337. Выполните умножение:

Решение:

1. \( 9 \frac{3}{7} \cdot \frac{5}{22} = \frac{9 \cdot 7 + 3}{7} \cdot \frac{5}{22} = \frac{63 + 3}{7} \cdot \frac{5}{22} = \frac{66}{7} \cdot \frac{5}{22} = \frac{6 \cdot 5}{7} = \frac{30}{7} = 4 \frac{2}{7} \)
2. \( 6 \frac{3}{8} \cdot \frac{16}{17} = \frac{6 \cdot 8 + 3}{8} \cdot \frac{16}{17} = \frac{48 + 3}{8} \cdot \frac{16}{17} = \frac{51}{8} \cdot \frac{16}{17} = \frac{3 \cdot 2}{1} = 6 \)
3. \( 2 \frac{1}{3} \cdot 1 \frac{1}{5} = \frac{2 \cdot 3 + 1}{3} \cdot \frac{1 \cdot 5 + 1}{5} = \frac{7}{3} \cdot \frac{6}{5} = \frac{7 \cdot 2}{5} = \frac{14}{5} = 2 \frac{4}{5} \)
4. \( 19 \frac{1}{2} \cdot 1 \frac{5}{9} = \frac{19 \cdot 2 + 1}{2} \cdot \frac{1 \cdot 9 + 5}{9} = \frac{38 + 1}{2} \cdot \frac{9 + 5}{9} = \frac{39}{2} \cdot \frac{14}{9} = \frac{13 \cdot 7}{1} = 91 \)
5. \( 2 \frac{1}{4} \cdot \frac{2}{27} = \frac{2 \cdot 4 + 1}{4} \cdot \frac{2}{27} = \frac{9}{4} \cdot \frac{2}{27} = \frac{1 \cdot 1}{2 \cdot 3} = \frac{1}{6} \)
6. \( 2 \frac{8}{11} \cdot 5 \frac{2}{15} = \frac{2 \cdot 11 + 8}{11} \cdot \frac{5 \cdot 15 + 2}{15} = \frac{22 + 8}{11} \cdot \frac{75 + 2}{15} = \frac{30}{11} \cdot \frac{77}{15} = \frac{2 \cdot 7}{1} = 14 \)
7. \( \frac{7}{9} \cdot 1 \frac{1}{14} \cdot 5 \frac{2}{5} = \frac{7}{9} \cdot \frac{1 \cdot 14 + 1}{14} \cdot \frac{5 \cdot 5 + 2}{5} = \frac{7}{9} \cdot \frac{15}{14} \cdot \frac{27}{5} = \frac{1 \cdot 3 \cdot 3}{1} = 9 \)
8. \( 2 \frac{2}{3} \cdot 1 \frac{1}{24} \cdot 5 \frac{2}{5} = \frac{2 \cdot 3 + 2}{3} \cdot \frac{1 \cdot 24 + 1}{24} \cdot \frac{5 \cdot 5 + 2}{5} = \frac{8}{3} \cdot \frac{25}{24} \cdot \frac{27}{5} = \frac{1 \cdot 5 \cdot 9}{1} = 45 \)

Ответ: 1) \( 4 \frac{2}{7} \); 2) \( 6 \); 3) \( 2 \frac{4}{5} \); 4) \( 91 \); 5) \( \frac{1}{6} \); 6) \( 14 \); 7) \( 9 \); 8) \( 45 \).