🔙 Quay lại trang tải sách pdf ebook Bài Tập Toán 4 Nâng Cao Theo Chủ Đề Ebooks Nhóm Zalo BÀI TẬP NÂNG CAO TOÁN 4 THEO CHỦ ĐỀ 1. Sè tù nhiªn - D·y sè tù nhiªn Bµi 11: T×m x , biÕt: a) x lµ sè trßn chôc vµ 28 < x < 48 b) x lµ sè tù nhiªn vµ 145 < x < 150 c) x lµ sè ch½n vµ 200 < x < 210 d) x lµ sè tù nhiªn vµ x < 3 e) x lµ sè tù nhiªn vµ 2 < x < 5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 12: Sè tù nhiªn x gåm mÊy ch÷ sè, biÕt sè ®ã: a) Cã ch÷ sè hµng cao nhÊt thuéc líp ngh×n? b) Cã ch÷ sè hµng cao nhÊt thuéc líp triÖu? c) BÐ h¬n 10? d) BÐ h¬n 1 000 000 vµ lín h¬n 1 00 000? e) §øng liÒn sau mét sè cã ba ch÷ sè? f) §øng liÒn tr-íc mét sè cã ba ch÷ sè? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 13: ViÕt sè tù nhiªn nhá nhÊt, biÕt sè ®ã: a) Gåm cã: - Mét ch÷ sè - Ba ch÷ sè - Ba ch÷ sè lÎ kh¸c nhau 1 b) Cã ®ñ n¨m ch÷ sè 5, 4, 7, 0, 1 c) Cã ba ch÷ sè mµ tæng c¸c ch÷ sè cña nã b»ng 20. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 14: T×m sè tù nhiªn x, biÕt: a) x lµ sè tù nhiªn bÐ nhÊt; b) x lµ sè liÒn sau sè 999; c) x lµ sè liÒn tr-íc sè 1001; d) x lµ sè võa lín h¬n 99 võa bÐ h¬n 1000; e) x lµ sè cã hai ch÷ sè vµ lín h¬n 15; f) x lµ sè cã ba ch÷ sè vµ bÐ h¬n 105; g) x lµ sè ë gi÷a sè 1 vµ sè 11; h) x lµ sè gi÷a sè tù nhiªn a vµ sè (a + 1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 16: H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè mµ tæng c¸c ch÷ sè cña nã b»ng 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 17: Cho 3 ch÷ sè 1; 2; 3. 2 a) H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau tõ 3 ch÷ sè ®· cho. b) TÝnh nhanh tæng c¸c sè võa viÕt ®-îc. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 18: Víi bèn ch÷ sè 1,2,3,4; a) H·y viÕt tÊt c¶ c¸c sè cã ®ñ bèn ch÷ sè Êy. b) TÝnh tæng cña tÊt c¶ c¸c sè ë c©u a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 19: Cho 5 ch÷ sè 0, 1, 2, 3, 6. a) H·y lËp tÊt c¶ c¸c sè cã bèn ch÷ sè kh¸c nhau tõ 5 ch÷ sè trªn? b) TÝnh nhanh tæng c¸c sè võa lËp ®-îc? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 22: Cho d·y sè: 2, 3, 4, 5, ..., 30, 31, 32, 33, 34. a) D·y sè trªn cã bao nhiªu sè h¹ng? b) TÝnh nhanh tæng cña d·y sè trªn? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 25: Cho d·y sè ch½n liªn tiÕp 2, 4, 6, 8, 10, ... , 2468. Hái d·y cã: a) Bao nhiªu sè h¹ng? b) Bao nhiªu ch÷ sè ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. BÀI TOÁN LIÊN QUAN DÃY SỐ THEO QUY LUẬT Cho các số 1;4;7;10;..................... a.Số 2221;2234 có thuộc dãy số đó không ? b.Số thứ 134 ,số thứ 205 là số nào ? c.Tính tổng của 50 số đầu của dãy số. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3/CẤU TẠO SỐ D¹ng 1: ViÕt sè TN tõ nh÷ng ch÷ sè cho tr-íc Bµi 2 : Cho 5 ch÷ sè : 0; 1; 2; 3; 4. a) H·y viÕt c¸c sè cã 4 ch÷ sè kh¸c nhau tõ 5 ch÷ sè ®· cho ? b) T×m sè ch½n lín nhÊt, sè lÎ nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 5 ch÷ sè ®· cho ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 1 : Cho bèn ch÷ sè : 0; 3; 8 vµ 9. a) ViÕt ®-îc tÊt c¶ bao nhiªu sè cã 4 ch÷ sè kh¸c nhau tõ 4 ch÷ sè ®· cho ? b) T×m sè lín nhÊt, sè nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 4 ch÷ sè ®· cho? c) T×m sè lÎ lín nhÊt, sè ch½n nhá nhÊt cã 4 ch÷ sè kh¸c nhau ®-îc viÕt tõ 4 ch÷ sè ®· cho ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D¹ng 2: C¸c bµi to¸n gi¶i b»ng ph©n tÝch sè : Bµi 1: T×m 1 sè TN cã 2 ch÷ sè, biÕt r»ng nÕu viÕt thªm ch÷ sè 9 vµo bªn tr¸i sè ®ã ta ®-îc mét sè lín gÊp 13 lÇn sè ®· cho ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 2: T×m mét sè cã 3 ch÷ sè, biÕt r»ng khi viÕt thªm ch÷ sè 5 vµo bªn ph¶i sè ®ã th× nã t¨ng thªm 1112 ®¬n vÞ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 3: T×m mét sè cã 2 ch÷ sè, biÕt r»ng khi viÕt thªm sè 21 vµo bªn tr¸i sè ®ã ta ®-îc mét sè lín gÊp 31 lÇn sè ph¶i t×m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Bµi 4: T×m mét sè cã 2 ch÷ sè, biÕt r»ng khi viÕt thªm ch÷ sè 5 vµo bªn ph¶i sè ®ã ta ®-îc sè míi lín h¬n sè ph¶i t×m lµ 230 ®¬n vÞ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D¹ng 3: Nh÷ng bµi to¸n vÒ xÐt c¸c ch÷ sè tËn cïng cña sè Bµi 1: Kh«ng lµm tÝnh, h·y cho biÕt ch÷ sè tËn cïng cña mçi kÕt qu¶ sau : ×( 1991 + 1992 +....+ 1999 ) a) ( 1991 + 1992 + ...+ 1999 ) – ( 11 + 12 + .....+ 19 ). c) 21 ×23 ×25 ×27 – 11 ×13 ×15 ×17 b) ( 1981 + 1982 + ...+ 1989 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 2 : Kh«ng lµm tÝnh, h·y xÐt xem kÕt qu¶ sau ®©y ®óng hay sai ? Gi¶i thÝch t¹i sao ? a) 136 ×136 – 42 = 1960 b) ab × ab- 8557 = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 3 : Kh«ng lµm tÝnh, h·y cho biÕt ch÷ sè tËn cïng cña mçi kÕt qu¶ sau : ×66 ×76 ×86 – 51 ×61 ×71 ×81 a) ( 1999 + 2378 + 4545 + 7956 ) – ( 315 + 598 + 736 + 89 ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . b) 56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 4 : Kh«ng lµm tÝnh, h·y xÐt xem kÕt qu¶ sau ®©y ®óng hay sai ? Gi¶i thÝch t¹i sao ? a) abc × abc- 853467 = 0 b) 11 × 21 × 31 × 41 – 19 × 25 × 37 = 110 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. C¸c bµi to¸n vÒ dÃy sè I. §iÒn thªm sè h¹ng vµo sau, gi÷a hoÆc tr-íc mét d·y sè Bµi 1. ViÕt tiÕp ba sè h¹ng vµo d·y sè sau : a) 1; 3; 4; 7; 11; 18;... b) 0; 2; 4; 6; 12; 22;... c) 0 ; 3; 7; 12;... d) 1; 2; 6; 24;... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 2 : T×m sè h¹ng ®Çu tiªn cña c¸c d·y sè sau : a). ...; 17; 19; 21. b). .: 64; 81; 100. BiÕt r»ng mçi d·y cã 10 sè h¹ng. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 3 : ViÕt tiÕp hai sè h¹ng cña d·y sè sau : a) 100; 93; 85; 76;..... b) 10; 13; 18; 26;... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II. X¸c ®Þnh sè a cã thuéc d·y ®· cho hay kh«ng Bµi 1: H·y cho biÕt: a) C¸c sè 50 vµ 133 cã thuéc d·y 90; 95; 100;...hay kh«ng ? b) Sè 1996 thuéc d·y 2;5;8;11;... hay kh«ng ? c) Sè nµo trong c¸c sè 666; 1000; 9999 thuéc d·y 3; 6; 12; 24;... hay kh«ng ? Gi¶i thÝch t¹i sao ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . III. T×m sè sè h¹ng cña d·y Bµi1. Cho d·y sè 11; 14; 17;.....;65; 68. a) H·y x¸c ®Þnh d·y sè trªn cã bao nhiªu sè h¹ng? b) NÕu ta tiÕp tôc kÐo dµi c¸c sè h¹ng cña d·y sè ®ã th× sè h¹ng thø 1996 lµ sè mÊy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 2 . Trong c¸c sè cã ba ch÷ sè, cã bao nhiªu sè chia hÕt cho 4? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 3: Cã bao nhiªu sè : cã 3 ch÷ sè khi chia cho 5 d- 1? D- 2 ? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IV. T×m tæng c¸c sè h¹ng cña d·y sè Bµi 1 . TÝnh tæng cña 50 sè lÎ ®Çu tiªn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bµi 2: T×m tæng cña : a) C¸c sè cã 2 ch÷ sè chia hÕt cho 3. b) C¸c sè cã 2 ch÷ sè chia cho 4 d- 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Bèn phÐp tÝnh víi sè tù nhiªn 5.1. PhÐp céng Bµi 1: T×m hai sè cã tæng b»ng 1149, biÕt r»ng nÕu gi÷ nguyªn sè lín vµ gÊp sè bÐ lªn 3 lÇn th× ta ®-îc tæng míi b»ng 2061. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 2: Hai sè cã tæng b»ng 6479, nÕu gi÷ nguyªn sè thø nhÊt, gÊp sè thø hai lªn 6 lÇn th× ®-îc tæng míi b»ng 6789. H·y t×m hai sè h¹ng ban ®Çu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 9 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: T×m hai sè cã tæng b»ng 140, biÕt r»ng nÕu gÊp sè h¹ng thø nhÊt lªn 5 lÇn vµ gÊp sè h¹ng thø hai lªn 3 lÇn th× tæng míi lµ 508. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 4: T×m hai sè tù nhiªn cã tæng lµ 254. NÕu viÕt thªm mét ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt vµ gi÷ nguyªn sè thø hai th× ®-îc tæng míi lµ 362. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 5: T×m hai sè cã tæng b»ng 586. NÕu viÕt thªm ch÷ sè 4 vµo bªn ph¶i sè thø hai vµ gi÷ nguyªn sè thø nhÊt th× tæng míi b»ng 716. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 36: Khi céng mét sè tù nhiªn víi 107, mét häc sinh ®· chÐp nhÇm sè h¹ng thø hai thµnh 1007 nªn ®- îc kÕt qu¶ lµ1996. T×m tæng ®óng cña hai sè h¹ng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 37: Hai sè cã tæng b»ng 6479, nÕu gi÷ nguyªn sè h¹ng thø nhÊt, gÊp sè h¹ng thø hai lªn 6 lÇn th× ®-îc tæng míi b»ng 65789. H·y t×m hai sè h¹ng ban ®Çu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 40: Cho sè cã hai ch÷ sè. NÕu viÕt sè ®ã theo thø tù ng-îc l¹i ta ®-îc sè míi bÐ h¬n sè ph¶i t×m. BiÕt tæng cña sè ®ã víi sè míi lµ 143. T×m sè ®· cho. 10 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 41: Tæng cña hai sè thay ®æi thÕ nµo nÕu mét sè h¹ng cña nã t¨ng thªm 300 ®¬n vÞ vµ gi÷ nguyªn sè h¹ng kia? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 42: Chu vi h×nh ch÷ nhËt sÏ thay ®æi thÕ nµo nÕu ta t¨ng chiÒu dµi thªm 3 mÐt vµ gi¶m chiÒu réng cña nã ®i 3m. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 43: Tæng cña hai sè lµ 69, nÕu gÊp 3 lÇn sè thø hai vµ gi÷ nguyªn sè thø nhÊt th× tæng míi lµ 87. T×m hai sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5.2. PhÐp trõ Bµi 1: T×m hai sè cã hiÖu lµ 23, biÕt r»ng nÕu gi÷ nguyªn sè trõ vµ gÊp sè bÞ trõ lªn 3 lÇn th× ®-îc hiÖu lµ 353. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 2: T×m hai sè cã hiÖu lµ 383, biÕt r»ng nÕu gi÷ nguyªn sè bÞ trõ vµ gÊp sè trõ lªn 4 lÇn th× ®-îc hiÖu míi lµ 158. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 11 .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: HiÖu cña hai sè tù nhiªn lµ 4441, nÕu viÕt thªm mét ch÷ sè 0 vµo bªn ph¶i sè trõ vµ gi÷ nguyªn sè bÞ trõ th× ®-îc hiÖu míi lµ 3298. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 4: HiÖu cña hai sè tù nhiªn lµ 134. ViÕt thªm mét ch÷ sè vµo bªn ph¶i cña sè bÞ trõ vµ gi÷ nguyªn sè trõ th× hiÖu míi lµ 2297. T×m ch÷ sè viÕt thªm vµ hai sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 45: TÝnh nhanh a) 32 - 13- 17 c) 1732 - 513 - 732 b) 45 - 12 - 5 - 23 d) 2834 - 150 -834 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 50: T×m tæng hai sè, biÕt hiÖu cña hai sè ®ã lµ 37 vµ hiÖu ®ã b»ng nöa sè bÐ. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 51: HiÖu cña hai sè thay ®æi thÕ nµo nÕu ta cïng t¨ng thªm (hay bít ®i) hai sè ®ã cïng mét sè. Cho vÝ dô? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 52: HiÖu cña hai sè lµ 27, nÕu ta cïng gÊp lªn ( hay gi¶m ®i) mçi sè ®ã 3 lÇn th× hiÖu míi lµ bao nhiªu? 