6. Вычислите: \(3\frac{1}{2} : \left(\frac{7}{9}-\frac{5}{2}\right)+4\cdot1\frac{1}{3}\).

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

\[\frac{7}{9}-\frac{5}{2}=\frac{14-45}{18}=-\frac{31}{18}.\]

\[\frac{7}{2}:\left(-\frac{31}{18}\right)=-\frac{63}{31},\qquad 4\cdot\frac{4}{3}=\frac{16}{3}.\]

\[-\frac{63}{31}+\frac{16}{3}=\frac{-189+496}{93}=\frac{307}{93}.\]

Ответ: \(\frac{307}{93}\).