14. $$4\frac{1}{6} \cdot \left(\frac{1}{2} - \frac{3}{5}\right) + \left(\frac{3}{4} + \frac{5}{6}\right) \cdot 6$$

INSIGHT

Решение:

1. \(\frac{1}{2} - \frac{3}{5} = \frac{1 \cdot 5 - 3 \cdot 2}{2 \cdot 5} = \frac{5 - 6}{10} = -\frac{1}{10}\)
2. \(4\frac{1}{6} = \frac{25}{6}\)
3. \(\frac{25}{6} \cdot \left(-\frac{1}{10}\right) = -\frac{25}{60} = -\frac{5}{12}\)
4. \(\frac{3}{4} + \frac{5}{6}\) Общий знаменатель для 4 и 6 — 12.
5. \(\frac{3 \cdot 3}{4 \cdot 3} + \frac{5 \cdot 2}{6 \cdot 2} = \frac{9 + 10}{12} = \frac{19}{12}\)
6. \(\frac{19}{12} \cdot 6 = \frac{19 \cdot 6}{12} = \frac{19}{2}\)
7. \(-\frac{5}{12} + \frac{19}{2} = -\frac{5}{12} + \frac{19 \cdot 6}{2 \cdot 6} = -\frac{5}{12} + \frac{114}{12} = \frac{109}{12}\)

Ответ: \(\frac{109}{12}\)