12 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 53: Kh«ng thùc hiÖn phÐp tÝnh, cã thÓ nãi ngay gi¸ trÞ biÓu thøc sau ®-îc kh«ng? a) A= 621 – ( 621 – 58) b) B = x- ( x- 60) c) C= 720 + ( 3927 – 720) d) D = x + ( 390 – x) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 54: T×m sè tù nhiÖn x, biÕt: a) 35- x < 35 – 5 b) x – 10 < 35 – 10 c) x – 10 < 45 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5.3. PhÐp nh©n Bµi 1: T×m tÝch cña 2 sè, biÕt r»ng nÕu gi÷ nguyªn thõa sè thø nhÊt vµ t¨ng thõa sè thø 2 lªn 4 lÇn th× ®-îc tÝch míi lµ 8400. Bµi gi¶i .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 13 Bµi 2: T×m 2 sè cã tÝch b»ng 5292, biÕt r»ng nÕu gi÷ nguyªn thõa sè thø nhÊt vµ t¨ng thõa sè thø hai thªm 6 ®¬n vÞ th× ®-îc tÝch míi b»ng 6048. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: T×m 2 sè cã tÝch b»ng 1932, biÕt r»ng nÕu gi÷ nguyªn mét thõa sè vµ t¨ng mét thõa sè thªm 8 ®¬n vÞ th× ®-îc tÝch míi b»ng 2604. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 58: Trong mét phÐp nh©n cã thõa sè thø hai lµ 64, khi thùc hiÖn phÐp nh©n mét ng-êi ®· viÕt c¸c tÝch riªng th¼ng cét víi nhau nªn kÕt qu¶ t×m ®-îc lµ 870. T×m tÝch ®óng cña phÐp nh©n? Bµi 59: Kh«ng tÝnh tæng, h·y biÕn ®æi tæng sau thµnh tÝch cã hai thõa sè . a) 462+273+315+630 c) 5555+6767+7878 b) 209+187+726+1078 d) 1997,1997+1998,1998+1999,1999 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 59: . So s¸nh A vµ B biÕt: a. A=73 x 73 B=72 x 74 b. A=1991 x 1999 B=1995 x 1995 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 60: TÝch cña hai sè thay ®æi thÕ nµo nÕu ta gÊp mét thõa sè lªn 2 lÇn vµ gi¶m thõa sè kia ®i 2 lÇn. Cho vÝ dô? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 61: TÝch cña hai sè thay ®æi thÕ nµo nÕu mçi thõa sè ®Òu gÊp lªn 3 lÇn. Cho vÝ dô? 14 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 62: T×m x ( Kh«ng thùc hiÖn phÐp tÝnh) a) 5×x = 5×195 b) ( x + 5) ×2009 = ( 19 + 5) ×2009 c) 35 ×x < 35 ×6 d) ( 15 – x) ×79 < ( 15 – 2) ×79 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 63: TÝch cña hai sè tù nhiªn lµ 65. NÕu mét sè t¨ng thªm 30 ®¬n vÞ vµ gi÷ nguyªn sè kia th× tÝch míi lµ 215.T×m hai sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 64: Khi nh©n mét sè víi 245, mét häc sinh ®· ®Æt c¸c tÝch riªng th¼ng cét nh- trong phÐp céng nªn t×m ra kÕt qu¶ lµ 4257. T×m tÝch ®óng cña phÐp nh©n ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 65: TÝnh gi¸ trÞ cña biÓu thøc sau b»ng c¸ch hîp lÝ: a) 54 ×113 + 54×113 + 113 b)( 532 ×7 - 266×14) ×( 532×7 + 266) c) 117 ×( 36 + 62) - 17×( 62 + 36) d)( 145 ×99 + 145) – ( 143 ×101 – 143) 21. T×m 3 sè lÎ liªn tiÕp mµ tÝch cña chóng lµ 105. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 15 .......................................................................................................................................................................... .......................................................................................................................................................................... 22. Cho A= 1×2 + 2×3 + 3×4 + …+ 19×20 TÝnh A×3 = ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 66: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ: a) 2009 ×867 + 2009 ×133 b) 2008×867 + 2009×133 TÝch cña hai sè tù nhiªn liªn tiÕp tõ 1 ®Õn 76 tËn cïng b»ng bao nhiªu ch÷ sè 0? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 67: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ: a) A = 1 + 1 + 1 + ...+ 1 – 999( cã 1000 sè 1) b) 4×113×25 - 5×112 ×20 c) ( 100 – 99 + 97 – 80 + 15) ×( 16 – 2 ×8) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 69: TÝnh b»ng c¸ch thuËn tiÖn a) 3×17 + 3×25 - 3×2 b) 123×15 - 123×5 c) 246 ×4 - 246×3 – 246 d) 789×9 - 789×8 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5.4. PhÐp CHIA Bµi 73: §Æt tÝnh råi tÝnh a) 256075 : 5 b) 369090 : 6 c)498479: 7 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 16 Bµi 74: T×m x: a) x×5 = 106570 b) 450906 : x = 6 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 76: TÝnh ( Theo mÉu) MÉu: 60 : 30 = 60 : ( 10 ×3) = 60 : 10 : 3 = 6 : 3 = 2 a) 90 : 30 b) 180 : 60 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 77: §Æt tÝnh råi tÝnh 552 : 24 450 : 27 540 : 45 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 79: §Æt tÝnh råi tÝnh 4725 : 15 8058: 34 5672 : 42 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 80: Ng-êi ta xÕp c¸c gãi kÑo vµo c¸c hép, mçi hép 30 gãi. Hái cã thÓ xÕp 2000 gãi kÑo vµo nhiÒu nhÊt bao nhiªu hép vµ cßn thõa bao nhiªu gãi kÑo? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 81: §Æt tÝnh råi tÝnh 3621: 213 8000 : 308 1682 : 209 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... ..........................................................................................................................................................................17 Bµi 84: Mua 52 bót bi hÕt 78 000 ®ång. Hái nÕu mçi bót bi ®ã gi¶m gi¸ 300 ®ång th× víi sè tiÒn 78 000 ®ång sÏ mua ®-îc bao nhiªu bót bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 85: Nam lµm mét phÐp chia cã d- lµ sè d- lín nhÊt cã thÓ cã. Sau ®ã Nam gÊp c¶ sè bÞ chia vµ sè chia lªn 3 lÇn. ë phÐp chia míi nµy, sè th-¬ng lµ 12 vµ sè d- lµ 24. T×m phÐp chia Nam thùc hiÖn ban ®Çu? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 86: Sè A chia cho 12 th× d- 8. NÕu gi÷ nguyªn sè chia th× sè A ph¶i thay ®æi thÕ nµo ®Ó th-¬ng t¨ng thªm 2 ®¬n vÞ vµ phÐp chia kh«ng cã d-? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 87: Mét phÐp chia cho 18 d- 8. §Ó phÐp chia kh«ng cßn d- vµ th-¬ng gi¶m ®i 2 lÇn th× ph¶i thay ®æi sè bÞ chia nh- thÕ nµo? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 88: Th-¬ng cña hai sè thay ®æi thÕ nµo nÕu ta gÊp sè bÞ chia vµ sè chia lªn cïng mét sè lÇn? Cho vÝ dô. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 89: Kh«ng thùc hiÖn phÐp tÝnh, t×m x: a) 2009 : x = 2009 : 2 b) ( x + 2) : 2009 = (2345 + 2) : 2009 c) x : 5 < 15 : 5 d) 35 : x > 35 : 5 .......................................................................................................................................................................... .......................................................................................................................................................................... 18 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 89: TÝnh gi¸ trÞ biÓu thøc sau b»ng c¸ch hîp lÝ: a) 1875 : 2 + 125 : 2 b) 0 : 36×( 32 + 17 + 99 – 68 + 1) c) ( m : 1 - m×1) : ( m×2009 + m + 1) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 90: H·y ®Æt dÊu ngoÆc vµo biÓu thøc : 3×15 + 18 : 6+ 3 ®Ó gi¸ trÞ cña biÓu thøc lµ : a) 47 b) Sè bÐ nhÊt cã thÓ cã c) Sè lín nhÊt cã thÓ cã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 91: TÝnh gi¸ trÞ biÓu thøc sau víi x = 1 vµ y = 0: a) A = ( 15 : x + 15×x) + 2009 ×y b) B = y : ( 119 ×x + 4512) + (756 : x – y) c) C = ( 10 + y) : ( 10 – y) – x + 10×x – 10 : x + y .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 6. DẠNG TOÁN TRUNG BÌNH CỘNG 4. Trong c¸c sè, nÕu cã mét sè lín h¬n møc trung b×nh céng cña c¸c sè n ®¬n vÞ th× trung b×nh céng cña c¸c sè ®ã b»ng tæng c¸c sè cßn l¹i céng víi n ®¬n vÞ råi chia cho sè l-îng c¸c sè h¹ng cßn l¹i ®ã. 19 VD: An cã 20 viªn bi, B×nh cã sè bi b»ng 21sè bi cña An. Chi cã sè bi h¬n møc trung b×nh céng cña ba b¹n lµ 6 viªn bi. Hái Chi cã bao nhiªu viªnn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5. Trong c¸c sè , nÕu mét sè kÐm trung b×nh céng cña c¸c sè ®ã n ®¬n vÞ th× trung b×nh céng cña c¸c sè ®ã b»ng tæng c¸c sè cßn l¹i trõ ®i n ®¬n vÞ råi chia sè c¸c sè h¹ng cßn l¹i. VD: An cã 20 bi, B×nh cã 20 bi. Chi cã sè bi kÐm trung b×nh céng cña c¶ ba b¹n lµ 6 bi. Hái Chi cã bao nhiªu bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 6. Bµi to¸n cã thªm mét sè h¹ng ®Ó møc trung b×nh céng cña tÊt c¶ t¨ng thªm n ®¬n vÞ, ta lµm nh sau: VD: Mét « t« trong ba giê ®Çu, mçi giê ®i ®-îc 40km, trong ba giê sau, mçi giê ®i ®-îc 50 km. NÕu muèn t¨ng trung b×nh céng mçi giê t¨ng thªm 1 km n÷a th× ®Õn giê thø 7, « t« ®ã cÇn ®i bao nhiªu km n÷a? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... VÝ dô 1: H·y t×m sè trung b×nh céng cña 1, 2, 3, 4, 5, 6, 7, 8, 9. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... VÝ dô3: An cã 20 nh·n vë, B×nh cã 20 nh·n vë. Chi cã sè nh·n vë kÐm trung b×nh céng cña ba b¹n lµ 6 nh·n vë. Hái Chi cã bao nhiªu n·nh vë? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... VÝ dô 4: 20 Cã bèn b¹n An, B×nh, Dòng, Minh cïng ch¬i bi. BiÕt An cã 18 viªn bi, B×nh cã 16 viªn bi, Dòng cã sè bi b»ng trung b×nh céng sè bi cña An vµ B×nh. Minh cã sè bi b»ng trung b×nh céng sè bi cña c¶ bèn b¹n. Hái B¹n Minh cã bao nhiªu viªn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 1: T×m sè trung b×nh céng cña c¸c sè c¸ch ®Òu nhau 4 ®¬n vÞ : 3, 7, 11, …,95, 99, 103. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 2: T×m sè trung b×nh céng cña c¸c sè : 4, 6, 8, 10, 12, 14, 16, 18. Em cã c¸ch nµo tÝnh nhanh sè trung b×nh céng cña c¸c sè trªn kh«ng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: Trung b×nh céng tuæi cña bè, mÑ, B×nh vµ Lan lµ 24 tuæi, trung b×nh céng tuæi cña bè. mÑ vµ Lan lµ 28 tuæi. T×m tuæi cña mçi ng-êi, biÕt tuæi B×nh gÊp ®«i tuæi Lan, tuæi Lan b»ng 61tuæi mÑ. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 5: Hai ng-êi ®i xe m¸y khëi hµnh cïng mét lóc tõ hai đ Þa ®iÓm c¸ch nhau 216km vµ ®i ng-îc chiÒu nhau. Hä ®i sau 3 giê th× gÆp nhau. Hái trung b×nh mét giê mçi ng-êi ®i ®i ®-îc bao nhiªu ki- l«- mÐt? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 21 Bµi 6: Con lîn vµ con chã nÆng 102kg, con lîn vµ con bß nÆng 231kg, con chã vµ con bß nÆng 177kg. Hái trung b×nh mçi con nÆng bao nhiªu ki-l«-gam? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 7: T×m sè cã ba ch÷ sè, biÕt trung b×nh céng ba ch÷ sè cña sè ®ã b»ng 6 vµ ch÷ sè hµng tr¨m gÊp ba ch÷ sè hµng chôc, ch÷ sè hµng chôc kÐm ch÷ sè hµng ®¬n vÞ lµ 2. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 8: Ba sè cã trung b×nh céng lµ 60. T×m ba sè ®ã, biÕt nÕu viÕt thªm mét ch÷ sè ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt th× ta ®-îc sè thø hai vµ sè thø nhÊt b»ng 41sè thø ba. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 12: ViÖt cã 18 bi, Nam cã 16 bi, Hoµ cã sè bi b»ng trung b×nh céng cña ViÖt vµ Nam, B×nh cã sè bi kÐm trung b×nh céng cña 4 b¹n lµ 6 bi. Hái B×nh cã bao nhiªu bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 13: Nh©n dÞp khai gi¶ng, Mai mua 10 quyÓn vë, Lan mua 12 quyÓn vë, §µo mua sè vë b»ng trung b×nh céng cña 2 b¹n trªn, Cóc mua h¬n trung b×nh céng cña c¶ 3 b¹n lµ 4 quyÓn. Hái Cóc mua bao nhiªu quyÓn vë? