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

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

Ответ: 7\(\frac{1}{2}\)

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

Ответ: 1\(\frac{1}{8}\)

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

Ответ: \(\frac{3}{5}\)

г) \(\frac{14}{55} : \frac{5}{21}\) = \(\frac{14}{55} \cdot \frac{21}{5}\) = \(\frac{14 \cdot 21}{55 \cdot 5}\) = \(\frac{2 \cdot 7 \cdot 3 \cdot 7}{5 \cdot 11 \cdot 5}\) = \(\frac{294}{275}\)

Ответ: \(\frac{294}{275}\)

д) \(\frac{121}{234} : \frac{11}{12}\) = \(\frac{121}{234} \cdot \frac{12}{11}\) = \(\frac{121 \cdot 12}{234 \cdot 11}\) = \(\frac{11 \cdot 11 \cdot 6 \cdot 2}{117 \cdot 2 \cdot 11}\) = \(\frac{11 \cdot 6}{117}\) = \(\frac{11 \cdot 2 \cdot 3}{3 \cdot 39}\) = \(\frac{22}{39}\)

Ответ: \(\frac{22}{39}\)