4.338 Решите уравнение: а) 1 3/4 : 3,75 = 4x : 15; б) 2 1/3 : 13 = 1/3 x : 4 1/3.

Решение: a) \(1\frac{3}{4} : 3,75 = 4x : 15\) \(\frac{7}{4} : \frac{15}{4} = 4x : 15\) \(\frac{7}{4} \cdot \frac{4}{15} = 4x : 15\) \(\frac{7}{15} = 4x : 15\) \(4x = 7\) \(x = \frac{7}{4} = 1\frac{3}{4}\) б) \(2\frac{1}{3} : 13 = \frac{1}{3}x : 4\frac{1}{3}\) \(\frac{7}{3} : 13 = \frac{1}{3}x : \frac{13}{3}\) \(\frac{7}{3 \cdot 13} = \frac{1}{3}x : \frac{13}{3}\) \(\frac{7}{39} = \frac{x}{3} \cdot \frac{3}{13}\) \(\frac{7}{39} = \frac{x}{13}\) \(x = \frac{7 \cdot 13}{39} = \frac{7}{3} = 2\frac{1}{3}\) Ответ: a) \(x = 1\frac{3}{4}\) б) \(x = 2\frac{1}{3}\)