453. Решите уравнение: 1) \(\frac{25}{27}x = \frac{5}{18}\); 2) \(\frac{13}{17}x = 39\); 3) \(4x = \frac{5}{7}\); 4) \(x : 2\frac{2}{15} = 1\frac{9}{16}\); 5) \(4\frac{4}{9} : x = \frac{5}{27}\); 6) \(1\frac{4}{9}x = 5,2\)

Решим уравнения: 1) $$\frac{25}{27}x = \frac{5}{18}$$ $$x = \frac{5}{18} \div \frac{25}{27}$$ $$x = \frac{5}{18} \cdot \frac{27}{25}$$ $$x = \frac{5 \cdot 27}{18 \cdot 25} = \frac{1 \cdot 3}{2 \cdot 5} = \frac{3}{10}$$ $$x = 0,3$$ 2) $$\frac{13}{17}x = 39$$ $$x = 39 \div \frac{13}{17}$$ $$x = 39 \cdot \frac{17}{13}$$ $$x = \frac{39 \cdot 17}{13} = \frac{3 \cdot 17}{1} = 51$$ $$x = 51$$ 3) $$4x = \frac{5}{7}$$ $$x = \frac{5}{7} \div 4$$ $$x = \frac{5}{7} \cdot \frac{1}{4}$$ $$x = \frac{5}{28}$$ 4) $$x : 2\frac{2}{15} = 1\frac{9}{16}$$ $$x : \frac{32}{15} = \frac{25}{16}$$ $$x = \frac{25}{16} \cdot \frac{32}{15}$$ $$x = \frac{25 \cdot 32}{16 \cdot 15} = \frac{5 \cdot 2}{1 \cdot 3} = \frac{10}{3}$$ $$x = 3\frac{1}{3}$$ 5) $$4\frac{4}{9} : x = \frac{5}{27}$$ $$\frac{40}{9} : x = \frac{5}{27}$$ $$x = \frac{40}{9} \div \frac{5}{27}$$ $$x = \frac{40}{9} \cdot \frac{27}{5}$$ $$x = \frac{40 \cdot 27}{9 \cdot 5} = \frac{8 \cdot 3}{1 \cdot 1} = 24$$ $$x = 24$$ 6) $$1\frac{4}{9}x = 5,2$$ $$\frac{13}{9}x = 5,2$$ $$x = 5,2 \div \frac{13}{9}$$ $$x = 5,2 \cdot \frac{9}{13}$$ $$x = \frac{5,2 \cdot 9}{13} = \frac{0,4 \cdot 9}{1} = 3,6$$ $$x = 3,6$$