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 14: Tuæi trung b×nh 11 cÇu thñ cña mét ®éi bãng ®¸ lµ 22 tuæi . NÕu kh«ng kÓ thñ m«n th× tuæi trung b×nh cña 10 cÇu thñ lµ 21 tuæi. Hái thñ m«n bao nhiªu tuæi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 22 Bµi 103: T×m trung b×nh céng cña c¸c sè : 4, 6, 8, 10, 12 14, 16, 18. Em cã c¸ch nµo tÝnh nhanh sè trung b×nh céng cña c¸c sè trªn kh«ng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 104: T×m sè cã ba ch÷ sè, biÕt truug b×nh céng ba ch÷ sè cña nã b»ng 5 vµ ch÷ sè hµng tr¨m gÊp ba ch÷ sè hµng chôc, ch÷ sè hµng chôc h¬n ch÷ sè hµng ®¬n vÞ lµ 1. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 105: Trung b×nh céng tuæi cña bè, mÑ, B×nh vµ Lan lµ 24 tuæi, trung b×nh céng tuæi cña bè, mÑ vµ Lan lµ 28 tuæi. T×m tuæi mçi ng-êi, biÕt tuæi B×nh gÊp ®«i tuæi Lan, tuæi Lan b»ng 61tuæi mÑ. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 106: Cã 4 b¹n An, B×nh, Dòng, Minh ch¬i bi. An cã 18 viªn, B×nh cã 16 viªn, Dòng cã sè bi b»ng TBC sè bi cña An vµ B×nh, Minh cã sè bi b»ng TBC sè bi cña c¶ 4 b¹n. Hái Minh cã bao nhiªu viªn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 107: TBC sè tuæi cña «ng , bè vµ ch¸u lµ 36 tuæi, TBC sè tuæi cña bè vµ cña ch¸u lµ 23, «ng h¬n ch¸u 54 tuæi. T×m tuæi mçi ng-êi. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 108: T×m 3 sè cã TBC b»ng 60, biÕt r»ng nÕu viÕt thªm 1 ch÷ sè 0 vµo bªn ph¶i sè thø nhÊt th× ®-îc sè thø hai vµ sè thø 3 gÊp 4 lÇn sè thø nhÊt. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 23 .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 109: ViÖt cã 18 viªn bi, Nam cã 16 bi, Hßa cã s« bi b»ng trung b×nh céng cña ViÖt vµ Nam, B×nh cã sè bi kÐm trung b×nh céng cña 4 b¹n lµ 6 bi. Hái B×nh cã bao nhiªu viªn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 110: Nh©n dÞp khai gi¶ng, Mai mua 10 quyÓn vë, Lan mua 12 quyÓn vë, §µo mua sè vë b»ng trung b×nh céng cña hai b¹n trªn, Cóc mua h¬n trung b×nh céng cña c¶ 3 b¹n lµ 4 quyÓn vë. Hái Cóc mua bao nhiªu quyÓn vë? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 112: Tuæi trung b×nh cña 11 cÇu thñ cña ®éi bãng ®¸ lµ 22 tuæi. NÕu kh«ng kÓ thñ m«n th× tuæi trung b×nh cña 10 cÇu thñ lµ 21 tuæi. Hái thñ m«n bao nhiªu tuæi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 113: Mét th¸ng ®iÓm cã 20 lÇn kiÓm tra, sau 10 lÇn kiÓm tra b¹n An thÊy ®iÓm trung b×nh cña m×nh lµ 7 ®iÓm. Hái cßn 10 lÇn kiÓm tra n÷a b¹n An ph¶i ®¹t ®-îc tÊt c¶ bao nhiªu ®iÓm ®Ó ®iÓm trung b×nh cña th¸ng lµ 8 ®iÓm. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 1: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở bằng trung bình cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 2: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở hơn trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... 24 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 3: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở kém trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 4: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở bằng trung bình cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 5: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở hơn trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 6: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở kém trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 7: Trung bình cộng của n số là 80 biết 1 trong các số đó là 100 .Nếu bỏ số 100 thì trung bình cộng các số còn lại là 78 tìm n. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 8: Có ba con ; gà, vịt, ngan . Hai con gà và vịt nặng tất cả là 5 kg . Hai con gà và ngan nặng tất cả là 9 kg . Hai con ngan và vịt nặng tất cả là 10 kg . Hỏi trung bình một con nặng mấy kg ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 25 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 10: Trung bình cộng của ba số là 50 . Tìm số thứ ba biết rằng nó bằng trung bình cộng của hai số đầu . Hướng dẫn giải .Dùng sơ đồ .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 11: Trung bình cộng của ba số là 35 . Tìm ba số đó biết rằng số thứ nhất gấp đôi số thứ hai, số thứ hai gấp đôi số thứ ba? Gợi ý Dùng sơ đồ .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 12: Tìm sáu số chẵn liên tiếp biết tổng của chúng là 90. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 13: Tìm trung bình cộng của tất cả các số có hai chữ số , mà chia hết cho 4 . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 14: Trung bình cộng số tuổi của hai anh em ít hơn tuổi anh là 4 tuổi . Hỏi anh hơn em mấy tuổi ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 15: Lớp 4 A có 40 học sinh , lớp 4B có 36 học sinh . Lóp 4 C có số học sinh ít hơn trunh bình cộng số học sinh của cả ba lớp là hai bạn . Tính số học sinh lớp 4 B. 26 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 16: Hai lớp 3A và 3B có tất cả 37 h/s .Hai lớp 3B và 3B có tất cả là 83 h/s. Hai lớp 3C vàg 3A có tất cả là 86 h/s . Hỏi: trung bình mỗi lớp có bao nhiêu học sinh ? Số học sinh của mỗi lớp là bao nhiêu em ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 17: Tuổi trung bình cộng của một đội bóng đá (11 người) là 22 tuổi. Nếu không kể đội trưởng, thì tuổi trung bình của 10 cầu thủ còn lại chỉ là 2. Tính tuổi của đội trưởng ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 18: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở bằng trung bình cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 19: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở hơn trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 20: Xe thứ nhất chở được 25 tấn hàng .xe thứ hai chở 35 tấn hàng .Xe thứ ba chở kém trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 27 Bài tập 21: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở bằng trung bình cộng 3 xe . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 22: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở hơn trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 23: Xe thứ nhất chở được 40 tấn hàng .xe thứ hai chở 50 tấn hàng .Xe thứ ba chở kém trung bình cộng 3 xe là 10 . Hỏi xe thứ 3 chở bao nhiêu tấn hàng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài tập 24: Ba lớp 4a;4b;4c; đi trồng cây . số cây của lớp 4a và 4b trồng được là 41 cây .Số cây của lớp 4b và lớp 4c trồng được là 43 cây . Số cây của 4c và 4a trồng được là 42 cây . Hỏi mỗi lớp trồng được bao nhiêu cây? .BàiGiải. Cả 3 lớp trồng được số cây là: (41+42+43 ): 2 =63 cây Lớp 4c trồng được số cây là 63- 41=22cây Lớp 4 b trồng số cây là: 43 -22= 21(Cây) Lớp 4 a trồng số cây là: 42 – 22 = 20 (cây) Đáp Số: Bài tập 25: An,Bình ,Chi đi câu cá . Cả ba bạn câu được 37 con cá . Nếu An câu thêm được 5 con cá và Bình câu giảm đi 3 con cá thí số cá ba bạn bằng nhau . Hỏi mỗi bạn câu được bao nhiêu con cá? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Ví dụ 1 : Tìm 3 số có trung bình cộng lớn hơn số thứ nhất 540, bé hơn số thứ hai là 1260 và gấp 31 lần số thứ ba. .......................................................................................................................................................................... .......................................................................................................................................................................... ..........................................................................................................................................................................28 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Ví dụ 2 : Đội tuyển học sinh giỏi khối 5 của một trường Tiểu học có 16 bạn. Biết rằng 2/5 số bạn nam nhiều hơn 1/2 số bạn nữ là 1 bạn. Hỏi đội tuyển có bao nhiêu bạn nam, bao nhiêu bạn nữ ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Ví dụ 3 : Một trường Tiểu học có số học sinh nam nhiều hơn số học sinh nữ là 40 học sinh. Trong đó 3/4 số bạn nam và 1/2 số bạn nữ đạt danh hiệu học sinh tiên tiến. Tính số học sinh nam và số học sinh nữ của trường đó. Biết số học sinh tiên tiến của trường đó là 530 bạn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 7. DẠNG TÌM HAI SỐ KHI BIẾT TỔNG VÀ HIỆU Bµi 1: Cã mét hép bi xanh vµ mét hép bi ®á, tæng sè bi cña 2 hép lµ 48 viªn bi. BiÕt r»ng nÕu lÊy ra ë hép bi ®á 10 viªn vµ lÊy ra ë hép bi xanh 2 viªn th× sè bi cßn l¹i trong 2 hép b»ng nhau. T×m sè bi cña mçi hép lóc ®Çu. Bµi gi¶i: .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... §¸p sè : 18 vµ 20 Bµi 2: Lan cã nhiÒu h¬n Hång 12 quyÓn truyÖn nhi ®ång. NÕu Hång mua thªm 8 quyÓn vµ Lan mua thªm 2 quyÓn th× 2 b¹n cã tæng céng 46 quyÓn. Hái mçi b¹n cã bao nhiªu quyÓn truyÖn nhi ®ång? ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè : 12 vµ 24 Bµi 3: Hai hép bi cã tæng céng 115 viªn, biÕt r»ng nÕu thªm vµo hép bi thø nhÊt 8 viªn vµ hép thø hai 17 viªn th× 2 hép cã sè bi b»ng nhau. Hái mçi hép cã bao nhiªu viªn bi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... §¸p sè 78 vµ 37 Bµi 4: T×m hai sè cã hiÖu b»ng 129, biÕt r»ng nÕu lÊy sè thø nhÊt céng víi sè thø hai råi céng víi tæng cña chóng th× ®-îc 2010. .......................................................................................................................................................................... .......................................................................................................................................................................... 29 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 5: T×m hai sè ch½n cã tæng b»ng 216, biÕt gi÷a chóng cã 5 sè ch½n .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 6: Tæng sè tuæi hiÖn nay cña bµ, cña HuÖ vµ cña H¶i lµ 80 tuæi. C¸ch ®©y 2 n¨m, tuæi bµ h¬n tæng sè tuæi cña HuÖ vµ H¶i lµ 54 tuæi, HuÖ nhiÒu h¬n H¶i 6 tuæi. Hái hiÖn nay mçi ng-êi bao nhiªu tuæi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 7: Hai ®éi trång c©y nhËn kÕ ho¹ch trång tÊt c¶ 872 c©y. Sau khi mçi ®éi hoµn thµnh 43kÕ ho¹ch cña m×nh, ®éi 1 trång nhiÒu h¬n sè c©y ®éi 2 trång lµ 54 c©y. Hái mçi ®éi nhËn trång theo kÕ ho¹ch lµ bao nhiªu c©y? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 115: T×m hai sè, biÕt tæng hai sè lµ sè lín nhÊt cã hai ch÷ sè. HiÖu hai sè lµ sè lÎ bÐ nhÊt cã hai ch÷ sè. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 116: T×m hai sè biÕt tæng hai sè lµ 100 vµ hiÖu hai sè lµ sè bÐ nhÊt cã hai ch÷ sè. