北师大四年级数学下册小数乘法简便计算最新整理.docx
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北师大四年级数学下册小数乘法简便计算最新整理
四年级下册小数练习题
一、脱式计算,能简算的要简算。
7.8×1.3+0.948-1.8×240.25×0.46×0.4
2.5×1.3+0.93.8×41-3.8(4+0.4)×2.5
0.27×3.8+0.27×6.22.9×100.127.5×101-27.5
40×0.63×0.253.62×25.7+3.62×74.30.25×4.87×4
18.8+23.6+26.4
10.95-3.74-4.26
95.59-(9.59+12.78)
25.6-(0.23+5.6)-1.77
13.75-(4.75+6.48)
7.83+2.34-0.83+6.66
3.82+2.9+0.18+9.1
5.93+0.19+2.81
25.48-((9.4-0.52)
3.07-0.38-
1.62
35.6-1.8-15.6-7.2
7.3+2.7-7.3+2.7
48.4+2.78+51.6-0.78
23.4+0.8-13.4-7.2
4.8+8.63+5.2+0.37
3.25+2.76+1.75
1.27+3.9+0.73+15.1
5.84-1.8-3.2
132.44-(58.74+19.44)
7.5+4.8-6.5
7.14-0.53-2.47
13.75-(3.75+6.48)13.45-4.68+2.55
47.8-7.45+8.2
36.8-4.5+6.98
49.8-9.6+8.815.2-6.8-3.45
1.76+0.65+3.24
0.134+2.66+0.8
7.5+4.9-6.33.45+1.79+0.65
4.85+8.63+0.37
1.76+3.44+0.35
36.54-1.76-8.668-2.45-1.02
23.4+3.4-0.23
6.02+3.6+1.98
3.07-0.38-1.627.5+4.9-6.5
36.8-3.9-
6.88
3.285+1.79+0.59
23.4-0.8+13.4
32+4.9-8.6
1.29+3.7+2.71
5.93+0.49+2.06
9-2.45-1.65
21+0.56+11.3
64.89-7.88-13.6
二、能简便的要简便计算。
12.5×8.2×80.23×1.4+0.23×8.6
0.125×(80+0.8)0.4×0.16×2.5
5.6×1017.85×991.15×99+1.15
16.2×101-16.245×0.78+5.5×7.8
2.8+7.2×0.810.34×2.5×0.41.25×11×4×0.8
8.93×5.7+8.93×3.3+8.934.82×102
0.7×0.46+0.7×0.545.6-4.34+7.34685.7-(15.3-4.8)
25.4-(15.3+7.7)3.6-1.28+3.093.8-0.46-1.723
25.6-(0.23+5.6)-1.7713.75-(4.75+6.48)7.83+2.34-
0.83+6.663.82+2.9+0.18+9.1
25.48-((9.4-0.52)35.6-1.8-15.6-7.25.93+0.19+2.81
7.3+2.7-7.3+2.73+5.2+0.373.07-0.38-1.62
48.4+2.78+51.6-0.7823.4+0.8-13.4-7.24.8+8.6
1.27+3.9+0.73+15.15.84-1.8-3.2132.44-(58.74+19.44)7.5+4.8-
6.513.45-4.68+2.55
3.25+2.76+1.7513.75-(3.75+6.48)7.14-0.53-2.47
47.8-7.45+8.236.8-4.5+6.9849.8-9.6+8.8
15.2-6.8-3.453.45+1.79+0.653.45+1.79+0.65
1.76+0.65+3.240.134+2.66+0.87.5+4.9-
6.34.85+8.63+0.371.76+3.44+0.3536.54-1.76-8.66
3.45+1.79+0.657.5+4.9-6.5
