Вычислите: \(\frac{9}{52}\cdot 4\frac{1}{3}\cdot\frac{1}{3}+\left(3\frac{2}{3}+2\frac{4}{5}\right)\cdot\frac{60}{97}+\frac{5}{36}\\cdot1\frac{4}{5}\).

Преобразуем смешанные числа в неправильные дроби:

\[4\frac{1}{3}=\frac{13}{3},\quad 3\frac{2}{3}=\frac{11}{3},\quad 2\frac{4}{5}=\frac{14}{5},\quad 1\frac{4}{5}=\frac{9}{5}.\]

\[\frac{9}{52}\cdot\frac{13}{3}\cdot\frac{1}{3}=\frac{3}{4}\cdot\frac{1}{3}\cdot\frac{1}{3}=\frac{1}{12}.\]

\[\left(\frac{11}{3}+\frac{14}{5}\right)\cdot\frac{60}{97}=\left(\frac{55}{15}+\frac{42}{15}\right)\cdot\frac{60}{97}=\frac{97}{15}\cdot\frac{60}{97}=4.\]

\[\frac{5}{36}\cdot\frac{9}{5}=\frac{1}{4}.\]

\[\frac{1}{12}+4+\frac{1}{4}=4+\frac{1+3}{12}=4+\frac{1}{3}=4\frac{1}{3}.\]

Ответ: \(4\frac{1}{3}\).