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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 : + 1992 +....+  (( 1991 a) ( 1991 + 1992 + ...+ 1999 ) – 11 + 12 + .....+ 19 ).1999 ) 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 : 86 – 51  )61 71  81 + 736 + 89 )  66+ 2378  76+4545 a) ( 1999 + 7956 –( 315 + 598 .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  b) 11  21 abc - 853467 = 0  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) c) C= 720 + ( 3927 – 720) b) B = x- ( x- 60) 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: b) 2008  867 + 2009  133 a) 2009  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 b) 123  15 - 123  5 a) 3  17 + 3  25 - 3  2 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
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