2) 1 7/48 : 2 2/5 − (9 1/6 · 4/15 + 2 5/9) · 2/5;

Преобразуем смешанные числа:

\(1\frac{7}{48}=\frac{55}{48}\), \(2\frac{2}{5}=\frac{12}{5}\), \(9\frac{1}{6}=\frac{55}{6}\), \(2\frac{5}{9}=\frac{23}{9}\).

\[\frac{55}{48}:\frac{12}{5}=\frac{55}{48}\cdot\frac{5}{12}=\frac{275}{576}.\]

\[\frac{55}{6}\cdot\frac{4}{15}+\frac{23}{9}=\frac{22}{9}+\frac{23}{9}=5.\]

\[\frac{275}{576}-5\cdot\frac{2}{5}=\frac{275}{576}-2=\frac{275-1152}{576}=-\frac{877}{576}=-1\frac{301}{576}.\]

Ответ: \(-1\frac{301}{576}\).