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

Решение:

1. \( 2\frac{4}{15} = \frac{2 \cdot 15 + 4}{15} = \frac{34}{15} \)
2. \( 2-1\frac{1}{15} = 2 - \frac{16}{15} = \frac{30-16}{15} = \frac{14}{15} \)
3. \( \frac{14}{15} : \frac{4}{9} = \frac{14}{15} \cdot \frac{9}{4} = \frac{14 \cdot 9}{15 \cdot 4} = \frac{7 \cdot 3}{5 \cdot 2} = \frac{21}{10} \)
4. \( \frac{21}{10} + \frac{2}{3} = \frac{21 \cdot 3 + 2 \cdot 10}{30} = \frac{63+20}{30} = \frac{83}{30} \)
5. \( \frac{34}{15} - \frac{83}{30} = \frac{34 \cdot 2 - 83}{30} = \frac{68-83}{30} = \frac{-15}{30} = -\frac{1}{2} \)

Ответ: -\(1/2).