Question

9．脫式計算，能簡便的要用簡便方法計算．
$\frac{3}{8}$×$\frac{5}{6}$÷$\frac{15}{16}$          　
$\frac{7}{30}$×0.6÷$\frac{7}{30}$×$\frac{5}{2}$          
$\frac{8}{17}$÷23+$\frac{1}{23}$×$\frac{9}{17}$
10÷$\frac{4}{25}$÷$\frac{5}{12}$　　　　　　
$\frac{3}{4}$×$\frac{4}{9}$+$\frac{4}{9}$÷$\frac{4}{3}$            
3-$\frac{6}{11}$÷$\frac{9}{22}$-$\frac{2}{3}$．

Answer 1

分析 ①把除法變成乘法，再約分計算．
②把小數(shù)變成分?jǐn)?shù)，把除法變成乘法，再約分計算．
③把除法變成乘法，再用乘法分配律計算．
④把除法變成乘法，再約分計算．
⑤把除法變成乘法，再用乘法分配律計算．
⑥把除法變成乘法，再用減法的性質(zhì)計算．

解答 解：①$\frac{3}{8}$×$\frac{5}{6}$÷$\frac{15}{16}$  
=$\frac{3}{8}$×$\frac{5}{6}$×$\frac{16}{15}$
=$\frac{1}{3}$

②$\frac{7}{30}$×0.6÷$\frac{7}{30}$×$\frac{5}{2}$       
=$\frac{7}{30}×\frac{3}{5}×\frac{30}{7}×\frac{5}{2}$
=$\frac{3}{2}$

③$\frac{8}{17}$÷23+$\frac{1}{23}$×$\frac{9}{17}$
=$\frac{8}{17}$×$\frac{1}{23}$+$\frac{1}{23}$×$\frac{9}{17}$
=（$\frac{8}{17}$+$\frac{9}{17}$）×$\frac{1}{23}$
=1×$\frac{1}{23}$
=$\frac{1}{23}$

④10÷$\frac{4}{25}$÷$\frac{5}{12}$　
=10×$\frac{25}{4}×\frac{12}{5}$
=150

⑤$\frac{3}{4}$×$\frac{4}{9}$+$\frac{4}{9}$÷$\frac{4}{3}$     
=$\frac{3}{4}$×$\frac{4}{9}$+$\frac{4}{9}$×$\frac{3}{4}$
=$（\frac{4}{9}+\frac{4}{9}）×\frac{3}{4}$
=$\frac{8}{9}×\frac{3}{4}$
=$\frac{2}{3}$

⑥$3-\frac{6}{11}÷\frac{9}{22}-\frac{2}{3}$
=$3-\frac{4}{3}-\frac{2}{3}$
=$3-（\frac{4}{3}+\frac{2}{3}）$
=3-2
=1

點評 本題主要考查分?jǐn)?shù)四則混合運算的計算順序和計算能力．