Выполните действия: а) 3 1/5 : (16 : 1 1/3); б) (1 − 2/5) : (2 6/11 : 56/121).

а) \(3\frac{1}{5}:\left(16:1\frac{1}{3}\right)\).

Преобразуем смешанные числа: \(3\frac{1}{5}=\frac{16}{5}\), \(1\frac{1}{3}=\frac{4}{3}\).

\(16:\frac{4}{3}=16\cdot\frac{3}{4}=12\).

\(\frac{16}{5}:12=\frac{16}{5}\cdot\frac{1}{12}=\frac{4}{15}\).

б) \(\left(1-\frac{2}{5}\right):\left(2\frac{6}{11}:\frac{56}{121}\right)\).

\(1-\frac{2}{5}=\frac{3}{5}\), \(2\frac{6}{11}=\frac{28}{11}\).

\(\frac{28}{11}:\frac{56}{121}=\frac{28}{11}\cdot\frac{121}{56}=\frac{11}{2}\).

\(\frac{3}{5}:\frac{11}{2}=\frac{3}{5}\cdot\frac{2}{11}=\frac{6}{55}\).

Ответ: а) \(\frac{4}{15}\); б) \(\frac{6}{55}\).