5.540 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.

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

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

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

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

Ответ: a) \(9\frac{3}{8}\); б) \(\frac{3}{4}\); в) \(\frac{104}{131}\); г) \(\frac{16}{125}\); д) 12; e) \(2\frac{1}{4}\).