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

Решение:

1. \( 9 \frac{3}{7} \cdot \frac{5}{22} = \frac{9 \cdot 7 + 3}{7} \cdot \frac{5}{22} = \frac{63 + 3}{7} \cdot \frac{5}{22} = \frac{66}{7} \cdot \frac{5}{22} = \frac{66^{3}}{7} \cdot \frac{5}{22^{1}} = \frac{3 \cdot 5}{7 \cdot 1} = \frac{15}{7} = 2 \frac{1}{7} \)
2. \( 6 \frac{3}{8} \cdot \frac{16}{17} = \frac{6 \cdot 8 + 3}{8} \cdot \frac{16}{17} = \frac{48 + 3}{8} \cdot \frac{16}{17} = \frac{51}{8} \cdot \frac{16}{17} = \frac{51^{3}}{8^{1}} \cdot \frac{16^{2}}{17} = \frac{3 \cdot 2}{1 \cdot 1} = 6 \)
3. \( 2 \frac{1}{3} \cdot 1 \frac{1}{5} = \frac{2 \cdot 3 + 1}{3} \cdot \frac{1 \cdot 5 + 1}{5} = \frac{7}{3} \cdot \frac{6}{5} = \frac{7}{3^{1}} \cdot \frac{6^{2}}{5} = \frac{7 \cdot 2}{1 \cdot 5} = \frac{14}{5} = 2 \frac{4}{5} \)
4. \( 19 \frac{1}{2} \cdot 1 \frac{5}{9} = \frac{19 \cdot 2 + 1}{2} \cdot \frac{1 \cdot 9 + 5}{9} = \frac{38 + 1}{2} \cdot \frac{9 + 5}{9} = \frac{39}{2} \cdot \frac{14}{9} = \frac{39^{13}}{2^{1}} \cdot \frac{14^{7}}{9^{3}} = \frac{13 \cdot 7}{1 \cdot 3} = \frac{91}{3} = 30 \frac{1}{3} \)
5. \( 2 \frac{1}{4} \cdot 2 \frac{2}{27} = \frac{2 \cdot 4 + 1}{4} \cdot \frac{2 \cdot 27 + 2}{27} = \frac{9}{4} \cdot \frac{54 + 2}{27} = \frac{9}{4} \cdot \frac{56}{27} = \frac{9^{1}}{4^{1}} \cdot \frac{56^{14}}{27^{3}} = \frac{1 \cdot 14}{1 \cdot 3} = \frac{14}{3} = 4 \frac{2}{3} \)
6. \( 2 \frac{8}{11} \cdot 5 \frac{2}{15} = \frac{2 \cdot 11 + 8}{11} \cdot \frac{5 \cdot 15 + 2}{15} = \frac{22 + 8}{11} \cdot \frac{75 + 2}{15} = \frac{30}{11} \cdot \frac{77}{15} = \frac{30^{2}}{11^{1}} \cdot \frac{77^{7}}{15^{1}} = \frac{2 \cdot 7}{1 \cdot 1} = 14 \)
7. \( \frac{7}{9} \cdot 1 \frac{1}{14} \cdot 5 \frac{2}{5} = \frac{7}{9} \cdot \frac{1 \cdot 14 + 1}{14} \cdot \frac{5 \cdot 5 + 2}{5} = \frac{7}{9} \cdot \frac{15}{14} \cdot \frac{27}{5} = \frac{7^{1}}{9^{1}} \cdot \frac{15^{5}}{14^{2}} \cdot \frac{27^{3}}{5^{1}} = \frac{1 \cdot 5 \cdot 3}{1 \cdot 2 \cdot 1} = \frac{15}{2} = 7 \frac{1}{2} \)
8. \( 2 \frac{2}{3} \cdot 1 \frac{1}{24} \cdot 5 \frac{2}{5} = \frac{2 \cdot 3 + 2}{3} \cdot \frac{1 \cdot 24 + 1}{24} \cdot \frac{5 \cdot 5 + 2}{5} = \frac{8}{3} \cdot \frac{25}{24} \cdot \frac{27}{5} = \frac{8^{1}}{3^{1}} \cdot \frac{25^{5}}{24^{3}} \cdot \frac{27^{9}}{5^{1}} = \frac{1 \cdot 5 \cdot 9}{1 \cdot 3 \cdot 1} = \frac{45}{3} = 15 \)

Ответ: 1) 2 1/7; 2) 6; 3) 2 4/5; 4) 30 1/3; 5) 4 2/3; 6) 14; 7) 7 1/2; 8) 15.