《小数乘法简便运算》（专项训练）-2026-2027学年五年级上册数学人教版

**基本信息** 以十大题型系统覆盖小数乘法简便运算，通过题型分类构建从基础到综合的知识逻辑，培养运算能力与推理意识。 **专项设计** |模块|题量/典例|题型特征|知识逻辑| |----|-----------|----------|----------| |顺展型|15题|含括号加减式与小数相乘|直接应用乘法分配律基础形式| |拆加/减型|各9题|乘数拆为整十/百数±小数|分配律拓展至凑整计算| |逆合/添“1”型|各14/15题|含相同因数的加减运算|逆向应用分配律及补“1”技巧| |拆倍/移小数点型|各6/11题|通过倍数转化或小数点移动构造相同因数|数感与运算律结合的变式应用| |拆分凑整/公式综合/交换结合律|各14/10/9题|拆分特殊数（如12.5=10+2.5）、多定律综合应用|从单一运算律到多方法融合，培养推理意识|

《小数乘法简便运算》十大题型 类型一：顺展型。 2.5×(4+0.8) 1.25×(8+0.8) 4.5×(20+0.6) 3.8×(10+0.5) (1.25−0.125)×8 (1.25+2.5)×0.8 0.8×(12.5−0.5)    (1.25+0.025)×8    9×(1.1+0.01) 12.5×(10+0.8) 3.6×(100+2) 5.7×(100−1) (10+0.8)×12.5 (12.5−3)×8 0.4×(2.5+22) 2.5×(4+0.8)=2.5×4+2.5×0.8=10+2=12 1.25×(8+0.8)=1.25×8+1.25×0.8=10+1=11 4.5×(20+0.6)=4.5×20+4.5×0.6=90+2.7=92.7 3.8×(10+0.5)=3.8×10+3.8×0.5=38+1.9=39.9 (1.25-0.125)×8=1.25×8-0.125×8=10-1=9 (1.25+2.5)×0.8=1.25×0.8+2.5×0.8=1+2=3 0.8×(12.5-0.5)=0.8×12.5-0.8×0.5=10-0.4=9.6 (1.25+0.025)×8=1.25×8+0.025×8=10+0.2=10.2 9×(1.1+0.01)=9×1.1+9×0.01=9.9+0.09=9.99 12.5×(10+0.8)=12.5×10+12.5×0.8=125+10=135 3.6×(100+2)=3.6×100+3.6×2=360+7.2=367.2 5.7×(100-1)=5.7×100-5.7×1=570-5.7=564.3 (10+0.8)×12.5=10×12.5+0.8×12.5=125+10=135 (12.5-3)×8=12.5×8-3×8=100-24=76 0.4×(2.5+22)=0.4×2.5+0.4×22=1+8.8=9.8 类型二：拆加型。 0.48×101 1.5×102 4.52×101 2.8×10.2 3.45×102 9.5×10.1    0.43×102 6.35×101 7.5×10.2 0.48×101=0.48×(100+1)=48+0.48=48.48 1.5×102=1.5×(100+2)=150+3=153 4.52×101=4.52×(100+1)=452+4.52=456.52 2.8×10.2=2.8×(10+0.2)=28+0.56=28.56 3.45×102=3.45×(100+2)=345+6.9=351.9 9.5×10.1=9.5×(10+0.1)=95+0.95=95.95 0.43×102=0.43×(100+2)=43+0.86=43.86 6.35×101=6.35×(100+1)=635+6.35=641.35 7.5×10.2=7.5×(10+0.2)=75+1.5=76.5 类型三：拆减型。 99×0.65 0.34 ×99 3.85×99 3.5×9.8 5.2×9.9 5.4×9.8 6.3×19.9 4.86×99 0.78×9.9 99×0.65=0.65×(100-1)=65-0.65=64.35 0.34×99=0.34×(100-1)=34-0.34=33.66 3.85×99=3.85×(100-1)=385-3.85=381.15 3.5×9.8=3.5×(10-0.2)=35-0.7=34.3 5.2×9.9=5.2×(10-0.1)=52-0.52=51.48 5.4×9.8=5.4×(10-0.2)=54-1.08=52.92 6.3×19.9=6.3×(20-0.1)=126-0.63=125.37 4.86×99=4.86×(100-1)=486-4.86=481.14 0.78×9.9=0.78×(10-0.1)=7.8-0.078=7.722 类型四：逆合型。 