Question

4．脱式计算，能简算的要简算．
$\frac{7}{12}$×$\frac{3}{4}$×$\frac{8}{21}$          $\frac{9}{14}$×$\frac{4}{7}$+$\frac{9}{14}$×$\frac{3}{7}$          （$\frac{2}{3}$+$\frac{5}{6}$）×12
10×$\frac{7}{9}$-$\frac{7}{9}$                56×$\frac{6}{7}$×$\frac{9}{8}$                    $\frac{4}{25}$-$\frac{4}{25}$×$\frac{2}{5}$．

Answer 1

分析 ①先乘前面两个数，再和第三个数相乘．
②用乘法分配律计算．a×（b+c）=ab+ac，或ab+ac=a×（b+c）．
③用乘法分配律计算．
④用乘法分配律计算．
⑤先乘后两个数，再和第一个数相乘．
⑥用乘法分配律计算．

解答 解：①$\frac{7}{12}×\frac{3}{4}×\frac{8}{21}$
=$\frac{21}{48}×\frac{8}{21}$
=$\frac{1}{6}$

②$\frac{9}{14}×\frac{4}{7}+\frac{9}{14}×\frac{3}{7}$
=$\frac{9}{14}×（\frac{4}{7}+\frac{3}{7}）$
=$\frac{9}{14}×1$
=$\frac{9}{14}$

③（$\frac{2}{3}$+$\frac{5}{6}$）×12
=12×$\frac{2}{3}$+$\frac{5}{6}$×12
=8+10
=18

④10×$\frac{7}{9}$-$\frac{7}{9}$   
=（10-1）×$\frac{7}{9}$
=9×$\frac{7}{9}$
=7

⑤56×$\frac{6}{7}$×$\frac{9}{8}$
=$56×（\frac{6}{7}×\frac{9}{8}）$
=$56×\frac{54}{56}$
=54

⑥$\frac{4}{25}$-$\frac{4}{25}$×$\frac{2}{5}$
=（1-$\frac{2}{5}$）×$\frac{4}{25}$
=$\frac{3}{5}×\frac{4}{25}$
=$\frac{12}{125}$

点评 脱式计算要观察算式的特点，灵活选用简便方法计算．