5.560 Вычислите: 1) \frac{1}{4} \cdot \frac{1}{4} \cdot \frac{2}{7}; 2) \frac{1}{3} \cdot \frac{7}{8} \cdot \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}

Решение:

1. $$\frac{1}{4} \cdot \frac{1}{4} \cdot \frac{2}{7} = \frac{1 \cdot 1 \cdot 2}{4 \cdot 4 \cdot 7} = \frac{2}{112} = \frac{1}{56}$$
2. $$\frac{1}{3} \cdot \frac{7}{8} \cdot \frac{9}{14} = \frac{1 \cdot 7 \cdot 9}{3 \cdot 8 \cdot 14} = \frac{63}{336} = \frac{9}{48} = \frac{3}{16}$$
3. $$\frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14} = \frac{1}{3} \cdot \frac{7}{8} \cdot \frac{14}{9} = \frac{1 \cdot 7 \cdot 14}{3 \cdot 8 \cdot 9} = \frac{98}{216} = \frac{49}{108}$$
4. $$\frac{6}{7} : \frac{5}{7} \cdot \frac{4}{9} = \frac{6}{7} \cdot \frac{7}{5} \cdot \frac{4}{9} = \frac{6 \cdot 7 \cdot 4}{7 \cdot 5 \cdot 9} = \frac{168}{315} = \frac{56}{105} = \frac{8}{15}$$

Ответ:

1. $$\frac{1}{56}$$
2. $$\frac{3}{16}$$
3. $$\frac{49}{108}$$
4. $$\frac{8}{15}$$