7.6×4.82+5.18×7.6 4.3×2.5+0.7×2.5 6.7×3.4+3.3×3.4 14.6×5.6−4.6×5.6 3.7×4.9−3.9×3.7 34.7×5.2+4.8×34.7 5.2×13.7+13.7×4.8 0.46×1.9+0.54×1.9 1.6×0.5−0.6×0.5 3.58×67+35.8×3.7 − 0.358×40 76.1×17−76.1×7 5.6×23−5.6×13−5.6×10  3.72×3.5+6.28×3.5 0.45×1.7+0.45×8.3  7.2×4.5−2.2×4.5 5.7×9.7+5.7×1.8−5.7×1.5  6.9×1.67−6.9×0.69+6.9×0.2 7.6×4.82+5.18×7.6=7.6×(4.82+5.18)=7.6×10=76 4.3×2.5+0.7×2.5=2.5×(4.3+0.7)=2.5×5=12.5 6.7×3.4+3.3×3.4=3.4×(6.7+3.3)=3.4×10=34 14.6×5.6-4.6×5.6=5.6×(14.6-4.6)=5.6×10=56 3.7×4.9-3.9×3.7=3.7×(4.9-3.9)=3.7×1=3.7 34.7×5.2+4.8×34.7=34.7×(5.2+4.8)=34.7×10=347 5.2×13.7+13.7×4.8=13.7×(5.2+4.8)=13.7×10=137 0.46×1.9+0.54×1.9=1.9×(0.46+0.54)=1.9×1=1.9 1.6×0.5-0.6×0.5=0.5×(1.6-0.6)=0.5×1=0.5 3.58×67+35.8×3.7-0.358×40 =3.58×67+3.58×37-3.58×4 =3.58×(67+37-4)=3.58×100=358 76.1×17-76.1×7=76.1×(17-7)=76.1×10=761 5.6×23-5.6×13-5.6×10=5.6×(23-13-10)=5.6×0=0 3.72×3.5+6.28×3.5=3.5×(3.72+6.28)=3.5×10=35 0.45×1.7+0.45×8.3=0.45×(1.7+8.3)=0.45×10=4.5 7.2×4.5-2.2×4.5=4.5×(7.2-2.2)=4.5×5=22.5 5.7×9.7+5.7×1.8-5.7×1.5 =5.7×(9.7+1.8-1.5)=5.7×10=57 6.9×1.67-6.9×0.69+6.9×0.2 =6.9×(1.67-0.69+0.2)=6.9×1.18=8.142 类型五：添 “1” 型。 5.13×99+5.13 0.04×29+0.04 0.78×99+0.78 7.34×99+7.34 34.95×101−34.95 1.78×99+1.78 50.8×101−50.8  2.5×39+2.5  6.7×99+6.7 56.5×99+56.5  9.7×99+9.7  4.2×99+4.2 3.8×99+3.8  9.2×101−9.2  78.9+78.9×9  4.7×1001−4.7 5.13×99+5.13=5.13×(99+1)=5.13×100=513 0.04×29+0.04=0.04×(29+1)=0.04×30=1.2 0.78×99+0.78=0.78×(99+1)=0.78×100=78 7.34×99+7.34=7.34×(99+1)=7.34×100=734 34.95×101-34.95=34.95×(101-1)=34.95×100=3495 1.78×99+1.78=1.78×(99+1)=1.78×100=178 50.8×101-50.8=50.8×(101-1)=50.8×100=5080 2.5×39+2.5=2.5×(39+1)=2.5×40=100 6.7×99+6.7=6.7×(99+1)=6.7×100=670 56.5×99+56.5=56.5×(99+1)=56.5×100=5650 9.7×99+9.7=9.7×(99+1)=9.7×100=970 4.2×99+4.2=4.2×(99+1)=4.2×100=420 3.8×99+3.8=3.8×(99+1)=3.8×100=380 9.2×101-9.2=9.2×(101-1)=9.2×100=920 78.9+78.9×9=78.9×(1+9)=78.9×10=789 4.7×1001-4.7=4.7×(1001-1)=4.7×1000=4700 类型六：拆倍法。 5.8×36+11.6×32  9.5×72−19×31 3.6×88+10.8×4  2.7×51−8.1×17 2.4×98+7.2  3.5×62+10.5×16 5.8×36+11.6×32 =5.8×36+5.8×2×32=5.8×(36+64)=5.8×100=580 9.5×72-19×31 =9.5×72-9.5×2×31=9.5×(72-62)=9.5×10=95 3.6×88+10.8×4 =3.6×88+3.6×3×4=3.6×(88+12)=3.6×100=360 2.7×51-8.1×17 =2.7×51-2.7×3×17=2.7×(51-51)=2.7×0=0 2.4×98+7.2 =2.4×98+2.4×3=2.4×(98+3)=2.4×101=242.4 3.5×62+10.5×16 =3.5×62+3.5×3×16=3.5×(62+48)=3.5×110=385 类型七：移小数点。 