簡便運(yùn)算的練習(xí)題和答案

1、(1)乘法交換律：aXb=bXa38X25X442X125X8運(yùn)算定律練習(xí)題乘法結(jié)合律：(aXb) Xc = aX (bXc)25X17X4(25X125) X (8X4)49X4X538X125X8X3(125X25)X45 X289X2(125X12) X8125X (12X4)(2)乘法交換律和結(jié)合律的變化練習(xí)125X64125X8844X25125X2425X28(3)加法交換律：a+b=b+a加法結(jié)合律：(a+b) +c=a+ (b+c)357+288+143158+395+105167+289+33129+235 + 171 + 165378+527+73169+78+2258+3

2、9+42+61138+293+62 + 107(4)乘法分配律：(a+b) Xc=aXc+bXc 正用練習(xí)(80+4) X25(20+4) X25(125+17) X825X (40+4)3)15X (20+(5)乘法分配律正用的變化練習(xí):36X325X41X2439X101125X88201(6)乘法分配律反用的練習(xí):34X72+34X2835X37+65X3785X82+85X1825X97+25X376X25+25X24(7)乘法分配律反用的變化練習(xí)：38 X 29+3875 X 299+7564 X199+6435X68+68+68X64思考題：(8)其他的一些簡便運(yùn)算。8004-25

3、60004-12536004-8-?558X101-5874X99【思路導(dǎo)航】在除法里，被除數(shù)和除數(shù)同時(shí)乘或除以一個(gè)相同的數(shù)，商不變。325 十 25=(325X4) 4- (25X4)=1300*100=13【練一練 1 】(1 ) 450W25( 2 ) 5254-25(3) 3500十125(4)10000一625(5)495004-900(6)9000三225【經(jīng)典例題二】計(jì)算25X125X4X8【思路導(dǎo)航】如果先把25與4相乘，可以得到100,同時(shí)把125與8相乘，可以得到1000； 再把100和1000相乘就可以了。運(yùn)用了乘法交換律和結(jié)合律。25X125X4X8=(25X4) X

4、(125X8)=100X1000=100000【練一練 2 ( 1 ) 125X15X8X425X24(3) 125X16125X25X32(4) 75X16(6) 25X5X64X125(5)(2)64X 45+64 X 71-64X16(3)=360十36+108一36=(1+3+5+7) 4-2=10+3=164-2=13【練一練 4 (1) (720+96)十246342+21=8(2) (4500-90)十45(3)(4) 8811一89(5) 73十36+105十36+14636(6) (0-10) 一 10(1) 125X34+125X66(2) 43X11+43X36+43X5

5、2+43=125X( 34+66 )=43 X(11+36+52+1)=125X100=43X100=12500【經(jīng)典例題三】計(jì)算：(1) 125X34+125X66(2) 43X11+43X36+43X52+43【思路導(dǎo)航】利用乘法分配律來計(jì)算這兩題4300【練一練3】計(jì)算下面各題:(1)125X64+125X3621X73+26X21+21【經(jīng)典例題四】計(jì)算(1) (360+108) 4-36(2) 1十2+3一2+5三2+7十2【思路導(dǎo)航】兩個(gè)數(shù)的和.差除以一個(gè)數(shù)，可以用這個(gè)數(shù)分別去除這兩個(gè)數(shù)，再求出兩個(gè)商 的和(差)。利用這一性質(zhì)，可以使計(jì)算筒便。(1) (360+108) 4-36(

6、2) 14-2+34-2+54-2+74-2【經(jīng)典例題五】158X61十79X3【思路導(dǎo)航】在乘除混合運(yùn)算中，如果算式中沒有括號，計(jì)算式可以根據(jù)運(yùn)算定律和性質(zhì)調(diào) 換乘數(shù)或者除數(shù)的位置，只要計(jì)算：數(shù)字跟著前面的符號一起移動。158X614-79X3=158-79X61X3=2X61X3=366【練一練5】計(jì)算下面各題：(1) 238X364-119X5(2) 138X274-69X50(3 )624X484-3124-8406X3124-1044-203【經(jīng)典例題六】計(jì)算下面各題：(1)103X964-16(2)200三(25三4)【思路導(dǎo)航】這兩道題都是乘除法混合運(yùn)算，我們可以根據(jù)這兩道題的特

