Вычислите: 1) \(\frac{1}{2} \cdot \frac{3}{7}\); 2) \(\frac{7}{10} \cdot \frac{5}{21}\); 3) \(\frac{5}{12} \cdot 3\); 4) \(\frac{5}{8} : \frac{3}{4}\); 5) \(1 : \frac{4}{7}\); 6) \(2 \frac{1}{3} : 7\).

Пошаговое решение:

1. \(\frac{1}{2} \cdot \frac{3}{7} = \frac{1 \cdot 3}{2 \cdot 7} = \frac{3}{14}\)
2. \(\frac{7}{10} \cdot \frac{5}{21} = \frac{7 \cdot 5}{10 \cdot 21} = \frac{35}{210} = \frac{1}{6}\)
3. \(\frac{5}{12} \cdot 3 = \frac{5 \cdot 3}{12} = \frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}\)
4. \(\frac{5}{8} : \frac{3}{4} = \frac{5}{8} \cdot \frac{4}{3} = \frac{5 \cdot 4}{8 \cdot 3} = \frac{20}{24} = \frac{5}{6}\)
5. \(1 : \frac{4}{7} = 1 \cdot \frac{7}{4} = \frac{7}{4} = 1\frac{3}{4}\)
6. \(2 \frac{1}{3} : 7 = \frac{7}{3} : 7 = \frac{7}{3} \cdot \frac{1}{7} = \frac{7 \cdot 1}{3 \cdot 7} = \frac{1}{3}\)

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