7. Вычислите: \(3\frac{2}{7} : \left(\frac{5}{6}-\frac{11}{3}\right)+7\cdot1\frac{4}{9}\).

\[3\frac{2}{7}=\frac{23}{7},\qquad 1\frac{4}{9}=\frac{13}{9}.\]

\[\frac{5}{6}-\frac{11}{3}=\frac{5}{6}-\frac{22}{6}=-\frac{17}{6}.\]

\[\frac{23}{7}:\left(-\frac{17}{6}\right)=-\frac{138}{119},\qquad 7\cdot\frac{13}{9}=\frac{91}{9}.\]

\[-\frac{138}{119}+\frac{91}{9}=\frac{-1242+10829}{1071}=\frac{9587}{1071}.\]

Ответ: \(\frac{9587}{1071}\).