Ответ:

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

\(7-\frac{16}{3}=\frac{5}{3}\).

\(\frac{5}{3}\cdot\frac{20}{27}=\frac{100}{81}=1\frac{19}{81}\).

Ответ: \(1\frac{19}{81}\).