Question

7．用你喜歡的方法計(jì)算．
$\frac{14}{15}$÷[（$\frac{4}{5}$+$\frac{2}{3}$）×$\frac{10}{11}$]
$\frac{2}{5}$-$\frac{2}{5}$×$\frac{3}{4}$÷$\frac{5}{2}$ 
$\frac{3}{7}$×$\frac{4}{5}$+$\frac{4}{7}$×$\frac{2}{5}$                          
（$\frac{1}{3}$+$\frac{1}{4}$+$\frac{1}{6}$）×12．

Answer 1

分析 ①$\frac{14}{15}$÷[（$\frac{4}{5}$+$\frac{2}{3}$）×$\frac{10}{11}$]，先算小括號(hào)里面的加法，再算中括號(hào)里面的乘法，最后算除法；
②$\frac{2}{5}$-$\frac{2}{5}$×$\frac{3}{4}$÷$\frac{5}{2}$，先算乘法、再算除法，最后算減法；
③$\frac{3}{7}$×$\frac{4}{5}$+$\frac{4}{7}$×$\frac{2}{5}$，運(yùn)用乘法分配律簡(jiǎn)算；                        
④（$\frac{1}{3}$+$\frac{1}{4}$+$\frac{1}{6}$）×12，運(yùn)用乘法分配律簡(jiǎn)算．

解答 解：①$\frac{14}{15}$÷[（$\frac{4}{5}$+$\frac{2}{3}$）×$\frac{10}{11}$]
=$\frac{14}{15}÷[\frac{22}{15}×\frac{10}{11}]$
=$\frac{14}{15}÷\frac{4}{3}$
=$\frac{14}{15}×\frac{3}{4}$
=$\frac{7}{10}$；

②$\frac{2}{5}$-$\frac{2}{5}$×$\frac{3}{4}$÷$\frac{5}{2}$ 
=$\frac{2}{5}-\frac{2}{5}×\frac{3}{4}×\frac{2}{5}$
=$\frac{2}{5}-$$\frac{3}{25}$
=$\frac{7}{25}$；

③$\frac{3}{7}$×$\frac{4}{5}$+$\frac{4}{7}$×$\frac{2}{5}$    
=$\frac{3}{7}×\frac{4}{5}+\frac{2}{7}×\frac{4}{5}$
=$（\frac{3}{7}+\frac{2}{7}）×\frac{4}{5}$
=$\frac{5}{7}×\frac{4}{5}$
=$\frac{4}{7}$；
                    
④（$\frac{1}{3}$+$\frac{1}{4}$+$\frac{1}{6}$）×12
=$\frac{1}{3}×12+\frac{1}{4}×12+\frac{1}{6}×12$
=4+3+2
=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．