23.4+3.4-0.236.02+3.6+1.983.07-0.38-1.62
36.8-3.9-6.883.285+1.79+0.5923.4-0.8+13.4
1.29+3.7+2.7121+0.56+11.332+4.9-8.65.93+0.49+2.069-2.45-
1.65
一、乘法交换律
a⨯b⨯c=a⨯c⨯b
0.25×8.5×412.5×0.96×0.80.25×0.73×40.25×16.2×4
二乘法结合律
(a⨯b)⨯c=a⨯(c⨯b)
4.36×12.5×80.95×0.25×435×0.2×0.50.75×50×0.4
三、乘法分配律
(a±
b)
⨯c
=a⨯c
±b⨯c
(1.25-0.125)×8(20-4)×0.25(2+0.4)×5(125+2.5)×0.8
四、乘法分配律逆应用
a⨯b±
a⨯c
=a(b
±c)
3.72×3.5+6.28×3.515.6×2.1-15.6×1.13.83×4.56+3.83×5.44
7.09×10.8-0.8×7.0927.5×3.7-7.5×3.73.9×2.7+3.9×7.3
10.6×0.35-9.6×0.357.6×0.8+0.2×7.6
五、把其中一个因数分成两个数的和或差,再按乘法分配律
0.8×100.10.79×990.85×1993.65×10.1
4.6×0.90.65×1014.8×10.13.6×102
0.39×1998.9×1.010.32×4033.65×10.1
0.85×9.90.65×101
六、拆分因数
1.25×2.5×323.2×0.25×12.50.25×3625×4.48.8×1.25
七、添加因数“1”
56.5×99+56.59.7×99+9.74.2×99+4.25.4×11-5.4
1.87×9.9+0.18712.7×9.9+1.27
八、更改因数的小数点位置
6.66×3.3+66.6×6746×57+23×864.8×7.8+78×0.52
3.14×0.68+31.4×0.032101×0.87-0.91×873.65×4.7-36.5×0.37
2.3×16+2.3×23+2.3314×0.043+3.14×7.2-31.4×0.15
5×1.03×0.232×1.250.45×9953×10.1
0.125×96
12.5×10.8
25×7.3×0.4
45×21-50×2.1
45×1.58+5.5×15.84.2×6.51+3.49×4.2
9.99×2.22+3.33×3.34
三、直接写得数
3.8×2=10×0.7=13.9×0=
50.8×100=
5.5×1=1.8×0.5=3.2×3=
13.1×0.3=
0.08×1.25=2.5×4=2.5×8=
0.5×0.2=
0.6×0.1=0.7×0.8=2.5×8×0=
125×0.8=
3.8×2=10×0.7=13.9×0=
508÷100=
5.5×1=1.8×0.5=
3.2×3=
13.1×0.3=
0.08×1.25=2.5×4=
2.5×8=
0.5×0.2=
0.6×0.1=0.7×0.8=
2.5×8×0=
125×0.8=
四、竖式计算
2.8×0.7=13×0.15=
0.39×0.6=
0.38×600=
7.05×2.4=0.46×7.9=
89.3×7.6=
60.5×400=
3.05×18=4.6×18.9=
40.5×4.2=
0.37×2.31=
3.8×0.12=
0.57×0.6=
6.4×0.5=
6.7×5.8=9.8×3.8=
7.8×6.4=
4.6×2.7=
4.5×2.7=
5×1.6=
3×0.6=
3×1.2=6.7×7.6=
5.4×7.8=
2.6×3.6=
3.5×1.7=8.3×2.6=
1.4×0.7=
4.5×2.8=
7.4×2.6=6.2×1.4=
5.4×2.6=
2.3×1.4=
3.7×1.8=4.5×2.3=
5.2×1.6=
3.6×0.8=
0.66×1.4=6.5×5.8=0.72×0.49=
0.42×0.28=
0.24×0.19=
2.4×1.3=
0.72×0.27=
0.78×0.32=
0.65×0.04=0.23×0.16=0.29×0.15=
0.16×0.19=
4×1.2=
