Question

15．用简便方法计算下面各题．
$\frac{5}{7}$×16×$\frac{21}{25}$                         
（$\frac{5}{6}$+$\frac{1}{3}$）÷$\frac{5}{12}$
$\frac{7}{8}$÷$\frac{9}{11}$+$\frac{1}{8}$÷$\frac{9}{11}$                  
$\frac{2}{9}$×$\frac{1}{5}$+$\frac{2}{9}$×$\frac{4}{5}$+$\frac{2}{9}$．

Answer 1

分析 $\frac{5}{7}$×16×$\frac{21}{25}$，运用乘法交换律和结合律简算；                        
（$\frac{5}{6}$+$\frac{1}{3}$）÷$\frac{5}{12}$，把除数转化为乘它的倒数，再运用乘法分配律简算；
$\frac{7}{8}$÷$\frac{9}{11}$+$\frac{1}{8}$÷$\frac{9}{11}$，把除数转化为乘它的倒数，再运用乘法分配律简算；             
$\frac{2}{9}$×$\frac{1}{5}$+$\frac{2}{9}$×$\frac{4}{5}$+$\frac{2}{9}$．运用乘法分配律简算．

解答 解：$\frac{5}{7}$×16×$\frac{21}{25}$   
=$16×（\frac{5}{7}×\frac{21}{25}）$
=$16×\frac{3}{5}$
=9.6；
                      
（$\frac{5}{6}$+$\frac{1}{3}$）÷$\frac{5}{12}$
=$（\frac{5}{6}+\frac{1}{3}）×\frac{12}{5}$
=$\frac{5}{6}×\frac{12}{5}+\frac{1}{3}×\frac{12}{5}$
=2$+\frac{4}{5}$
=$2\frac{4}{5}$；

$\frac{7}{8}$÷$\frac{9}{11}$+$\frac{1}{8}$÷$\frac{9}{11}$    
=$（\frac{7}{8}+\frac{1}{8}）×\frac{11}{9}$
=$1×\frac{11}{9}$
=$\frac{11}{9}$；
              
$\frac{2}{9}$×$\frac{1}{5}$+$\frac{2}{9}$×$\frac{4}{5}$+$\frac{2}{9}$
=$\frac{2}{9}×（\frac{1}{5}+\frac{4}{5}+1）$
=$\frac{2}{9}×2$
=$\frac{4}{9}$．

点评 此题考查的目的是理解掌握分数四则混合运算的顺序以及它们的计算法则，并且能够灵活选择简便方法进行计算．