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 117: T×m hai sè biÕt hiÖu hai sè lµ sè lín nhÊt cã 1 ch÷ sè vµ tæng hai sè lµ sè lín nhÊt cã ba ch÷ sè. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 30 .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 118: T×m hai sè ch½n cã tæng b»ng 220, biÕt r»ng ë gi÷a chóng cã 3 sè ch½n. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 119: Tæng cña hai sè ch½n lµ 38. H·y t×m hai sè biÕt r»ng gi÷a chóng chØ cã 3 sè lÎ. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 120: Tæng cña ba sè lÎ liªn tiÕp lµ 75,h·y t×m ba sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 121: Anh h¬n em 5 tuæi. BiÕt r»ng 5 n¨m n÷a th× tæng sè tuæi cña hai anh em lµ 25. TÝnh sè tuæi cña mçi ng-êi hiÖn nay? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 122: TÝnh diÖn tÝch cña miÕng ®Êt h×nh ch÷ nhËt cã chu vi lµ 256 m vµ chiÒu dµi h¬n chiÒu réng 32m .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 123: Mét m¶nh v-ên h×nh ch÷ nhËt cã chu vi b»ng chu vi thöa ruéng h×nh vu«ng c¹nh 80m. NÕu gi¶m chiÒu dµi m¶nh v-ên ®i 30m vµ t¨ng chiÒu réng thªm 10m th× m¶nh v-ên sÏ cã h×nh vu«ng. TÝnh diÖn tÝch m¶nh v-ên. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 124: T×m hai sè cã hiÖu b»ng 129, biÕt r»ng nÕu lÊy sè thø nhÊt céng víi sè thø hai råi céng tæng cña chóng th× ®-îc 2010 .......................................................................................................................................................................... .......................................................................................................................................................................... 31 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 8. DẠNG TÌM HAI SỐ KHI BIẾT 2 HIỆU SỐ Bài toán: Để chuẩn bị cho năm học mới, hai bạn Vĩnh và Kim đi mua sắm sách vở. Vĩnh mua 15 quyển vở, Kim mua nhiều hơn hơn Vĩnh 5 quyển vở cùng loại và phải trả nhiều hơn Vĩnh 20.000 đồng. Hỏi mỗi bạn phải trả bao nhiêu tiền mua vở? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 3. Bài tập cần luyện: *Bài tập 1: Một hiệu sách, lần thứ nhất bán được 27 quyển vở. Lần thứ hai bán được 40 quyển vở cùng loại và nhận nhiều tiền hơn lần trước 52.000 đồng. Hỏi mỗi lần bán hiệu sách nhận bao nhiêu tiền? (GV phân tích tương tự như bài toán trên). .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... *Bài tập 2: Hồng mua 3 cái bút và 5 quyển vở hết 39.000 đồng. Hoa mua 3 cái bút và 9 quyển vở cùng loại như Hồng hết 51.000 đồng. Tính giá tiền một cây bút, một quyển vở? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 4. Bài tập về nhà: Chị Vĩnh mua 2 mét vải xanh và 6 mét vải hoa. Chị Linh mua 2 mét vải xanh và 9 mét vải hoa cùng loại. Chị Vĩnh phải trả 380.000 đồng. Chị Linh phải trả 530.000 đồng. Tính giá tiền một mét vải mỗi loại? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 32 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 1: Hiện nay, Minh 10 tuổi ,em Minh 6 ,còn mẹ của Minh 36 tuổi .Hỏi bao nhiêu năm nữa tuổi mẹ bằng tổng số tuổi của hai anh em. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2 : Bể thứ nhất chứa 1200 lít nước . Bể thứ 2 chứa 1000 lít nước .Khi bể không có nứớc người ta cho 2 vòi cùng chảy 1 lúc vào 2 bể . Vòi thứ nhất mỗi giờ chảy được 200 lít .Vòi thứ 2 mỗi giờ chảy được 150 lít. Hỏi sau bao lâu số nước còn lại ở 2 bể bằng nhau. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3: Cùng 1 lúc xe máy và xe đạp cùng đi về phía thành phố xe máy cách xe đạp 60km. Vận tốc xe máy là 40 km/h vận tốc xe đạp là 25 km/h. Hỏi sau bao lâu xe máy đuổi kịp xe đạp. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4 : Một con Chó Đuổi theo một con thỏ .Con chó cách con thỏ 20m.Mỗi bước con thỏ nhẩy được 30cm,con chó nhảy được 50 cm.Hỏi sau bao nhiêu bước con chó bắt được con thỏ ? Biết rằng con thỏ nhảy được 1 bước thì con chó cũng nhảy được 1 bước. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5 Hai bác thợ mộc nhận bàn ghế về đống .Bác thứ nhất nhận 60 bộ .Bác thứ 2 nhận 45 bộ . Cứ 1 tuần bác thứ nhất đóng được 5 bộ ,bác thứ hai đóng được 2 bộ . Hỏi sau bao lâu số ghế còn lại của 2 bác bằng nhau. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 33 Bài 6:Hai bác thợ mộc nhận bàn ghế về đống .Bác thứ nhất nhận 120 bộ .Bác thứ 2 nhận 80 bộ . Cứ 1 tuần bác thứ nhất đóng được 12 bộ ,bác thứ hai đóng được 4 bộ .Hỏi sau bao lâu số ghế còn lại của bác thứ nhất bằng 1/2 số bộ bàn ghế của bác thứ 2. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 7: Hai bể nước có dung tích bằng nhau .Cùng 1 lúc người ta cho 2 vòi nước chảy vào 2 bể .Vòi thứ nhất mỗi giờ chảy được 50 lít nước .Vòi thứ 2 mỗi giờ chảy được 30 lít nước . Sau khi bể thứ nhất đầy nước thì bể thứ 2 phải chảy thêm 600 lít nữa mới đầy .Hỏi dung tích của bể là bao nhiêu lít nước? (Tham khảo thêm Đề thi và phần Bài tập mở rộng) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 9. DẠNG TOÁN LIÊN QUAN ĐẾN CHIA HẾT Bµi 1: Tõ 3 ch÷ sè 0, 1, 2. H·y viÕt tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau chia hÕt cho 2. ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ Bµi 2: ViÕt tÊt c¶ c¸c sè chia hÕt cho 5 cã 4 ch÷ sè kh¸c nhau tõ 4 ch÷ sè 0, 1, 2 , 5. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: Em h·y viÕt vµo dÊu * ë sè 86* mét ch÷ sè ®Ó ®-îc sè cã 3 ch÷ sè vµ lµ sè: a) Chia hÕt cho 2 b) chia hÕt cho 3 c) Chia hÕt cho 5 d) chia hÕt cho 9 e) Chia hÕt cho c¶ 2 vµ 5 g) Chia hÕt cho c¶ 3 vµ 9 ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ Bµi 4: chia hÕt cho 5 vµ 9. H·y t×m c¸c ch÷ sè x, y sao cho 17x8y .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 34 ........................................................ ........................................................ Bµi 5: T×m x, y ®Ó x765ychia hÕt cho 3 vµ 5. .......................................................................................................................................................................... ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè: Y = 0 ta cã c¸c sè : x= 3, 6 9 Y = 5 ta cã x = 14,7 Bµi 6: T×m x vµ y ®Ó sè 1996xychia hÕt cho 2, 5 vµ 9. .......................................................................................................................................................................... ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ Bµi 7: T×m a vµ b ®Ó 56a3bchia hÕt cho 36. ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè: ( Chia hết cho 36 thì tổng của 56a3b chia hết cho 4 và 9) 1a83blµ sè tù nhiªn. Bµi 8: T×m tÊt c¶ c¸c ch÷ sè a vµ b ®Ó ph©n sè 45 ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ 1a83bchia hết cho 5 và 9) §¸p sè: ( Chia hết cho 45 thì tổng của 45 Bµi 9: T×m x ®Ó 37+2x5chia hÕt cho 3. .......................................................................................................................................................................... ........................................................ ........................................................ ........................................................ ........................................................ ........................................................ §¸p sè: 37 + 2 + 5 = 41 vËy x = 1, 4 , 7 35 Bµi 10: T×m a vµ b ®Ó sè a391bchia hÕt cho 9 vµ chia cho 5 d- 1. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 11: T×m tÊt c¶ c¸c sè cã 3 ch÷ sè kh¸c nhau abc, biÕt: 32 ac. 7= b B= 2 th× ac = 2 x 9 = 18 B= 5 th× ac = 2 x 19 = 39 B= 8 th× ac = 2 x 29 = 54 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 1. ViÕt c©c sè tù nhiªn theo dÊu hiÖu chia hÕt Bµi 2 : Cho 4 ch÷ sè 0; 1; 5; 8. H·y lËp c¸c sè cã 3 ch÷ sè kh¸c nhau tõ 4 ch÷ sè ®· cho tho¶ m·n ®iÒu kiÖn: a) Chia hÕt cho 3 ? b) Chia hÕt cho 2 vµ 5 ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 2. Dïng dÊu hiÖu chia hÕt ®Ó ®iÒn c¸c ch÷ sè ch-a biÕt. Bµi 2: Cho sè b = xy2008thay x vµ y sao cho sè b chia hÕt cho 2, 5 vµ 3. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 3.bµi to¸n vÒ vËn dông tÝnh chÊt chia hÕt cña mét tæng vµ mét hiÖu. Bµi 1: Kh«ng lµm phÐp tÝnh, h·y xÐt xem c¸c tæng vµ hiÖu d-íi ®©y cã chia hÕt cho 3 hay kh«ng? a) 240 + 123 b) 240 – 123 c) 459 + 690 + 1236 d) 2454 + 374 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 36 Bµi 2: Tæng kÕt n¨m häc 2007- 2008, mét tr-êng tiÓu häc cã 462 häc sinh tiªn tiÕn vµ 195 häc sinh giái. Ban gi¸m hiÖu dù ®Þnh th-ëng cho mçi häc sinh giái nhiÒu h¬n häc sinh tiªn tiÕn 2 quyÓn vë. C« v¨n phßng nhÈm tÝnh ph¶i mua 1996 quyÓn th× ®ñ ph¸t th-ëng. Hái c« v¨n phßng ®· tÝnh ®óng hay sai? Gi¶i thÝch t¹i sao ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 4.C¸c bµi to¸n vÒ phÐp chia cã d-. 5xy Cho a = . H·y thay x, y b»ng nh÷ng ch÷ sè thÝch hîp ®Ó d-îc mét sè cã 3 ch÷ sè kh¸c nhau chia cho 2,3 vµ 5 ®Òu d- 4. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5. VËn dông tÝnh chÊt chia hÕt vµ phÐp chia cã d- ®Ó gi¶i c¸c bµi to¸n cã lêi v¨n. Bµi 3: Mét cöa hµng då s¾t cã 7 thïng ®ùng 2 lo¹i ®inh 5 ph©n vµ 10 ph©n (mçi thïng chØ ®ùng mét lo¹i ®inh). Sè ®inh trong mçi thïng theo thø tù lµ 24kg, 26kg, 30kg, 37kg, 41kg, 55kg vµ 58 kg. Sau khi b¸n hÕt 6 thïng vµ chØ cßn mét thïng ®inh 10 ph©n, ng-êi b¸n hµng thÊy r»ng trong sè ®inh ®· b¸n, ®inh 10 ph©n gÊp 3 lÇn ®inh 10 ph©n. Hái cöa hµng ®· cã bao nhiªu kil«gam ®inh mçi lo¹i? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 1: Trong giờ tập thể dục của lớp 4a thầy giáo cho các bạn học sinh xép hàng .lúc thì cho xép hàng 8 ,lúc xép hàng 6,lúc lại xép hàng 4,hàng 3 hàng 2 vẫn thấy vừa đủ .Các bạn tính xem lớp 4a có bao nhiêu bạn biết biết số học sinh là số nhỏ hơn 48. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2:Mẹ có một số táo mẹ xếp vào đĩa .Khi xếp vào đĩa mẹ nhận thấy nếu xếp mỗi đĩa 9 quả hay 12 quả thì cũng vừa hết .Hỏi mẹ có bao nhiêu quả táo ? biết số táo lớn hơn 30 nhỏ hơn 40 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3:ở một bến cảng có ba con tàu A,B,C Tàu a cứ 3 ngày cặp bến 1 lần ,tàu B là 4 ngày cặp bến 1 lần ,tàu C là 5 ngày .Nếu một hôm nào đó cả ba tàu cùng cặp bến thì hỏi sau bao nhiêu ngày ba tàu lại cùng cặp bến. 37 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4:Trong giờ tập thể dục của lớp 4 b thầy giáo cho các bạn học sinh xép hàng .lúc thì cho xép hàng 8 ,lúc xép hàng 6,lúc lại xép hàng 4,hàng 3 hàng 2 đều thấy hàng cuối thiếi 1 người .Các bạn tính xem lớp 4b có bao nhiêu bạn .Biết biết số học sinh là số nhỏ hơn 48. