6. Вычислите: \(\frac{7}{10}\) - \(\frac{9}{49}\) : (3-\(\frac{13}{14}\)) + \(\frac{2}{5}\). Запишите полностью решение и ответ.

Решение:

1. \(3 - \frac{13}{14} = \frac{42}{14} - \frac{13}{14} = \frac{29}{14}\)
2. \(\frac{9}{49} : \frac{29}{14} = \frac{9}{49} \times \frac{14}{29} = \frac{9 \times 2}{7 \times 29} = \frac{18}{203}\)
3. \(\frac{7}{10} - \frac{18}{203} = \frac{7 \times 203}{10 \times 203} - \frac{18 \times 10}{203 \times 10} = \frac{1421}{2030} - \frac{180}{2030} = \frac{1241}{2030}\)
4. \(\frac{1241}{2030} + \frac{2}{5} = \frac{1241}{2030} + \frac{2 \times 406}{5 \times 406} = \frac{1241}{2030} + \frac{812}{2030} = \frac{2053}{2030}\)

Ответ: \(\frac{2053}{2030}\)