Решите уравнение: 1) \(\frac{8}{9}x = \frac{2}{9};\) 2) \(\frac{5}{9}x = 1;\) 3) \(\frac{4}{7}x = 16;\) 4) \(5x = \frac{4}{5};\) 5) \(x : \frac{9}{16} = \frac{32}{45};\) 6) \(\frac{25}{42} : x = \frac{5}{6}.\)

Ответ: 1) \(x = \frac{1}{4}\); 2) \(x = \frac{9}{5}\); 3) \(x = 28\); 4) \(x = \frac{4}{25}\); 5) \(x = \frac{2}{5}\); 6) \(x = \frac{5}{7}\)

Решение:

1. \(\frac{8}{9}x = \frac{2}{9}\)
\(x = \frac{2}{9} : \frac{8}{9}\) \(x = \frac{2}{9} \cdot \frac{9}{8}\) \(x = \frac{2 \cdot 9}{9 \cdot 8}\) \(x = \frac{1}{4}\)
2. \(\frac{5}{9}x = 1\)
\(x = 1 : \frac{5}{9}\) \(x = 1 \cdot \frac{9}{5}\) \(x = \frac{9}{5}\)
3. \(\frac{4}{7}x = 16\)
\(x = 16 : \frac{4}{7}\) \(x = 16 \cdot \frac{7}{4}\) \(x = \frac{16 \cdot 7}{4}\) \(x = 4 \cdot 7 = 28\)
4. \(5x = \frac{4}{5}\)
\(x = \frac{4}{5} : 5\) \(x = \frac{4}{5} \cdot \frac{1}{5}\) \(x = \frac{4}{25}\)
5. \(x : \frac{9}{16} = \frac{32}{45}\)
\(x = \frac{32}{45} \cdot \frac{9}{16}\) \(x = \frac{32 \cdot 9}{45 \cdot 16}\) \(x = \frac{2 \cdot 1}{5 \cdot 1}\) \(x = \frac{2}{5}\)
6. \(\frac{25}{42} : x = \frac{5}{6}\)
\(x = \frac{25}{42} : \frac{5}{6}\) \(x = \frac{25}{42} \cdot \frac{6}{5}\) \(x = \frac{25 \cdot 6}{42 \cdot 5}\) \(x = \frac{5 \cdot 1}{7 \cdot 1}\) \(x = \frac{5}{7}\)

Ответ: 1) \(x = \frac{1}{4}\); 2) \(x = \frac{9}{5}\); 3) \(x = 28\); 4) \(x = \frac{4}{25}\); 5) \(x = \frac{2}{5}\); 6) \(x = \frac{5}{7}\)