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5:Trong giờ tập thể dục của lớp 4C thầy giáo cho các bạn học sinh xếp hàng .lúc thì cho xếp hàng 8, lúc xếp hàng 6, lúc lại xếp hàng 4, hàng 3 hàng 2 đều thấy thừa 1 người .Các bạn tính xem lớp 4c có bao nhiêu bạn biết số học sinh là số nhỏ hơn 48. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 6 : Mẹ có một số táo mẹ xếp vào đĩa .Khi xếp vào đĩa mẹ nhận thấy nếu xếp mỗi đĩa 9 quả hay 12 quả thì đĩa cuối đều thiếu 2 quả .Hỏi mẹ có bao nhiêu quả táo ? biết số táo lớn hơn 30 nhỏ hơn 40. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 7: Một ông tướng cầm quân đi dẹp giặc .Ông cho quân xép hàng 10 thì thấy hàng cuối thiếu 1 người, thấy vậy ông lại cho quân xếp hàng 9 thì thấy hàng cuối vẫn thiếu 1 người; thế là ông lại cho quân xếp hàng 8 thì hàng cuối vẫn thiếu 1 người. Ông bèn cho xếp hàng 7;6;5;4;3;2 đều vẫn như vậy . Tính hộ xem ông tướng có bao nhiêu quân biết số quân của ông ít hơn 5000 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 38 10. BÀI TOÁN CÓ NỘI DUNG HÌNH HỌC Bài 3:Một thửa ruộng hình chữ nhật có chu vi 100m .Người ta tăng chiều dài lên 1/3 chiều dài thì chu vi hình chữ nhật mới là 120m. Tính diện tích thửa ruộng ban đầu . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4:Một thửa ruộng hình chữ nhật có chu vi 100m .Người ta giảm chiều dài đi 1/3 chiều dài thì chu vi hình chữ nhật mới là 80m. Tính diện tích thửa ruộng ban đầu . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5:Một thửa ruộng hình chữ nhật có chu vi 110m . Nếu tăng chiều rộng 5 m và giảm chiều dài 5 m thì diện tích thửa ruộng không thay đổi .Tính diện tích thửa ruộng 39 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 6:Một thửa đất hình vuông trên thửa đất đó người ta đào một cái ao hình vuông cạnh cái ao cách đều cạnh thửa đất .Chu vi cái ao kém chu vi thửa đất là 64 m.Tính diện tích cái ao biết diện tích phần dất còn lại là 600m2. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 7:Bác An có một mảnh đất vườn chữ nhật .ở một góc vườn bác đào một cái ao hình vuông có 1 cạnh cách chiều rộng mảnh vườn 33 m còn cạnh kia cách chiều dài mảnh vườn là 17 m .Biết diện tích phần đất còn lại là 1311m2 . Tính diện tích mảnh vườn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 8:Một thửa ruộng hình chữ nhật có chu vi 200 m .chiều dài hình chữ nhật hơn 2 lần chiều rộng là 10m.Tính diện tích thửa ruộng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 9:Một thửa ruộng hình chữ nhật có chu vi 160 m .chiều dài hình chữ nhật kém 2 lần chiều rộng là 10m.Tính diện tích thửa ruộng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 10:Một thửa ruộng hình chữ nhật có chu vi 200 m Dọc theo chiều dài người ta ngăn thửa ruộng thành 2 thửa ruộng nhỏ .Biết 1 trong 2 thửa ruộng là hình vuông và chu vi thửa ruộng hình vuông nhỏ hơn chu vi thửa ruộng hình chữ nhật nhỏ là 20m Tính diện tích thửa ruộng ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... 40 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 11:Một thửa ruộng hình chữ nhật có chu vi 160 m Dọc theo chiều dài người ta ngăn thửa ruộng thành 2 thửa ruộng nhỏ .Biết 1 trong 2 thửa ruộng là hình vuông và chu vi thửa ruộng hình vuông lớn hơn chu vi thửa ruộng hình chữ nhật nhỏ là 20m Tính diện tích thửa ruộng ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 12:Một thửa ruộng hình chữ nhật có chiều dài gấp 3 lần chiều rộng . Nếu tăng chiều rộng 5m và giảm chiều dài 5 m thì diện tích tăng thêm 300m2 . Tính diện tích thửa ruộng ban đầu .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 13: Một hình chữ nhật, nếu tăng chiều rộng để bằng chiều dài của nó thì diện tích tăng thêm 20m2, còn khi giảm chiều dài cho bằng chiều rộng thì diện tích giảm 16 m2. Tính diện tích hình chữ nhật .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 14 Một hình chữ nhật có diện tích 135m2 . Chiều dài bằng 3/5 chiều rộng .Tính chu vi hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 15: Một cái sân hình chũ nhật có chu vi 110m. Người ta tăng chiều rộng lên 5m thì sân trở thành hình vuông . tính diện tích cái sân ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 16 Một mảnh vườn hình chữ nhật có chu vi 180 m nếu giảm chiều dài 10 m thì mảnh vườn trở thành mảnh vườn hình vuông .Tính diện tích mảnh vườn ban đầu . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 41 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 17 Một mảnh vườn hình chữ nhật có chu vi 150 m .Nếu giảm chiều dài 10m và tăng chiều rộng 5m thì được một hình chữ nhật mới có chiều dài gấp 4 chiều rộng .Tính diện tích mảnh vườn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 18 Một hình chữ nhật có chiều dài gấp 3 chiều rộng . Nếu tăng chiều rộng lên 24 m thì được hình chữ nhật mới có chiều dài gấp 3 chiều rộng. Tính diện tích hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 19 Một mảnh vườn hình chữ nhật có chiều dài gấp 4 lần chiều rộng . Nếu tăng chiều dài 5m và giảm chiều rộng 5 m thì diện tích giảm đi 256m2. Tính diện tích mảnh vườn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 20 Một cái ao hình chữ nhật có chu vi 120 m .Dọc theo chiều dài người ta ngăn cái ao thành 2 ao nhỏ (Hình vẽ). Tổng chu vi 2 ao mới tạo thành la 180 m .Tính diện tích cái ao ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 21 Sân trường em hình vuông .Để tăng thêm diện tích nhà trường đã mở rộng về mỗi phía 3m thì diện tích tăng thêm là 196 m2 . Hỏi trước đây sân trường em có diện tích là bao nhiêu m2? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 42 Bài 22: Bác Hà có hai tấm kính hình chữ nhật. Chiều rộng của mỗi tấm kính bằng 1/2 chiều dài của nó và chiều dài của tấm kính nhỏ đúng bằng chiều rộng của tấm kính to. Bác ghép hai tấm kính sát vào nhau và đặt lên bàn có diện tích 90 dm2 thì vừa khít. Hãy tính kích thước của mỗi tấm kính đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 23: Khu vườn hình chữ nhật có nửa chu vi 108m. Nếu giảm chiều dài 3m và tăng chiều rộng thêm 3m thì được hình vuông . Tính diện tích hình vuông. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 24: Hình chữ nhật có chu vi 84m. Nếu bớt chiều rộng 5m và bớt chiều dài 7m thì được hình vuông. Tính chiều dài và chiều rộng hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 25: Hình chữ nhật có nửa chu vi 86m. Nếu giảm chiều dài 9m và tăng chiều rộng thêm 5m thì được hình vuông . Tính diện tích hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 26: Hình chữ nhật có chu vi 216m. Nếu giảm chiều rộng 5m và giảm chiều dài 21m thì được hình vuông. Tính diện tích hình vuông đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 27: Hình chữ nhật có chu vi gấp 10 lần chiều rộng. Chiều dài bằng 88m. Tính chiều rộng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 28: Hình chữ nhật có chu vi gấp 12 lần chiều rộng. Chiều dài bằng 120m. Tính diện tích hình chữ nhật. 43 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 29: Hình chữ nhật có chu vi gấp 14 lần chiều rộng. Chiều dài hơn chiều rộng 80m. Tính chiều dài và chiều rộng hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 30: Hình chữ nhật có chu vi gấp 16 lần chiều rộng. Chiều dài hơn chiều rộng 198m. Tính diện tích hình chữ nhật đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 31: Hình chữ nhật có nửa chu vi 99m. Nếu tăng chiều rộng thêm 5m và giảm chiều dài đi 5m thì diện tích không thay đổi. Tính chiều dài và chiều rộng hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 32: Hình chữ nhật có chu vi 160m. Nếu tăng chiều rộng thêm 10m và giảm chiều dài đi 10m thì diện tích không thay đổi. Tính diện tích hình chữ nhật đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 33: Hình chữ nhật có chu vi gấp 3 lần chiều dài. Chiều rộng bằng 5m. Tính diện tích hình chữ nhật đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 44 Bài 34: Hình chữ nhật có chu vi gấp 3 lần chiều dài. Chiều rộng kém chiều dài 5m. Tính diện tích hình chữ nhật đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 35: Hình chữ nhật có chu vi 48m. Nếu tăng chiều dài 6m thì được hình chữ nhật mới có chiều dài gấp 2 lần chiều rộng. Tính chiều dài và chiều rộng hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 36: Hình chữ nhật có chu vi 64cm. Nếu giảm chiều rộng 2cm, thêm chiều dài 2cm thì được hình chữ nhật mới có chiều dài gấp 3 lần chiều rộng. Tính chiều dài và chiều rộng hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 37: Trung bình cộng chiều dài và chiều rộng hình chữ nhật là 18m, chiều dài hơn chiều rộng 6m. Tính chiều dài và chiều rộng hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 38: Trung bình cộng chiều dài và chiều rộng hình chữ nhật là 32m, chiều dài gấp 3 lần chiều rộng 6m. Tính diện tích hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 39: Hình chữ nhật có chiều dài gấp 3 lần chiều rộng. Nếu giảm chiều rộng đi 2m và tăng chiều dài thêm 2m thì diện tích giảm đi 68m2 . Tính diện tích hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 45 .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 40: Hình chữ nhật có chiều dài gấp 4 lần chiều rộng. Nếu giảm chiều dài đi 3m và tăng chiều rộng thêm 3m thì diện tích tăng thêm 108m2 . Tính chiều dài và chiều rộng hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 41: Hình chữ nhật có chiều dài gấp 5 lần chiều rộng. Nếu giảm chiều rộng đi 2m và giảm chiều dài đi 2m thì diện tích giảm đi 140m2 . Tính diện tích hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 42: Hình chữ nhật có chiều dài gấp 5 lần chiều rộng. Nếu tăng chiều dài thêm 5m và tăng chiều rộng thêm 5m thì diện tích tăng thêm 475m2 . Tính diện tích hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 43: Một thửa hình chữ nhật có chiều rộng bằng 1/2 chiều dài. Tính diện tích thửa đất. Biết rằng nếu tăng chiều rộng 15m và giảm chiều dài 9m thì thửa đất trở thành hình vuông. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 44: Nếu bớt một cạnh hình vuông là 7m và bớt một cạnh khác 25m thì được hình chữ nhật có chiều dài gấp 3 lần chiều rộng. Tính chu vi và diện tích của hình vuông. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 45: Trên một miếng đất hình vuông, người ta đào một cái ao hình vuông để thả cá. Sau khi đào xong thì diện tích còn 1280m2. Tính diện tích miếng hình vuông ban đầu. Biết rằng cạnh ao kém cạnh miếng đất 32m. