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

1) \(\frac{1}{4}:\frac{1}{4} \cdot \frac{2}{7} = \frac{1}{4} \cdot \frac{4}{1} \cdot \frac{2}{7} = \frac{1 \cdot 4 \cdot 2}{4 \cdot 1 \cdot 7} = \frac{8}{28} = \frac{2}{7}\)

2) \(\frac{1}{6} \cdot \frac{3}{7}: \frac{5}{14} = \frac{1 \cdot 3}{6 \cdot 7}: \frac{5}{14} = \frac{3}{42}: \frac{5}{14} = \frac{3}{42} \cdot \frac{14}{5} = \frac{3 \cdot 14}{42 \cdot 5} = \frac{42}{210} = \frac{1}{5}\)

3) \(\frac{1}{3}:\frac{7}{8} :\frac{9}{14} = \frac{1}{3} \cdot \frac{8}{7} \cdot \frac{14}{9} = \frac{1 \cdot 8 \cdot 14}{3 \cdot 7 \cdot 9} = \frac{112}{189} = \frac{16}{27}\)

4) \(\frac{6}{7}:\frac{5}{7} \cdot \frac{4}{9} = \frac{6}{7} \cdot \frac{7}{5} \cdot \frac{4}{9} = \frac{6 \cdot 7 \cdot 4}{7 \cdot 5 \cdot 9} = \frac{168}{315} = \frac{8}{15}\)

Ответ: 1) \(\frac{2}{7}\), 2) \(\frac{1}{5}\), 3) \(\frac{16}{27}\), 4) \(\frac{8}{15}\)