7、點(diǎn)，采用加括號和 去括號的方法，使計(jì)算簡便?？梢愿爬椋豪ㄌ柷伴L乘號，加、去括號不改號，括號前長除 號，田、去括號要改號。(1) 103X964-16(2) 200-r (254-4)=103X (96 + 16)=2004-25X4=103X6=8X4=618 =32【練一練6】計(jì)算下面各題：(2)1000十(125*4)(1)612X3664-183(3) (13X8X5X6) 一 (4X5X6)(4) 241X345十678一345X (678子241)【經(jīng)典例題七】計(jì)算：(1) 68X62(2) 85X85【思路導(dǎo)航】這兩題的形式叫做“頭同尾合十”它們的計(jì)算方法是：先用兩個(gè)因數(shù)的個(gè)位數(shù)

8、 相乘，并把積直接寫在末尾，如果積不滿10,十位上要補(bǔ)寫0,然后再將兩個(gè)因數(shù)的十位數(shù) 乘它本身加1的和，積寫在兩個(gè)個(gè)位數(shù)積的前面。(1) 68X62第一步8X2=16,第二步6X (6+1)二42,合起來是4216(2) 85X85第一步5X5=25,第二步是8X (8+1) =72,合起來是7225【練一練 7 I ( 1 ) 23X27( 2 ) 46X44( 3 )55X55(4) 91X99【經(jīng)典例題八】計(jì)算：26X11【思路導(dǎo)航】一個(gè)兩位數(shù)乘11的方法是：用兩位數(shù)的頭作積的頭，用兩位數(shù)的尾作積的尾, 用這個(gè)兩位數(shù)的兩個(gè)數(shù)字之和作積的中間數(shù)（如果相加滿十，則把和的十位數(shù)“1”加到頭上。

9、 26X11第一步2作積的頭，第二步6作積的尾，第三步2+6=8作中間， 合起來是286。【練一練8計(jì)算（1） 53X1165X11(2) 39X11(4) 98X11【經(jīng)典例題九】計(jì)算:358X11【思路導(dǎo)航】三位數(shù)乘11,用三位數(shù)的頭作積的頭，用三位數(shù)的尾作積的尾，用三位數(shù)前兩 位數(shù)字組成的數(shù)加厚兩位數(shù)字組成的數(shù)的和作積的中間數(shù)。358X11,第一步用3作積的頭，第二步用8作積的尾，在用35+58=93,合起來是3938?！揪氁痪?】計(jì)算（1）353X11(2)654X11(3)896X11【練一練 1(1 )4504-25(2 )5254-25(3) 35004-125(4)lOOOO-

10、r-625(5)495004-900(6) 90004-225【練25X24練 2)(1)125X15X8X4(3) 125X16(4 )75X16125X25X32(6) 25X5X64X125【練一練3】計(jì)算下面各題：(1)125X64+125X36(2)64X 45+64 X 71-64X16(3)21X73+26X21+21【練一練 4)(1)(720+96)4-24(2)(4500-90)+45(3)6342+21(4) 88114-89(5) 73十36+105三36+146十36(6) (0-10) 4-10【練一練5】計(jì)算下面各題：(1) 238X364-119X5(2) 13

11、8X274-69X50(3) 624X48十312三8(4) 406X312一 104十203【練一練6】計(jì)算下面各題：(1) 612X366十 183(2) 1000十(1254-4)(3) (13X8X5X6) 一 (4X5X6)(4) 241X3454-678345X(6784-241)【練一練7】（1 ） 23X27(2) 46X44(3)55X55(4) 91X99【練一練8計(jì)算（1） 53X11(2) 39X11(3)65X11(4) 98X11【練一練9 1計(jì)算(1 )353X11(2 )654X11(3) 896X11簡便計(jì)算專題訓(xùn)練158+262+138375+219+381

12、+2255001-247-1021-232(181+2564) +2719378+44+114+242+222276+228+353+219(375+1034)+(966+125)(2130+783+270)+101799+999+9999+999997755-(2187+755)2214+638+2863065-738-1065899+3442357-183-317-3572365-1086-214497-2992370+19953999+4981883-39812X2575X24138X25X4(13X125)X(3X8)(12+24+80) X50704X25簡便計(jì)算練習(xí)題225X32X

13、12532X (25+125)88X125102X7658X98178X101-17884X36+64X8475X99+2X7583X102-83X298X199123X18-123X3+85X12350X(34X4)X325X (24+16)178X99+17879X42+79+79X5773004-254-48100+4+75168004-120301004-2100320004-40021500 + 125497004-7001248一243150-7-1548004-25簡便計(jì)算練習(xí)題32356- (1356-721)1235- (1780-1665)75X27+19X2 531X87

