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(4)下面算式的积在$\frac{1}{5}和\frac{1}{4}$之间的是(
①$\frac{1}{4}×\frac{1}{2}$ ②$\frac{3}{5}×\frac{5}{6}$ ③$\frac{21}{20}×\frac{3}{14}$
③
)。①$\frac{1}{4}×\frac{1}{2}$ ②$\frac{3}{5}×\frac{5}{6}$ ③$\frac{21}{20}×\frac{3}{14}$
答案
③
解析
①$\frac{1}{4}×\frac{1}{2}=\frac{1}{8}=0.125$，$\frac{1}{5}=0.2$，$0.125＜0.2$，不在范围内；②$\frac{3}{5}×\frac{5}{6}=\frac{1}{2}=0.5$，$\frac{1}{4}=0.25$，$0.5＞0.25$，不在范围内；③$\frac{21}{20}×\frac{3}{14}=\frac{9}{40}=0.225$，$0.2＜0.225＜0.25$，在范围内。
(5)下列可以用百分数表示的是(
①甲数是乙数的1.5倍 ②一筐苹果重8.5kg ③小红比小明矮0.3dm
①
)。①甲数是乙数的1.5倍 ②一筐苹果重8.5kg ③小红比小明矮0.3dm
答案
①
解析
百分数表示一个数是另一个数的百分之几，不能表示具体数量。①中“甲数是乙数的1.5倍”表示两个数的倍数关系，可转化为百分数；②“8.5kg”和③“0.3dm”是具体数量，不能用百分数表示。故①可以用百分数表示。
(1)直接写出得数。
$\frac{2}{3}×\frac{9}{8}=$
$\frac{5}{4}×\frac{7}{15}=$
$\frac{2}{3}×\frac{9}{8}=$
$\frac{3}{4}$
$6÷\frac{1}{3}=$18
$\frac{3}{8}×3=$$\frac{9}{8}$
$\frac{5}{4}×\frac{7}{15}=$
$\frac{7}{12}$
$28×\frac{5}{14}=$10
$5÷\frac{1}{50}=$250
答案
$\frac{3}{4}$；18；$\frac{9}{8}$；$\frac{7}{12}$；10；250
(2)下面各题怎样简便就怎样算。
$\frac{5}{12}÷\frac{1}{8}+\frac{1}{12}×8$ $\frac{12}{5}×(\frac{5}{6}+\frac{3}{4})$
$(\frac{1}{3}-\frac{1}{4})÷\frac{1}{12}$ $\frac{4}{5}÷[(\frac{3}{4}-\frac{1}{6})×\frac{4}{7}]$
$\frac{5}{12}÷\frac{1}{8}+\frac{1}{12}×8$ $\frac{12}{5}×(\frac{5}{6}+\frac{3}{4})$
$(\frac{1}{3}-\frac{1}{4})÷\frac{1}{12}$ $\frac{4}{5}÷[(\frac{3}{4}-\frac{1}{6})×\frac{4}{7}]$
答案
（1）$4$；（2）$\frac{19}{5}$；（3）$1$；（4）$\frac{12}{5}$
解析
（1）$\frac{5}{12}÷\frac{1}{8}+\frac{1}{12}×8$
$=\frac{5}{12}×8+\frac{1}{12}×8$
$=(\frac{5}{12}+\frac{1}{12})×8$
$=\frac{6}{12}×8$
$=\frac{1}{2}×8$
$=4$
（2）$\frac{12}{5}×(\frac{5}{6}+\frac{3}{4})$
$=\frac{12}{5}×\frac{5}{6}+\frac{12}{5}×\frac{3}{4}$
$=2+\frac{9}{5}$
$=\frac{10}{5}+\frac{9}{5}$
$=\frac{19}{5}$
（3）$(\frac{1}{3}-\frac{1}{4})÷\frac{1}{12}$
$=(\frac{1}{3}-\frac{1}{4})×12$
$=\frac{1}{3}×12-\frac{1}{4}×12$
$=4-3$
$=1$
（4）$\frac{4}{5}÷[(\frac{3}{4}-\frac{1}{6})×\frac{4}{7}]$
$=\frac{4}{5}÷[(\frac{9}{12}-\frac{2}{12})×\frac{4}{7}]$
$=\frac{4}{5}÷[\frac{7}{12}×\frac{4}{7}]$
