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

Решение:

1. \(3 - \frac{13}{14} = \frac{42}{14} - \frac{13}{14} = \frac{29}{14}\)
2. \(\frac{25}{49} : \frac{29}{14} = \frac{25}{49} \times \frac{14}{29} = \frac{25 \times 2}{7 \times 29} = \frac{50}{203}\)
3. \(\frac{5}{6} - \frac{50}{203} = \frac{5 \times 203}{6 \times 203} - \frac{50 \times 6}{203 \times 6} = \frac{1015}{1218} - \frac{300}{1218} = \frac{715}{1218}\)
4. \(\frac{715}{1218} + \frac{1}{2} = \frac{715}{1218} + \frac{1 \times 609}{2 \times 609} = \frac{715}{1218} + \frac{609}{1218} = \frac{1324}{1218} = \frac{662}{609}\)

Ответ: \(\frac{662}{609}\)