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.

Ответ:

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

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

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

г) \[\frac{14}{55} \cdot \frac{5}{21} = \frac{14 \cdot 5}{55 \cdot 21} = \frac{2 \cdot 1}{11 \cdot 3} = \frac{2}{33}\]

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

Ответ: