639. 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) \(2\frac{1}{7}:1\frac{11}{14}\); з) \(3\frac{3}{5}:1\frac{11}{25}\);

a)

$$\frac{4}{9}:\frac{3}{8} = \frac{4}{9} \cdot \frac{8}{3} = \frac{4 \cdot 8}{9 \cdot 3} = \frac{32}{27} = 1\frac{5}{27}$$

б)

$$\frac{3}{7}:\frac{9}{14} = \frac{3}{7} \cdot \frac{14}{9} = \frac{3 \cdot 14}{7 \cdot 9} = \frac{3 \cdot 2 \cdot 7}{7 \cdot 3 \cdot 3} = \frac{2}{3}$$

в)

$$\frac{86}{113}:\frac{43}{51} = \frac{86}{113} \cdot \frac{51}{43} = \frac{2 \cdot 43 \cdot 3 \cdot 17}{113 \cdot 43} = \frac{2 \cdot 3 \cdot 17}{113} = \frac{102}{113}$$

г)

$$\frac{27}{64}:9 = \frac{27}{64} \cdot \frac{1}{9} = \frac{27}{64 \cdot 9} = \frac{3 \cdot 9}{64 \cdot 9} = \frac{3}{64}$$

д)

$$8:\frac{2}{3} = 8 \cdot \frac{3}{2} = \frac{8 \cdot 3}{2} = \frac{4 \cdot 2 \cdot 3}{2} = 4 \cdot 3 = 12$$

е)

$$7:3 = \frac{7}{3} = 2\frac{1}{3}$$

ж)

$$2\frac{1}{7}:1\frac{11}{14} = \frac{15}{7} : \frac{25}{14} = \frac{15}{7} \cdot \frac{14}{25} = \frac{15 \cdot 14}{7 \cdot 25} = \frac{3 \cdot 5 \cdot 2 \cdot 7}{7 \cdot 5 \cdot 5} = \frac{3 \cdot 2}{5} = \frac{6}{5} = 1\frac{1}{5}$$

з)

$$3\frac{3}{5}:1\frac{11}{25} = \frac{18}{5} : \frac{36}{25} = \frac{18}{5} \cdot \frac{25}{36} = \frac{18 \cdot 25}{5 \cdot 36} = \frac{18 \cdot 5 \cdot 5}{5 \cdot 2 \cdot 18} = \frac{5}{2} = 2\frac{1}{2}$$

Ответ: a) \(1\frac{5}{27}\); б) \(\frac{2}{3}\); в) \(\frac{102}{113}\); г) \(\frac{3}{64}\); д) 12; е) \(2\frac{1}{3}\); ж) \(1\frac{1}{5}\); з) \(2\frac{1}{2}\).