5.541 Вычислите: a) 5:; б) :; в) :; г) : ; д) : 2 3 1 1 14 5 121 11 3 8 3 12 36 55 21 234 12

Ответ: а) 7.5, б) \(\frac{9}{8}\), в) \(\frac{3}{5}\), г) \(\frac{2}{15}\), д) \(\frac{121}{204}\)

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

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

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

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

д) \(\frac{121}{234} : \frac{11}{12} = \frac{121}{234} \cdot \frac{12}{11} = \frac{11}{1} \cdot \frac{2}{11} = \frac{11 \cdot 2}{39 \cdot 1} = \frac{22}{39}\)

Ответ: а) 7.5, б) \(\frac{9}{8}\), в) \(\frac{3}{5}\), г) \(\frac{294}{275}\), д) \(\frac{22}{39}\)