Найдите значение выражения: \(2\frac{4}{15}−\left(2−\frac{1}{15}\right)\cdot\frac49+\frac23\).

\(2\frac4{15}=\frac{34}{15}\), а \(2−\frac1{15}=\frac{29}{15}\).

\[\frac{34}{15}−\frac{29}{15}\cdot\frac49+\frac23=\frac{34}{15}−\frac{116}{135}+\frac{90}{135}=\frac{306−116+90}{135}=\frac{280}{135}=\frac{56}{27}=2\frac{2}{27}.\]

Ответ: \(\frac{56}{27}=2\frac{2}{27}\).