三升四暑期奥数培优讲义-4-03-乘除巧算4-讲义-教师

第3讲乘除巧算

［学习目标］

1、熟练掌握乘除运算中的技巧；

2、能进行复杂的乘除混合运算。

【知识梳理］"H

1、找朋友:5X2=10,25X4=100,125X8=1000；

2、运算律：交换律、结合律、分配律；

3、填减括号：需要变号要变号；

4、埼殊简算规则：如123X11、46X44……；

5、平方差公式：a2-b2=(a+b)x(a-b)<.

［典例精析方

【例1】简算：

(1)8X25X4X125(2)16X125(3)125X25X5X64X17

=(25X4)X(8X125)=2X8X125=125X25X5X8X4X2X17

=100X1000=2X1000=1000X100X10X17

=100000=2000=17000000

【趁热打铁-1】简算:

(1)25X42X4(2)125X17X8(3)25X125X4X8

=17X125X8=25X4X125X8

=25X4X42

=17X1000=100X1000

=100X42

=17000=100000

=4200

【例2】巧算:

(1)42004-25(2)340004-125(3)128+9+16+9

=(4200X4)4-(25X4)=(34000X8)4-(125X8)=(128+16)4-9

=16800^-100=2720004-1000=1444-9

=168=272=16

【趁热打铁-2】巧算：

(1)72004-25(2)32704-5(3)887+8-87+8

二(7200X4)+(25X4)=(3270X2)4-(5X2)=(887-87)4-8

=288004-100=65404-10=8004-8

二288二654=100

【例3】巧算：

(1)56X101(2)29X99(3)25X41

=56X100+56X1=29X100-29X1=25X40125X1

=5656=2900-29=1000+25

=2871=1025

【趁热打铁-3】简算:

(1)32X102(2)78X999(3)125X792

=78X1000-78X1

=78000-78

=77922

=32X100+32X2=125X800-125X8

=3200+64=100000-1000

=3264=99000

【例4】巧算:

(1)25X11(2)234X11(3)6753X11

=275=2574=74283

【趁热打铁-4】速算：

(1)125X11(2)5321X11(3)74251X11

=1375=58531=816761

【例5】巧算:

(1)45X45(2)67X63(3)46X66(4)36X76

=2025=4221=3036=2736

【趁热打铁-5】速算：

(1)35X35(2)77X73(3)94X14(4)81X21

=1225=5621=1316=1701

【例6】先观察，再动手计算:

(1)102X98(2)201X199(3)304X296

=(100+2)X(100-2)=(200+1)X(200+)=(300+4)X(300-4)

=100X100-2X2=200X200-1X1=300X300-4X4

=10000-4=40000-1=90000-16

二9996=39999=89984

【趁热打铁-6】怎样简便就怎样计算:

(1)101X99(2)305X295(3)402X398

=(100+1)X(100-1)=(300+5)X(300-5)=(400+2)X(400-2)

=100X100-1X1=300X300-5X5=400X400-4X2

=10000-1=90000-25=160000-4

=9999=89975=159996

【例7】先观察，再动手计算:

(1)132X48H-16(2)32X(1214-16)(3)728X94-8

=132X(484-16)

=324-16X121=728+8X9

=132X3

=2X121=91X9

=396

二242=819

(4)2100+25+4(5)1864-(64-9)(6)1894-(7X9)

=21004-(25X4)=1864-6X9=1894-94-7

=21004-100=31X9=214-7

=21=279=3

【趁热打铁-7】用简便方法计算卜面各题:

(1)105X724-9(2)48X(242+24)(3)287X114-7

=105X(724-9)二48/24X242=2874-7X11

=105X8=2X242=41X11

=484

二840二451

(4)3500+5+7⑸260+(10+3)(6)1054-(7X5)

=3500+(5X7)=2604-10X3=1054-74-5

=35004-35=26X3=154-5

=100=78=3

【例8】计算：(48X56X72)+(24X28X36)

=(484-24)X(56+28)X(72+36)

=2X2X2

【趁热打铁-8】计算：(44X38X51X28)+(11X17X19X14)

=(444-11)X(384-19)X(514-17)X(28+14)

=4X2X3X2

=48

【例9】计算：14-(24-3)4-(34-4)4-(44-5)~r....4-(20204-2021)4-(20214-2022)

=14-2X34-3X44-4X54-....4-2020X20214-2021X2022

=1011

【趁热打铁-9】20004-(2+3)T(34-4)+(4+5)L....4-(20204-2021)L(20214-2022)

=20004-2X34-3X44-4X54-....4-2020X20214-2021X2022

=2022000

【例10】计算：

(1)123456789X9=1111111101(2)123456789X18=2222222202

【趁热打铁TO】计算：

(1)123456789X36=4444444404(2)123456789X81=9999999909

【过关精炼】

1、计算：

(1)128X25X5X125(2)125X15X8X4(3)25X5X64X125

=2X4X25X2X5X8X125=125X8X15X4=25X4X5X2X125X8

=2X100X10X1000=1000X60=1OOX1OX1000

=2000000=60000=1000000

(4)32004-25(5)100004-625(6)90004-225

=(3200X4)4-(25X4)=(10000X2X8)+(625X2X8)=(9000X4)4-(225X4)

=128004-100=1600004-10000=360004-900

=128=16二40

2、计算：

(1)238X36^-119X5(2)200=(25+4)

二(238+119)X5X36=2004-25X4

=2X5X36=(200X4X4)4-(25X4)

=360=32004-100

=32

(3)406X312+104+203(4)(78X56X72)+(14X39X24)

=(4064-203)X(3124-104)=(784-39)X(56+(4)X(724-24)

=2X3