9) \(2\frac{3}{5} : \left(1\frac{12}{30}-1\frac{10}{27}\right)\)

1. \(1\frac{12}{30}=1\frac{2}{5}\), \(1\frac{10}{27}=1\frac{10}{27}\).
2. \(1\frac{2}{5}-1\frac{10}{27}=\frac{2}{5}-\frac{10}{27}=\frac{54-50}{135}=\frac{4}{135}\).
3. \(2\frac{3}{5}:\frac{4}{135}=\frac{13}{5}\cdot\frac{135}{4}=\frac{351}{4}=87\frac{3}{4}\).

Ответ: \(87\frac{3}{4}\).