14. Тип 13 № 1956 / Вычислите:$$\frac{4}{3}+(-8\frac{1}{9}+5\frac{8}{5}\cdot3\frac{1}{8}):\frac{7}{6}$$ Запишите полностью решение и ответ.

Вычислим:

$$\frac{4}{3}+(-8\frac{1}{9}+5\frac{8}{5}\cdot3\frac{1}{8}):\frac{7}{6}$$

1) $$5\frac{8}{5} \cdot 3\frac{1}{8} = \frac{33}{5} \cdot \frac{25}{8} = \frac{33 \cdot 5}{8} = \frac{165}{8} = 20\frac{5}{8}$$

2) $$-8\frac{1}{9}+20\frac{5}{8} = -\frac{73}{9} + \frac{165}{8} = \frac{-73 \cdot 8 + 165 \cdot 9}{72} = \frac{-584 + 1485}{72} = \frac{901}{72} = 12\frac{37}{72}$$

3) $$12\frac{37}{72} : \frac{7}{6} = \frac{901}{72} : \frac{7}{6} = \frac{901}{72} \cdot \frac{6}{7} = \frac{901}{12 \cdot 7} = \frac{901}{84} = 10\frac{61}{84}$$

4) $$\frac{4}{3} + 10\frac{61}{84} = \frac{4}{3} + \frac{901}{84} = \frac{4 \cdot 28}{84} + \frac{901}{84} = \frac{112}{84} + \frac{901}{84} = \frac{1013}{84} = 12\frac{5}{84}$$

Ответ: $$12\frac{5}{84}$$