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

1) \(\frac{8}{9}x = \frac{2}{9};\)

\(x = \frac{2}{9} : \frac{8}{9}\)

\(x = \frac{2}{9} \cdot \frac{9}{8}\)

\(x = \frac{2 \cdot 9}{9 \cdot 8}\)

\(x = \frac{1 \cdot 1}{1 \cdot 4}\)

\(x = \frac{1}{4}\)

Ответ: \(\frac{1}{4}\)

3) \(\frac{4}{7}x = 16;\)

\(x = 16 : \frac{4}{7}\)

\(x = 16 \cdot \frac{7}{4}\)

\(x = \frac{16 \cdot 7}{4}\)

\(x = \frac{4 \cdot 7}{1}\)

\(x = 28\)

Ответ: 28

5) \(x \cdot \frac{9}{16} = \frac{32}{45}\)

\(x = \frac{32}{45} : \frac{9}{16}\)

\(x = \frac{32}{45} \cdot \frac{16}{9}\)

\(x = \frac{32 \cdot 16}{45 \cdot 9}\)

\(x = \frac{512}{405}\)

\(x = 1\frac{107}{405}\)

Ответ: \(1\frac{107}{405}\)