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 46 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 46: Cho hai hình chữ nhật A và B. Diện tích hình A hơn hình B là 300m2, chu vi hình A hơn hình B là 20m. Tính diện tích mỗi hình chữ nhật. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 47: Một mảnh đất hình chữ nhật có chiều rộng bằng 1/5 chiều dài, nếu tăng mỗi chiều thêm 5m thì mảnh đất hình chữ nhật có diện tích mới hơn diện tích cũ là 300m2. Tính diện tích mảnh đất hình chữ nhật sau khi mở rộng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 48: Một mảnh đất hình chữ nhật có chiều dài hơn chiều rộng 15m, nếu tăng mỗi chiều thêm 5m thì mảnh đất hình chữ nhật có diện tích mới hơn diện tích cũ là 600m2. Tính diện tích mảnh đất hình chữ nhật ban đầu. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 49: Ở chính giữa một mảnh đất hình vuông người ta đào một cái ao cũng hình vuông. Cạnh ao song song và cách đều đám đất 2m. Tính diện tích cái ao biết diện tích mảnh đất hơn diện tích cái ao là 64m2. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 50: Tính diện tích hình chữ nhật biết 3 lần chiều rộng 2 lần chiều dài bằng 62m, 2 lần chiều rộng 3 lần chiều dài bằng 68m. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 51: Một khu đất hình chữ nhật có chu vi bằng 286m. CHiều dài hơn chiều rộng 5m. Người ta mở rộng chiều dài và chiều rộng khu đất them một đoạn bằng nhau để được khu đất mới có chiều dài gấp đôi chiều rộng. Tính diện tích khu đất mới. (Tham khảo thêm Đề thi và phần Bài tập mở rộng) 47 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 11/®¬n vÞ ®o Bµi 28: C« Mai cã 2kg ®-êng, c« ®· dïng 41sè ®-êng ®ã ®Ó lµm b¸nh. Hái c« Mai cßn l¹i bao nhiªu gam ®-êng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 48 Bµi 29: ViÕt sè thÝch hîp vµo chç chÊm: 1 phót = ...gi©y 3 phót = . .......gi©y 2 phót 10 gi©y = ...gi©y 61phót = .......gi©y 51thÕ kØ = . ...n¨m .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 30: ViÕt tiÕp vµo chç chÊm: a) N¨m 40, Hai Bµ Tr-ng phÊt cê khëi nghÜa chèng l¹i ¸ch thèng trÞ cña nhµ H¸n, n¨m ®ã thuéc thÕ kØ ... b)Lª Lîi lªn ng«i vua vµo n¨m 1428. N¨m ®ã thuéc thÕ kØ ... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 31: Khoanh vµo ch÷ ®Æt tr-íc c©u tr¶ lêi ®óng: Ngµy 23 th¸ng 5 lµ thø 3. Ngµy 1 th¸ng 6 cïng n¨m ®ã lµ: A. Thø t- B. Thø n¨m C. Thø s¸u D. Thø b¶y .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 12. DẠNG TOÁN LIÊN QUAN ĐẾN CHUYỂN TỪ A SANG B ; B SANG C; C SANG ... Bài 1: Ba kho chứa 560 tấn thóc .Nếu chuyển 30 tấn từ kho thứ nhất sang kho thứ 2 Sau đó chuyển 25 tấn từ kho thứ 2 sang kho thứ 3 rồi chuyển 12 tấn từ kho thứ 3 sang kho thứ nhất thì số thóc ở 3 kho bằng nhau .Tính số thóc mỗi kho. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 49 .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2 Ba kho chứa 240 tấn thóc .Nếu chuyển 25 tấn từ kho thứ nhất sang kho thứ 2 Sau đó chuyển 35 tấn từ kho thứ 2 sang kho thứ 3 thì số thóc ở 3 kho bằng nhau .Tính số thóc mỗi kho. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3: Ba lớp 4a;4b;4c. đi trồng cây cả 3 lớp trồng được 120 .Số cây lớp 4a và 4 b trồng được là 70 cây ;số cây lớp 4b và 4c là 90 cây ;số cây lớp 4c và 4a là 80 cây . Tính số cây mỗi lớp . (Tham khảo thêm Đề thi và phần Bài tập mở rộng) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 13.DẠNG TOÁN KHỬ Bài 1: Mua 3 lọ mực và 4 cái bút hết 25000 đồng . Mua 5 lọ mực và 4 cái bút hết 31000 đồng . Tính giá tiền mỗi loại. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 50 .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2: Minh mua 5 quyển vở và 8 quyển sách hết 75500 đồng. Tâm mua 3 quyển sách và 10 quyển vở hết 73000 đồng. Tính giá tiền mỗi loại. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3: Mua 3 m vải hoa và 7 m vải xanh hết 370 000 đồng . Mua 4 m vải hoa và 5 m vai xanh phải trả 320 000 Đồng. Tính giá tiền 1m vải mỗi loại. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4: Minh mua 5 quyển vở và 8 quyển sách hết 42000 đồng. Biết một quyển sách có giá gấp 2 lần 1 quyển vở. Tính giá tiền mỗi loại .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... *Bài tập 1: Để học thủ công, tổ Một mua 10 cái kéo và 5 túi giấy màu hết tất cả 50.000 đồng. Tổ Hai cũng mua 8 cái kéo và 10 túi giấy màu như thế hết tất cả 52.000 đồng. Tính giá tiền một cái kéo, giá tiền một túi giấy màu? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... *Bài tập 2: Văn phòng trường em lần đầu mua 24 cây bút bic và 12 cây bút chì hết tất cả 60.000 đồng. Lần sau mua 10 cây bút bic và 8 cây bút chì hết tất cả 28.000 đồng. Hãy tính giá tiền mỗi cây bút từng loại? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... *Bài tập 3: Cô Thu mua 1 mét lụa và 1 mét vải hết tất cả 50.000 đồng. Cô Đông mua 1mét lụa 2 và 52mét vải cùng loại như thế hết tất cả 23.000 đồng. Hỏi cô Xuân mua 8 mét lụa và 15 mét vải cùng loại như thế phải trả bao nhiêu tiền? .......................................................................................................................................................................... .......................................................................................................................................................................... 51 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 4. Bài tập về nhà: Bạn Mai mua 3 lọ mực đỏ và 2 lọ mực xanh giá 23.000 đồng. Bạn Lan cũng mua 2 lọ mực đỏ và 3 lọ mực xanh mực như thế hết 22.000 đồng. Tính giá tiền một lọ mực mỗi loại? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 14. MỘT SỐ BÀI TOÁN VỀ TÍNH TUỔI Bài 1: Năm nay con 4 tuổi và kém cha 35 tuổi. Hỏi sau bao nhiêu năm nữa thì 2 lần tuổi cha bằng 7 lần tuổi con ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 52 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2: Cách đây 3 năm, em lên 5 tuổi và kém anh 8 tuổi. Hỏi cách đây mấy năm thì tuổi anh gấp 3 lần tuổi em ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3: Tuổi cha năm nay gấp 4 lần tuổi con và tổng số tuổi của 2 cha con cộng lại là 50 tuổi. Hãy tính tuổi của 2 cha con khi tuổi cha gấp 4 lần tuổi con. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4: Hùng hơn Cường 6 tuổi, biết rằng 74tuổi của Hùng bằng 32tuổi của Cường. Tính tuổi của mỗi người. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5: Năm nay tuổi mẹ gấp 3 lần tuổi con. 8 năm trước tuổi mẹ gấp 7 lần tuổi con.Tìm tuổi mỗi người hiện nay. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 6: Tuổi của bà, của mẹ và của Mai năm nay cộng được 100 năm.Bạn hãy tính tuổi của mỗi người, biết rằng, tuổi của Mai có bao nhiêu ngày thì tuổi của mẹ có bấy nhiêu tuần và tuổi của Mai có bao nhiêu tháng thì tuổi của bà có bấy nhiêu năm. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 7: Tuổi em năm nay nhiều hơn hiệu số tuổi của 2 chị em là 15. Tổng số tuổi của 2 chị em cùng nhỏ hơn 2 lần tuổi của chị là 3. Tính tuổi mỗi người. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 53 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 8: 8 năm về trước tổng số tuổi của ba cha con cộng lại là 48. 8 năm sau cha hơn con lớn 26 tuổi và hơn con nhỏ 34 tuổi. Tính tuổi của mỗi người hiện nay. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 9: Hai năm trước đây tuổi hai chú cháu cộng lại bằng 24. Hỏi sau mấy năm nữa thì tuổi chú gấp 4 lần tuổi cháu? Biết rằng 2 năm trước tuổi cháu có bao nhiêu ngày thì tuổi chú có bấy nhiêu tuần . .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 10: Tuổi em hiện nay gấp 2 lần tuổi em khi anh bằng tuổi em hiện nay.Khi tuổi em bằng tuổi anh hiện nay thì 2 lần tuổi em lớn hơn tuổi anh lúc đó 15 tuổi. Tính tuổi hiện nay của mỗi người. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 11: Khi tuổi chị bằng tuổi em hiện nay thì tuổi chị lớn hơn 3 lần tuổi em là 3 tuổi. đến khi chị 34 tuổi thì tuổi em bằng tuổi chị hiện nay.Tìm tuổi của 2 chị em hiện nay. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 12: Tuổi bố năm nay gấp 2,3 lần tuổi con. 25 năm về trước, tuổi bố gấp 8,3 lần tuổi con. Hỏi khi tuổi bố gấp 3 lần tuổi con thì con bao nhiêu tuổi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 13: Hai người bạn gặp nhau. Một người hỏi bạn mình :" Các con của anh bao nhiêu tuổi?" Người thứ hai trả lời: "Tôi có hai đứa con trai : tuổi tôi gấp 4 lần tuổi đứa thứ nhất và gấp 7lần đứa thứ hai". Hỏi ông bố bao nhiêu tuổi và các con của ông bao nhiêu tuổi? 54 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 14: Ba người có tên là A, B, C cùng ở trong 1 buồng của toa xe lửa. Trong khi trò chuyện mới biết rằng: - Nếu đổi chỗ các chữ số trong tuổi của A thì được tuổi của B - Hiệu của tuổi giữa A và B gấp đôi số tuổi của C - Tuổi của B gấp 10 lần tuổi của C Hỏi mỗi người bao nhiêu tuổi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 15 : Người ta hỏi một ông già rằng ông đã tham gia quân đội trong bao lâu, ông trả lời:Số năm tham gia quân đội của tôi bằng 1/27 tuổi của tôi hay bằng 1/7 tuổi của cháu tôi hoặc bằng đúng tuổi của con trai tôi. Ngoài ra tuổi của tôi gần số 90 hơn là gần số 100. Hỏi ông già đã tham gia quân đội trong bao lâu? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 16 : An hỏi Hà: “ Năm nay anh bao nhiêu tuổi? ” Anh Hà trả lời: “ Nếu sang năm lấy tuổi của anh nhân với 6 sẽ được một số có 3 chữ số trong đó chữ số hàng trăm là 1, còn chữ số hàng chục và chữ số hàng đơn vị chính là chữ số hàng hàng chục và chữ số hàng đơn vị của tuổi anh khi đó”. Hỏi anh Hà năm nay bao nhiêu tuổi? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 17: Vào năm mới tuổi bố nhiều hơn tuổi anh là 29, tuổi mẹ nhiều hơn tuổi em là 25, hiệu của tuổi bố và tuổi mẹ gấp đôi hiệu của tuổi anh và tuổi em. Tính tuổi của mỗi người (bố, mẹ, anh và em) biết rằng tổng số tuổi của bốn người là 90. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 18: Ngày đầu năm 1991, bác Nam hỏi anh Việt: - Năm nay cháu bao nhiêu tuổi? - Tuổi cháu năm nay đúng bằng tổng các chữ số của năm sinh - anh Việt trả lời. 55 Thế mà bác Nam tính ra ngay tuổi của anh Việt. Bác gật gù nói: - Lúc bác bằng tuổi cháu hiện nay, bác đang tham gia kháng chiến chống Pháp, và năm ấy cũng có tổng các chữ số bằng tuổi cháu. Anh Việt cũng tính đúng tuổi của bác Nam. Hỏi anh Việt và bác Nam sinh năm nào? