1. Вычислите: $$\frac{9}{10}\cdot\left(\frac{11}{12}-\frac{2}{9}\right)$$.

$$\frac{9}{10}\cdot\left(\frac{11}{12}-\frac{2}{9}\right)$$

1) $$\frac{11}{12}-\frac{2}{9}=\frac{11 \cdot 3}{12 \cdot 3}-\frac{2 \cdot 4}{9 \cdot 4}=\frac{33}{36}-\frac{8}{36}=\frac{33-8}{36}=\frac{25}{36}$$

2) $$\frac{9}{10}\cdot\frac{25}{36}=\frac{9 \cdot 25}{10 \cdot 36}=\frac{9 \cdot 5 \cdot 5}{2 \cdot 5 \cdot 9 \cdot 4}=\frac{5}{2 \cdot 4}=\frac{5}{8}$$

Ответ: $$\frac{5}{8}$$