Вычислите: $$2\frac{4}{15}-\left(2-1\frac{1}{15}\right):\frac{4}{9}+\frac{2}{3}$$

Решим пример по действиям:

1. $$2-1\frac{1}{15} = 2 - \frac{16}{15} = \frac{30}{15} - \frac{16}{15} = \frac{14}{15}$$
2. $$\frac{14}{15} : \frac{4}{9} = \frac{14}{15} \cdot \frac{9}{4} = \frac{14 \cdot 9}{15 \cdot 4} = \frac{7 \cdot 3}{5 \cdot 2} = \frac{21}{10} = 2\frac{1}{10}$$
3. $$2\frac{4}{15} = \frac{34}{15}$$
4. $$\frac{34}{15} - 2\frac{1}{10} = \frac{34}{15} - \frac{21}{10} = \frac{34 \cdot 2}{15 \cdot 2} - \frac{21 \cdot 3}{10 \cdot 3} = \frac{68}{30} - \frac{63}{30} = \frac{5}{30} = \frac{1}{6}$$
5. $$\frac{1}{6} + \frac{2}{3} = \frac{1}{6} + \frac{2 \cdot 2}{3 \cdot 2} = \frac{1}{6} + \frac{4}{6} = \frac{5}{6}$$

Ответ: $$\frac{5}{6}$$