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) $$\frac{121}{234} : \frac{9}{8}$$

a) $$5 : \frac{2}{3} = 5 \cdot \frac{3}{2} = \frac{5 \cdot 3}{2} = \frac{15}{2} = 7\frac{1}{2}$$ б) $$\frac{3}{8} : \frac{1}{3} = \frac{3}{8} \cdot \frac{3}{1} = \frac{3 \cdot 3}{8 \cdot 1} = \frac{9}{8} = 1\frac{1}{8}$$ в) $$\frac{1}{12} : \frac{5}{36} = \frac{1}{12} \cdot \frac{36}{5} = \frac{1 \cdot 36}{12 \cdot 5} = \frac{36}{60} = \frac{3 \cdot 12}{5 \cdot 12} = \frac{3}{5}$$ г) $$\frac{14}{55} : \frac{5}{21} = \frac{14}{55} \cdot \frac{21}{5} = \frac{14 \cdot 21}{55 \cdot 5} = \frac{2 \cdot 7 \cdot 3 \cdot 7}{5 \cdot 11 \cdot 5} = \frac{294}{275}$$ д) $$\frac{121}{234} : \frac{9}{8} = \frac{121}{234} \cdot \frac{8}{9} = \frac{121 \cdot 8}{234 \cdot 9} = \frac{121 \cdot 8}{26 \cdot 9 \cdot 9} = \frac{968}{2106} = \frac{484}{1053}$$