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

Решение:

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

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