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

Решим примеры на деление дробей.

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) $$ \frac{64}{131} : \frac{32}{52} = \frac{64}{131} \cdot \frac{52}{32} = \frac{64 \cdot 52}{131 \cdot 32} = \frac{2 \cdot 4}{1 \cdot 32} = \frac{8}{131} $$.

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

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

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

ж) $$ 1 \frac{3}{7} : 1 \frac{1}{14} = \frac{10}{7} : \frac{15}{14} = \frac{10}{7} \cdot \frac{14}{15} = \frac{10 \cdot 14}{7 \cdot 15} = \frac{2 \cdot 2}{1 \cdot 3} = \frac{4}{3} = 1 \frac{1}{3} $$.

и) $$ 3 \frac{8}{19} : 5 \frac{15}{38} = \frac{65}{19} : \frac{205}{38} = \frac{65}{19} \cdot \frac{38}{205} = \frac{65 \cdot 38}{19 \cdot 205} = \frac{1 \cdot 2}{1 \cdot 1} = \frac{2}{1} = 2 $$.

з) $$ 2 \frac{1}{3} : 7 \frac{1}{9} = \frac{7}{3} : \frac{64}{9} = \frac{7}{3} \cdot \frac{9}{64} = \frac{7 \cdot 9}{3 \cdot 64} = \frac{7 \cdot 3}{1 \cdot 64} = \frac{21}{64} $$.

к) $$ 4 \frac{17}{36} : 19 \frac{1}{6} = \frac{161}{36} : \frac{115}{6} = \frac{161}{36} \cdot \frac{6}{115} = \frac{161 \cdot 6}{36 \cdot 115} = \frac{161}{6 \cdot 115} = \frac{161}{690} $$.

Ответ: a) $$9 \frac{3}{8}$$; б) $$ \frac{3}{4} $$, в) $$ \frac{8}{131} $$, г) $$ \frac{16}{125} $$, д) $$12$$, e) $$2 \frac{1}{4}$$, ж) $$1 \frac{1}{3}$$, и) $$2$$, з) $$ \frac{21}{64} $$, к) $$ \frac{161}{690} $$.