5.541 Вычислите: a) \(5 : \frac{2}{3}\); б) \(\frac{3}{8} : \frac{1}{3}\); в) \(\frac{1}{12} : \frac{5}{36}\); г) \(\frac{14}{55} : \frac{5}{2}\).

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

Ответ: 7,5

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\(\frac{1}{8}\).

Ответ: 1\(\frac{1}{8}\)

в) \(\frac{1}{12} : \frac{5}{36}\) = \(\frac{1}{12} \cdot \frac{36}{5}\) = \(\frac{1 \cdot 36}{12 \cdot 5}\) = \(\frac{1 \cdot 3}{1 \cdot 5}\) = \(\frac{3}{5}\) = 0,6.

Ответ: 0,6

г) \(\frac{14}{55} : \frac{5}{2}\) = \(\frac{14}{55} \cdot \frac{2}{5}\) = \(\frac{14 \cdot 2}{55 \cdot 5}\) = \(\frac{28}{275}\).

Ответ: \(\frac{28}{275}\)