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1. 下面的计算正确吗？ 正确的画“√”，错误的画“×”并改正。
(1) $\frac{4}{15}÷\frac{7}{12}=\frac{4}{15}×\frac{7}{12}=\frac{7}{45}$ (
改正:
(2) $\frac{8}{25}÷5=\frac{25}{8}×\frac{1}{5}=\frac{5}{8}$ (
改正:
(1) $\frac{4}{15}÷\frac{7}{12}=\frac{4}{15}×\frac{7}{12}=\frac{7}{45}$ (
×
)改正:
$\frac{4}{15}÷\frac{7}{12}=\frac{4}{15}×\frac{12}{7}=\frac{16}{35}$
(2) $\frac{8}{25}÷5=\frac{25}{8}×\frac{1}{5}=\frac{5}{8}$ (
×
)改正:
$\frac{8}{25}÷5=\frac{8}{25}×\frac{1}{5}=\frac{8}{125}$
答案
1. (1) × 改正：$\frac{4}{15}÷\frac{7}{12}=\frac{4}{15}×\frac{12}{7}=\frac{16}{35}$
(2) × 改正：$\frac{8}{25}÷5=\frac{8}{25}×\frac{1}{5}=\frac{8}{125}$
(2) × 改正：$\frac{8}{25}÷5=\frac{8}{25}×\frac{1}{5}=\frac{8}{125}$
2. 计算下面各题。
$\frac{2}{3} ÷ \frac{4}{7} =$
$12 ÷ \frac{4}{5} =$
$\frac{4}{9} ÷ \frac{3}{10} =$
$\frac{39}{25} ÷ \frac{13}{15} =$
$\frac{49}{60} ÷ \frac{14}{15} =$
$\frac{17}{36} ÷ \frac{17}{25} =$
$6 ÷ \frac{12}{11} =$
$\frac{13}{20} ÷ \frac{5}{4} =$
$\frac{2}{3} ÷ \frac{4}{7} =$
$12 ÷ \frac{4}{5} =$
$\frac{4}{9} ÷ \frac{3}{10} =$
$\frac{39}{25} ÷ \frac{13}{15} =$
$\frac{49}{60} ÷ \frac{14}{15} =$
$\frac{17}{36} ÷ \frac{17}{25} =$
$6 ÷ \frac{12}{11} =$
$\frac{13}{20} ÷ \frac{5}{4} =$
答案
$\frac{2}{3} ÷ \frac{4}{7} = \frac{7}{6}$
$12 ÷ \frac{4}{5} = 15$
$\frac{4}{9} ÷ \frac{3}{10} = \frac{40}{27}$
$\frac{39}{25} ÷ \frac{13}{15} = \frac{9}{5}$
$\frac{49}{60} ÷ \frac{14}{15} = \frac{7}{8}$
$\frac{17}{36} ÷ \frac{17}{25} = \frac{25}{36}$
$6 ÷ \frac{12}{11} = \frac{11}{2}$
$\frac{13}{20} ÷ \frac{5}{4} = \frac{13}{25}$
$12 ÷ \frac{4}{5} = 15$
$\frac{4}{9} ÷ \frac{3}{10} = \frac{40}{27}$
$\frac{39}{25} ÷ \frac{13}{15} = \frac{9}{5}$
$\frac{49}{60} ÷ \frac{14}{15} = \frac{7}{8}$
$\frac{17}{36} ÷ \frac{17}{25} = \frac{25}{36}$
$6 ÷ \frac{12}{11} = \frac{11}{2}$
$\frac{13}{20} ÷ \frac{5}{4} = \frac{13}{25}$
3. 下面的计算对吗？ 对的画“√”，错的画“×”并改正。
$\frac{3}{10}÷\frac{3}{5}×\frac{2}{3}$
$=\frac{3}{10}÷\frac{2}{5}$
$=\frac{3}{4}$（
改正：
$\frac{8}{15}×\frac{3}{4}÷\frac{8}{15}×\frac{3}{4}$
$=(\frac{8}{15}×\frac{3}{4})÷(\frac{8}{15}×\frac{3}{4})$
$=1$（
