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

Решение:

1) \(\frac{1}{4} \cdot \frac{1}{4}:\frac{2}{7} = \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{7}{2} = \frac{1 \cdot 1 \cdot 7}{4 \cdot 4 \cdot 2} = \frac{7}{32}\)

2) \(\frac{1}{6} \cdot \frac{3}{7}:\frac{5}{14} = \frac{1}{6} \cdot \frac{3}{7} \cdot \frac{14}{5} = \frac{1 \cdot 3 \cdot 14}{6 \cdot 7 \cdot 5} = \frac{1 \cdot 1 \cdot 2}{2 \cdot 1 \cdot 5} = \frac{1}{5}\)

3) \(\frac{1}{3}:\frac{7}{8} \cdot \frac{9}{14} = \frac{1}{3} \cdot \frac{8}{7} \cdot \frac{9}{14} = \frac{1 \cdot 8 \cdot 9}{3 \cdot 7 \cdot 14} = \frac{1 \cdot 8 \cdot 3}{1 \cdot 7 \cdot 14} = \frac{24}{98} = \frac{12}{49}\)

4) \(\frac{6}{7}:\frac{5}{7} \cdot \frac{4}{9} = \frac{6}{7} \cdot \frac{7}{5} \cdot \frac{4}{9} = \frac{6 \cdot 7 \cdot 4}{7 \cdot 5 \cdot 9} = \frac{6 \cdot 1 \cdot 4}{1 \cdot 5 \cdot 9} = \frac{24}{45} = \frac{8}{15}\)