5.540 Найдите частное: a) \(\frac{5}{4} : \frac{2}{15}\); б) \(\frac{2}{3} : \frac{8}{9}\); в) \(\frac{64}{181} : \frac{32}{52}\); г) \(\frac{64}{125} : 4\); д) 9 : \(\frac{3}{4}\); e) 9 : 4.

Ответ: a) \(9 \frac{3}{8}\); б) \(\frac{3}{4}\); в) \(\frac{32}{181} \cdot \frac{26}{1}\); г) \(\frac{16}{125}\); д) 12; e) \(\frac{9}{4}\)

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

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) \(\frac{64}{181} : \frac{32}{52} = \frac{64}{181} \cdot \frac{52}{32} = \frac{2 \cdot 32 \cdot 52}{181 \cdot 32} = \frac{2 \cdot 52}{181} = \frac{104}{181}\)

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

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

е) \(9 : 4 = \frac{9}{4}\)

Ответ: a) \(9 \frac{3}{8}\); б) \(\frac{3}{4}\); в) \(\frac{104}{181}\); г) \(\frac{16}{125}\); д) 12; e) \(\frac{9}{4}\)