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

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