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1. $\frac{8}{11} ÷ \frac{9}{11} = □ ÷ □ = \frac{□}{□}$ $\frac{3}{8} ÷ \frac{5}{6} = \frac{□}{24} ÷ \frac{□}{24} = \frac{□}{□}$ $\frac{3}{4} ÷ \frac{6}{7} = (\frac{3}{4} × \frac{□}{□}) ÷ (\frac{6}{7} × \frac{□}{□}) = \frac{□}{□}$
答案
8，9，$\frac{8}{9}$；9，20，$\frac{9}{20}$；$\frac{7}{6}$，$\frac{7}{6}$，$\frac{7}{8}$
解析
1. $\frac{8}{11} ÷ \frac{9}{11} = 8 ÷ 9 = \frac{8}{9}$；
2. $\frac{3}{8} = \frac{9}{24}$，$\frac{5}{6} = \frac{20}{24}$，所以$\frac{3}{8} ÷ \frac{5}{6} = \frac{9}{24} ÷ \frac{20}{24} = \frac{9}{20}$；
3. 除以一个分数等于乘这个分数的倒数，$\frac{6}{7}$的倒数是$\frac{7}{6}$，所以$\frac{3}{4} ÷ \frac{6}{7} = (\frac{3}{4} × \frac{7}{6}) ÷ (\frac{6}{7} × \frac{7}{6}) = \frac{21}{24} ÷ 1 = \frac{7}{8}$
2. $\frac{3}{8} = \frac{9}{24}$，$\frac{5}{6} = \frac{20}{24}$，所以$\frac{3}{8} ÷ \frac{5}{6} = \frac{9}{24} ÷ \frac{20}{24} = \frac{9}{20}$；
3. 除以一个分数等于乘这个分数的倒数，$\frac{6}{7}$的倒数是$\frac{7}{6}$，所以$\frac{3}{4} ÷ \frac{6}{7} = (\frac{3}{4} × \frac{7}{6}) ÷ (\frac{6}{7} × \frac{7}{6}) = \frac{21}{24} ÷ 1 = \frac{7}{8}$
2. 把结果相等的算式用线连起来。
$\frac{2}{3} ÷ 4$ $\frac{3}{7} ÷ 4$ $\frac{8 ÷ 4}{9}$ $\frac{8}{5} ÷ 4$
$\frac{3}{7} × \frac{1}{4}$ $\frac{8}{5 × 4}$ $\frac{2}{3} × \frac{1}{4}$ $\frac{8}{9} × \frac{1}{4}$
$\frac{2}{3} ÷ 4$ $\frac{3}{7} ÷ 4$ $\frac{8 ÷ 4}{9}$ $\frac{8}{5} ÷ 4$
$\frac{3}{7} × \frac{1}{4}$ $\frac{8}{5 × 4}$ $\frac{2}{3} × \frac{1}{4}$ $\frac{8}{9} × \frac{1}{4}$
答案
$\frac {1}{7}$
$\frac {4}{3}$
$\frac {2}{17}$
20
$\frac {7}{6}$
2
$\frac {1}{2}$
$\frac {3}{2}$
$\frac {6}{5}$
$\frac {9}{4}$
$\frac {21}{20}$
$\frac {6}{5}$
3. $\frac{14}{17} ÷ 7 = \frac{14}{17} × (\quad)$ $15 ÷ \frac{3}{4} = 15 × (\quad)$
$= (\quad)$ $= (\quad)$
$\frac{3}{7} ÷ \frac{6}{7} = \frac{3}{7} × (\quad)$ $\frac{3}{4} ÷ \frac{1}{2} = \frac{3}{4} × (\quad)$
$= (\quad)$ $= (\quad)$
$\frac{7}{8} ÷ \frac{5}{6} = \frac{7}{8} × (\quad)$ $\frac{8}{15} ÷ \frac{4}{9} = \frac{8}{15} × (\quad)$
$= (\quad)$ $= (\quad)$
$= (\quad)$ $= (\quad)$
$\frac{3}{7} ÷ \frac{6}{7} = \frac{3}{7} × (\quad)$ $\frac{3}{4} ÷ \frac{1}{2} = \frac{3}{4} × (\quad)$
$= (\quad)$ $= (\quad)$
$\frac{7}{8} ÷ \frac{5}{6} = \frac{7}{8} × (\quad)$ $\frac{8}{15} ÷ \frac{4}{9} = \frac{8}{15} × (\quad)$
$= (\quad)$ $= (\quad)$
答案
$\frac{1}{7}$，$\frac{4}{3}$，$\frac{2}{17}$，$20$；
$\frac{7}{6}$，$2$，$\frac{1}{2}$，$\frac{3}{2}$；
$\frac{6}{5}$，$\frac{9}{4}$，$\frac{21}{20}$，$\frac{6}{5}$。（按题中空顺序）
（由于为填空题，按顺序将答案填入即可，无选项）
解析
分数除法的计算法则是将除数取倒数，然后将除法转化为乘法进行计算。
1. $\frac{14}{17} ÷ 7 = \frac{14}{17} × \frac{1}{7} = \frac{14 × 1}{17 × 7} = \frac{2}{17}$；
2. $15 ÷ \frac{3}{4} = 15 × \frac{4}{3} = \frac{15 × 4}{3} = 20$；
3. $\frac{3}{7} ÷ \frac{6}{7} = \frac{3}{7} × \frac{7}{6} = \frac{3 × 7}{7 × 6} = \frac{1}{2}$；
4. $\frac{3}{4} ÷ \frac{1}{2} = \frac{3}{4} × 2 = \frac{3 × 2}{4} = \frac{3}{2}$；
5. $\frac{7}{8} ÷ \frac{5}{6} = \frac{7}{8} × \frac{6}{5} = \frac{7 × 6}{8 × 5} = \frac{21}{20}$；
6. $\frac{8}{15} ÷ \frac{4}{9} = \frac{8}{15} × \frac{9}{4} = \frac{8 × 9}{15 × 4} = \frac{6}{5}$。
4. 计算。
$\frac{11}{12} ÷ \frac{5}{9}$ $\frac{10}{21} ÷ \frac{5}{7}$ $\frac{15}{28} ÷ \frac{3}{4}$ $\frac{7}{8} ÷ \frac{2}{3}$
$\frac{11}{12} ÷ \frac{5}{9}$ $\frac{10}{21} ÷ \frac{5}{7}$ $\frac{15}{28} ÷ \frac{3}{4}$ $\frac{7}{8} ÷ \frac{2}{3}$
答案
$=\frac {11}{12}×\frac {9}{5}$
$=\frac {33}{20}$
$=\frac {10}{21}×\frac {7}{5}$
$=\frac {2}{3}$
$=\frac {15}{28}×\frac {4}{3}$
$=\frac {5}{7}$
$=\frac {7}{8}×\frac {3}{2}$
$=\frac {21}{16}$
$=\frac {33}{20}$
$=\frac {10}{21}×\frac {7}{5}$
$=\frac {2}{3}$
$=\frac {15}{28}×\frac {4}{3}$
$=\frac {5}{7}$
$=\frac {7}{8}×\frac {3}{2}$
$=\frac {21}{16}$
