1059 Найти неизвестный член пропорции: 1) 10 : \( \frac{1}{8} \) = x : \( 1\frac{1}{4} \); 2) x : 0,75 = 9\( \frac{1}{2} \) : 14\( \frac{1}{4} \), 3) \( \frac{x}{15} = \frac{1.456}{1.05} \)

Решение:

1) \( 10 : \frac{1}{8} = x : 1\frac{1}{4} \)

\( 10 \cdot \frac{1}{8} \) = \( x \cdot 1\frac{1}{4} \)

\( \frac{10}{8} = x \cdot \frac{5}{4} \)

\( \frac{5}{4} = x \cdot \frac{5}{4} \)

\( x = \frac{5}{4} : \frac{5}{4} = 1 \)

2) \( x : 0.75 = 9\frac{1}{2} : 14\frac{1}{4} \)

\( x \cdot 14\frac{1}{4} = 0.75 \cdot 9\frac{1}{2} \)

\( x \cdot \frac{57}{4} = \frac{3}{4} \cdot \frac{19}{2} \)

\( x \cdot \frac{57}{4} = \frac{57}{8} \)

\( x = \frac{57}{8} : \frac{57}{4} = \frac{57}{8} \cdot \frac{4}{57} = \frac{1}{2} = 0.5 \)

3) \( \frac{x}{15} = \frac{1.456}{1.05} \)

\( x \cdot 1.05 = 15 \cdot 1.456 \)

\( x \cdot 1.05 = 21.84 \)

\( x = 21.84 : 1.05 = 20.8 \)

Ответ: 1) 1; 2) 0.5; 3) 20.8.