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

1) \(\frac{1}{4} \cdot \frac{1}{4} : \frac{2}{7} = \frac{1}{16} : \frac{2}{7} = \frac{1}{16} \cdot \frac{7}{2} = \frac{7}{32}\)

2) \(\frac{1}{3} : \frac{7}{8} \cdot \frac{9}{14} = \frac{1}{3} \cdot \frac{8}{7} \cdot \frac{9}{14} = \frac{1 \cdot 8 \cdot 9}{3 \cdot 7 \cdot 14} = \frac{72}{294} = \frac{12}{49}\)

3) \(\frac{1}{3} : \frac{7}{8} : \frac{9}{14} = \frac{1}{3} \cdot \frac{8}{7} : \frac{9}{14} = \frac{8}{21} \cdot \frac{14}{9} = \frac{8 \cdot 14}{21 \cdot 9} = \frac{112}{189} = \frac{16}{27}\)

4) \(\frac{6}{7} : \frac{5}{7} \cdot \frac{4}{9} = \frac{6}{7} \cdot \frac{7}{5} \cdot \frac{4}{9} = \frac{6 \cdot 7 \cdot 4}{7 \cdot 5 \cdot 9} = \frac{168}{315} = \frac{8 \cdot 21}{15 \cdot 21} = \frac{8}{15}\)

Ответ: 1) \(\frac{7}{32}\); 2) \(\frac{12}{49}\); 3) \(\frac{16}{27}\); 4) \(\frac{8}{15}\)