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 19: Trả lời về tuổi của mình, 1 người đàn ông nói như sau: "Cứ vào sinh nhật của tôi, cha tôi lại giết 1 con cừu để ăn mừng, bộ da cừu ông xếp vào 1 chỗ. Tôi lớn lên lấy vợ cũng sinh được 1 thằng con trai, vào sinh nhật nào của nó tôi cũng lại giết cừu, cất bộ da vào 1 chỗ. Năm nay số da cừu của tôi bằng số da cừu của nó. Hỏi tuổi người đàn ông và con trai của ông ta là bao nhiêu? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 20: Trong giờ nghỉ ở một hội nghị, các đồng nghiệp hỏi một giáo sư xem ông ta có mấy con và chúng bao nhiêu tuổi. Giáo sư trả lời: - Tôi có 3 con trai. Có sự trùng hợp lý thú là ngày sinh của chúng đều là ngày hôm nay, tuổi chúng cộng lại bằng ngày hôm nay và đem nhân với nhau thì tích là 36. Một đồng nghiệp nói: - Chỉ như vậy thì chưa xác định được tuổi của bọn trẻ. - Ồ, đúng vây. Tôi quên không nói thêm rằng: Khi chúng tôi chờ sinh đứa thứ 3 thì 2 đứa lớn đã được gửi về quê với ông bà. - Xin cám ơn ngài, giờ thì tôi đã biết tuổi của bọn trẻ rồi. Vậy tuổi của mỗi cậu con trai là bao nhiêu và ngày hôm đó là ngày nào trong tháng? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 1 Hiện nay tuổi em bằng 2/3 tuổi anh .Đến khi tuổi em bằng tuổi anh hiện nay thì tổng số tuổi của hai anh em là 49 tuổi . tính tuổi hiện nay của mỗi người. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2 Hiện nay bố gấp 6 lần tuổi con . 4 năm nữa bố gấp 4 lần tuổi con .Tính tuổi hiên nay của mỗi người. 56 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3 Tổng số tuổi của ông ,bố và cháu là 120 tuổi .Tính tuổi mỗi người biết tuổi ông là bao nhiêu năm thì cháu bấy nhiêu tháng và cháu bao nhiêu ngày thì bố bấy nhiêu tuần .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4 Hiện nay tuổi mẹ gấp 4 lần tuỏi con . Năm năm nữa tuổi mẹ gấp 3 lần tuổi con .Tính tuổi hiện nay của mỗi người. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5: Tuổi của con hiện nay bằng 1/2 hiệu tuổi của bố và tuổi con. Bốn năm trước, tuổi con bằng 1/3 hiệu tuổi của bố và tuổi con. Hỏi khi tuổi con bằng 1/4 hiệu tuổi của bố và tuổi của con thì tuổi của mỗi người là bao nhiêu ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 57 15. BÀI TOÁN GIẢ THIẾT TẠM VÝ dô 2: 12 con võa gµ võa thá, c¶ th¶y ®Õm ®-îc 32 ch©n. Hái cã bao nhiªu con gµ, bao nhiªu con thá. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... VÝ dô: Cã 18 « t« gåm 3 lo¹i: Lo¹i 4 b¸nh chë ®-îc 5 tÊn, lo¹i 6 b¸nh chë ®-îc 6 tÊn vµ lo¹i 8 b¸nh chë ®-îc 6 tÊn. 18 xe ®ã chë ®-îc tÊt c¶ 101 tÊn hµng, vµ cã tÊt c¶ 106 b¸nh xe. Hái mçi lo¹i cã bao nhiªu xe? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi to¸n 1: Cã 10 xe chë g¹o gåm hai lo¹i. Lo¹i 1 xe chë ®-îc 43 t¹ vµ lo¹i 1 xe chë ®-îc 32 t¹. TÊt c¶ ®· chë ®-îc 39 tÊn 8 t¹ g¹o. Hái cã bao nhiªu xe mçi lo¹i? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi to¸n 2: Cã 8 sät ®ùng tÊt c¶ 1120 qu¶ võa cam võa quýt. Mçi sät cam ®ùng ®-îc 75 qu¶, mçi sät quýt ®ùng ®-îc 179 qu¶. Hái mçi lo¹i cã bao nhiªu qu¶? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi to¸n 3: Mét bÕp ¨n mua 200 con võa Õch võa cua bÓ. Tæng sè ch©n ®Õm ®-îc lµ 1400 ch©n (cµng cua xem nh- ch©n cua). Hái cã bao nhiªu con mçi lo¹i. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 58 Bµi to¸n 4: Cã 15 « t« gåm 3 lo¹i: Lo¹i 4 b¸nh chë ®-îc 5 tÊn, lo¹i 6 b¸nh chë ®-îc 10 tÊn vµ lo¹i 6 b¸nh chë ®-îc 8 tÊn. 15 xe ®ã chë ®-îc tÊt c¶ 121 tÊn hµng, vµ cã tÊt c¶ 84 b¸nh xe. Hái mçi lo¹i cã bao nhiªu xe. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi to¸n 5: Cã 15 « t« gåm 3 lo¹i, lo¹i 4 b¸nh chë 5 tÊn, lo¹i 4 b¸nh chë 6 tÊn, lo¹i 6 b¸nh chë 8 tÊn. Hái sè xe mçi lo¹i lµ bao nhiªu, biÕt tæng sè b¸nh xe lµ 70 b¸nh, tæng sè hµng chë ®-îc lµ 93 tÊn. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 16. CÁC BÀI TOÁN LIÊN QUAN TRỒNG CÂY 59 17. MỘT SỐ BÀI TOÁN GIẢI NGƯỢC TỪ CUỐI Bài 1: Lan có một số nhãn vở .Lan tặng Mai 1/2 số nhãn vở và 1chiếc .Lan tặng Hoà 1/2 số nhãn vở còn lại và 2 chiếc .Lan tặng Nga 1/2 số nhãn vở còn lại sau 2 lần và 3 chiếc .Cuối cùng Lan còn lại 6 chíêc cho Mình .Hỏi Lan có tất cả bao nhiêu nhãn vở ,và tặng mỗi bạn bao nhiêu nhãn vở. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2, Một bà đem trứng đi chợ bán .Lần đầu bà bán 1/2 số trứng và 1/2 quả trứng .Lần 2 bà bán 1/2 số trứng còn lại và 1/2 quả trứng .Lần thứ 3 bà bán 1/2 Số trứng còn lại sau 2 lần đầu và 1/2 quả trứng nữa thì vừa hết . Hỏi bà đem ra chợ bán bao nhiêu quả trứng. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3: Mai có một số bông hồng ,Mai tặng Nga 1/2 số hoa Mai có .Tặng Đào 1/2 số còn lại .Cuối cùng Mai còn 7 Bông dành cho mình .Hỏi Mai đã tặng mỗi bạn bao nhiêu bông hoa. (Tham khảo thêm Đề thi và phần Bài tập mở rộng) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 1. T×m mét sè biÕt r»ng, sè ®ã trõ 80, ®-îc bao nhiªu nh©n víi 5 råi céng víi 192 th× b»ng 792. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 2. MÑ cho hai anh em mét sè tiÒn ®Ó mua s¸ch. NÕu anh cho em mét sè tiÒn ®óng b»ng sè tiÒn cña em, råi em l¹i cho anh mét sè tiÒn ®óng b»ng sè tiÒn cßn l¹i cña anh th× em cã 35000 ®ång vµ anh cã 30000 ®ång. Hái mÑ ®· cho mçi ng-êi bao nhiªu tiÒn ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 60 3. Cã ba hép bi A, B, C. LÇn ®Çu chuyÓn 10 bi tõ hép A sang hép B vµ 15 bi tõ hép C sang hép B. LÇn thø hai chuyÓn 6 bi tõ hép A sang hép B vµ 9 bi tõ hép B sang hép C. LÇn thø ba chuyÓn 20 bi tõ hép C sang hép A vµ 18 bi tõ hép B sang hép A. LÇn thø t- chuyÓn 9 bi tõ hép A sang hép B vµ 7 bi tõ hép C sang hép B, th× cuèi cïng hép A cã 190 bi, hép B cã 350 bi, hép C cã 280 bi. Hái lóc ®Çu mçi hép cã bao nhiªu bi ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 4. Mét ng-êi ra chî b¸n cam. LÇn thø nhÊt b¸n 1/2 sè cam céng thªm 1/2 qu¶. LÇn thø hai b¸n 1/2 sè cam cßn l¹i céng thªm 1/2 qu¶. LÇn thø ba b¸n 1/2 sè cam cßn l¹i céng thªm 1/2 qu¶. LÇn thø t- b¸n 1/2 sè cam cßn l¹i céng 1/2 qu¶ th× võa hÕt. TÝnh sè cam ng-êi ®ã ®em b¸n. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 5. (To¸n cæ). Mét tªn tham lam gÆp mét con quû ë c¹nh chiÕc cÇu. Tªn nµy than phiÒn vÒ nçi nghÌo khæ cña m×nh. Con quû nãi r»ng " T«i cã thÓ gióp anh. Cø mçi lÇn anh ®i qua cÇu th× sè tiÒn cña anh sÏ ®-îc t¨ng gÊp ®«i; nh-ng ngay sau ®ã anh ph¶i tr¶ cho t«i 24 xu. B»ng lßng chø ?". Tªn tham lam b»ng lßng nh- thÕ. Sau khi h¾n ®i qua cÇu ba lÇn th× thÊy trong tói cña m×nh kh«ng cßn mét xu nµo. Hái lóc ®Çu tªn tham lam cã bao nhiªu tiÒn ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 6. Trong mét buæi lao ®éng trång c©y ®Çu xu©n, líp 5A ®· chia sè c©y cho c¸c tæ lÇn l-ît nh- sau: Tæ Mét trång 20 c©y vµ 4/ 100 sè c©y cßn l¹i; Tæ Hai trång 21 c©y vµ 4/100 sè c©y cßn l¹i; Tæ Ba trång 22 c©y vµ 4/100 sè c©y cßn l¹i; …………………………………………………. Cø chia nh- vËy cho ®Õn tæ cuèi cïng th× võa hÕt sè c©y vµ sè c©y mçi tæ ®em trång ®Òu b»ng nhau. Hái líp 5 A cã mÊy tæ vµ mçi tæ ®-îc chia bao nhiªu c©y ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 7. Trong hép cã 130 bi. Hai b¹n ch¬i trß bèc bi. Mçi lÇn cã thÓ lÊy tõ 1 ®Õn 6 bi. Ai lÊy ®-îc viªn bi cuèi cïng ng-êi ®ã th¾ng cuéc. B¹n ®-îc bèc tr-íc, theo b¹n nªn lÊy nh- thÕ nµo ®Ó b¹n lu«n lµ ng-êi th¾ng cuéc ? .......................................................................................................................................................................... .......................................................................................................................................................................... 61 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 18. DẠNG TOÁN CÔNG VIỆC Bài 1:Bác An làm một công việc hết 8 giờ .Bác Bình cũng công việc ấy hết 5 giờ .Hỏi nếu 2 bác cùng làm công việc ấy thi sau bao nhiêu giờ sẽ hoàn thành? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2: Nếu bể không có nước vòi thứ nhất chảy trong 3 giờ sẽ đầy bể.Nếu bể không có nước vòi thứ 2 chảy trong 5 giờ sẽ đầy bể .Hỏi nếu bể không có nước cùng 1 lúc cho cả 2 vòi chảy trì trong bao lâu sẽ đầy bể? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3: Bác Minh làm Một công việc hết 8 giờ .Bác Tâm cũng công việc ấy làm hết 5 giờ . Đầu tiên bác Minh làm một mình sau khi làm được 4 giờ thì bác Tâm đến làm cùng với bác Minh .Hỏi sau bao nhiêu lâu nữa thì hai bác làm xong công việc đó? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 4:Bác An làm một công việc hết 8 giờ .Bác Bình cũng công việc ấy hết 5 giờ .Lúc đâu 2 bác cùng làm nhưng sau khi làm được 3 giờ do bận công việc nên bác Bình phải đi làm việc khác .Hỏi bác An còn phải làm bao lâu nữa mới hoàn thành công việc ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 5: Nếu bể không có nước vòi thứ nhất chảy trong 4 giờ sẽ đầy bể.Nếu bể không có nước vòi thứ 2 chảy trong 5 giờ sẽ đầy bể .Khi bể không có nước người ta cho 2 vòi cùng chảy vào bể sau khi chảy được 2 giờ người ta tắt vòi thứ nhất để vòi thứ 2 chảy tiếp .Hỏi sau bao nhiêu thời gian nữa thì bể đầy nước? (Tham khảo thêm Đề thi và phần Bài tập mở rộng) .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 62 .......................................................................................................................................................................... Bài 1 : Sơn và Hải nhận làm chung một công việc. Nếu một mình Sơn làm thì sau 3 giờ sẽ xong việc, còn nếu Hải làm một mình thì sau 6 giờ sẽ xong công việc đó. Hỏi cả hai người cùng làm thì sau mấy giờ sẽ xong công việc đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2 : Hai vòi nước cùng chảy vào bể nước thì sau 1 giờ 12 phút sẽ đầy bể. Nếu một mình vòi thứ nhất chảy thì sau 2 giờ sẽ đầy bể. Hỏi nếu một mình vòi thứ hai chảy thì mấy giờ đầy bể ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 3 : Ba người dự định đắp xong một con đường. Người thứ nhất có thể đắp xong con đường đó trong 3 tuần. Người thứ hai có thể đắp xong một con đường dài gấp 3 lần con đường đó trong 8 tuần. Người thứ ba có thể đắp xong một con đường dài gấp 5 lần con đường đó trong 12 tuần. Hỏi cả ba người cùng đắp con đường dự định ban đầu thì sẽ hoàn thành trong bao nhiêu giờ, nếu mỗi tuần làm việc 45 giờ ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 63 19.BÀI TOÁN CHIA GIA TÀI *Đề : Một ông nhà giàu khi vợ đang mang thai thì mắc bệnh hiểm nghèo, trước lúc lâm chung ông ta để lại “Di chúc ” : Sau khi qua đời nếu vợ sinh con trai thì gia tài cho con trai 2/3 và vợ 1/3; Nếu sinh con gái thì con gái 1/3; vợ 1/3; còn lại 1/3 làm từ thiện. Nhưng thực tế sau khi ông ta chết, vọ sinh đôi : 1 con trai và 1 con gái. Hỏi Tòa án dân sự phải xử chia gia tài cho họ như thế nào ? Mỗi người được hưởng bao nhiêu phần ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... *Đề : Một ông nhà giàu khi vợ đang mang thai thì mắc bệnh hiểm nghèo, trước lúc lâm chung ông ta để lại “Di chúc ” : Sau khi qua đời nếu vợ sinh con trai thì gia tài cho con trai 2/3 và vợ 1/3; Nếu sinh con gái thì con gái 1/3; vợ 1/3; còn lại 1/3 làm từ thiện. Nhưng thực tế sau khi ông ta chết, vọ sinh đôi : 1 con trai và 1 con gái. Hỏi Tòa án dân sự phải xử chia gia tài cho họ như thế nào ? Mỗi người được hưởng bao nhiêu phần ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 64 20.DÙNG SƠ ĐỒ DIỆN TÍCH ĐỂ GIẢI TOÁN BA ĐẠI LƯỢNG Bài 1: Một ôtô đi từ Vinh đến Hà Nội dự định đi với vận tốc 30 km/h. Nhưng do trời mưa nên chỉ đi được 25 km/h, nên đến Hà Nội muộn mất 2 giờ so với thời gian dự định. Tính quãng đường Vinh - Hà Nội? