П.20 Выполните действие: a) 16/27 : 9/4 б) 42/5 : 5/7 в) 7/12 : 3/12 г) 14/55 : 7/22

Решение:

а) \(\frac{16}{27} : \frac{9}{4} = \frac{16}{27} × \frac{4}{9} = \frac{16 × 4}{27 × 9} = \frac{64}{243}\)

б) \(\frac{42}{5} : \frac{5}{7} = \frac{42}{5} × \frac{7}{5} = \frac{42 × 7}{5 × 5} = \frac{294}{25}\)

в) \(\frac{7}{12} : \frac{3}{12} = \frac{7}{12} × \frac{12}{3} = \frac{7}{3}\)

г) \(\frac{14}{55} : \frac{7}{22} = \frac{14}{55} × \frac{22}{7} = \frac{14 × 22}{55 × 7} = \frac{(2 × 7) × (2 × 11)}{(5 × 11) × 7} = \frac{2 × 2}{5} = \frac{4}{5}\)

Ответ: а) \(\frac{64}{243}\); б) \(\frac{294}{25}\); в) \(\frac{7}{3}\); г) \(\frac{4}{5}\).