639. Выполните деление: a) 4/9 : 2/8; б) 3/7 : 9/14; в) 86/113 : 43/51; г) 27/64 д) 8: e) 7:

Решение:

1. $$\frac{4}{9} : \frac{2}{8} = \frac{4}{9} \cdot \frac{8}{2} = \frac{4 \cdot 8}{9 \cdot 2} = \frac{32}{18} = \frac{16}{9} = 1\frac{7}{9}$$
2. $$\frac{3}{7} : \frac{9}{14} = \frac{3}{7} \cdot \frac{14}{9} = \frac{3 \cdot 14}{7 \cdot 9} = \frac{42}{63} = \frac{2}{3}$$
3. $$\frac{86}{113} : \frac{43}{51} = \frac{86}{113} \cdot \frac{51}{43} = \frac{86 \cdot 51}{113 \cdot 43} = \frac{2 \cdot 43 \cdot 3 \cdot 17}{113 \cdot 43} = \frac{2 \cdot 3 \cdot 17}{113} = \frac{102}{113}$$
4. $$\frac{27}{64} : 8 = \frac{27}{64} : \frac{8}{1} = \frac{27}{64} \cdot \frac{1}{8} = \frac{27 \cdot 1}{64 \cdot 8} = \frac{27}{512}$$
5. $$7 : 1 = 7$$

Ответ:

1. $$1\frac{7}{9}$$
2. $$\frac{2}{3}$$
3. $$\frac{102}{113}$$
4. $$\frac{27}{512}$$
5. $$7$$