Вычислите: 1) \(\frac{3}{8} \cdot \frac{8}{9}\) 2) \(14 \cdot \frac{7}{8}\) 3) \(5 \frac{1}{4}\) 4) \(\frac{5}{11} \cdot \frac{4}{15}\) 5) \(18 \cdot \frac{2}{9}\) 6) \(\frac{3}{7} \cdot 21\) 7) \(15 \cdot 2 \frac{3}{5}\) 8) \(\frac{9}{14} \cdot \frac{5}{12}\) 9) \(15 \cdot \frac{9}{10}\) 10) \(\frac{4}{9} \cdot 6\) 11) \(1 \frac{3}{7} \cdot 2 \frac{4}{5}\)

Решение:

1. \( \frac{3}{8} \cdot \frac{8}{9} = \frac{3 \cdot 8}{8 \cdot 9} = \frac{3}{9} = \frac{1}{3} \)
2. \( 14 \cdot \frac{7}{8} = \frac{14 \cdot 7}{8} = \frac{98}{8} = \frac{49}{4} = 12\frac{1}{4} \)
3. \( 5 \frac{1}{4} \) - это число, а не выражение для вычисления.
4. \( \frac{5}{11} \cdot \frac{4}{15} = \frac{5 \cdot 4}{11 \cdot 15} = \frac{20}{165} = \frac{4}{33} \)
5. \( 18 \cdot \frac{2}{9} = \frac{18 \cdot 2}{9} = \frac{36}{9} = 4 \)
6. \( \frac{3}{7} \cdot 21 = \frac{3 \cdot 21}{7} = \frac{63}{7} = 9 \)
7. \( 15 \cdot 2 \frac{3}{5} = 15 \cdot \frac{13}{5} = \frac{15 \cdot 13}{5} = 3 \cdot 13 = 39 \)
8. \( \frac{9}{14} \cdot \frac{5}{12} = \frac{9 \cdot 5}{14 \cdot 12} = \frac{45}{168} = \frac{15}{56} \)
9. \( 15 \cdot \frac{9}{10} = \frac{15 \cdot 9}{10} = \frac{135}{10} = \frac{27}{2} = 13\frac{1}{2} \)
10. \( \frac{4}{9} \cdot 6 = \frac{4 \cdot 6}{9} = \frac{24}{9} = \frac{8}{3} = 2\frac{2}{3} \)
11. \( 1 \frac{3}{7} \cdot 2 \frac{4}{5} = \frac{10}{7} \cdot \frac{14}{5} = \frac{10 \cdot 14}{7 \cdot 5} = \frac{140}{35} = 4 \)

Ответ: 1) \(\frac{1}{3}\); 2) \(12\frac{1}{4}\); 3) \(5\frac{1}{4}\); 4) \(\frac{4}{33}\); 5) \(4\); 6) \(9\); 7) \(39\); 8) \(\frac{15}{56}\); 9) \(13\frac{1}{2}\); 10) \(2\frac{2}{3}\); 11) \(4\).