7. Вычислите: \(\frac{3}{10}\) - \(\frac{9}{25}\) : (4-\(\frac{9}{10}\)) + \(\frac{4}{7}\). Запишите полностью решение и ответ.

Решение:

1. \(4 - \frac{9}{10} = \frac{40}{10} - \frac{9}{10} = \frac{31}{10}\)
2. \(\frac{9}{25} : \frac{31}{10} = \frac{9}{25} \times \frac{10}{31} = \frac{9 \times 2}{5 \times 31} = \frac{18}{155}\)
3. \(\frac{3}{10} - \frac{18}{155} = \frac{3 \times 31}{10 \times 31} - \frac{18 \times 2}{155 \times 2} = \frac{93}{310} - \frac{36}{310} = \frac{57}{310}\)
4. \(\frac{57}{310} + \frac{4}{7} = \frac{57 \times 7}{310 \times 7} + \frac{4 \times 310}{7 \times 310} = \frac{399}{2170} + \frac{1240}{2170} = \frac{1639}{2170}\)

Ответ: \(\frac{1639}{2170}\)