78. Выполните деление: 1) \(\frac{5}{6} : \frac{4}{7}\); 2) \(\frac{6}{35} : \frac{48}{49}\); 3) \(\frac{8}{15} : \frac{32}{75}\); 4) \(\frac{45}{56} : \frac{54}{49}\)

**Решение:** 1) \(\frac{5}{6} : \frac{4}{7} = \frac{5}{6} \cdot \frac{7}{4} = \frac{5 \cdot 7}{6 \cdot 4} = \frac{35}{24} = 1\frac{11}{24}\) 2) \(\frac{6}{35} : \frac{48}{49} = \frac{6}{35} \cdot \frac{49}{48} = \frac{6 \cdot 49}{35 \cdot 48} = \frac{1 \cdot 7}{5 \cdot 8} = \frac{7}{40}\) 3) \(\frac{8}{15} : \frac{32}{75} = \frac{8}{15} \cdot \frac{75}{32} = \frac{8 \cdot 75}{15 \cdot 32} = \frac{1 \cdot 5}{1 \cdot 4} = \frac{5}{4} = 1\frac{1}{4}\) 4) \(\frac{45}{56} : \frac{54}{49} = \frac{45}{56} \cdot \frac{49}{54} = \frac{45 \cdot 49}{56 \cdot 54} = \frac{5 \cdot 7}{8 \cdot 6} = \frac{35}{48}\) **Ответ:** 1) \(1\frac{11}{24}\); 2) \(\frac{7}{40}\); 3) \(1\frac{1}{4}\); 4) \(\frac{35}{48}\)