8. Вычислите: \( \frac{5}{6} - \frac{25}{49} : (3-1\frac{13}{14}) + \frac{1}{2} \)

Решение:

1. \( 3-1\frac{13}{14} = 3 - \frac{27}{14} = \frac{42-27}{14} = \frac{15}{14} \)
2. \( \frac{25}{49} : \frac{15}{14} = \frac{25}{49} \cdot \frac{14}{15} = \frac{25 \cdot 14}{49 \cdot 15} = \frac{5 \cdot 2}{7 \cdot 3} = \frac{10}{21} \)
3. \( \frac{5}{6} - \frac{10}{21} = \frac{5 \cdot 7 - 10 \cdot 2}{42} = \frac{35-20}{42} = \frac{15}{42} = \frac{5}{14} \)
4. \( \frac{5}{14} + \frac{1}{2} = \frac{5 + 1 \cdot 7}{14} = \frac{5+7}{14} = \frac{12}{14} = \frac{6}{7} \)

Ответ: \(6/7).