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:\(\frac{3}{2}\)?

a) \(\frac{5}{4} : \frac{2}{15}\)

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

Ответ: \(9\frac{3}{8}\)

б) \(\frac{2}{3} : \frac{8}{9}\)

1. \(\frac{2}{3} : \frac{8}{9} = \frac{2}{3} \cdot \frac{9}{8} = \frac{2 \cdot 9}{3 \cdot 8} = \frac{2 \cdot 3 \cdot 3}{3 \cdot 2 \cdot 4} = \frac{3}{4}\)

Ответ: \(\frac{3}{4}\)

в) \(\frac{64}{131} : \frac{32}{52}\)

1. \(\frac{64}{131} : \frac{32}{52} = \frac{64}{131} \cdot \frac{52}{32} = \frac{64 \cdot 52}{131 \cdot 32} = \frac{32 \cdot 2 \cdot 4 \cdot 13}{131 \cdot 32} = \frac{2 \cdot 4 \cdot 13}{131} = \frac{104}{131}\)

Ответ: \(\frac{104}{131}\)

г) \(\frac{64}{125} : 4\)

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

Ответ: \(\frac{16}{125}\)

д) 9:\(\frac{3}{2}\)

1. \(9 : \frac{3}{2} = \frac{9}{1} : \frac{3}{2} = \frac{9}{1} \cdot \frac{2}{3} = \frac{9 \cdot 2}{1 \cdot 3} = \frac{3 \cdot 3 \cdot 2}{3} = 6\)

Ответ: 6