7×4.6=6×0.37=0.28×0.27=
0.75×0.42=
2.3×1.9=
8×0.64=
2.7×0.8=
10×4.2=7.1×3.9=
4.3×1.4=
2.6×1.6=
0.8×0.3=0.65×0.4=0.91×0.6=
1.8×1.6=
4.8×0.5=
3.2×0.4=
9.8×4.8=
12×8.3=
15.2×6.5=20.1×11.1=13.34×10.32=
6.52×0.48=
6.3×5.1=
8.7×3.6=
14.3×4.3=
1.5×0.54=
10×4.2=2.47×3.24=
2.98×0.56=
5.64×1.78=
8.02×0.98=7.1×3.9=2.8×11.39=
12.53×4.67=
7.2×6.45=
1.65×3.35=7.96×1.45=60×1.27=
6.07×4.89=
5×0.41=
0.9×0.5=2×0.7=1.2×4.3=
5.4×2.7=6×2.9=3.7×1.7=4.2×0.8=7.5×2.5=
2.2×4.3=
9.5×7.1=
3.5×1.6=
5.2×2.8=
7.8×1.6=
9.6×4.1=10×4.2=
5.1×2.5=
4.1×3.4=
1.2×3.8=9.6×4.1=7.8×1.6=
3.5×1.6=
4.4×1.4=
2.9×2.1=
3.5×1.2=
4.8×3.4=
6.9×2.5=2.5×7.8=
8×5.4=
6.9×2.5=
2×3.5=6.8×2.2=
4.7×5.4=
4.1×8.8=
2.2×5.5=9.6×2.1=
1.7×3.8=
7.4×3.6=
0.8×0.23=1.6×2.4=4.7×3.5=
1.2×3.6=
1.5×3.8=
2.8×1.2=7.3×2.7=7.3×2.7=
6.2×3.7=
4.2×3.9=
0.54×0.65=
7.5×5.2=
0.7×0.5=0.32×0.47=8.3×6.3=
7.2×0.42=
0.48×0.52=
0.8×0.25=43.5×0.65=0.32×0.16=
0.35×0.55=
0.87×0.8=
0.24×0.08=
0.92×0.37=
1.4×0.6=3.6×4.2=
0.72×0.48=
6.8×3.2=
7.1×3.4=0.42×0.66=0.32×0.68=
2.8×7.2=
0.65×0.19=
3.09×1.2=
3.25×5.64=
0.25×0.47=
0.82×0.18=7.8×2.4=0.45×0.18=
0.4×0.16=
8.2×1.8=
0.73×0.27=
8×3.2=
9.8×4.8=
3×2.4=2.8×0.9=
1.29×0.18=
5.1×0.8=
10×0.3=
8.9×4.9=
6.8×0.7=
8×0.72=6.6×3.4=6.4×1.3=
1.2×0.8=
7.3×6.2=
8.7×3.6=
12.3×0.7=
0.8×9.2=
4.7×1.9=5.1×3.9=1.4×0.6=
3.8×6.4=0.6×7.45=4.9×0.1=4.5×3.2=1.8×0.9=
6.5×0.5=10.5×6.5=
7.5×0.5=0.78×0.28=12.8×2.8=9.6×2.3=
3.8×0.12=0.8×0.08=10×7.4=7.5×3.2=0.42×0.58=
0.8×0.15=2.5×0.4=8.2×2.6=
1.4×0.7=2.5×4.6=0.5×9.8=6.7×2.6=7.2×5.9=
8.7×3.6=5.69×2.48=2.9×4.1=
9.1×6.7=2.03×1.2=8.6×4.9=1.3×2.03=
9.46×7.21=1.56×2.24=3.5×1.25=0.75×0.4=20×0.78=
4.8×4.2=5.7×3=4.9×1.7=1.34×0.8=2×0.75=
8.7×0.03=0.2×0.09=
8.5×2.5=3.4×1.4=0.68×0.42=7.82×7.2=2×9.1=
0.48×0.52=8.1×5.1=0.78×0.24=0.8×0.18=0.89×0.25=
1×0.98=0.9×0.1=1×0.8=4.5×4=5.6×4=
5.7×3.3=10×4.4=6×6.6=9.5×2.7=1×0.55=
五、列式计算。
1、甲数是15.24,比乙数多7.6,乙数是多少?
