4. $$\left(5\frac{1}{16} - 1\frac{1}{8}\right) \cdot \left(\frac{5}{6} + \frac{3}{14}\right)$$

INSIGHT

Решение:

1. \(5\frac{1}{16} = \frac{5 \cdot 16 + 1}{16} = \frac{81}{16}\)
2. \(1\frac{1}{8} = \frac{1 \cdot 8 + 1}{8} = \frac{9}{8}\)
3. \(\frac{81}{16} - \frac{9}{8} = \frac{81}{16} - \frac{9 \cdot 2}{8 \cdot 2} = \frac{81 - 18}{16} = \frac{63}{16}\)
4. \(\frac{5}{6} + \frac{3}{14}\) Общий знаменатель для 6 и 14 — 42.
5. \(\frac{5 \cdot 7}{6 \cdot 7} + \frac{3 \cdot 3}{14 \cdot 3} = \frac{35 + 9}{42} = \frac{44}{42} = \frac{22}{21}\)
6. \(\frac{63}{16} \cdot \frac{22}{21} = \frac{63 \cdot 22}{16 \cdot 21} = \frac{(3 \cdot 21) \cdot (2 \cdot 11)}{(16) \cdot 21} = \frac{3 \cdot 2 \cdot 11}{16} = \frac{6 \cdot 11}{16} = \frac{3 \cdot 11}{8} = \frac{33}{8}\)

Ответ: \(\frac{33}{8}\)