3. 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) \(9:4\).

а) \(\frac{5}{4}:\frac{2}{15}\)

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

б) \(\frac{2}{3}:\frac{8}{9}\)

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

в) \(\frac{64}{131}:\frac{32}{52}\)

$$\frac{64}{131}:\frac{32}{52} = \frac{64}{131} \cdot \frac{52}{32} = \frac{64 \cdot 52}{131 \cdot 32} = \frac{3328}{4192} = \frac{104}{131}$$

г) \(\frac{64}{125}:4\)

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

д) \(9:\frac{3}{4}\)

$$9:\frac{3}{4} = \frac{9}{1}:\frac{3}{4} = \frac{9}{1} \cdot \frac{4}{3} = \frac{9 \cdot 4}{1 \cdot 3} = \frac{36}{3} = 12$$

е) \(9:4\)

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

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