337. Выполните умножение: 1) \(9\frac{3}{7}\cdot\frac{5}{22}\); 2) \(6\frac{3}{8}\cdot\frac{16}{17}\); 3) \(2\frac{1}{3}\cdot1\frac{1}{5}\); 4) \(19\frac{1}{2}\cdot1\frac{5}{9}\); 5) \(2\frac{1}{4}\cdot2\frac{2}{27}\); 6) \(2\frac{8}{11}\cdot5\frac{2}{15}\); 7) \(\frac{7}{9}\cdot1\frac{1}{14}\cdot5\frac{2}{5}\); 8) \(2\frac{2}{3}\cdot1\frac{1}{24}\cdot5\frac{2}{5}\).

1. Переведём смешанное число в неправильную дробь: \(9\frac{3}{7}=\frac{66}{7}\).
   \[\frac{66}{7}\cdot\frac{5}{22}=\frac{15}{7}=2\frac{1}{7}.\]
2. \(6\frac{3}{8}=\frac{51}{8}\).
   \[\frac{51}{8}\cdot\frac{16}{17}=6.\]
3. \(2\frac{1}{3}=\frac{7}{3}\), \(1\frac{1}{5}=\frac{6}{5}\).
   \[\frac{7}{3}\cdot\frac{6}{5}=\frac{14}{5}=2\frac{4}{5}.\]
4. \(19\frac{1}{2}=\frac{39}{2}\), \(1\frac{5}{9}=\frac{14}{9}\).
   \[\frac{39}{2}\cdot\frac{14}{9}=\frac{91}{3}=30\frac{1}{3}.\]
5. \(2\frac{1}{4}=\frac{9}{4}\), \(2\frac{2}{27}=\frac{56}{27}\).
   \[\frac{9}{4}\cdot\frac{56}{27}=\frac{14}{3}=4\frac{2}{3}.\]
6. \(2\frac{8}{11}=\frac{30}{11}\), \(5\frac{2}{15}=\frac{77}{15}\).
   \[\frac{30}{11}\cdot\frac{77}{15}=14.\]
7. \(1\frac{1}{14}=\frac{15}{14}\), \(5\frac{2}{5}=\frac{27}{5}\).
   \[\frac{7}{9}\cdot\frac{15}{14}\cdot\frac{27}{5}=\frac{9}{2}=4\frac{1}{2}.\]
8. \(2\frac{2}{3}=\frac{8}{3}\), \(1\frac{1}{24}=\frac{25}{24}\), \(5\frac{2}{5}=\frac{27}{5}\).
   \[\frac{8}{3}\cdot\frac{25}{24}\cdot\frac{27}{5}=15.\]

Ответ: 1) \(2\frac{1}{7}\); 2) \(6\); 3) \(2\frac{4}{5}\); 4) \(30\frac{1}{3}\); 5) \(4\frac{2}{3}\); 6) \(14\); 7) \(4\frac{1}{2}\); 8) \(15\).