$$\begin{aligned}&7\frac{2}{7} + 8\frac{3}{8}:32 = \frac{7 \cdot 7 + 2}{7} + \frac{8 \cdot 8 + 3}{8}:32 = \frac{49+2}{7} + \frac{64+3}{8}:32 = \frac{51}{7} + \frac{67}{8}:32 =\\&= \frac{51}{7} + \frac{67}{8} \cdot \frac{1}{32} = \frac{51}{7} + \frac{67}{8 \cdot 32} = \frac{51}{7} + \frac{67}{256} = \frac{51 \cdot 256 + 67 \cdot 7}{7 \cdot 256} = \frac{13056 + 469}{1792} = \frac{13525}{1792} = 7\frac{1021}{1792}\\
&\text{Ответ: } \frac{13525}{1792} = 7\frac{1021}{1792}\end{aligned}$$