5.541 Вычислите: a) 5 : 2/3; б) 3/8 : 1/3; в) 1/12 : 5/36; г) 14/55 : 5/21; д) 121/234 : 11/12; е) 9/8 : 5/8 ⋅ 3/10.

a)

\[5 : \frac{2}{3} = 5 \cdot \frac{3}{2} = \frac{5 \cdot 3}{2} = \frac{15}{2} = 7\frac{1}{2}\]

б)

\[\frac{3}{8} : \frac{1}{3} = \frac{3}{8} \cdot \frac{3}{1} = \frac{3 \cdot 3}{8} = \frac{9}{8} = 1\frac{1}{8}\]

в)

\[\frac{1}{12} : \frac{5}{36} = \frac{1}{12} \cdot \frac{36}{5} = \frac{1 \cdot 36}{12 \cdot 5} = \frac{3 \cdot 12}{12 \cdot 5} = \frac{3}{5}\]

г)

\[\frac{14}{55} : \frac{5}{21} = \frac{14}{55} \cdot \frac{21}{5} = \frac{14 \cdot 21}{55 \cdot 5} = \frac{2 \cdot 7 \cdot 3 \cdot 7}{5 \cdot 11 \cdot 5} = \frac{294}{275} = 1\frac{19}{275}\]

д)

\[\frac{121}{234} : \frac{11}{12} = \frac{121}{234} \cdot \frac{12}{11} = \frac{121 \cdot 12}{234 \cdot 11} = \frac{11 \cdot 11 \cdot 2 \cdot 6}{39 \cdot 6 \cdot 11} = \frac{11 \cdot 2}{39} = \frac{22}{39}\]

е)

\[\frac{9}{8} : \frac{5}{8} \cdot \frac{3}{10} = \frac{9}{8} \cdot \frac{8}{5} \cdot \frac{3}{10} = \frac{9 \cdot 8 \cdot 3}{8 \cdot 5 \cdot 10} = \frac{9 \cdot 3}{5 \cdot 10} = \frac{27}{50}\]

Ответ: a) 7 1/2; б) 1 1/8; в) 3/5; г) 1 19/275; д) 22/39; е) 27/50