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11. 计算下面各题,怎样简便就怎样计算。
$(\frac{5}{12} + \frac{1}{8}) ÷ \frac{1}{24}$
$23 - \frac{8}{9} × \frac{3}{4} ÷ \frac{1}{27}$
$\frac{7}{9} ÷ \frac{11}{5} - \frac{5}{11} × \frac{2}{9}$
$36 ÷ \frac{2}{3} ÷ \frac{3}{5}$
$\frac{5}{8} - \frac{1}{4} × (\frac{8}{9} ÷ \frac{2}{3})$
$2\frac{5}{7} - \frac{3}{8} ÷ \frac{5}{8} - \frac{2}{5}$
$(\frac{5}{12} + \frac{1}{8}) ÷ \frac{1}{24}$
$23 - \frac{8}{9} × \frac{3}{4} ÷ \frac{1}{27}$
$\frac{7}{9} ÷ \frac{11}{5} - \frac{5}{11} × \frac{2}{9}$
$36 ÷ \frac{2}{3} ÷ \frac{3}{5}$
$\frac{5}{8} - \frac{1}{4} × (\frac{8}{9} ÷ \frac{2}{3})$
$2\frac{5}{7} - \frac{3}{8} ÷ \frac{5}{8} - \frac{2}{5}$
答案
$(\frac{5}{12} + \frac{1}{8}) ÷ \frac{1}{24}$
$=(\frac{5}{12} + \frac{1}{8})×24$
$=\frac{5}{12}×24 + \frac{1}{8}×24$
$=10 + 3$
$=13$
$23 - \frac{8}{9} × \frac{3}{4} ÷ \frac{1}{27}$
$=23 - \frac{2}{3}×27$
$=23 - 18$
$=5$
$\frac{7}{9} ÷ \frac{11}{5} - \frac{5}{11} × \frac{2}{9}$
$=\frac{7}{9}×\frac{5}{11} - \frac{5}{11}×\frac{2}{9}$
$=(\frac{7}{9} - \frac{2}{9})×\frac{5}{11}$
$=\frac{5}{9}×\frac{5}{11}$
$=\frac{25}{99}$
$36 ÷ \frac{2}{3} ÷ \frac{3}{5}$
$=36×\frac{3}{2}×\frac{5}{3}$
$=36×(\frac{3}{2}×\frac{5}{3})$
$=36×\frac{5}{2}$
$=90$
$\frac{5}{8} - \frac{1}{4} × (\frac{8}{9} ÷ \frac{2}{3})$
$=\frac{5}{8} - \frac{1}{4}×(\frac{8}{9}×\frac{3}{2})$
$=\frac{5}{8} - \frac{1}{4}×\frac{4}{3}$
$=\frac{5}{8} - \frac{1}{3}$
$=\frac{15}{24} - \frac{8}{24}$
$=\frac{7}{24}$
$2\frac{5}{7} - \frac{3}{8} ÷ \frac{5}{8} - \frac{2}{5}$
$=2\frac{5}{7} - \frac{3}{8}×\frac{8}{5} - \frac{2}{5}$
$=2\frac{5}{7} - \frac{3}{5} - \frac{2}{5}$
$=2\frac{5}{7} - (\frac{3}{5} + \frac{2}{5})$
$=2\frac{5}{7} - 1$
$=1\frac{5}{7}$
$=(\frac{5}{12} + \frac{1}{8})×24$
$=\frac{5}{12}×24 + \frac{1}{8}×24$
$=10 + 3$
$=13$
$23 - \frac{8}{9} × \frac{3}{4} ÷ \frac{1}{27}$
$=23 - \frac{2}{3}×27$
$=23 - 18$
$=5$
$\frac{7}{9} ÷ \frac{11}{5} - \frac{5}{11} × \frac{2}{9}$
$=\frac{7}{9}×\frac{5}{11} - \frac{5}{11}×\frac{2}{9}$
$=(\frac{7}{9} - \frac{2}{9})×\frac{5}{11}$
$=\frac{5}{9}×\frac{5}{11}$
$=\frac{25}{99}$
$36 ÷ \frac{2}{3} ÷ \frac{3}{5}$
$=36×\frac{3}{2}×\frac{5}{3}$
$=36×(\frac{3}{2}×\frac{5}{3})$
$=36×\frac{5}{2}$
$=90$
$\frac{5}{8} - \frac{1}{4} × (\frac{8}{9} ÷ \frac{2}{3})$
$=\frac{5}{8} - \frac{1}{4}×(\frac{8}{9}×\frac{3}{2})$
$=\frac{5}{8} - \frac{1}{4}×\frac{4}{3}$
$=\frac{5}{8} - \frac{1}{3}$
