10. Вычислите: \(2\frac{2}{3} : \left(\frac{5}{9}-\frac{20}{3}\right)+14\cdot1\frac{3}{4}\).

\[2\frac{2}{3}=\frac{8}{3},\qquad 1\frac{3}{4}=\frac{7}{4}.\]

\[\frac{5}{9}-\frac{20}{3}=\frac{5}{9}-\frac{60}{9}=-\frac{55}{9}.\]

\[\frac{8}{3}:\left(-\frac{55}{9}\right)=-\frac{24}{55},\qquad 14\cdot\frac{7}{4}=\frac{49}{2}.\]

\[-\frac{24}{55}+\frac{49}{2}=\frac{-48+2695}{110}=\frac{2647}{110}.\]

Ответ: \(\frac{2647}{110}\).