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 : \(\frac{3}{4}\).

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\(\frac{3}{8}\)

Ответ: 9\(\frac{3}{8}\)

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

Ответ: \(\frac{3}{4}\)

в) \(\frac{64}{131} : \frac{32}{52}\) = \(\frac{64}{131} \cdot \frac{52}{32}\) = \(\frac{64 \cdot 52}{131 \cdot 32}\) = \(\frac{2 \cdot 32 \cdot 4 \cdot 13}{131 \cdot 32}\) = \(\frac{2 \cdot 4 \cdot 13}{131}\) = \(\frac{8 \cdot 13}{131}\) = \(\frac{104}{131}\)

Ответ: \(\frac{104}{131}\)

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

Ответ: \(\frac{16}{125}\)

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

Ответ: 12