1. Вычислите: (1$$\frac{8}{13} * \frac{13}{42} + 5\frac{5}{7} : \frac{8}{21}): (8\frac{1}{8} + 3\frac{1}{2})

Выполним вычисление по действиям:

1. $$1\frac{8}{13} * \frac{13}{42} = \frac{13+8}{13} * \frac{13}{42} = \frac{21}{13} * \frac{13}{42} = \frac{21*13}{13*42} = \frac{1}{2}$$
2. $$5\frac{5}{7} : \frac{8}{21} = \frac{5*7+5}{7} : \frac{8}{21} = \frac{40}{7} : \frac{8}{21} = \frac{40}{7} * \frac{21}{8} = \frac{40*21}{7*8} = \frac{5*3}{1*1} = 15$$
3. $$\frac{1}{2} + 15 = 15\frac{1}{2} = \frac{15*2+1}{2} = \frac{31}{2}$$
4. $$8\frac{1}{8} + 3\frac{1}{2} = \frac{8*8+1}{8} + \frac{3*2+1}{2} = \frac{65}{8} + \frac{7}{2} = \frac{65}{8} + \frac{7*4}{2*4} = \frac{65}{8} + \frac{28}{8} = \frac{65+28}{8} = \frac{93}{8}$$
5. $$\frac{31}{2} : \frac{93}{8} = \frac{31}{2} * \frac{8}{93} = \frac{31*8}{2*93} = \frac{31*4}{1*93} = \frac{4}{3} = 1\frac{1}{3}$$

Ответ: $$1\frac{1}{3}$$