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

а) \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{24}{72} = \frac{1}{3}

б) \frac{10}{7}:\frac{3}{4} \cdot \frac{5}{14} = \frac{10}{7} \cdot \frac{4}{3} \cdot \frac{5}{14} = \frac{10 \cdot 4 \cdot 5}{7 \cdot 3 \cdot 14} = \frac{200}{294} = \frac{100}{147}

в) \frac{9}{8}:\frac{5}{8} \cdot \frac{3}{10} = \frac{9}{8} \cdot \frac{8}{5} \cdot \frac{3}{10} = \frac{9 \cdot 8 \cdot 3}{8 \cdot 5 \cdot 10} = \frac{216}{400} = \frac{27}{50}