4. Выполните действия: \(\frac9{10}\cdot1\frac1{14}:2\frac47\cdot24-2\frac4{15}:\left(1\frac15-\frac23\right)\).

Преобразуем смешанные числа: \(1\frac1{14}=\frac{15}{14}\), \(2\frac47=\frac{18}{7}\), \(2\frac4{15}=\frac{34}{15}\), \(1\frac15=\frac65\).

\(\frac9{10}\cdot\frac{15}{14}:\frac{18}{7}\cdot24-\frac{34}{15}:\left(\frac65-\frac23\right)\)

\(=\frac9{10}\cdot\frac{15}{14}\cdot\frac7{18}324-\frac{34}{15}:\frac8{15}\)

\(=9-\frac{34}{15}\cdot\frac{15}{8}=9-\frac{17}{4}=\frac{19}{4}=4\frac34\).

Ответ: \(4\frac34\).