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

Давай выполним вычисления по порядку: 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) \(\frac{1}{6}\) \(\cdot\) \(\frac{3}{7}\) \(\cdot\) \(\frac{5}{14}\) = \(\frac{1 \cdot 3 \cdot 5}{6 \cdot 7 \cdot 14}\) = \(\frac{15}{588}\) = \(\frac{5}{196}\) 3) \(\frac{1}{3}\) \(\cdot\) \(\frac{7}{8}\) \(\cdot\) \(\frac{9}{14}\) = \(\frac{1 \cdot 7 \cdot 9}{3 \cdot 8 \cdot 14}\) = \(\frac{63}{336}\) = \(\frac{3}{16}\) 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) \(\frac{1}{56}\); 2) \(\frac{5}{196}\); 3) \(\frac{3}{16}\); 4) \(\frac{40}{147}\)