1) \(\frac{5}{6} : \frac{7}{4} = \frac{5}{6} \cdot \frac{4}{7} = \frac{5 \cdot 4}{6 \cdot 7} = \frac{5 \cdot 2 \cdot 2}{2 \cdot 3 \cdot 7} = \frac{5 \cdot 2}{3 \cdot 7} = \frac{10}{21}\)
2) \(\frac{8}{13} : \frac{7}{9} = \frac{8}{13} \cdot \frac{9}{7} = \frac{8 \cdot 9}{13 \cdot 7} = \frac{72}{91}\)
3) \(\frac{6}{35} : \frac{48}{49} = \frac{6}{35} \cdot \frac{49}{48} = \frac{6 \cdot 49}{35 \cdot 48} = \frac{6 \cdot 7 \cdot 7}{5 \cdot 7 \cdot 6 \cdot 8} = \frac{7}{5 \cdot 8} = \frac{7}{40}\)
4) \(\frac{7}{8} : \frac{91}{32} = \frac{7}{8} \cdot \frac{32}{91} = \frac{7 \cdot 32}{8 \cdot 91} = \frac{7 \cdot 8 \cdot 4}{8 \cdot 7 \cdot 13} = \frac{4}{13}\)
5) \(\frac{8}{15} : \frac{32}{75} = \frac{8}{15} \cdot \frac{75}{32} = \frac{8 \cdot 75}{15 \cdot 32} = \frac{8 \cdot 15 \cdot 5}{15 \cdot 8 \cdot 4} = \frac{5}{4}\)
6) \(\frac{45}{56} : \frac{54}{49} = \frac{45}{56} \cdot \frac{49}{54} = \frac{45 \cdot 49}{56 \cdot 54} = \frac{5 \cdot 9 \cdot 7 \cdot 7}{8 \cdot 7 \cdot 6 \cdot 9} = \frac{5 \cdot 7}{8 \cdot 6} = \frac{35}{48}\)
7) \(\frac{9}{32} : 36 = \frac{9}{32} \cdot \frac{1}{36} = \frac{9}{32 \cdot 36} = \frac{9}{32 \cdot 9 \cdot 4} = \frac{1}{32 \cdot 4} = \frac{1}{128}\)
8) \(9 : \frac{3}{7} = 9 \cdot \frac{7}{3} = \frac{9 \cdot 7}{3} = \frac{3 \cdot 3 \cdot 7}{3} = 3 \cdot 7 = 21\)
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