33. Вычислите: а) \(\frac{3}{31}\cdot5\); \(\frac{5}{34}\cdot9\); \(\frac{3}{50}\cdot3\); \(\frac{3}{29}\cdot4\); \(\frac{3}{14}\cdot6\); \(\frac{7}{8}\cdot11\); \(\frac{9}{11}\cdot100\); б) \(4\frac{2}{35}\cdot7\); \(\frac{4}{27}\cdot10\); \(1\frac{3}{14}\cdot5\); \(7\frac{1}{9}\cdot6\); \(11\frac{1}{8}\cdot7\); \(\frac{7}{8}\cdot32\); \(12\frac{5}{121}\cdot4\).

Умножаем числитель дроби на натуральное число; смешанные числа перед умножением переводим в неправильные дроби.

1. \(\frac{3}{31}\cdot5=\frac{15}{31}\).
2. \(\frac{5}{34}\cdot9=\frac{45}{34}=1\frac{11}{34}\).
3. \(\frac{3}{50}\cdot3=\frac{9}{50}\).
4. \(\frac{3}{29}\cdot4=\frac{12}{29}\).
5. \(\frac{3}{14}\cdot6=\frac{18}{14}=1\frac{2}{7}\).
6. \(\frac{7}{8}\cdot11=\frac{77}{8}=9\frac{5}{8}\).
7. \(\frac{9}{11}\cdot100=\frac{900}{11}=81\frac{9}{11}\).
8. \(4\frac{2}{35}\cdot7=\frac{142}{35}\cdot7=\frac{142}{5}=28\frac{2}{5}\).
9. \(\frac{4}{27}\cdot10=\frac{40}{27}=1\frac{13}{27}\).
10. \(1\frac{3}{14}\cdot5=\frac{17}{14}\cdot5=\frac{85}{14}=6\frac{1}{14}\).
11. \(7\frac{1}{9}\cdot6=\frac{64}{9}\cdot6=\frac{128}{3}=42\frac{2}{3}\).
12. \(11\frac{1}{8}\cdot7=\frac{89}{8}\cdot7=\frac{623}{8}=77\frac{7}{8}\).
13. \(\frac{7}{8}\cdot32=28\).
14. \(12\frac{5}{121}\cdot4=\frac{145}{121}\cdot4=\frac{580}{121}=4\frac{96}{121}\).