0.75×5.7+2.5×0.57 70.8×0.27+7.08×7.3 3.25×3.5+32.5×0.65 0.37×42.6+3.7×5.74 6.4×5.3−0.64×43 0.64×38.5+6.4×61.5 5.1×28+0.51×720 5.1×18+1.7×46 1.2×34+0.12×660 1.7×28+3.4×36 8.5×9.2−0.85×82 0.75×5.7+2.5×0.57 =7.5×0.57+2.5×0.57=0.57×(7.5+2.5)=5.7 70.8×0.27+7.08×7.3 =7.08×2.7+7.08×7.3=7.08×(2.7+7.3)=70.8 3.25×3.5+32.5×0.65 =3.25×3.5+3.25×6.5=3.25×(3.5+6.5)=32.5 0.37×42.6+3.7×5.74 =3.7×4.26+3.7×5.74=3.7×(4.26+5.74)=37 6.4×5.3-0.64×43 =6.4×5.3-6.4×4.3=6.4×(5.3-4.3)=6.4 0.64×38.5+6.4×61.5 =6.4×3.85+6.4×61.5=6.4×(3.85+61.5)=418.24 5.1×28+0.51×720 =5.1×28+5.1×72=5.1×(28+72)=510 5.1×18+1.7×46 =1.7×54+1.7×46=1.7×(54+46)=170 1.2×34+0.12×660 =1.2×34+1.2×66=1.2×(34+66)=120 1.7×28+3.4×36 =1.7×28+1.7×72=1.7×(28+72)=170 8.5×9.2-0.85×82 =8.5×9.2-8.5×8.2=8.5×(9.2-8.2)=8.5 类型八： 拆分凑整。 5.6×0.125 1.25×8.8 1.25×6.4×0.25 0.32×2.5×12.5 4.8×12.5 1.25×32 0.125×72 0.25×96 0.75×48 0.5×86 0.88 × 25 0.125×32 1.25×4.8 0.25×0.44 5.6×0.125=0.7×(8×0.125)=0.7×1=0.7 1.25×8.8=1.25×8×1.1=10×1.1=11 1.25×6.4×0.25=(1.25×8)×(0.8×0.25)=10×0.2=2 0.32×2.5×12.5=(0.4×2.5)×(0.8×12.5)=1×10=10 4.8×12.5=0.6×(8×12.5)=0.6×100=60 1.25×32=1.25×8×4=10×4=40 0.125×72=0.125×8×9=1×9=9 0.25×96=0.25×4×24=1×24=24 0.75×48=0.75×4×12=3×12=36 0.5×86=43 0.88×25=0.22×(4×25)=0.22×100=22 0.125×32=0.125×8×4=1×4=4 1.25×4.8=1.25×8×0.6=10×0.6=6 0.25×0.44=0.25×4×0.11=1×0.11=0.11 类型九：公式综合。 0.8×0.25×0.4×1.25 0.04×12.5×2.5×0.8 3.78×9.9+0.378 12.5×2.2×0.8×0.5 0.25×0.32×12.5×5 0.45×1.25×2×8 9.99×111+3.33×667 23.6×47+23.6×52+23.6 99.9×4.5+33.3×1.5 1.9×90+1.9×9−99×1.8 2.6×12+2.6×17+29×7.4 0.8×0.25×0.4×1.25=(0.8×1.25)×(0.25×0.4)=1×0.1=0.1 0.04×12.5×2.5×0.8=(0.04×2.5)×(12.5×0.8)=0.1×10=1 3.78×9.9+0.378=3.78×9.9+3.78×0.1=3.78×(9.9+0.1)=37.8 12.5×2.2×0.8×0.5=(12.5×0.8)×(2.2×0.5)=10×1.1=11 0.25×0.32×12.5×5=(0.25×0.4)×(0.8×12.5)×5=0.1×10×5=5 0.45×1.25×2×8=(0.45×2)×(1.25×8)=0.9×10=9 9.99×111+3.33×667 =3.33×333+3.33×667=3.33×(333+667)=3330 23.6×47+23.6×52+23.6=23.6×(47+52+1)=2360 99.9×4.5+33.3×1.5 =33.3×13.5+33.3×1.5=33.3×(13.5+1.5)=499.5 1.9×90+1.9×9-99×1.8 =1.9×99-99×1.8=99×(1.9-1.8)=9.9 2.6×12+2.6×17+29×7.4 =2.6×29+29×7.4=29×(2.6+7.4)=290 类型十：乘法交换律、结合律 4.67×0.25×4 0.25×0.9×0.8 5.2×0.2×5 2.5×3.1×4 8×3.82×1.25 0.25×3.86×4 12.5×6.75×0.8 6.4×12.5×5×0.25 8.8×12.5 35×1.25×2×0.8 4.67×0.25×4=4.67×(0.25×4)=4.67×1=4.67 0.25×0.9×0.8=(0.25×0.8)×0.9=0.2×0.9=0.18 5.2×0.2×5=5.2×(0.2×5)=5.2×1=5.2 2.5×3.1×4=(2.5×4)×3.1=10×3.1=31 8×3.82×1.25=(8×1.25)×3.82=10×3.82=38.2 0.25×3.86×4=(0.25×4)×3.86=1×3.86=3.86 12.5×6.75×0.8=(12.5×0.8)×6.75=10×6.75=67.5 6.4×12.5×5×0.25 =(8×12.5)×(0.8×5×0.25)=100×1=100 8.8×12.5=1.1×(8×12.5)=1.1×100=110 35×1.25×2×0.8=(35×2)×(1.25×0.8)=70×1=70 学科网（北京）股份有限公司 $《小数乘法简便运算》十 类型一：顺展型。 2.5×(4+0.8) 1.25×(8+0.8) 3.8×(10+0.5) (1.25-0.125)×8 0.8×(12.5-0.5) (1.25+0.025)×8 12.5×(10+0.8) 3.6×(100+2) (10+0.8)×12.5 (12.5-3)×8 2.5×(4+0.8)=2.5×4+2.5×0.8=10+2=12 1.25×(8+0.8)=1.25×8+1.25×0.8=10+1=11 4.5×(20+0.6)=4.5×20+4.5×0.6=90+2.7=92.7 3.8×(10+0.5)=3.8×10+3.8×0.5=38+1.9=39.9 (1.25-0.125)×8=1.25×8-0.125×8=10-1=9 (1.25+2.5)×0.8=1.25×0.8+2.5×0.8=1+2=3 大题型 4.5×(20+0.6) (1.25+2.5)×0.8 9×(1.1+0.01) 5.7×(100-1) 0.4×(2.5+22) 0.8×(12.5-0.5)=0.8×12.5-0.8×0.5=10-0.4=9.6 (1.25+0.025)×8=1.25×8+0.025×8=10+0.2=10.2 9×(1.1+0.01)=9×1.1+9×0.01=9.9+0.09=9.99 12.5×(10+0.8)=12.5×10+12.5×0.8=125+10=135 3.6×(100+2)=3.6×100+3.6×2=360+7.2=367.2 5.7×(100-1)=5.7×100-5.7×1=570-5.7=564.3 (10+0.8)×12.5=10×12.5+0.8×12.5=125+10=135 (12.5-3)×8=12.5×8-3×8=100-24=76 0.4×(2.5+22)=0.4×2.5+0.4×22=1+8.8=9.8 类型二：拆加型。 0.48×101 1.5×102 2.8×10.2 3.45×102 0.43×102 6.35×101 0.48×101=0.48×(100+1)=48+0.48=48.48 1.5×102=1.5×(100+2)=150+3=153 4.52×101=4.52×(100+1)=452+4.52=456.52 2.8×10.2=2.8×(10+0.2)=28+0.56=28.56 3.45×102=3.45×(100+2)=345+6.9=351.9 9.5×10.1=9.5×(10+0.1)=95+0.95=95.95 0.43×102=0.43×(100+2)=43+0.86=43.86 4.52×101 9.5×10.1 7.5×10.2 6.35×101=6.35×(100+1)=635+6.35=641.35 7.5×10.2=7.5×(10+0.2)=75+1.5=76.5 类型三：拆减型。 99×0.65 0.34×99 3.5×9.8 5.2×9.9 6.3×19.9 4.86×99 99×0.65=0.65×(100-1)=65-0.65=64.35 0.34×99=0.34×(100-1)=34-0.34=33.66 3.85×99=3.85×(100-1)=385-3.85=381.15 3.5×9.8=3.5×(10-0.2)=35-0.7=34.3 5.2×9.9=5.2×(10-0.1)=52-0.52=51.48 5.4×9.8=5.4×(10-0.2)=54-1.08=52.92 6.3×19.9=6.3×(20-0.1)=126-0.63=125.37 4.86×99=4.86×(100-1)=486-4.86=481.14 0.78×9.9=0.78×(10-0.1)=7.8-0.078=7.722 类型四：逆合型。 