78. Выполните деление: 1) \(\frac{5}{7}: \frac{4}{5}\); 2) \(\frac{6}{35}: \frac{18}{49}\); 3) \(\frac{27}{28}: \frac{9}{56}\); 4) \(\frac{28}{45}: \frac{63}{40}\)

Решим примеры на деление дробей.

1) \(\frac{5}{7}: \frac{4}{5} = \frac{5}{7} \cdot \frac{5}{4} = \frac{5 \cdot 5}{7 \cdot 4} = \frac{25}{28}\)

2) \(\frac{6}{35}: \frac{18}{49} = \frac{6}{35} \cdot \frac{49}{18} = \frac{6 \cdot 49}{35 \cdot 18} = \frac{6 \cdot 7 \cdot 7}{5 \cdot 7 \cdot 6 \cdot 3} = \frac{7}{5 \cdot 3} = \frac{7}{15}\)

3) \(\frac{27}{28}: \frac{9}{56} = \frac{27}{28} \cdot \frac{56}{9} = \frac{27 \cdot 56}{28 \cdot 9} = \frac{9 \cdot 3 \cdot 28 \cdot 2}{28 \cdot 9} = 3 \cdot 2 = 6\)

4) \(\frac{28}{45}: \frac{63}{40} = \frac{28}{45} \cdot \frac{40}{63} = \frac{28 \cdot 40}{45 \cdot 63} = \frac{4 \cdot 7 \cdot 8 \cdot 5}{9 \cdot 5 \cdot 9 \cdot 7} = \frac{4 \cdot 8}{9 \cdot 9} = \frac{32}{81}\)

Ответ: 1) \(\frac{25}{28}\); 2) \(\frac{7}{15}\); 3) 6; 4) \(\frac{32}{81}\)