10) \(18\frac{1}{5} : \left(2\frac{12}{30}-2\frac{5}{6}\right)\)

1. \(2\frac{12}{30}=2\frac{2}{5}\).
2. \(2\frac{2}{5}-2\frac{5}{6}=\frac{2}{5}-\frac{5}{6}=\frac{12-25}{30}=-\frac{13}{30}\).
3. \(18\frac{1}{5}:-\frac{13}{30}=\frac{91}{5}\cdot\frac{30}{-13}=-42\).

Ответ: \(-42\).