3. Решите уравнение: 1) 5/13 x = 2/13; 2) 8/9 x = 1; 3) 6/7 x = 24; 4) 7x = 3/4; 5) x : 3/11 = 22/27; 6) 15/52 : x = 5/13.

Решим уравнения.

1. $$\frac{5}{13}x = \frac{2}{13}$$ $$x = \frac{2}{13} : \frac{5}{13}$$ $$x = \frac{2}{13} \times \frac{13}{5} = \frac{2 \times 13}{13 \times 5} = \frac{2}{5}$$
2. $$\frac{8}{9}x = 1$$ $$x = 1 : \frac{8}{9}$$ $$x = 1 \times \frac{9}{8} = \frac{9}{8} = 1 \frac{1}{8}$$
3. $$\frac{6}{7}x = 24$$ $$x = 24 : \frac{6}{7}$$ $$x = 24 \times \frac{7}{6} = \frac{24 \times 7}{6} = \frac{6 \times 4 \times 7}{6} = 4 \times 7 = 28$$
4. $$7x = \frac{3}{4}$$ $$x = \frac{3}{4} : 7$$ $$x = \frac{3}{4} \times \frac{1}{7} = \frac{3}{28}$$
5. $$x : \frac{3}{11} = \frac{22}{27}$$ $$x = \frac{22}{27} \times \frac{3}{11} = \frac{22 \times 3}{27 \times 11} = \frac{11 \times 2 \times 3}{9 \times 3 \times 11} = \frac{2}{9}$$
6. $$\frac{15}{52} : x = \frac{5}{13}$$ $$x = \frac{15}{52} : \frac{5}{13}$$ $$x = \frac{15}{52} \times \frac{13}{5} = \frac{15 \times 13}{52 \times 5} = \frac{3 \times 5 \times 13}{4 \times 13 \times 5} = \frac{3}{4}$$

Ответ: 1) 2/5; 2) 9/8; 3) 28; 4) 3/28; 5) 2/9; 6) 3/4