Question

16．下面各題，怎樣簡便怎樣算．
$\frac{8}{13}$÷7+$\frac{1}{7}$×$\frac{6}{13}$
$\frac{1}{2}$×$\frac{2}{5}$+$\frac{9}{10}÷\frac{9}{20}$
166÷$\frac{167}{166}$
$\frac{8}{13}$÷4×$\frac{5}{6}$
（$\frac{7}{12}-\frac{5}{18}$）×36
$\frac{3}{5}$÷0.8÷$\frac{1}{12}$．

Answer 1

分析 ①把除法變成乘法，用乘法分配律計算．
②先算乘除法再算加減法．
③把除法變成乘法，用乘法分配律計算．
④先算除法再算乘法．
⑤用乘法分配律計算．
⑥從左往右計算．

解答 解：①$\frac{8}{13}$÷7+$\frac{1}{7}$×$\frac{6}{13}$
=$\frac{1}{7}$×（$\frac{6}{13}$+$\frac{8}{13}$）
=$\frac{1}{7}×\frac{14}{13}$
=$\frac{2}{13}$

②$\frac{1}{2}$×$\frac{2}{5}$+$\frac{9}{10}÷\frac{9}{20}$
=$\frac{1}{5}+2$
=$2\frac{1}{5}$

③$166÷\frac{167}{166}$
=$166×\frac{166}{167}$
=$（167-1）×\frac{166}{167}$
=$167×\frac{166}{167}-\frac{166}{167}$
=$166-\frac{166}{167}$
=$165\frac{1}{167}$

④$\frac{8}{13}$÷4×$\frac{5}{6}$
=$\frac{2}{13}×\frac{5}{6}$
=$\frac{10}{78}$
=$\frac{5}{39}$

⑤（$\frac{7}{12}-\frac{5}{18}$）×36
=36×$\frac{7}{12}-\frac{5}{18}$×36
=21-10
=11

⑥$\frac{3}{5}$÷0.8÷$\frac{1}{12}$
=$\frac{3}{4}×12$
=9

點評 本題考查了解答脫式計算的計算能力．重點是乘法分配律計算方法的應用．