5.560 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}: \frac{5}{7} \cdot \frac{4}{9}.

1) Вычислим \frac{1}{4}:\frac{1}{4} \cdot \frac{2}{7}.

\frac{1}{4}:\frac{1}{4} = 1;

1 \cdot \frac{2}{7} = \frac{2}{7}.

2) Вычислим \frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14}.

\frac{1}{3} \cdot \frac{7}{8} = \frac{7}{24};

\frac{7}{24} : \frac{9}{14} = \frac{7}{24} \cdot \frac{14}{9} = \frac{7 \cdot 14}{24 \cdot 9} = \frac{98}{216} = \frac{49}{108}.

3) Вычислим \frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14}.

\frac{1}{3} \cdot \frac{7}{8} = \frac{7}{24};

\frac{7}{24} : \frac{9}{14} = \frac{7}{24} \cdot \frac{14}{9} = \frac{7 \cdot 14}{24 \cdot 9} = \frac{98}{216} = \frac{49}{108}.

4) Вычислим \frac{6}{7}: \frac{5}{7} \cdot \frac{4}{9}.

\frac{6}{7}: \frac{5}{7} = \frac{6}{7} \cdot \frac{7}{5} = \frac{6}{5};

\frac{6}{5} \cdot \frac{4}{9} = \frac{6 \cdot 4}{5 \cdot 9} = \frac{24}{45} = \frac{8}{15}.

Ответ: 1) \frac{2}{7}; 2) \frac{49}{108}; 3) \frac{49}{108}; 4) \frac{8}{15}.