Вычислите: \(2\frac{4}{3}-\left(\frac{4}{5}-\frac{8}{12}\right)-7:3\frac{1}{2}\).

\(2\frac{4}{3}=\frac{10}{3}\), а \(\frac{8}{12}=\frac{2}{3}\).

\[\frac{10}{3}-\left(\frac{4}{5}-\frac{2}{3}\right)-7:\frac{7}{2}\]

\[\frac{4}{5}-\frac{2}{3}=\frac{12-10}{15}=\frac{2}{15},\qquad 7:\frac{7}{2}=7\cdot\frac{2}{7}=2.\]

\[\frac{10}{3}-\frac{2}{15}-2=\frac{50}{15}-\frac{2}{15}-\frac{30}{15}=\frac{18}{15}=\frac{6}{5}=1\frac{1}{5}.\]

Ответ: \(1\frac{1}{5}\).