7.6×4.82+5.18×7.6 4.3×2.5+0.7×2.5 3.85×99 5.4×9.8 0.78×9.9 6.7×3.4+3.3×3.4 14.6×5.6-4.6×5.6 3.7×4.9-3.9×3.7 34.7×5.2+4.8×34.7 5.2×13.7+13.7×4.8 0.46×1.9+0.54×1.91.6×0.5-0.6×0.5 3.58×67+35.8×3.7-0.358×40 76.1×17-76.1×7 5.6×23-5.6×13-5.6×10 3.72×3.5+6.28×3.5 0.45×1.7+0.45×8.3 7.2×4.5-2.2×4.5 5.7×9.7+5.7×1.8-5.7×1.5 6.9×1.67-6.9×0.69+6.9×0.2 7.6×4.82+5.18×7.6=7.6×(4.82+5.18)=7.6×10=76 4.3×2.5+0.7×2.5=2.5×(4.3+0.7)=2.5×5=12.5 6.7×3.4+3.3×3.4=3.4×(6.7+3.3)=3.4×10=34 14.6×5.6-4.6×5.6=5.6×(14.6-4.6)=5.6×10=56 3.7×4.9-3.9×3.7=3.7×(4.9-3.9)=3.7×1=3.7 34.7×5.2+4.8×34.7=34.7×(5.2+4.8)=34.7×10=347 5.2×13.7+13.7×4.8=13.7×(5.2+4.8)=13.7×10=137 0.46×1.9+0.54×1.9=1.9×(0.46+0.54)=1.9×1=1.9 1.6×0.5-0.6×0.5=0.5×(1.6-0.6)=0.5×1=0.5 3.58×67+35.8×3.7-0.358×40 =3.58×67+3.58×37-3.58×4 =3.58×(67+37-4)=3.58×100=358 76.1×17-76.1×7=76.1×(17-7)=76.1×10=761 5.6×23-5.6×13-5.6×10=5.6×(23-13-10)=5.6×0=0 3.72×3.5+6.28×3.5=3.5×(3.72+6.28)=3.5×10=35 0.45×1.7+0.45×8.3=0.45×(1.7+8.3)=0.45×10=4.5 7.2×4.5-2.2×4.5=4.5×(7.2-2.2)=4.5×5=22.5 5.7×9.7+5.7×1.8-5.7×1.5 =5.7×(9.7+1.8-1.5)=5.7×10=57 6.9×1.67-6.9×0.69+6.9×0.2 =6.9×(1.67-0.69+0.2)=6.9×1.18=8.142 类型五：添“1”型。 5.13×99+5.13 0.04×29+0.04 0.78×99+0.78 7.34×99+7.34 34.95×101-34.95 1.78×99+1.78 088=00I×8'8=(T+66)×8'8=8'8+66×8'g 0Z=00I×乙五=(I+66)X乙五=乙五+66×乙五 026=00I×L6=(1+66)XL6=L6+66×L6 0999=00I×999=(I+66)×999=999+66×999 029=00L×L9=(T+66)×L9=29+66×ㄥ9 00I=0b×9Z=(I+68)X9Z=9Z+68×9Z 080S=00I×809=(I-I0I)×8^09=80S-I0I×809 8LI=00I×8LT=(I+66)×8LI=8LT+66×82T 96t8=00I×96五8=(I-I0I)×96五8=968-I0I×96五8 五8L=00IX五8L=(I+66)X8L=8L+66X五8L 8L=00I×8L0=(I+66)×820=8L0+66X8L0 Z1=08×00=(1+6Z)×00=00+6Z×00 CIS=00IXCI'S=(I+66)XCI'S=CI '9+66XCI'g ㄥ五-I00IXㄥ五 6×68+6`8L 乙6-I0IX乙6 8'8+66×8‘8 乙五+66XZ五 L6+66×ㄥ6 999+66X999 ㄥ9+66×ㄥ9 9Z+68×9Z 809-I0IX809 9.2×101-9.2=9.2×(101-1)=9.2×100=920 78.9+78.9×9=78.9×(1+9)=78.9×10=789 4.7×1001-4.7=4.7×(1001-1)=4.7×1000=4700 类型六：拆倍法。 