Ответ:

\(1\frac{1}{9}=\frac{10}{9}\), \(2\frac{2}{5}=\frac{12}{5}\).

\(\frac{10}{9}\cdot\frac{12}{5}=\frac{120}{45}=\frac{8}{3}=2\frac{2}{3}\).

Ответ: \(2\frac{2}{3}\).