14、0+13X3104X(25X65+25X28)(300+6)x12(13+24)x825x (4+8)125x(35+8)84x101504x2578x10225x20499x6499x16638x99999x9999X13+1325+199X2532X16+14X3278X4+78X3+78X3125X32X825X32X12588X12572X1253600 十 25*42簡便計(jì)算練習(xí)題48100一 4 十 75273-73-27278+463+22+37732+580+268214- (86+14)787- (87-29)576-285+85825-657+57871-299157-99

15、3000 十 125 一 81250+25-5847-527-2731034+780320+102425+14+186365- (65+118)455- (155+230)690-177+77755-287+87363-199968-599178X101-17883X102-83X217X23-23X735X127-35X16-11X35簡便計(jì)算練習(xí)題5容易出錯(cuò)類型（共五種類型）600-604-1520X44-20X4736-35X2025X4十25X498-18X5+2556X84-56X8280-804-12X6*12X6175-75十2580-20X2+6025X84-25X836X94

16、-36X936-36-7-6-6100+45-100+4525X84-15X97+3(25X8)100+1-100+11000+8-1000+848X99+15+95X28102+1-102+125+75-25+7540+360+20-1065+35X1313+24X8672-36+64324-68+32100-36+6426X39+61X26簡便計(jì)算練習(xí)題6356X9-56X999X55+5578X101-7852X76+47X76+76134X56-134+45X13448X52X2-4X4825X23X (40+4)999X999+1999184+98695+202864-199738-

17、301380+476+120(569+468) + (432+131)704X25256-147-53373-129+29189- (89+74)28X4X25125X32X259X72X125720 + 16 十 5簡便計(jì)算練習(xí)題76304-42456- (256-36)102X35 98X42158+262+138375+219+381+2255001-247-1021-232(181+2564) +2719378+44+114+242+222276+228+353+219(375+1034)+(966+125)(2130+783+270)+101799+999+9999+99999775

18、5-(2187+755)2214+638+2863065-738-1065899+3442357-183-317-3572365-1086-214497-2992370+19953999+498簡便計(jì)算練習(xí)題81883-39812X2575X24138X25X425X32X125(13X125)X(3X8)32X(25+125)(12+24+80) X5088X125102X76178X101-17884X36+64X8475X99+2X7598X199123X18-123X3+85X12350X(34X4)X325 X (24+16)178X99+17879X42+79+79X57)7300

19、+25 十 48100+4+75158+262+1381248-r 2421500一125簡便計(jì)算練習(xí)題931504-154800 子 25375+219+381+2255001-247-1021-232(181+2564) +2719(375+1034)+(966+125)378+44+114+242+222276+228+353+219(2130+783+270)+101799+999+9999+999997755-(2187+755)2214+638+2863065-738-1065899+3442357-183-317-3572365-1086-214497-2992370+19953

20、999+4981883-39812X25筒便計(jì)算練習(xí)題1075X24138X25X4(13X125)X(3X8)(12+24+80) X50704X2525X32X12532X(25+125)88X125102X7658X98178X101-17884X36+64X8475X99+2X7583X102-83X298X199123X18-123X3+85X12350X(34X4)X325X (24+16)178X99+17879X42+79+79X57215004-125168004-1207300+25 一 48100-4十 75筒便計(jì)算練習(xí)題11(a+b) + c 二 a + (b+c)+

21、+ + + + abc = a (b+c) 10 -一 (+ )(a X b) Xc = a X (b X c)25 X XX 32 XXc X (a+b) = cXa + cXbX 201XX 99簡便計(jì)算練習(xí)題12X + XX 99 +X4- 2x +十8a -7-b-r C =a 4- (b X c)4-(X8)4-( X )9304-5 (+ )十2 .5 X(4 +-X8X99X +X-X簡便計(jì)算練習(xí)題13+_+ +_+X X4X32 XX-XX-4-4X + X5158+262+138簡便計(jì)算專題訓(xùn)練375+219+381+2255001-247-1021-232(181+2564

22、) +2719378+44+114+242+222276+228+353+219(375+1034)+(966+125)(2130+783+270)+101799+999+9999+999997755-(2187+755)2214+638+2863065-738-1065899+3442357-183-317-3572365-1086-214497-2992370+19953999+4981883-39812X2575X24178X101-17884X36+64X8475X99+2X7583X102-83X298X199123X18-123X3+85X12350X(34X4)X325X (24