5.8×36+11.6×32 9.5×72-19×31 3.6×88+10.8×4 2.7×51-8.1×17 2.4×98+7.2 3.5×62+10.5×16 5.8×36+11.6×32 =5.8×36+5.8×2×32=5.8×(36+64)=5.8×100=580 9.5×72-19×31 =9.5×72-9.5×2×31=9.5×(72-62)=9.5×10=95 3.6×88+10.8×4 =3.6×88+3.6×3×4=3.6×(88+12)=3.6×100=360 2.7×51-8.1×17 =2.7×51-2.7×3×17=2.7×(51-51)=2.7×0=0 2.4×98+7.2 =2.4×98+2.4×3=2.4×(98+3)=2.4×101=242.4 3.5×62+10.5×16 =3.5×62+3.5×3×16=3.5×(62+48)=3.5×110=385 类型七：移小数点。 0.75X5.7+2.5×0.57 70.8×0.27+7.08×7.3 3.25×3.5+32.5×0.65 0.37×42.6+3.7×5.74 6.4×5.3-0.64×43 0.64×38.5+6.4×61.5 5.1×28+0.51×720 5.1×18+1.7×46 1.2×34+0.12×660 1.7×28+3.4×36 8.5×9.2-0.85×82 0.75×5.7+2.5×0.57 =7.5×0.57+2.5×0.57=0.57×(7.5+2.5)=5.7 70.8×0.27+7.08×7.3 =7.08×2.7+7.08×7.3=7.08×(2.7+7.3)=70.8 3.25×3.5+32.5×0.65 =3.25×3.5+3.25×6.5=3.25×(3.5+6.5)=32.5 0.37×42.6+3.7×5.74 =3.7×4.26+3.7×5.74=3.7×(4.26+5.74)=37 6.4×5.3-0.64×43 =6.4×5.3-6.4×4.3=6.4×(5.3-4.3)=6.4 0.64×38.5+6.4×61.5 =6.4×3.85+6.4×61.5=6.4×(3.85+61.5)=418.24 5.1×28+0.51×720 =5.1×28+5.1×72=5.1×(28+72)=510 5.1×18+1.7×46 =1.7×54+1.7×46=1.7×(54+46)=170 1.2×34+0.12×660 =1.2×34+1.2×66=1.2×(34+66)=120 1.7×28+3.4×36 =1.7×28+1.7×72=1.7×(28+72)=170 8.5×9.2-0.85×82 =8.5×9.2-8.5×8.2=8.5×(9.2-8.2)=8.5 类型八：拆分凑整。 5.6×0.125 1.25×8.8 1.25×6.4×0.25 0.32×2.5×12.5 4.8×12.5 1.25×32 0.125×720.25×96 0.75×480.5×86 0.88×25 0.125×32 1.25×4.8 0.25×0.44 5.6×0.125=0.7×(8×0.125)=0.7×1=0.7 1.25×8.8=1.25×8×1.1=10×1.1=11 1.25×6.4×0.25=(1.25×8)×(0.8×0.25)=10×0.2=2 0.32×2.5×12.5=(0.4×2.5)×(0.8×12.5)=1×10=10 4.8×12.5=0.6×(8×12.5)=0.6×100=60 1.25×32=1.25×8×4=10×4=40 0.125×72=0.125×8×9=1×9=9 0.25×96=0.25×4×24=1×24=24 0.75×48=0.75×4×12=3×12=36 0.5×86=43 0.88×25=0.22×(4×25)=0.22×100=22 0.125×32=0.125×8×4=1×4=4 1.25×4.8=1.25×8×0.6=10×0.6=6 0.25×0.44=0.25×4×0.11=1×0.11=0.11 类型九：公式综合。 0.8×0.25×0.4×1.25 0.04×12.5×2.5×0.8 II=I'IXOI=(9OXX(80X9ZI=90X80X7ZX9'ZI 8L8=(10+66)X8L‘8=I0×8L8+66×8L8=8L80+66×8ㄥ8 I=0I×I0=(80X9ZI)×(9Z×00)=80×9Z×9I×00 I0=I0×I=(匝0×9Z0)×(9ZT×80)=9ZT×五0×9Z0X80 五2×6Z+2IX9Z+ZIX9乙 8T×66-6×6I+06X6I 9T×8`88+9五X6`66 9`8Z+Z9×9`Z+Lb×9`8乙 L99×888+III×66'6 8×ZX9ZI×9五'0 9×9ZIXZ80X9Z0 90X80X乙ZX9ZI 8280+66×8ㄥ‘8 0.25×0.32×12.5×5=(0.25×0.4)×(0.8×12.5)×5=0.1×10×5=5 0.45×1.25×2×8=(0.45×2)×(1.25×8)=0.9×10=9 