60 Вычислите: 1) \frac{1}{4} : \frac{1}{4} \cdot \frac{2}{7}; 2) \frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14}; 3) \frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14}; 4) \frac{6}{7} \cdot \frac{5}{7} \cdot \frac{4}{9}

Решение:

1. \[\frac{1}{4} : \frac{1}{4} \cdot \frac{2}{7} = 1 \cdot \frac{2}{7} = \frac{2}{7}\]
2. \[\frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14} = \frac{7}{24} : \frac{9}{14} = \frac{7}{24} \cdot \frac{14}{9} = \frac{7 \cdot 14}{24 \cdot 9} = \frac{7 \cdot 7}{12 \cdot 9} = \frac{49}{108}\]
3. \[\frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14} = \frac{7}{24} : \frac{9}{14} = \frac{7}{24} \cdot \frac{14}{9} = \frac{7 \cdot 14}{24 \cdot 9} = \frac{7 \cdot 7}{12 \cdot 9} = \frac{49}{108}\]
4. \[\frac{6}{7} \cdot \frac{5}{7} \cdot \frac{4}{9} = \frac{6 \cdot 5 \cdot 4}{7 \cdot 7 \cdot 9} = \frac{2 \cdot 5 \cdot 4}{7 \cdot 7 \cdot 3} = \frac{40}{147}\]

Ответ: 1) \(\frac{2}{7}\); 2) \(\frac{49}{108}\); 3) \(\frac{49}{108}\); 4) \(\frac{40}{147}\)