146. Решите уравнение: a) \(\frac{7}{12}:y = \frac{2}{3}\); б) \(1\frac{3}{7}z + \frac{7}{8} = 1\frac{3}{8}\); в) \(\frac{7}{9}x - \frac{5}{18}x + \frac{1}{4}x = \frac{1}{6}\).

а) \(\frac{7}{12}:y = \frac{2}{3}\)

\(y = \frac{7}{12} : \frac{2}{3}\)

\(y = \frac{7}{12} \cdot \frac{3}{2}\)

\(y = \frac{7}{4 \cdot 2} = \frac{7}{8}\)

Ответ: \(\frac{7}{8}\)

б) \(1\frac{3}{7}z + \frac{7}{8} = 1\frac{3}{8}\)

\(\frac{10}{7}z = 1\frac{3}{8} - \frac{7}{8}\)

\(\frac{10}{7}z = \frac{11}{8} - \frac{7}{8}\)

\(\frac{10}{7}z = \frac{4}{8} = \frac{1}{2}\)

\(z = \frac{1}{2} : \frac{10}{7}\)

\(z = \frac{1}{2} \cdot \frac{7}{10}\)

\(z = \frac{7}{20}\)

Ответ: \(\frac{7}{20}\)

в) \(\frac{7}{9}x - \frac{5}{18}x + \frac{1}{4}x = \frac{1}{6}\)

\(\frac{28x - 10x + 9x}{36} = \frac{1}{6}\)

\(\frac{27x}{36} = \frac{1}{6}\)

\(\frac{3x}{4} = \frac{1}{6}\)

\(3x = \frac{4}{6} = \frac{2}{3}\)

\(x = \frac{2}{3} : 3\)

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

Ответ: \(\frac{2}{9}\)