№ 4. Найдите значение выражения: a) \frac{\frac{9}{10} - \frac{1}{5}}{\frac{1}{2}}; б) \frac{\frac{5}{12}}{\frac{2}{3} + \frac{1}{6}}; в) 1\frac{3}{4} \cdot (\frac{7}{15} - \frac{3}{10}).

a) \frac{\frac{9}{10} - \frac{1}{5}}{\frac{1}{2}} = \frac{\frac{9}{10} - \frac{2}{10}}{\frac{1}{2}} = \frac{\frac{7}{10}}{\frac{1}{2}} = \frac{7}{10} : \frac{1}{2} = \frac{7}{10} \cdot \frac{2}{1} = \frac{7 \cdot 2}{10 \cdot 1} = \frac{14}{10} = \frac{7}{5} = 1\frac{2}{5}

б) \frac{\frac{5}{12}}{\frac{2}{3} + \frac{1}{6}} = \frac{\frac{5}{12}}{\frac{4}{6} + \frac{1}{6}} = \frac{\frac{5}{12}}{\frac{5}{6}} = \frac{5}{12} : \frac{5}{6} = \frac{5}{12} \cdot \frac{6}{5} = \frac{5 \cdot 6}{12 \cdot 5} = \frac{30}{60} = \frac{1}{2}

в) 1\frac{3}{4} \cdot (\frac{7}{15} - \frac{3}{10}) = \frac{7}{4} \cdot (\frac{14}{30} - \frac{9}{30}) = \frac{7}{4} \cdot \frac{5}{30} = \frac{7}{4} \cdot \frac{1}{6} = \frac{7 \cdot 1}{4 \cdot 6} = \frac{7}{24}

Ответ: а) 1\frac{2}{5}; б) \frac{1}{2}; в) \frac{7}{24}