Найдите частное: а) \(\frac{5}{4}:\frac{2}{15}\); б) \(\frac{2}{3}:\frac{8}{9}\); в) \(\frac{64}{131}:\frac{32}{52}\); г) \(\frac{64}{125}:4\); д) 9:\(\frac{3}{4}\); е) 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\(\frac{17}{36}:19\frac{1}{6}\)

Решение:

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

Ответ: 9\(\frac{3}{8}\)

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

Ответ: \(\frac{3}{4}\)

в) \(\frac{64}{131}:\frac{32}{52}=\frac{64}{131}\cdot \frac{52}{32}=\frac{64\cdot 52}{131\cdot 32}=\frac{2\cdot 52}{131}=\frac{104}{131}\)

Ответ: \(\frac{104}{131}\)

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

Ответ: \(\frac{16}{125}\)

д) \(9:\frac{3}{4}=\frac{9}{1}:\frac{3}{4}=\frac{9}{1}\cdot \frac{4}{3}=\frac{9\cdot 4}{1\cdot 3}=\frac{36}{3}=12\)

Ответ: 12

е) \(9:4=\frac{9}{1}:\frac{4}{1}=\frac{9}{4}=2\frac{1}{4}\)

Ответ: 2\(\frac{1}{4}\)

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

Ответ: 1\(\frac{1}{3}\)

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

Ответ: \(\frac{21}{64}\)

и) \(3\frac{8}{19}:5\frac{15}{38}=\frac{65}{19}:\frac{205}{38}=\frac{65}{19}\cdot \frac{38}{205}=\frac{65\cdot 38}{19\cdot 205}=\frac{1\cdot 2}{1\cdot \frac{205}{65}}=\frac{2}{3.15}\approx 0.63\)

Ответ: \(\approx 0.63\)

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

Ответ: \(\frac{161}{690}\)