5.486 Найдите произведение: a) \(\frac{8}{9} \cdot \frac{3}{4}\) b) \(\frac{11}{45} \cdot \frac{9}{22}\) c) \(\frac{51}{29} \cdot \frac{58}{85}\) d) \(\frac{1}{4} \cdot \frac{4}{5} \cdot \frac{5}{6}\)

а) \(\frac{8}{9} \cdot \frac{3}{4} = \frac{8 \cdot 3}{9 \cdot 4} = \frac{24}{36}\). Сократим на 12: \(\frac{24}{36} = \frac{2}{3}\) б) \(\frac{11}{45} \cdot \frac{9}{22} = \frac{11 \cdot 9}{45 \cdot 22} = \frac{99}{990}\). Сократим на 99: \(\frac{99}{990} = \frac{1}{10}\) в) \(\frac{51}{29} \cdot \frac{58}{85} = \frac{51 \cdot 58}{29 \cdot 85} = \frac{2958}{2465}\). Сократим на 29: \(\frac{51 \cdot 2}{1 \cdot 85} = \frac{102}{85}\) г) \(\frac{1}{4} \cdot \frac{4}{5} \cdot \frac{5}{6} = \frac{1 \cdot 4 \cdot 5}{4 \cdot 5 \cdot 6} = \frac{20}{120}\). Сократим на 20: \(\frac{20}{120} = \frac{1}{6}\) Ответ: a) \(\frac{2}{3}\) b) \(\frac{1}{10}\) c) \(\frac{102}{85}\) d) \(\frac{1}{6}\)