1. Выполни действие: a) \(\frac{5}{7}:\frac{3}{8}\); б) \(\frac{5}{9}:\frac{10}{27}\); в) \(4\frac{4}{9}:2\frac{2}{3}\); г) 32:\(\frac{8}{9}\); д) \(\frac{12}{13}:6\).

1. Выполним действия:

а) \(\frac{5}{7}:\frac{3}{8} = \frac{5}{7} \cdot \frac{8}{3} = \frac{5 \cdot 8}{7 \cdot 3} = \frac{40}{21} = 1\frac{19}{21}\)

б) \(\frac{5}{9}:\frac{10}{27} = \frac{5}{9} \cdot \frac{27}{10} = \frac{5 \cdot 27}{9 \cdot 10} = \frac{1 \cdot 3}{1 \cdot 2} = \frac{3}{2} = 1\frac{1}{2}\)

в) \(4\frac{4}{9}:2\frac{2}{3} = \frac{4 \cdot 9 + 4}{9} : \frac{2 \cdot 3 + 2}{3} = \frac{40}{9} : \frac{8}{3} = \frac{40}{9} \cdot \frac{3}{8} = \frac{40 \cdot 3}{9 \cdot 8} = \frac{5 \cdot 1}{3 \cdot 1} = \frac{5}{3} = 1\frac{2}{3}\)

г) \(32:\frac{8}{9} = 32 \cdot \frac{9}{8} = \frac{32 \cdot 9}{8} = \frac{4 \cdot 9}{1} = 36\)

д) \(\frac{12}{13}:6 = \frac{12}{13} : \frac{6}{1} = \frac{12}{13} \cdot \frac{1}{6} = \frac{12 \cdot 1}{13 \cdot 6} = \frac{2 \cdot 1}{13 \cdot 1} = \frac{2}{13}\)

Ответ: а) \(1\frac{19}{21}\); б) \(1\frac{1}{2}\); в) \(1\frac{2}{3}\); г) 36; д) \(\frac{2}{13}\).