Вычислите: $$\frac{9}{10}+\frac{4}{9}:(2-1\frac{11}{21})-1\frac{2}{3}$$. Запишите полностью решение и ответ.

Решение:

1. $$2-1\frac{11}{21} = 2 - \frac{32}{21} = \frac{42}{21} - \frac{32}{21} = \frac{10}{21}$$
2. $$\frac{4}{9} : \frac{10}{21} = \frac{4}{9} \cdot \frac{21}{10} = \frac{2}{3} \cdot \frac{7}{5} = \frac{14}{15}$$
3. $$\frac{9}{10} + \frac{14}{15} = \frac{27}{30} + \frac{28}{30} = \frac{55}{30} = \frac{11}{6}$$
4. $$\frac{11}{6} - 1\frac{2}{3} = \frac{11}{6} - \frac{5}{3} = \frac{11}{6} - \frac{10}{6} = \frac{1}{6}$$

Ответ: $$\frac{1}{6}$$