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

а) $$\frac{\frac{9}{10} - \frac{1}{5}}{\frac{1}{2}} = \frac{\frac{9}{10} - \frac{1 \times 2}{5 \times 2}}{\frac{1}{2}} = \frac{\frac{9}{10} - \frac{2}{10}}{\frac{1}{2}} = \frac{\frac{7}{10}}{\frac{1}{2}} = \frac{7}{10} \cdot \frac{2}{1} = \frac{7 \cdot 2}{10 \cdot 1} = \frac{7 \cdot 1}{5 \cdot 1} = \frac{7}{5} = 1\frac{2}{5}$$

б) $$\frac{\frac{5}{12}}{\frac{2}{3} + \frac{1}{6}} = \frac{\frac{5}{12}}{\frac{2 \times 2}{3 \times 2} + \frac{1}{6}} = \frac{\frac{5}{12}}{\frac{4}{6} + \frac{1}{6}} = \frac{\frac{5}{12}}{\frac{5}{6}} = \frac{5}{12} \cdot \frac{6}{5} = \frac{5 \cdot 6}{12 \cdot 5} = \frac{1 \cdot 1}{2 \cdot 1} = \frac{1}{2}$$

в) $$\frac{1}{2} - \frac{3}{4} \cdot (\frac{7}{15} - \frac{3}{10}) = \frac{1}{2} - \frac{3}{4} \cdot (\frac{7 \times 2}{15 \times 2} - \frac{3 \times 3}{10 \times 3}) = \frac{1}{2} - \frac{3}{4} \cdot (\frac{14}{30} - \frac{9}{30}) = \frac{1}{2} - \frac{3}{4} \cdot \frac{5}{30} = \frac{1}{2} - \frac{3 \cdot 5}{4 \cdot 30} = \frac{1}{2} - \frac{1 \cdot 1}{4 \cdot 6} = \frac{1}{2} - \frac{1}{24} = \frac{1 \times 12}{2 \times 12} - \frac{1}{24} = \frac{12}{24} - \frac{1}{24} = \frac{11}{24}$$

Ответ: а) $$1\frac{2}{5}$$; б) $$\frac{1}{2}$$; в) $$\frac{11}{24}$$