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) \(\frac{121}{234} : \frac{11}{12}\)

Ответ: a) 7,5; б) 1,125; в) 0,6; г) \(\frac{294}{275}\); д) \(\frac{22}{39}\)

a) \(5 : \frac{2}{3} = 5 \cdot \frac{3}{2} = \frac{5 \cdot 3}{2} = \frac{15}{2} = 7.5\)

б) \(\frac{3}{8} : \frac{1}{3} = \frac{3}{8} \cdot \frac{3}{1} = \frac{3 \cdot 3}{8} = \frac{9}{8} = 1.125\)

в) \(\frac{1}{12} : \frac{5}{36} = \frac{1}{12} \cdot \frac{36}{5} = \frac{1 \cdot 36}{12 \cdot 5} = \frac{36}{60} = 0.6\)

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

Ответ: a) 7,5; б) 1,125; в) 0,6; г) \(\frac{294}{275}\); д) \(\frac{22}{39}\)