12. Вычислите: 4: \(\frac{20}{23}\) + \(\frac{2}{15}\) \(\cdot\) (\(\frac{4}{7}\) - 4\(\frac{11}{14}\)). Запишите полностью решение и ответ.

Ответ: \(\frac{23}{5} = 4\frac{3}{5}\)

1. \(\frac{4}{7} - 4\frac{11}{14} = \frac{4}{7} - \frac{67}{14} = \frac{8}{14} - \frac{67}{14} = -\frac{59}{14}\)
2. \(\frac{2}{15} \cdot (-\frac{59}{14}) = -\frac{2 \cdot 59}{15 \cdot 14} = -\frac{118}{210} = -\frac{59}{105}\)
3. \(4 : \frac{20}{23} = 4 \cdot \frac{23}{20} = \frac{4 \cdot 23}{20} = \frac{92}{20} = \frac{23}{5}\)
4. \(\frac{23}{5} + (-\frac{59}{105}) = \frac{23 \cdot 21}{5 \cdot 21} - \frac{59}{105} = \frac{483}{105} - \frac{59}{105} = \frac{424}{105}\)
5. \(\frac{424}{105} = 4\frac{4}{105}\)

Ответ: \(\frac{424}{105} = 4\frac{4}{105}\)