Общий знаменатель: \(48\).
\(\frac{3}{16}=\frac{9}{48}\), \(\frac{7}{24}=\frac{14}{48}\), \(\frac{1}{12}=\frac{4}{48}\).
\(2\frac{9}{48}+1\frac{14}{48}+3\frac{4}{48}=6\frac{27}{48}=6\frac{9}{16}\).
Ответ: \(6\frac{9}{16}\).