9.99×111+3.33×667 =3.33×333+3.33×667=3.33×(333+667)=3330 23.6×47+23.6×52+23.6=23.6×(47+52+1)=2360 99.9×4.5+33.3×1.5 =33.3×13.5+33.3×1.5=33.3×(13.5+1.5)=499.5 1.9×90+1.9×9-99×1.8 =1.9×99-99×1.8=99×(1.9-1.8)=9.9 2.6×12+2.6×17+29×7.4 =2.6×29+29×7.4=29×(2.6+7.4)=290 类型十：乘法交换律、结合律 4.67×0.25×4 0.25×0.9×0.8 5.2×0.2×5 2.5×3.1×4 8×3.82×1.25 0.25×3.86×4 12.5×6.75×0.8 6.4×12.5×5×0.25 8.8×12.5 35×1.25×2×0.8 4.67×0.25×4=4.67×(0.25×4)=4.67×1=4.67 0.25×0.9×0.8=(0.25×0.8)×0.9=0.2×0.9=0.18 5.2×0.2×5=5.2×(0.2×5)=5.2×1=5.2 2.5×3.1×4=(2.5×4)×3.1=10×3.1=31 8×3.82×1.25=(8×1.25)×3.82=10×3.82=38.2 0.25×3.86×4=(0.25×4)×3.86=1×3.86=3.86 12.5×6.75×0.8=(12.5×0.8)×6.75=10×6.75=67.5 6.4×12.5×5×0.25 =(8×12.5)×(0.8×5×0.25)=100×1=100 8.8×12.5=1.1×(8×12.5)=1.1×100=110 35×1.25×2×0.8=(35×2)×(1.25×0.8)=70×1=70 《小数乘法简便运算》十大题型 类型一：顺展型。 2.5×(4+0.8) 1.25×(8+0.8) 4.5×(20+0.6) 3.8×(10+0.5) (1.25−0.125)×8 (1.25+2.5)×0.8 0.8×(12.5−0.5)    (1.25+0.025)×8    9×(1.1+0.01) 12.5×(10+0.8) 3.6×(100+2) 5.7×(100−1) (10+0.8)×12.5 (12.5−3)×8 0.4×(2.5+22) 类型二：拆加型。 0.48×101 1.5×102 4.52×101 2.8×10.2 3.45×102 9.5×10.1    0.43×102 6.35×101 7.5×10.2 类型三：拆减型。 99×0.65 0.34 ×99 3.85×99 3.5×9.8 5.2×9.9 5.4×9.8 6.3×19.9 4.86×99 0.78×9.9 类型四：逆合型。 7.6×4.82+5.18×7.6 4.3×2.5+0.7×2.5 6.7×3.4+3.3×3.4 14.6×5.6−4.6×5.6 3.7×4.9−3.9×3.7 34.7×5.2+4.8×34.7 5.2×13.7+13.7×4.8 0.46×1.9+0.54×1.9 1.6×0.5−0.6×0.5 3.58×67+35.8×3.7 − 0.358×40 76.1×17−76.1×7 5.6×23−5.6×13−5.6×10  3.72×3.5+6.28×3.5 0.45×1.7+0.45×8.3  7.2×4.5−2.2×4.5 5.7×9.7+5.7×1.8−5.7×1.5  6.9×1.67−6.9×0.69+6.9×0.2 类型五：添 “1” 型。 5.13×99+5.13 0.04×29+0.04 0.78×99+0.78 7.34×99+7.34 34.95×101−34.95 1.78×99+1.78 50.8×101−50.8  2.5×39+2.5  6.7×99+6.7 56.5×99+56.5  9.7×99+9.7  4.2×99+4.2 3.8×99+3.8  9.2×101−9.2  78.9+78.9×9  4.7×1001−4.7 类型六：拆倍法。 5.8×36+11.6×32  9.5×72−19×31 3.6×88+10.8×4  2.7×51−8.1×17 2.4×98+7.2  3.5×62+10.5×16 类型七：移小数点。 0.75×5.7+2.5×0.57 70.8×0.27+7.08×7.3 3.25×3.5+32.5×0.65 0.37×42.6+3.7×5.74 6.4×5.3−0.64×43 0.64×38.5+6.4×61.5 5.1×28+0.51×720 5.1×18+1.7×46 1.2×34+0.12×660 1.7×28+3.4×36 8.5×9.2−0.85×82 类型八： 拆分凑整。 