23、+16)178X99+178138X25X4(13X125)X(3X8)(12+24+80) X50704X25簡便計(jì)算練習(xí)題225X32X12532X (25+125)88X125102X7658X9879X42+79+79X577300+25 一 48100+4 一 7516800+120301004-2100320004-40021500一125497004-70012484-2431504-1548004-25簡便計(jì)算練習(xí)題32356- (1356-721)1235- (1780-1665)75X27+19X2 531X870+13X3104X(25X65+25X28)25x(4+8)

24、125x(35+8)(300+6)x12(13+24)x884x101504x2578x10225x20499x6499x16638x99999x9999X13+1325+199X2532X16+14X3278X4+78X3+78X3125X32X825X32X12588X12572X1253600 十 25*4簡便計(jì)算練習(xí)題48100 一 4*7530004-1254-81250 一 25*5273-73-27847-527-273278+463+22+37732+580+2681034+780320+102425+14+186214- (86+14)787- (87-29)365- (65

25、+118)455- (155+230)576-285+85825-657+57690-177+77755-287+87871-299157-99363-199968-599178X101-17883X102-83X217X23-23X735X127-35X16-11X35簡便計(jì)算練習(xí)題5容易出錯(cuò)類型（共五種類型）600-60-r 15736-35X2020X44-20X425X4十25X498-18X5+25456X84-56X812X64-12X6280-80三175-75+2580-20X2+6025X84-25X836X9+36X936-36十6-6100+45-100+4525X8 一

26、(15X97+325X8)100+1-100+11000+8-1000+848X99+15+95X28102+1-102+125+75-25+7540+3604-20-1065+35X1313+24X8672-36+64324-68+32100-36+6426X39+61X26簡便計(jì)算練習(xí)題6356X9-56X999X55+5578X101-7852X76+47X76+76134X56-134+45X13448X52X2-4X4825X23X (40+4)999X999+1999184+98695+202864-199738-301380+476+120(569+468) + (432+131

27、)704X25256-147-53373-129+29189- (89+74)28X4X25125X32X259X72X125720 + 16 十 5簡便計(jì)算練習(xí)題76304-42456- (256-36)102X35 98X42158+262+138375+219+381+2255001-247-1021-232(181+2564) +2719378+44+114+242+222276+228+353+219(375+1034)+(966+125)(2130+783+270)+101799+999+9999+999997755-(2187+755)2214+638+2863065-738-1

28、065899+3442357-183-317-3572365-1086-214497-2992370+1995簡便計(jì)算練習(xí)題83999+498138X25X41883-39812X2575X2425X32X125178X101-178(13X125)X(3X8)(12+24+80) X5032X(25+125)88X125102X7684X36+64X8475X99+2X7598X199123X18-123X3+85X12350X(34X4)X379X42+79+79X5725X (24+16)178X99+17873004-254-481004-44-75158+262+13812484-2

29、4簡便計(jì)算練習(xí)題931504-154800F25215004-125375+219+381+2255001-247-1021-232(181+2564) +2719378+44+114+242+222276+228+353+219(375+1034) + (966+125)(2130+783+270)+101799+999+9999+999997755-(2187+755)2214+638+2863065-738-1065899+3442357-183-317-3572365-1086-214497-2992370+19953999+4981883-39812X25簡便計(jì)算練習(xí)題1075X24

30、138X25X4(13X125)X(3X8)(12+24+80) X50704X2525X32X12532X(25+125)88X125102X7658X98178X101-17884 X 36+64 X8475 X 99+2 X 7583X102-83X298X199123X18-123X3+85X12350X(34X4)X325X (24+16)178X99+17879X42+79+79X57215004-12516800十1207300 一 25 一 48100*475簡便計(jì)算練習(xí)題11 (a+b) + c = a + (b+c)+ + + + +abc = a (b+c)10 - 一一

31、 (+ )(a X b) Xc = a X (b X c)25 X XX 32 Xc X (a+b) = cXa + cXbX 201XX 99簡便計(jì)算練習(xí)題12X + XX 99 +23 X + X+ +X 4-X十4 + XX X4X32 X2 .5 X(4+-X8XX99X+X-X1X + XX XXX-F4X + X5第一類：加357+288+143265+73+135 72+68+28129+235+171+16517+145+23+35999+99+9+36+7+8+102+103+104第二類：減400-256-449998+3+99+998+3+9517-53-47284-15

32、9-41258-42-16545-167-145478-47-178344- (144+37)236- (177+36)88X12572X125125第三類：乘45X4X523X5X225X9X48X (125X13)(250X125) X (4X8)X 64X2542X125X8X5 第四類：乘(12+50 ) X4018X12525X4X88X125125 X ( 40-4 )76X10325X4499X999X7842X25第五類：乘45X37+37X5528X21+28X7917X23-23X738X46+64X3899X32+3246+46X5939X8+6X39-39X4167X2

