9. Вычислите: 4 \(\frac{1}{6}:(1\frac{1}{2}-\frac{3}{5})+(\frac{2}{5}+\frac{5}{6})\cdot 6\). Запишите решение и ответ.

1) \(1\frac{1}{2}-\frac{3}{5}=\frac{3}{2}-\frac{3}{5}=\frac{3 \cdot 5 -3 \cdot 2}{10}=\frac{15-6}{10}=\frac{9}{10}\)

2) \(4\frac{1}{6}: \frac{9}{10}=\frac{25}{6}:\frac{9}{10}=\frac{25}{6} \cdot \frac{10}{9}=\frac{25 \cdot 10}{6 \cdot 9}=\frac{25 \cdot 5}{3 \cdot 9}=\frac{125}{27}=4\frac{17}{27}\)

3) \(\frac{2}{5}+\frac{5}{6}=\frac{2 \cdot 6 +5 \cdot 5}{30}=\frac{12+25}{30}=\frac{37}{30}\)

4) \(\frac{37}{30} \cdot 6 = \frac{37 \cdot 6}{30}=\frac{37}{5}=7\frac{2}{5}\)

5) \(4\frac{17}{27}+7\frac{2}{5}=4\frac{17 \cdot 5}{27 \cdot 5}+7\frac{2 \cdot 27}{5 \cdot 27}=4\frac{85}{135}+7\frac{54}{135}=11\frac{139}{135}=12\frac{4}{135}\)

Ответ: \(12\frac{4}{135}\)