Question

5．计算下面各题打星号的要简算．
19.5×0.2-2.07÷23                          
$\frac{3}{8}$×[$\frac{8}{9}$÷（$\frac{5}{6}$-$\frac{3}{4}$）]
※（$\frac{2}{29}$+$\frac{3}{23}$）×29×23
※$\frac{17}{24}$×$\frac{1}{5}$+$\frac{7}{24}$÷5+$\frac{1}{5}$．

Answer 1

分析 ①先算乘法和除法，再算减法；
②先算小括号的减法，再算除法，最后算乘法；
③运用乘法分配律可简算；
④先把除法变成乘法，再逆用乘法分配律简算．

解答 解：①19.5×0.2-2.07÷23  
=3.9-0.09
=3.81
                        
②$\frac{3}{8}$×[$\frac{8}{9}$÷（$\frac{5}{6}$-$\frac{3}{4}$）]
=$\frac{3}{8}$×[$\frac{8}{9}$÷（$\frac{10}{12}$$-\frac{9}{12}$）]
=$\frac{3}{8}$×[$\frac{8}{9}$$÷\frac{1}{12}$]
=$\frac{3}{8}$×[$\frac{8}{9}$×12]
=$\frac{3}{8}$×$\frac{32}{3}$
=4

③（$\frac{2}{29}$+$\frac{3}{23}$）×29×23
=$\frac{2}{29}$×29×23+$\frac{3}{23}$×29×23
=46+87
=133

④$\frac{17}{24}$×$\frac{1}{5}$+$\frac{7}{24}$÷5+$\frac{1}{5}$
=$\frac{17}{24}$×$\frac{1}{5}$+$\frac{7}{24}$×$\frac{1}{5}$$+\frac{1}{5}$
=（$\frac{17}{24}$$+\frac{7}{24}$+1）×$\frac{1}{5}$
=2×$\frac{1}{5}$
=$\frac{2}{5}$

点评 此题考查小数、分数四则混合运算顺序和灵活运用运算定律，分析数据找到正确的计算方法．