5.24 Найдите х из пропорции: 1) 2,5x : 14 = : 30; 2) 36: 35 = : 1

Ответ: 1) \(x = \frac{14}{75}\); 2) \(x = \frac{7}{72}\)

1. 1) 2,5x : 14 = \(\frac{1}{7}\) : 30
   • Представим 2,5 в виде обыкновенной дроби: 2,5 = \(\frac{5}{2}\)
   • \(\frac{5}{2}\)x = \(\frac{14 \cdot 1}{7 \cdot 30}\)
   • \(\frac{5}{2}\)x = \(\frac{14}{210}\)
   • \(\frac{5}{2}\)x = \(\frac{1}{15}\)
   • x = \(\frac{1 \cdot 2}{15 \cdot 5}\)
   • x = \(\frac{2}{75}\)
2. 2) 36 : 35 = \(\frac{1}{5}\)x : \(\frac{1}{12}\)
• \(\frac{36}{35}\) = \(\frac{x}{5} \cdot \frac{12}{1}\)
• \(\frac{36}{35}\) = \(\frac{12x}{5}\)
• x = \(\frac{36 \cdot 5}{35 \cdot 12}\)
• x = \(\frac{3 \cdot 1}{7 \cdot 1}\)
• x = \(\frac{3}{7}\)

Ответ: 1) \(x = \frac{14}{75}\); 2) \(x = \frac{7}{72}\)