改正：
$\frac{3}{10}÷\frac{3}{5}×\frac{2}{3}$
$=\frac{3}{10}÷\frac{2}{5}$
$=\frac{3}{4}$（
×
）改正：
$\frac{8}{15}×\frac{3}{4}÷\frac{8}{15}×\frac{3}{4}$
$=(\frac{8}{15}×\frac{3}{4})÷(\frac{8}{15}×\frac{3}{4})$
$=1$（
×
）改正：
答案
3. (1) × 改正：$\frac{3}{10}÷\frac{3}{5}×\frac{2}{3}=\frac{3}{10}×\frac{5}{3}×\frac{2}{3}=\frac{1}{2}×\frac{2}{3}=\frac{1}{3}$
(2) × 改正：$\frac{8}{15}×\frac{3}{4}÷\frac{8}{15}×\frac{3}{4}=\frac{8}{15}÷\frac{8}{15}×\frac{3}{4}×\frac{3}{4}=1×\frac{3}{4}×\frac{3}{4}=\frac{9}{16}$
(2) × 改正：$\frac{8}{15}×\frac{3}{4}÷\frac{8}{15}×\frac{3}{4}=\frac{8}{15}÷\frac{8}{15}×\frac{3}{4}×\frac{3}{4}=1×\frac{3}{4}×\frac{3}{4}=\frac{9}{16}$
4. 计算下面各题，能简算的要简算。
$\frac{8}{9} × \frac{3}{14} ÷ \frac{10}{21}$
$\frac{7}{11} ÷ 7 + \frac{7}{11} × \frac{6}{7}$
$4 ÷ ( \frac{1}{3} - \frac{1}{5} ) ÷ \frac{1}{2}$
$( \frac{3}{4} + \frac{1}{2} - \frac{5}{12} ) ÷ \frac{25}{24}$
$\frac{5}{6} × \frac{13}{10} - \frac{5}{6} ÷ \frac{10}{3}$
$\frac{5}{9} × \frac{8}{21} + \frac{13}{21} ÷ \frac{9}{5}$
$\frac{8}{9} × \frac{3}{14} ÷ \frac{10}{21}$
$\frac{7}{11} ÷ 7 + \frac{7}{11} × \frac{6}{7}$
$4 ÷ ( \frac{1}{3} - \frac{1}{5} ) ÷ \frac{1}{2}$
$( \frac{3}{4} + \frac{1}{2} - \frac{5}{12} ) ÷ \frac{25}{24}$
$\frac{5}{6} × \frac{13}{10} - \frac{5}{6} ÷ \frac{10}{3}$
$\frac{5}{9} × \frac{8}{21} + \frac{13}{21} ÷ \frac{9}{5}$
答案
$\frac{8}{9} × \frac{3}{14} ÷ \frac{10}{21} = \frac{2}{5}$
$\frac{7}{11} ÷ 7 + \frac{7}{11} × \frac{6}{7} = \frac{7}{11}$
$4 ÷ ( \frac{1}{3} - \frac{1}{5} ) ÷ \frac{1}{2} = 60$
$( \frac{3}{4} + \frac{1}{2} - \frac{5}{12} ) ÷ \frac{25}{24} = \frac{4}{5}$
$\frac{5}{6} × \frac{13}{10} - \frac{5}{6} ÷ \frac{10}{3} = \frac{5}{6}$
$\frac{5}{9} × \frac{8}{21} + \frac{13}{21} ÷ \frac{9}{5} = \frac{5}{9}$
$\frac{7}{11} ÷ 7 + \frac{7}{11} × \frac{6}{7} = \frac{7}{11}$
$4 ÷ ( \frac{1}{3} - \frac{1}{5} ) ÷ \frac{1}{2} = 60$
$( \frac{3}{4} + \frac{1}{2} - \frac{5}{12} ) ÷ \frac{25}{24} = \frac{4}{5}$
$\frac{5}{6} × \frac{13}{10} - \frac{5}{6} ÷ \frac{10}{3} = \frac{5}{6}$
$\frac{5}{9} × \frac{8}{21} + \frac{13}{21} ÷ \frac{9}{5} = \frac{5}{9}$
