Question

15．用簡(jiǎn)便方法計(jì)算下面各題．
$\frac{5}{7}$×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×$\frac{21}{25}$，運(yùn)用乘法交換律和結(jié)合律簡(jiǎn)算；                        
（$\frac{5}{6}$+$\frac{1}{3}$）÷$\frac{5}{12}$，把除數(shù)轉(zhuǎn)化為乘它的倒數(shù)，再運(yùn)用乘法分配律簡(jiǎn)算；
$\frac{7}{8}$÷$\frac{9}{11}$+$\frac{1}{8}$÷$\frac{9}{11}$，把除數(shù)轉(zhuǎn)化為乘它的倒數(shù)，再運(yùn)用乘法分配律簡(jiǎn)算；             
$\frac{2}{9}$×$\frac{1}{5}$+$\frac{2}{9}$×$\frac{4}{5}$+$\frac{2}{9}$．運(yùn)用乘法分配律簡(jiǎn)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$+\frac{4}{5}$
=$2\frac{4}{5}$；

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

點(diǎn)評(píng) 此題考查的目的是理解掌握分?jǐn)?shù)四則混合運(yùn)算的順序以及它們的計(jì)算法則，并且能夠靈活選擇簡(jiǎn)便方法進(jìn)行計(jì)算．