5.541 Вычислите: а) \(5 : \frac{2}{3}\); б) \(\frac{3}{8} : \frac{1}{3}\); в) \(\frac{1}{12} : \frac{5}{36}\); г) \(\frac{14}{55} : \frac{5}{21}\); д) \(\frac{121}{234} : \frac{11}{12}\)?

а) \(5 : \frac{2}{3} = 5 \cdot \frac{3}{2} = \frac{15}{2} = 7\frac{1}{2}\). б) \(\frac{3}{8} : \frac{1}{3} = \frac{3}{8} \cdot \frac{3}{1} = \frac{9}{8} = 1\frac{1}{8}\). в) \(\frac{1}{12} : \frac{5}{36} = \frac{1}{12} \cdot \frac{36}{5} = \frac{36}{60}\). Сокращаем на 12: \(\frac{3}{5}\). г) \(\frac{14}{55} : \frac{5}{21} = \frac{14}{55} \cdot \frac{21}{5} = \frac{14 \cdot 21}{55 \cdot 5} = \frac{294}{275}\). д) \(\frac{121}{234} : \frac{11}{12} = \frac{121}{234} \cdot \frac{12}{11} = \frac{121 \cdot 12}{234 \cdot 11}\). Сокращаем 121 и 11 на 11 и 12 и 234 на 6: \(\frac{11 \cdot 2}{39} = \frac{22}{39}\). Ответ: а) \(7\frac{1}{2}\), б) \(1\frac{1}{8}\), в) \(\frac{3}{5}\), г) \(\frac{294}{275}\), д) \(\frac{22}{39}\).