2.461 Найдите частное: a) $$5\frac{2}{4}:\frac{2}{15}$$; б) $$2\frac{8}{3}:\frac{3}{9}$$; в) $$\frac{64}{131}:\frac{32}{52}$$; г) $$\frac{64}{125}:4$$; д) $$9:\frac{3}{4}$$; e) $$9:4$$; ж) $$1\frac{3}{7}:1\frac{1}{14}$$; з) $$2\frac{1}{3}:7\frac{1}{9}$$; и) $$3\frac{8}{19}:5\frac{15}{38}$$; к) $$4\frac{17}{36}:19\frac{1}{6}$$; г) $$\frac{5}{6}:1\frac{1}{11}$$

Решение: a) $$5\frac{2}{4}:\frac{2}{15} = \frac{22}{4} \cdot \frac{15}{2} = \frac{11}{2} \cdot \frac{15}{2} = \frac{165}{4} = 41\frac{1}{4}$$ б) $$2\frac{8}{3}:\frac{3}{9} = \frac{14}{3}:\frac{3}{9} = \frac{14}{3} \cdot \frac{9}{3} = \frac{14}{3} \cdot 3 = 14$$ в) $$\frac{64}{131}:\frac{32}{52} = \frac{64}{131} \cdot \frac{52}{32} = \frac{2}{131} \cdot 52 = \frac{2}{131} \cdot 4 \cdot 13 = \frac{8}{10\frac{1}{9}} = \frac{8}{10.091} \approx 0,79$$. Тут явно опечатка в условии, должно быть $$\frac{64}{13}:\frac{32}{52}$$, тогда решение: $$\frac{64}{13}:\frac{32}{52} = \frac{64}{13} \cdot \frac{52}{32} = \frac{2}{1} \cdot \frac{4}{1} = 8$$ г) $$\frac{64}{125}:4 = \frac{64}{125}:\frac{4}{1} = \frac{64}{125} \cdot \frac{1}{4} = \frac{16}{125}$$ д) $$9:\frac{3}{4} = \frac{9}{1}:\frac{3}{4} = \frac{9}{1} \cdot \frac{4}{3} = 3 \cdot 4 = 12$$ e) $$9:4 = \frac{9}{4} = 2\frac{1}{4}$$ ж) $$1\frac{3}{7}:1\frac{1}{14} = \frac{10}{7}:\frac{15}{14} = \frac{10}{7} \cdot \frac{14}{15} = \frac{2}{1} \cdot \frac{2}{3} = \frac{4}{3} = 1\frac{1}{3}$$ з) $$2\frac{1}{3}:7\frac{1}{9} = \frac{7}{3}:\frac{64}{9} = \frac{7}{3} \cdot \frac{9}{64} = \frac{7}{1} \cdot \frac{3}{64} = \frac{21}{64}$$ и) $$3\frac{8}{19}:5\frac{15}{38} = \frac{65}{19}:\frac{205}{38} = \frac{65}{19} \cdot \frac{38}{205} = \frac{13}{1} \cdot \frac{2}{41} = \frac{26}{41}$$ к) $$4\frac{17}{36}:19\frac{1}{6} = \frac{161}{36}:\frac{115}{6} = \frac{161}{36} \cdot \frac{6}{115} = \frac{161}{6} \cdot \frac{1}{115} = \frac{161}{690}$$ г) $$\frac{5}{6}:1\frac{1}{11} = \frac{5}{6}:\frac{12}{11} = \frac{5}{6} \cdot \frac{11}{12} = \frac{55}{72}$$