3. $$1\frac{31}{35} : \left(2 - \frac{8}{9} : 1\frac{19}{45}\right)$$

INSIGHT

Решение:

1. \(1\frac{19}{45} = \frac{45 + 19}{45} = \frac{64}{45}\)
2. \(\frac{8}{9} : \frac{64}{45} = \frac{8}{9} \cdot \frac{45}{64} = \frac{8 \cdot 45}{9 \cdot 64} = \frac{1 \cdot 5}{1 \cdot 8} = \frac{5}{8}\)
3. \(2 - \frac{5}{8} = \frac{16 - 5}{8} = \frac{11}{8}\)
4. \(1\frac{31}{35} = \frac{35 + 31}{35} = \frac{66}{35}\)
5. \(\frac{66}{35} : \frac{11}{8} = \frac{66}{35} \cdot \frac{8}{11} = \frac{66 \cdot 8}{35 \cdot 11} = \frac{6 \cdot 8}{35 \cdot 1} = \frac{48}{35}\)

Ответ: \(\frac{48}{35}\)