$=\frac{15}{24} - \frac{8}{24}$
$=\frac{7}{24}$
$2\frac{5}{7} - \frac{3}{8} ÷ \frac{5}{8} - \frac{2}{5}$
$=2\frac{5}{7} - \frac{3}{8}×\frac{8}{5} - \frac{2}{5}$
$=2\frac{5}{7} - \frac{3}{5} - \frac{2}{5}$
$=2\frac{5}{7} - (\frac{3}{5} + \frac{2}{5})$
$=2\frac{5}{7} - 1$
$=1\frac{5}{7}$
12. 解下列方程。
$\frac{4}{5}x = 28$
$\frac{3}{7}x - \frac{1}{2} = \frac{3}{7}$
$\frac{3}{7}x ÷ \frac{1}{2} = 1$
$x + \frac{1}{6}x = \frac{14}{9}$
$\frac{4}{5}x = 28$
$\frac{3}{7}x - \frac{1}{2} = \frac{3}{7}$
$\frac{3}{7}x ÷ \frac{1}{2} = 1$
$x + \frac{1}{6}x = \frac{14}{9}$
答案
$\frac{4}{5}x = 28$
$x = 28 ÷ \frac{4}{5}$
$x = 28 × \frac{5}{4}$
$x = 35$
$\frac{3}{7}x - \frac{1}{2} = \frac{3}{7}$
$\frac{3}{7}x = \frac{3}{7} + \frac{1}{2}$
$\frac{3}{7}x = \frac{6}{14} + \frac{7}{14}$
$\frac{3}{7}x = \frac{13}{14}$
$x = \frac{13}{14} ÷ \frac{3}{7}$
$x = \frac{13}{14} × \frac{7}{3}$
$x = \frac{13}{6}$
$\frac{3}{7}x ÷ \frac{1}{2} = 1$
$\frac{3}{7}x = 1 × \frac{1}{2}$
$\frac{3}{7}x = \frac{1}{2}$
$x = \frac{1}{2} ÷ \frac{3}{7}$
$x = \frac{1}{2} × \frac{7}{3}$
$x = \frac{7}{6}$
$x + \frac{1}{6}x = \frac{14}{9}$
$\frac{7}{6}x = \frac{14}{9}$
$x = \frac{14}{9} ÷ \frac{7}{6}$
$x = \frac{14}{9} × \frac{6}{7}$
$x = \frac{4}{3}$
$x = 28 ÷ \frac{4}{5}$
$x = 28 × \frac{5}{4}$
$x = 35$
$\frac{3}{7}x - \frac{1}{2} = \frac{3}{7}$
$\frac{3}{7}x = \frac{3}{7} + \frac{1}{2}$
$\frac{3}{7}x = \frac{6}{14} + \frac{7}{14}$
$\frac{3}{7}x = \frac{13}{14}$
$x = \frac{13}{14} ÷ \frac{3}{7}$
$x = \frac{13}{14} × \frac{7}{3}$
$x = \frac{13}{6}$
$\frac{3}{7}x ÷ \frac{1}{2} = 1$
$\frac{3}{7}x = 1 × \frac{1}{2}$
$\frac{3}{7}x = \frac{1}{2}$
$x = \frac{1}{2} ÷ \frac{3}{7}$
$x = \frac{1}{2} × \frac{7}{3}$
$x = \frac{7}{6}$
$x + \frac{1}{6}x = \frac{14}{9}$
$\frac{7}{6}x = \frac{14}{9}$
$x = \frac{14}{9} ÷ \frac{7}{6}$
$x = \frac{14}{9} × \frac{6}{7}$
$x = \frac{4}{3}$
13. 王师傅要做一批灯笼,$\frac{20}{3}小时做了这批灯笼的\frac{1}{12}$,照这样计算,$\frac{60}{7}$小时能做这批灯笼的几分之几？
答案
$\frac{3}{28}$
解析
首先求出王师傅每小时完成这批灯笼的几分之几，即工作效率。
工作效率=工作总量÷工作时间=$\frac{1}{12}÷\frac{20}{3}=\frac{1}{12}×\frac{3}{20}=\frac{1}{80}$
再用求出的工作效率乘以$\frac{60}{7}$小时，即可求出$\frac{60}{7}$小时能做这批灯笼的几分之几。
工作总量=工作效率×工作时间=$\frac{1}{80}×\frac{60}{7}=\frac{3}{28}$
工作效率=工作总量÷工作时间=$\frac{1}{12}÷\frac{20}{3}=\frac{1}{12}×\frac{3}{20}=\frac{1}{80}$
再用求出的工作效率乘以$\frac{60}{7}$小时，即可求出$\frac{60}{7}$小时能做这批灯笼的几分之几。
工作总量=工作效率×工作时间=$\frac{1}{80}×\frac{60}{7}=\frac{3}{28}$
