11) \(3\frac{1}{2}:(1\frac{4}{15}+2\frac{9}{10})\)

\(3\frac{1}{2}=\frac{7}{2}\), \(1\frac{4}{15}=\frac{19}{15}\), \(2\frac{9}{10}=\frac{29}{10}\).

В скобках: \(\frac{19}{15}+\frac{29}{10}=\frac{38+87}{30}=\frac{125}{30}=\frac{25}{6}\).

\(\frac{7}{2}:\frac{25}{6}=\frac{7}{2}\cdot\frac{6}{25}=\frac{21}{25}.\)

Ответ: \(\frac{21}{25}\).