№8. * $$\left(1\frac{8}{13} \cdot \frac{13}{42} + 5\frac{5}{7} : \frac{8}{21}\right) : \left(\frac{8}{8} + 3\frac{1}{2}\right);$$

1) \(1\frac{8}{13} \cdot \frac{13}{42} = \frac{1 \cdot 13 + 8}{13} \cdot \frac{13}{42} = \frac{21}{13} \cdot \frac{13}{42} = \frac{21 \cdot 13}{13 \cdot 42} = \frac{21}{42} = \frac{1}{2}\) 2) \(5\frac{5}{7} : \frac{8}{21} = \frac{5 \cdot 7 + 5}{7} : \frac{8}{21} = \frac{40}{7} : \frac{8}{21} = \frac{40}{7} \cdot \frac{21}{8} = \frac{40 \cdot 21}{7 \cdot 8} = \frac{5 \cdot 3}{1 \cdot 1} = 15\) 3) \(\frac{1}{2} + 15 = 15\frac{1}{2} = \frac{15 \cdot 2 + 1}{2} = \frac{31}{2}\) 4) \(\frac{8}{8} + 3\frac{1}{2} = 1 + 3\frac{1}{2} = 4\frac{1}{2} = \frac{4 \cdot 2 + 1}{2} = \frac{9}{2}\) 5) \(\frac{31}{2} : \frac{9}{2} = \frac{31}{2} \cdot \frac{2}{9} = \frac{31 \cdot 2}{2 \cdot 9} = \frac{31}{9} = 3\frac{4}{9}\) Ответ: \(3\frac{4}{9}\)