5.541 Вычислите: a) 5 : \(\frac{2}{3}\); б) \(\frac{1}{12} : \frac{5}{36}\); в) \(\frac{3}{4} : \frac{3}{8}\); г) \(\frac{14}{55} : \frac{5}{21}\); д) \(\frac{12}{9} : \frac{8}{3}\)?

a) 5 : \(\frac{2}{3}\)

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

Ответ: \(7\frac{1}{2}\)

б) \(\frac{1}{12} : \frac{5}{36}\)

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

Ответ: \(\frac{3}{5}\)

в) \(\frac{3}{4} : \frac{3}{8}\)

1. \(\frac{3}{4} : \frac{3}{8} = \frac{3}{4} \cdot \frac{8}{3} = \frac{3 \cdot 8}{4 \cdot 3} = \frac{3 \cdot 4 \cdot 2}{4 \cdot 3} = 2\)

Ответ: 2

г) \(\frac{14}{55} : \frac{5}{21}\)

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

Ответ: \(\frac{294}{275}\)

д) \(\frac{12}{9} : \frac{8}{3}\)

1. \(\frac{12}{9} : \frac{8}{3} = \frac{12}{9} \cdot \frac{3}{8} = \frac{12 \cdot 3}{9 \cdot 8} = \frac{4 \cdot 3 \cdot 3}{3 \cdot 3 \cdot 4 \cdot 2} = \frac{1}{2}\)

Ответ: \(\frac{1}{2}\)