5.541 Вычислите: a) 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) \(\frac{121}{234}:\frac{11}{12}\).

Выполним деление дробей:

а) \(5:\frac{2}{3} = \frac{5}{1} \cdot \frac{3}{2} = \frac{5 \cdot 3}{1 \cdot 2} = \frac{15}{2} = 7\frac{1}{2}\)

б) \(\frac{3}{8}:\frac{1}{3} = \frac{3}{8} \cdot \frac{3}{1} = \frac{3 \cdot 3}{8 \cdot 1} = \frac{9}{8} = 1\frac{1}{8}\)

в) \(\frac{1}{12}:\frac{5}{36} = \frac{1}{12} \cdot \frac{36}{5} = \frac{1 \cdot 36}{12 \cdot 5} = \frac{3}{5}\)

г) \(\frac{14}{55}:\frac{5}{21} = \frac{14}{55} \cdot \frac{21}{5} = \frac{14 \cdot 21}{55 \cdot 5} = \frac{294}{275} = 1\frac{19}{275}\)

д) \(\frac{121}{234}:\frac{11}{12} = \frac{121}{234} \cdot \frac{12}{11} = \frac{11 \cdot 12}{234} = \frac{132}{234} = \frac{22}{39} \)

Ответ: а) \(7\frac{1}{2}\); б) \(1\frac{1}{8}\); в) \(\frac{3}{5}\); г) \(1\frac{19}{275}\); д) \(\frac{22}{39}\).