2、3.58加上7.08与5.1的差,和是多少?
六、解决问题。
1、小红用20元钱买文具,买钢笔用去6.7元,买文具盒用去9.8元,还剩下多少钱?
2、爸爸用两条长度分别是1.27米、1.35米的绳子接起来捆扎报纸。
接口处共用去绳子0.25米,接好后的绳子有多长?
3、一桶油连桶共重12.65千克,用去一半后,连桶还重6.85千克,原来的桶里
有油多少千克?
二、减法中的巧算
1.减法的性质:
a-b-c=a-(b+c)
巧算下面各题:
①300-73-27②7.42-(3.42+1.5)③4723-(723+189)
三、加减混合式的巧算
1.去括号和添括号的法则
在只有加减运算的算式里,如果括号前面是“+”号,则不论去掉括号或添上括号,括号里面的运算符号都不变;如果括号前面是“-”号,则不论去掉括号或添上括号,括号里面的运算符号都要改变,“+”变“-”,“-”变“+”,即:
a+(b+c+d)=a+b+c+da-(b+a+d)=a-b-c-d
a-(b-c)=a-b+c2.带符号“搬家”
325+46-125+54
=325-125+46+54
=(325-125)+(46+54)
=200+100
=300
注意:
每个数前面的运算符号是这个数的符号.如+46,-125,+54.而325前面虽然没有符号,应看作是+325。
3.找“基准数”法
几个比较接近于某一整数的数相加时,选这个整数为“基准数”。
计算78+76+83+82+77+80+79+85
二、用简便方法计算:
536+(541+464)+459
588+264+148
8996+3458+7546
4995-(995-480)
1870-280-520
4250-294+94
478-128+122-72
464-545+99+345
537-(543-163)-57
小数乘法的简便运算
947+(372-447)-572
一、乘法交换律与结合律的运用。
提示1:
以下计算中,有的需要把一个小数拆成两个数相乘,要注意拆分后两数
相乘的大小应该与原数相等,特别是小数的位数。
如3.2=0.8×4
3.2=0.4×80.32=0.04×80.32=0.08×45.6=0.8×75.6=0.7×8
0.56=0.07×80.56=0.08×70.48=0.12×40.48=0.04×12
提示2:
应用乘法结合律解题的口诀是连乘用结合
提示3:
应用乘法结合律解题的格式是a×b×c=a×(b×c)最后一个步骤是“×”,
不要看成是“+”.如2.5×0.48=2.5×0.04×12=0.1×12=1.2
4.56×0.4×2.512.5×2.7×0.812.5×3.2×0.25
2.5×0.4812.5×5.625×0.36
乘法分配律的运用。
提示1:
A组中的一个因数都具备一个特点,都接近整数1、10、100等,这样的数就可以拆分成两个数相加或者相减。
如10.4=(10+0.4)9.9=(10-0.9)0.99=(10-0.01)
但也有这样的数8.8=(8+0.8)4.4=(4+0.4)0.48=(0.4+0.08)
提示2:
应用乘法分配律解题的口诀是乘加乘减用分配
提示3:
应用乘法分配律解题的格式是(a+b)×c=a×c+b×c最后一个步骤是
“+”,不要看成是“×”.
