Ответ:

\(1\frac{7}{9}=\frac{16}{9}\), \(1\frac{19}{36}=\frac{55}{36}\).

\(\frac{15}{32}:\frac{55}{36}=\frac{15}{32}\cdot\frac{36}{55}=\frac{27}{88}\).

\(\frac{16}{9}\cdot\frac{27}{88}=\frac{6}{11}\).

Ответ: \(\frac{6}{11}\).