Выполните действия: $$\left(9-2\frac{2}{3}\cdot2\frac{1}{7}\right)\cdot\frac{21}{46}$$.

Решение:

1) $$2\frac{2}{3}\cdot2\frac{1}{7} = \frac{2\cdot3+2}{3}\cdot\frac{2\cdot7+1}{7} = \frac{8}{3}\cdot\frac{15}{7} = \frac{8\cdot15}{3\cdot7} = \frac{8\cdot3\cdot5}{3\cdot7} = \frac{8\cdot5}{7} = \frac{40}{7}$$

2) $$9 - \frac{40}{7} = \frac{9}{1} - \frac{40}{7} = \frac{9^{(7}}{1} - \frac{40^{(1}}{7} = \frac{9\cdot7 - 40}{7} = \frac{63-40}{7} = \frac{23}{7}$$

3) $$\frac{23}{7} \cdot \frac{21}{46} = \frac{23\cdot21}{7\cdot46} = \frac{23\cdot3\cdot7}{7\cdot2\cdot23} = \frac{3}{2} = 1\frac{1}{2}$$

Ответ: $$1\frac{1}{2}$$