如2.5×0.48=2.5×(0.4+0.08)=2.5×0.4+2.5×0.08=1+0.2=1.2
不是=1+0.2=2
提示4:
应用乘法分配律解题的最后一步,有时是数字比较大的两个数相加减,
口算容易出错,这时就要打草稿竖式计算。
0.25×10.412.5×8.89.9×0.35
3.7×1.8-2.7×1.895.7×0.28+6.3×0.28-0.28×2
1.08×9+1.08
比较乘法结合律与分配律在简便运算时的区别。
下面各题用两种方法简算。
12.5×8.812.5×8.80.25×4.80.25×4.8
二、变一变,能简算
48×0.56+44×0.48
我来试一试:
表面上看来,左右两边没有相同的因数,不能使用乘法分配律。
0.279×343+0.657×2790.264×519+264×0.4819.16×1.53-0.053×
91.6
三、拓展提高。
99.99×0.8+11.11×2.8314×0.043+3.14×7.2-31.4×0.15
小数除法的简便运算
小数除法的简便计算与整数除法的简便计算一样,用到的是除法性质。
除法性质1、A÷B÷C=A÷(B×C)
如:
42÷2.8=42÷(0.7×4)=42÷0.7÷4=60÷4=15
如:
420÷2.5÷4=420÷(2.5×4)=420÷10=42
除法性质2、(a-b)÷c=a÷c-b÷c
除法性质3、A÷(B÷C)=A÷B×C
除法性质4、A×(B÷C)=A×B÷C
小数乘除法的递等式计算
小数乘除法的递等式计算方法与整数的一样,能简便的要简便,
但也有的是不能简便比如:
3.6+6.4×0.5不能掉进先加后乘的陷阱里。
3.6×5+15×6.4不能掉进应用乘法分配率的陷阱里。
73.8-1.64-13.8-5.3666.86-8.66-1.34
0.25×16.2×4
3.72×3.5+6.28×3.536.8-3.9-6.12
5.48-(9.4-0.52)
4.8×7.8+78×0.523.6×1026.4×0.25+3.6÷4
32+4.9-0.94.8-4.8×0.5(1.25-0.125)×8
4.8×100.156.5×9.9+56.57.09×10.8-0.8×7.09
4.02+5.4+0.985.17-1.8-3.213.75-(3.75+6.48)
3.68+7.56-2.687.85+2.34-0.85+4.66
35.6-1.8-15.6-7.2
3.82+2.9+0.18+9.19.6+4.8-3.6
7.14-0.53-2.47
5.27+2.86-0.66+1.6313.35-4.68+2.65
47.8-7.45+8.8
0.398+0.36+3.6415.75+3.59-0.59+14.25
42.5-(6.07+1.13)
4.2÷3.5320÷1.25÷818.76×9.9+18.76
3.52÷2.5÷0.44.78÷0.2+3.443.9-4.1+6.1-5.9
0.49÷1.41.25×2.5×323.6-0.6×2
3.65×10.13.6-3.6×0.815.2÷0.25÷4
5.6÷3.59.6÷0.8÷0.44.2×99+4.2
0.89×100.1146.5-(23+46.5)17.8÷(1.78×4)
5.83×2+4.27(45.9-32.7)÷8÷0.1259.7×99+9.7
4.36×12.5×815.6×13.1-15.6-15.6×2.10.65×101
27.5×3.7-7.5×3.78.54÷2.5÷0.4
3.83×4.56+3.83×5.44
6048+975-3045498×396048+75-3005
648×75-30056098+935-1045404×24-758
1048+975-345640×75÷35
878×2968×975-345
9948+275-3045690×6÷35
68+975-34568+975÷345
648+75-35685+975-345
68+975-345548×975-3045
48×975-3046748+975-5045
6048+975-30450.425×0,38÷0,01
20.5-1.074-8.35×5.5
748+95-45
48×975-3045
0.425×0,38÷0,01
20.5-1.074-8.35×5.5
52.8÷0.75×0.25
45×(267+143)
(2448+864)÷23
327+9664÷32×25
727+9660÷30×25
586-45×81÷27
58-45×80÷25
3.68÷4.6+6.32
368÷46+632
604×24-758
644×14-858
604×24-758
408×59
478×39278×39
478×19
10.8/15+7/3-8/5408-12×24(46+28)×60
42×50-1715÷532+105÷5(108+47)×52
420×(327-238)(4121+2389)÷7671×1