Question

15．简算
102.31×59=
$\frac{1}{7}$×102.31+40$\frac{6}{7}$×102.31=
1$\frac{3}{7}$×$\frac{4}{5}$+2$\frac{4}{7}$×$\frac{4}{5}$+$\frac{4}{5}$=

Answer 1

分析 （1）利用乘法分配律简算；
（2）（3）逆用乘法分配律简算．

解答 解：（1）102.31×59
=102.31×（60-1）
=102.31×60-102.31×1
=6138.6-102.31
=6036.29     

（2）$\frac{1}{7}$×102.31+40$\frac{6}{7}$×102.31
=（$\frac{1}{7}$×+40$\frac{6}{7}$）×102.31
=41×102.31
=4194.71；    

（3）1$\frac{3}{7}$×$\frac{4}{5}$+2$\frac{4}{7}$×$\frac{4}{5}$+$\frac{4}{5}$
=（1$\frac{3}{7}$+2$\frac{4}{7}$+1）×$\frac{4}{5}$
=5×$\frac{4}{5}$
=4．

点评 掌握乘法分配律是解决问题的关键．