10. \((11\frac{5}{11}-8\frac{21}{22}):1\frac{2}{3}\)

\[(11\frac{5}{11}-8\frac{21}{22}):1\frac{2}{3}=\left(\frac{126}{11}-\frac{197}{22}\right):\frac{5}{3}\]

\[=\left(\frac{252-197}{22}\right)\cdot\frac{3}{5}=\frac{55}{22}\cdot\frac{3}{5}=\frac{5}{2}\cdot\frac{3}{5}=\frac{3}{2}\]

Ответ: \(\frac{3}{2}\).