Выполните деление: a) \(\frac{4}{9} : \frac{3}{8}\); б) \(\frac{3}{7} : \frac{9}{14}\); в) \(\frac{86}{113} : \frac{43}{51}\); г) \(\frac{27}{64} : 9\); д) \(8 : \frac{2}{3}\); е) \(7 : 3\); ж) \(2\frac{1}{7}\); з) \(3\frac{3}{5}\)

Решение:

1. а) \(\frac{4}{9} : \frac{3}{8} = \frac{4}{9} \cdot \frac{8}{3} = \frac{32}{27}\)
2. б) \(\frac{3}{7} : \frac{9}{14} = \frac{3}{7} \cdot \frac{14}{9} = \frac{1}{1} \cdot \frac{2}{3} = \frac{2}{3}\)
3. в) \(\frac{86}{113} : \frac{43}{51} = \frac{86}{113} \cdot \frac{51}{43} = \frac{2 \cdot 43}{113} \cdot \frac{51}{43} = \frac{2 \cdot 51}{113} = \frac{102}{113}\)
4. г) \(\frac{27}{64} : 9 = \frac{27}{64} \cdot \frac{1}{9} = \frac{3 \cdot 9}{64} \cdot \frac{1}{9} = \frac{3}{64}\)
5. д) \(8 : \frac{2}{3} = 8 \cdot \frac{3}{2} = 4 \cdot 3 = 12\)
6. е) \(7 : 3 = \frac{7}{3} = 2\frac{1}{3}\)
7. ж) \(2\frac{1}{7} = \frac{2 \cdot 7 + 1}{7} = \frac{15}{7}\)
8. з) \(3\frac{3}{5} = \frac{3 \cdot 5 + 3}{5} = \frac{18}{5}\)

Ответ: а) \(\frac{32}{27}\); б) \(\frac{2}{3}\); в) \(\frac{102}{113}\); г) \(\frac{3}{64}\); д) 12; е) \(\frac{7}{3}\); ж) \(\frac{15}{7}\); з) \(\frac{18}{5}\)