8. $$\left(\frac{4}{5} + \frac{4}{7}\right) \cdot \left(3\frac{3}{8} + 2\frac{11}{4}\right)$$

INSIGHT

Решение:

1. \(\frac{4}{5} + \frac{4}{7} = \frac{4 \cdot 7 + 4 \cdot 5}{5 \cdot 7} = \frac{28 + 20}{35} = \frac{48}{35}\)
2. \(3\frac{3}{8} = \frac{3 \cdot 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}\)
3. \(2\frac{11}{4} = \frac{2 \cdot 4 + 11}{4} = \frac{8 + 11}{4} = \frac{19}{4}\)
4. \(\frac{27}{8} + \frac{19}{4} = \frac{27}{8} + \frac{19 \cdot 2}{4 \cdot 2} = \frac{27 + 38}{8} = \frac{65}{8}\)
5. \(\frac{48}{35} \cdot \frac{65}{8} = \frac{48 \cdot 65}{35 \cdot 8} = \frac{(6 \cdot 8) \cdot (5 \cdot 13)}{(5 \cdot 7) \cdot 8} = \frac{6 \cdot 13}{7} = \frac{78}{7}\)

Ответ: \(\frac{78}{7}\)