5.542 Выполните действия: а) \(\frac{3}{8} : \frac{3}{4} \cdot \frac{2}{3}\); б) \(\frac{10}{7} : \frac{3}{4} : \frac{5}{14}\); в) \(\frac{9}{8} : \frac{5}{2} : \frac{3}{10}\).

a) \(\frac{3}{8} : \frac{3}{4} \cdot \frac{2}{3}\) = \(\frac{3}{8} \cdot \frac{4}{3} \cdot \frac{2}{3}\) = \(\frac{3 \cdot 4 \cdot 2}{8 \cdot 3 \cdot 3}\) = \(\frac{4 \cdot 2}{8 \cdot 3}\) = \(\frac{8}{24}\) = \(\frac{1}{3}\)

Ответ: \(\frac{1}{3}\)

б) \(\frac{10}{7} : \frac{3}{4} : \frac{5}{14}\) = \(\frac{10}{7} \cdot \frac{4}{3} \cdot \frac{14}{5}\) = \(\frac{10 \cdot 4 \cdot 14}{7 \cdot 3 \cdot 5}\) = \(\frac{2 \cdot 5 \cdot 4 \cdot 2 \cdot 7}{7 \cdot 3 \cdot 5}\) = \(\frac{2 \cdot 4 \cdot 2}{3}\) = \(\frac{16}{3}\) = 5\(\frac{1}{3}\)

Ответ: 5\(\frac{1}{3}\)

в) \(\frac{9}{8} : \frac{5}{2} : \frac{3}{10}\) = \(\frac{9}{8} \cdot \frac{2}{5} \cdot \frac{10}{3}\) = \(\frac{9 \cdot 2 \cdot 10}{8 \cdot 5 \cdot 3}\) = \(\frac{3 \cdot 3 \cdot 2 \cdot 2 \cdot 5}{2 \cdot 4 \cdot 5 \cdot 3}\) = \(\frac{3 \cdot 2}{4}\) = \(\frac{6}{4}\) = \(\frac{3}{2}\) = 1\(\frac{1}{2}\)

Ответ: 1\(\frac{1}{2}\)