5. Вычислить а) \(\frac{7}{9}:5\frac{2}{5};\) б) \(\frac{9}{13}:\frac{26}{27};\) в) \(4\frac{2}{5}:2\frac{4}{7};\) г) \(2\frac{5}{8}:16;\) д) \(\frac{3}{8}:\frac{6}{5};\) e) \(\frac{24}{25}:12\); ж) \(2\frac{5}{8}:\frac{1}{8}\times 3\)

1. а) \(\frac{7}{9}:5\frac{2}{5} = \frac{7}{9}:\frac{27}{5} = \frac{7}{9} \cdot \frac{5}{27} = \frac{7 \cdot 5}{9 \cdot 27} = \frac{35}{243}\)
2. б) \(\frac{9}{13}:\frac{26}{27} = \frac{9}{13} \cdot \frac{27}{26} = \frac{9 \cdot 27}{13 \cdot 26} = \frac{243}{338}\)
3. в) \(4\frac{2}{5}:2\frac{4}{7} = \frac{22}{5}:\frac{18}{7} = \frac{22}{5} \cdot \frac{7}{18} = \frac{11}{5} \cdot \frac{7}{9} = \frac{11 \cdot 7}{5 \cdot 9} = \frac{77}{45} = 1\frac{32}{45}\)
4. г) \(2\frac{5}{8}:16 = \frac{21}{8}:16 = \frac{21}{8} \cdot \frac{1}{16} = \frac{21}{128}\)
5. д) \(\frac{3}{8}:\frac{6}{5} = \frac{3}{8} \cdot \frac{5}{6} = \frac{1}{8} \cdot \frac{5}{2} = \frac{5}{16}\)
6. e) \(\frac{24}{25}:12 = \frac{24}{25} \cdot \frac{1}{12} = \frac{2}{25} \cdot \frac{1}{1} = \frac{2}{25}\)
7. ж) \(2\frac{5}{8}:\frac{1}{8}\times 3 = \frac{21}{8}:\frac{1}{8} \cdot 3 = \frac{21}{8}:\frac{3}{8} = \frac{21}{8} \cdot \frac{8}{3} = \frac{21}{3} = 7\)

Ответ: а) \(\frac{35}{243}\); б) \(\frac{243}{338}\); в) \(1\frac{32}{45}\); г) \(\frac{21}{128}\); д) \(\frac{5}{16}\); e) \(\frac{2}{25}\); ж) 7

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