5.765 Найдите частное: a) $$\frac{5}{4} : \frac{2}{15}$$; б) $$\frac{2}{3} : \frac{8}{9}$$; в) $$\frac{64}{131} : \frac{32}{52}$$; г) $$\frac{64}{125} : 4$$; д) $$9 : \frac{3}{4}$$; e) $$9 : 4$$.

a) $$\frac{5}{4} : \frac{2}{15} = \frac{5}{4} \cdot \frac{15}{2} = \frac{5 \cdot 15}{4 \cdot 2} = \frac{75}{8} = 9 \frac{3}{8}$$

б) $$\frac{2}{3} : \frac{8}{9} = \frac{2}{3} \cdot \frac{9}{8} = \frac{2 \cdot 9}{3 \cdot 8} = \frac{18}{24} = \frac{3}{4}$$

в) $$\frac{64}{131} : \frac{32}{52} = \frac{64}{131} \cdot \frac{52}{32} = \frac{64 \cdot 52}{131 \cdot 32} = \frac{3328}{4192} = \frac{32}{131} \cdot \frac{52}{32} = \frac{208}{131} = 1 \frac{77}{131}$$

г) $$\frac{64}{125} : 4 = \frac{64}{125} \cdot \frac{1}{4} = \frac{64 \cdot 1}{125 \cdot 4} = \frac{64}{500} = \frac{16}{125}$$

д) $$9 : \frac{3}{4} = 9 \cdot \frac{4}{3} = \frac{9 \cdot 4}{3} = \frac{36}{3} = 12$$

e) $$9 : 4 = \frac{9}{4} = 2 \frac{1}{4}$$

Ответ: a) $$9 \frac{3}{8}$$; б) $$\frac{3}{4}$$; в) $$1 \frac{77}{131}$$; г) $$\frac{16}{125}$$; д) $$12$$; e) $$2 \frac{1}{4}$$