5.560 Вычислите: 1 1 2 1 7 9 1 7 9 6.54 1) — : — . —; 2) — . — : —; 3) — . — : —; 4) — . — . —. 4 4 7' 3 8 14' 3 8 14' 7 7 9

Ответ:

1. \(\frac{1}{4} : \frac{1}{4} \cdot \frac{2}{7} = (\frac{1}{4} \cdot \frac{4}{1}) \cdot \frac{2}{7} = 1 \cdot \frac{2}{7} = \frac{2}{7}\)
2. \(\frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14} = \frac{1 \cdot 7}{3 \cdot 8} : \frac{9}{14} = \frac{7}{24} : \frac{9}{14} = \frac{7}{24} \cdot \frac{14}{9} = \frac{7 \cdot 14}{24 \cdot 9} = \frac{98}{216} = \frac{49}{108}\)
3. \(\frac{1}{3} \cdot \frac{7}{8} : \frac{9}{14} = \frac{1 \cdot 7}{3 \cdot 8} : \frac{9}{14} = \frac{7}{24} : \frac{9}{14} = \frac{7}{24} \cdot \frac{14}{9} = \frac{7 \cdot 14}{24 \cdot 9} = \frac{98}{216} = \frac{49}{108}\)
4. \(\frac{6}{7} \cdot \frac{5}{7} \cdot \frac{4}{9} = \frac{6 \cdot 5 \cdot 4}{7 \cdot 7 \cdot 9} = \frac{120}{441} = \frac{40}{147}\)

Ответ: 1) \(\frac{2}{7}\); 2) \(\frac{49}{108}\); 3) \(\frac{49}{108}\); 4) \(\frac{40}{147}\)