Ответ:

\(1\frac{5}{9}:\frac{7}{24}=\frac{14}{9}\cdot\frac{24}{7}=\frac{16}{3}\).

\(7-\frac{16}{3}=\frac{5}{3}\), затем \(\frac{5}{3}:\frac{20}{27}=\frac{5}{3}\cdot\frac{27}{20}=\frac{9}{4}\).

Ответ: \(\frac{9}{4}\).