5.6×0.125 1.25×8.8 1.25×6.4×0.25 0.32×2.5×12.5 4.8×12.5 1.25×32 0.125×72 0.25×96 0.75×48 0.5×86 0.88 × 25 0.125×32 1.25×4.8 0.25×0.44 类型九：公式综合。 0.8×0.25×0.4×1.25 0.04×12.5×2.5×0.8 3.78×9.9+0.378 12.5×2.2×0.8×0.5 0.25×0.32×12.5×5 0.45×1.25×2×8 9.99×111+3.33×667 23.6×47+23.6×52+23.6 99.9×4.5+33.3×1.5 1.9×90+1.9×9−99×1.8 2.6×12+2.6×17+29×7.4 类型十：乘法交换律、结合律 4.67×0.25×4 0.25×0.9×0.8 5.2×0.2×5 2.5×3.1×4 8×3.82×1.25 0.25×3.86×4 12.5×6.75×0.8 6.4×12.5×5×0.25 8.8×12.5 35×1.25×2×0.8 学科网（北京）股份有限公司 $类型一：顺展型。 2.5×(4+0.8) 3.8×(10+0.5) 0.8×(12.5-0.5) 12.5×(10+0.8) (10+0.8)×12.5 类型二：拆加型。 0.48×101 《小数乘法简便运算》 1.25×(8+0.8) (1.25-0.125)×8 (1.25+0.025)×8 3.6×(100+2) (12.5-3)×8 1.5×102 十大题型 4.5×(20+0.6) (1.25+2.5)×0.8 9×(1.1+0.01) 5.7×(100-1) 0.4×(2.5+22) 4.52×101 2.8×10.2 0.43×102 类型三：拆减型。 99×0.65 3.5×9.8 6.3×19.9 类型四：逆合型。 7.6×4.82+5.18×7.6 3.45×102 6.35×101 0.34×99 5.2×9.9 4.86×99 4.3X2.5+0.7×2.5 9.5×10.1 7.5×10.2 3.85×99 5.4×9.8 0.78×9.9 6.7×3.4+3.3×3.4 14.6×5.6-4.6×5.6 3.7×4.9-3.9×3.7 34.7×5.2+4.8×34.7 5.2×13.7+13.7×4.8 0.46×1.9+0.54×1.91.6×0.5-0.6×0.5 3.58×67+35.8×3.7-0.358×40 76.1×17-76.1×7 5.6×23-5.6×13-5.6×10 3.72×3.5+6.28×3.5 0.45×1.7+0.45×8.3 7.2×4.5-2.2×4.5 5.7×9.7+5.7×1.8-5.7×1.5 6.9×1.67-6.9×0.69+6.9×0.2 类型五：添“1”型。 5.13×99+5.13 7.34×99+7.34 50.8×101-50.8 56.5×99+56.5 3.8×99+3.8 4.7×1001-4.7 类型六：拆倍法。 5.8×36+11.6×32 0.04×29+0.04 34.95×101-34.95 2.5×39+2.5 9.7×99+9.7 9.2×101-9.2 9.5×72 0.78×99+0.78 1.78×99+1.78 6.7×99+6.7 4.2×99+4.2 78.9+78.9×9 19×31 3.6×88+10.8×4 2.4×98+7.2 类型七：移小数点。 0.75×5.7+2.5×0.57 3.25×3.5+32.5×0.65 6.4×5.3-0.64×43 5.1×28+0.51×720 2.7×51-8.1×17 3.5×62+10.5×16 70.8×0.27+7.08×7.3 0.37×42.6+3.7×5.74 0.64×38.5+6.4×61.5 5.1×18+1.7×46 1.2×34+0.12×660 8.5×9.2-0.85×82 类型八：拆分凑整。 5.6×0.125 0.32×2.5×12.5 0.125×720.25×96 0.125×32 1.7×28+3.4×36 1.25×8.8 1.25×6.4×0.25 4.8×12.5 1.25×32 0.75×480.5×86 0.88×25 1.25×4.8 0.25×0.44 类型九：公式综合。 0.8×0.25×0.4×1.25 3.78×9.9+0.378 0.25×0.32×12.5×5 9.99×111+3.33×667 99.9×4.5+33.3×1.5 2.6×12+2.6×17+29×7.4 8I×66-6×6I+06×6T 9'gZ+Z9X98乙+L五X9'gZ 8×Z×9zIX9五0 90X80XZZ×9ZI 80×9Z×9ZI×00 类型十：乘法交换律、 4.67×0.25×4 2.5×3.1×4 12.5×6.75×0.8 35×1.25×2×0.8 结合律 0.25×0.9×0.8 8×3.82×1.25 6.4×12.5×5×0.25 5.2×0.2×5 0.25×3.86×4 8.8×12.5