4.338 Решите уравнение: а) 1\(\frac{3}{4}\) : 3,75 = 4x : 15; б) \(\frac{1}{2}\) : 13 = \(\frac{1}{3}\)x : 4\(\frac{1}{3}\).

Ответ: a) x = 1,25; б) x = 0,048

Решение:

1. a) \(1\frac{3}{4} : 3,75 = 4x : 15\)
   • \(\frac{7}{4} : \frac{15}{4} = \frac{4x}{15}\)
   • \(\frac{7}{4} \cdot \frac{4}{15} = \frac{4x}{15}\)
   • \(\frac{7}{15} = \frac{4x}{15}\)
   • \(4x = 7\)
   • \(x = \frac{7}{4} = 1,75\)
2. б) \(\frac{1}{2} : 13 = \frac{1}{3}x : 4\frac{1}{3}\)
   • \(\frac{1}{2} : 13 = \frac{1}{26}\)
   • \(\frac{1}{3}x : \frac{13}{3} = \frac{x}{3} \cdot \frac{3}{13} = \frac{x}{13}\)
   • \(\frac{1}{26} = \frac{x}{13}\)
   • \(x = \frac{13}{26} = \frac{1}{2} = 0,5\)

Ответ: a) x = 1,75; б) x = 0,5