$=\frac{4}{5}÷\frac{1}{3}$
$=\frac{4}{5}×3$
$=\frac{12}{5}$
$=\frac{5}{12}×8+\frac{1}{12}×8$
$=(\frac{5}{12}+\frac{1}{12})×8$
$=\frac{6}{12}×8$
$=\frac{1}{2}×8$
$=4$
（2）$\frac{12}{5}×(\frac{5}{6}+\frac{3}{4})$
$=\frac{12}{5}×\frac{5}{6}+\frac{12}{5}×\frac{3}{4}$
$=2+\frac{9}{5}$
$=\frac{10}{5}+\frac{9}{5}$
$=\frac{19}{5}$
（3）$(\frac{1}{3}-\frac{1}{4})÷\frac{1}{12}$
$=(\frac{1}{3}-\frac{1}{4})×12$
$=\frac{1}{3}×12-\frac{1}{4}×12$
$=4-3$
$=1$
（4）$\frac{4}{5}÷[(\frac{3}{4}-\frac{1}{6})×\frac{4}{7}]$
$=\frac{4}{5}÷[(\frac{9}{12}-\frac{2}{12})×\frac{4}{7}]$
$=\frac{4}{5}÷[\frac{7}{12}×\frac{4}{7}]$
$=\frac{4}{5}÷\frac{1}{3}$
$=\frac{4}{5}×3$
$=\frac{12}{5}$
5. 解下列方程。
$\frac{1}{12}x-\frac{2}{5}×\frac{5}{9}= \frac{3}{4}$ $x+\frac{1}{4}x= \frac{1}{4}$ $x÷\frac{5}{6}= \frac{3}{8}$
$\frac{1}{12}x-\frac{2}{5}×\frac{5}{9}= \frac{3}{4}$ $x+\frac{1}{4}x= \frac{1}{4}$ $x÷\frac{5}{6}= \frac{3}{8}$
答案
1. 对于方程 $\frac{1}{12}x - \frac{2}{5} × \frac{5}{9} = \frac{3}{4}$：
$\begin{aligned}\frac{1}{12}x - \frac{2}{9} = \frac{3}{4}, \\ \frac{1}{12}x = \frac{3}{4} + \frac{2}{9}, \\ \frac{1}{12}x = \frac{27}{36} + \frac{8}{36}, \\ \frac{1}{12}x = \frac{35}{36}, \\ x = \frac{35}{36} × 12, \\ x = \frac{35}{3} .\end{aligned}$
2. 对于方程 $x + \frac{1}{4}x = \frac{1}{4}$：
$\begin{aligned}\frac{5}{4}x = \frac{1}{4}, \\ x = \frac{1}{4} × \frac{4}{5}, \\ x = \frac{1}{5} .\end{aligned}$
3. 对于方程 $x ÷ \frac{5}{6} = \frac{3}{8}$：
$\begin{aligned}x = \frac{3}{8} × \frac{5}{6}, \\ x = \frac{5}{16} .\end{aligned}$
$\begin{aligned}\frac{1}{12}x - \frac{2}{9} = \frac{3}{4}, \\ \frac{1}{12}x = \frac{3}{4} + \frac{2}{9}, \\ \frac{1}{12}x = \frac{27}{36} + \frac{8}{36}, \\ \frac{1}{12}x = \frac{35}{36}, \\ x = \frac{35}{36} × 12, \\ x = \frac{35}{3} .\end{aligned}$
2. 对于方程 $x + \frac{1}{4}x = \frac{1}{4}$：
$\begin{aligned}\frac{5}{4}x = \frac{1}{4}, \\ x = \frac{1}{4} × \frac{4}{5}, \\ x = \frac{1}{5} .\end{aligned}$
3. 对于方程 $x ÷ \frac{5}{6} = \frac{3}{8}$：
$\begin{aligned}x = \frac{3}{8} × \frac{5}{6}, \\ x = \frac{5}{16} .\end{aligned}$