33、+167X3+167X528X225-2X225-6X225(42+25) X125+ (18+15) X12523X2X4+25X4X2+27X1X8+25X8X199X22+33X34第六類：除360+4+98004-54-86004-124-5480-54-482404-54-124204-3524004-2578004-125第七類：加減197+102354-10892+99127-98323+189-123248-86+48672-36+64(6467-832) + (1832-1467)1530+ (592-530) -192(2+4+6+98+100)-(1+3+5+97+99)

34、第八類：乘除960X464-48990004-121X113702X384-12346404- (164-4)10004- (1254-4)第九類：加減乘除(98+147) 4-49(230-23) 4-23(250-25) 4-251736 三 28+1064*28125X (860+240+12)700+612 一 12X4(37+15) X85+13602005X-2006X158+262+138(181+2564) +2719375+219+381+225378+44+114+242+2225001-247-1021-232276+228+353+219(375+1034)+(966+

35、125)(2130+783+270)+101799+999+9999+999997755(2187+755)738-10652214+638+2863065-899+3441086-2142357-183-317-3572365 -4972993999+498188339875X242370+199512X25138X25X4(12+24+80) X50(13X125)X(3X8)25X32X125簡便計(jì)算練習(xí)題2704X2532X (25+125)88X125102X7658X98178X101 一17884X36+64X8475X99+2X7583X2123X3+85X12398X1998

36、3X102123X1850X(34X4)X325 X(24+16)178X99+17879X42+79+79X577300 十 25+481004-44-75168004-1203 01004-210032000十400215004-125497004-70012484-2431504-1548004-25簡便計(jì)算練習(xí)題32356- (1356-721)51235- (1780-1665)75X27+19X231X870+13X310(300+6)x124X(25X65+25X28)25x(4+8)125x(35+8)(13+24)x884x101504x2578x10225x20499x64

37、99x16638x99999x9932X16+14X3299X13+1325+199X2578X4+78X3+78X3125X32X872X12525X32X12588X125簡便計(jì)算練習(xí)題43600+25 子 48100-44-753000-1254-812504-254-5273-73-27847-527-273278+463+22+37186732+580+2681034+780320+102425+14+214- (86+14)(155+230)787- (87-29)365- (65+118)455-825-657+57690-177+77576-285+85755-287+8787

38、1-299157-99363-199968-599簡便計(jì)算練習(xí)題5600-60十1520X44-20X4736-35X2025X4 25X498-18X5+2556X8*56X8280-80十412X64-12X6175-75十2525X84-25X836X9+36X980-20X2+6036-364-6-6(25X8)100+45-100+4515X97+325X84-100+1-100+11000+85+95X2848X99+11000+8102+1-102+165+35X1325+75-25+7513+24X840+36020-10672-36+64100-36+64324-68+32簡

39、便計(jì)算練習(xí)題626X39 + 61X265578X101-78356X9 -56X999X55 +52X76+47X76 + 764X48134X56-134+45X13448X52X2-25X23X (40+4)+202999X999+1999184+98695864-199738-301380+476+120(569+468) + (432+ 131)704X25256-147-53一(89+74)373-129 + 2918928X4X25X125125X32X259X72簡便計(jì)算練習(xí)題77204-164-5102X35 98X42630*42456 - (256-36)158+262+

40、138232375+219+381+225(181+2564) +27195001247-1021 一378+44+114+242+222(375+1034)+(966+125)276+228+353+219(2130+783+270)+1017(2187+755)99+999+9999+999992214+638+28677553065-738-1065357899+3442357-183-317-2365-1086-214497-2992370+1995簡便計(jì)算練習(xí)題8 3999+49839812X2575X241883138X25X425X32X125(13X125)X(3X8)(12+

41、24+80) X5032X (25+125)88X125102X76178X101-17884 X 36+64 X 8475X99+2X7598X199123X18-123X3+85X12350X(34X4)X325 X(24+16)178X99+17879X42+79+79X5773004-254-48100 一 4一 75158+262+138簡便計(jì)算練習(xí)題912484-24215004-125 375+219+381+22531504-1548004-25378+44+114+242+2225001-247-1021-232(181+2564) +2719276+228+353+219(375+1034)+(966+125)99+999+9999+999997755 一(2130+783+270)+1017(2187+755)2214+638+2863065-738-1065899+3442357-183-317-3572365-1086-214497-2992370+19953999+49812X2575X24138X25X4)X(3X8)(12+24