5.558 Найдите частное: а) \frac{7}{9}:\frac{7}{18}; б) \frac{1}{4}:\frac{1}{3}; в) \frac{3}{4}:\frac{7}{9}; г) \frac{3}{7}:\frac{1}{14}; д) \frac{6}{11}:6; е) \frac{9}{13}:3; ж) \frac{5}{7}:\frac{1}{7}; з) \frac{15}{22}:5.

Решение:

1. a) $$\frac{7}{9}:\frac{7}{18} = \frac{7}{9} \cdot \frac{18}{7} = \frac{7 \cdot 18}{9 \cdot 7} = \frac{18}{9} = 2$$
2. б) $$\frac{1}{4}:\frac{1}{3} = \frac{1}{4} \cdot \frac{3}{1} = \frac{1 \cdot 3}{4 \cdot 1} = \frac{3}{4}$$
3. в) $$\frac{3}{4}:\frac{7}{9} = \frac{3}{4} \cdot \frac{9}{7} = \frac{3 \cdot 9}{4 \cdot 7} = \frac{27}{28}$$
4. г) $$\frac{3}{7}:\frac{1}{14} = \frac{3}{7} \cdot \frac{14}{1} = \frac{3 \cdot 14}{7 \cdot 1} = \frac{3 \cdot 2}{1 \cdot 1} = 6$$
5. д) $$\frac{6}{11}:6 = \frac{6}{11} \cdot \frac{1}{6} = \frac{6 \cdot 1}{11 \cdot 6} = \frac{1}{11}$$
6. е) $$\frac{9}{13}:3 = \frac{9}{13} \cdot \frac{1}{3} = \frac{9 \cdot 1}{13 \cdot 3} = \frac{3 \cdot 1}{13 \cdot 1} = \frac{3}{13}$$
7. ж) $$\frac{5}{7}:\frac{1}{7} = \frac{5}{7} \cdot \frac{7}{1} = \frac{5 \cdot 7}{7 \cdot 1} = \frac{5}{1} = 5$$
8. з) $$\frac{15}{22}:5 = \frac{15}{22} \cdot \frac{1}{5} = \frac{15 \cdot 1}{22 \cdot 5} = \frac{3 \cdot 1}{22 \cdot 1} = \frac{3}{22}$$

Ответ:

1. a) 2
2. б) $$\frac{3}{4}$$
3. в) $$\frac{27}{28}$$
4. г) 6
5. д) $$\frac{1}{11}$$
6. е) $$\frac{3}{13}$$
7. ж) 5
8. з) $$\frac{3}{22}$$