Ответ:

\(1\frac{19}{45}=\frac{64}{45}\).

\(\frac{8}{9}:\frac{64}{45}=\frac{8}{9}\cdot\frac{45}{64}=\frac{5}{8}\).

\(2-\frac{5}{8}=\frac{11}{8}\).

\(\frac{31}{35}:\frac{11}{8}=\frac{31}{35}\cdot\frac{8}{11}=\frac{248}{385}\).

Ответ: \(\frac{248}{385}\)