10) \(1\frac{1}{12}:(1\frac{13}{18}-2\frac{5}{9})\)

\(1\frac{1}{12}=\frac{13}{12}\), \(1\frac{13}{18}=\frac{31}{18}\), \(2\frac{5}{9}=\frac{23}{9}\).

\(\frac{13}{12}:\left(\frac{31}{18}-\frac{46}{18}\right)=\frac{13}{12}:\left(-\frac{5}{6}\right)=\frac{13}{12}\cdot\left(-\frac{6}{5}\right)=-\frac{13}{10}\).

Ответ: \(-\frac{13}{10}\).