2.463 Найдите значение выражения: a) \frac{4}{5}:1\frac{1}{6}+(2\frac{1}{3}-\frac{3}{7}):1\frac{1}{3};

а) $$\frac{4}{5}:1\frac{1}{6}+(2\frac{1}{3}-\frac{3}{7}):1\frac{1}{3} = \frac{4}{5}:\frac{7}{6}+(\frac{7}{3}-\frac{3}{7}):\frac{4}{3} = \frac{4}{5} \cdot \frac{6}{7}+(\frac{7 \cdot 7 - 3 \cdot 3}{3 \cdot 7}):\frac{4}{3} = \frac{24}{35}+(\frac{49-9}{21}):\frac{4}{3} = \frac{24}{35}+\frac{40}{21}:\frac{4}{3} = \frac{24}{35}+\frac{40}{21} \cdot \frac{3}{4} = \frac{24}{35}+\frac{40 \cdot 3}{21 \cdot 4} = \frac{24}{35}+\frac{10 \cdot 1}{7 \cdot 1} = \frac{24}{35}+\frac{10}{7} = \frac{24 + 10 \cdot 5}{35} = \frac{24+50}{35} = \frac{74}{35} = 2\frac{4}{35}$$

Ответ: $$2\frac{4}{35}$$