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 2: Bố bạn An năm nay 30 tuổi. Nếu lấy số tuổi bố bạn An cách đây 5 năm và số tuổi của An bây giờ cộng với 2 rồi nhân hai số đó với nhau thì cũng bằng số tuổi bố bạn An bây giờ nhân với số tuổi bạn An bây giờ. Tính tuổi bạn An bây giờ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 65 TOÁN 4 – HỌC KÌ 2 NÂNG CAO THEO CHỦ ĐỀ ph©n sè 21/ph©n sè - RÚT GỌN PHÂN SỐ Bài 137: Viết các phân số sau theo thứ tự từ bé đến lớn: 76;73;74 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 141: So sánh 3+ c) 109 a) 43+ 42 b) 87 8 8+ 10 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 149: Khu đất nhà Lan có53diện tích đất làm nhà, 72diện tích dùng để trồng rau. Hỏi: a)Diện tích đất làm nhà và trồng rau bằng bao nhiêu phần diện tích của khu vườn? a) Diện tích làm nhà nhiêu hơn diện tích trồng rau bao nhiêu phần diện tích khu đất? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 150: Tìm x 7+ x = c) 229 x + = b) 23 a)34 3 3 x − = d) 92 4 12 11 9− x =2 66 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 151: Trong số các bài kiểm tra giữa kì II của khối lớp 4, có73số bài đạt điểm khá. Biết số bài đạt 29 điểm khá và giỏi là35 số bài kiểm tra. Hỏi số bài đạt điểm giỏi chiếm bao nhiêu phân số bài kiểm tra? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 154: T×m sè tù nhiªn x sao cho: 75 4< < x 7 10 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 155: T×m hai ph©n sè biÕt r»ng hai ph©n sè ®ã ®Òu cã mÉu sè lµ 8, c¸c tö sè cÇn t×m lµ hai sè tù nhiªn liªn tiÕp vµ ph©n sè 53n»m gi÷a hai ph©n sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 156: T×m hai ph©n sè biÕt r»ng hai ph©n sè ®ã ®Òu cã tö sè lµ 1, c¸c mÉu sè ph¶i t×m lµ hai sè tù nhiªn liªn tiÕp vµ ph©n sè 8413n»m gi÷a hai ph©n sè ®ã. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 67 22/So s¸nh ph©n sè Bµi 1: So s¸nh c¸c ph©n sè sau b»ng c¸ch hîp lÝ nhÊt: 1999PhÇn bï 1998vµ 2000 a) 1712vµ 157d) 1999 1999vµ 1112So s¸nh víi 1 b) 2001 c) 2713vµ 4127PhÇn bï g) 4723vµ 4524( Trung gian) .......................................................................................................................................................................... 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Bµi 2: So s¸nh c¸c ph©n sè sau b»ng c¸ch hîp lÝ nhÊt: a) 2515vµ 75PhÇn bï d) 83vµ 4917 SS víi 15/49 27Trung gian26/120 e) 1547vµ 3529( TS > MS) b) 6013vµ 100 1993vµ 998 c) 1995 997(997x2) SS phÇn bï g) 2716vµ 2915SS 16/29 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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.......................................................................................................................................................................... 69 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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Bµi 3: So s¸nh c¸c ph©n sè sau b»ng c¸ch hîp lÝ nhÊt: a) 1513vµ 2523 (SS phÇn bï) c) 2512vµ 4925 SS 24/49 b) 2823vµ 2724SS Trung gian .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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Bµi 157: So s¸nh b»ng c¸ch hîp lÝ 2007vµ 2008 1313vµ 1413 b) 1122 vµ 511 c) 813vµ 27 d) 2006 a)73vµ 7733; 1414 2006 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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.......................................................................................................................................................................... 71 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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Bµi 158: Kh«ng quy ®ång mÉu sè h·y so s¸nh c¸c ph©n sè 2007vµ2009 a)2008 2008 b)32vµ43 c)132vµ143 d)145vµ112 e)65vµ109 g)7877vµ7978 h)1817vµ1918 i)2120vµ2221 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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.......................................................................................................................................................................... .......................................................................................................................................................................... 72 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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Bµi 159: So s¸nh b»ng c¸ch hîp lÝ 2007vµ2004 2005 c)2006 2007vµ2007 a)9697vµ9596 b)2006 2008 d)2425vµ2324 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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.......................................................................................................................................................................... 73 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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Bµi 160: Kh«ng quy ®ång mÉu sè h·y so s¸nh a)94vµ103 b)1911vµ1813 c)9745vµ9647 d)3120vµ3319 e)4645vµ4744 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 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Bµi 161: H·y chøng tá r»ng c¸c ph©n sè sau b»ng nhau 13= = 7= = b)127127 1313 131313 77 777 123= c)151515 a)999 123123 9 99 127 15 1515 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 162: So s¸nh c¸c ph©n sè sau víi 1 1991 1999 34 34 × × b) 1995 1995 a) 33 35 × × .......................................................................................................................................................................... .......................................................................................................................................................................... 75 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 163: So s¸nh c¸c ph©n sè sau (víi n lµ sè tù nhiªn) a) 21 n vµ 43 + n b) n + 3 + n vµ 41 n + n + n n − + .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 164: So s¸nh c¸c ph©n sè sau(a lµ sè tù nhiªn kh¸c 0) a +1vµ 23 a b) a + 6 + a vµ 71 a) a a + a a + + .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 23/ TÌM PHÂN SỐ CỦA MỘT SỐ Bài 165: Lớp 4A có 27 học sinh, trong đó số bạn nữ bằng 32số học sinh cả lớp. Tìm số học sinh nam? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 166: Lớp 4B có 10 bạn nữ, số bạn nam bằng23số bạn nữ. Tìm số bạn nam? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 167: Một sân trường hình chữ nhật có chiều rộng bằng 90m, chiều dài bằng 34chiều rộng. Tính diện tích sân trường đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 76 .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 168: Nam có 27 viên bi gồm hai màu vàng và đỏ, trong đó số bi màu vàng bằng 32tổng số bi. Tìm số bi màu đỏ? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 169: An có 10 quyển vở, Bình có số vở bằng23số vở của An. Bình có bao nhiêu quyển vở? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bài 170: Một sân trường hình chữ nhật có chiều dài bằng 90m, chiều rộng bằng 32chiều dài. Tính diện tích sân trường đó. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 171: C¶ 3 ng-êi thî lµm c«ng ®-îc 270 000 ®ång. Ng-êi thø nhÊt ®-îc 21sè tiÒn, ng-êi thø hai ®-îc 2sè tiÒn. TÝnh tiÒn cña ng-êi thø ba. 5 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 17 2: Hai ng-êi chia nhau 720 000 ®ång. Ng-êi thø nhÊt ®-îc 61sè tiÒn, ng-êi thø hai ®-îc 81sè tiÒn, sè tiÒn cßn l¹i lµ cña ng-êi thø ba. Hái ng-êi thø ba ®-îc bao nhiªu tiÒn? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 77 Bµi 1: C¶ ba ng-êi thî lµm c«ng ®-îc 270000 ®ång. Ng-êi thø nhÊt ®-îc 31sè tiÒn. Ng-êi thø hai ®-îc 2sè tiÒn. TÝnh sè tiÒn cña ng-êi thø ba. 5 .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 2: Hai ng-êi chia nhau 720000 ®ång. Ng-êi thø nhÊt ®-îc 61sè tiÒn. Ng-êi thø hai ®-îc 81sè tiÒn. Sè tiÒn cßn l¹i lµ cña ng-êi thø ba. Hái ng-êi thø ba ®-îc chia bao nhiªu tiÒn? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 3: Ba b¹n chia nhau 30 qu¶ cam. Nam lÊy 52sè cam, Ph-îng lÊy sè cam b»ng 54sè cam cña Mai. Hái mçi b¹n ®-îc bao nhiªu qu¶ cam? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 4: Hai anh em cã tÊt c¶ 40 viªn bi, biÕt 31sè bi cña em b»ng 51sè bi cña anh. TÝnh sè bi cña mçi ng-êi. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 5: HiÖn nay mÑ h¬n con 24 tuæi, biÕt31tuæi cña con b»ng 111tuæi cña mÑ.TÝnh tuæi cña mçi ng-êi. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 78 .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 6: Líp 5A cã 21sè häc sinh n÷ b»ng 51sè häc sinh nam. BiÕt sè häc sinh n÷ kÐm sè häc sinh nam lµ 15 b¹n. TÝnh sè häc sinh n÷ vµ sè häc sinh nam. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 7: Líp 5A cã 35 häc sinh, biÕt 51sè häc sinh nam b»ng 21sè häc sinh n÷. TÝnh sè häc sinh nam vµ häc sinh n÷. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 8: Ba khu vùc A, B, C cã tæng sè d©n lµ 12000 ng-êi. TÝnh sè d©n mçi khu vùc, biÕt 32sè d©n khu vùc A b»ng 105sè d©n khu vùc B vµ b»ng 104sè d©n khu vùc C. .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... Bµi 9: Hai anh em ®i mua s¸ch hÕt 112000 ®ång. BiÕt 53sè tiÒn s¸ch cña em b»ng 31sè tiÒn cña anh. Hái mçi ng-êi mua hÕt bao nhiªu tiÒn s¸ch? .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... .......................................................................................................................................................................... 79