13. Решите пропорции: 1) x : 12 = 4 3/4 : 7 1/8; 2) 6 1/2 : x = 6 5/6 : 4,1; 3) 3 1/5 : x : 1,5 = 4 2/7 : 3/14; 4) 8 1/19 : 1 1/2 = 2 3/6 : 0,8x

1) \(x:12=4\frac{3}{4}:7\frac{1}{8}\).

\(x=12\cdot\frac{4\frac{3}{4}}{7\frac{1}{8}}=12\cdot\frac{19/4}{57/8}=12\cdot\frac{2}{3}=8\).

2) \(6\frac{1}{2}:x=6\frac{5}{6}:4.1\).

\(\frac{13/2}{x}=\frac{41/6}{41/10}=\frac{5}{3}\), поэтому \(x=\frac{13}{2}\cdot\frac{3}{5}=\frac{39}{10}=3.9\).

3) \(3\frac{1}{5}:x:1.5=4\frac{2}{7}:\frac{3}{14}\). По свойству пропорции: \(\frac{3\frac{1}{5}}{x}=\frac{4\frac{2}{7}}{\frac{3}{14}}\cdot1.5\).

\(\frac{16/5}{x}=\frac{30/7}{3/14}\cdot\frac{3}{2}=20\), откуда \(x=\frac{16}{100}=\frac{4}{25}=0.16\).

4) \(8\frac{1}{19}:1\frac{1}{2}=2\frac{3}{6}:0.8x\).

\(\frac{153/19}{3/2}=\frac{5/2}{0.8x}\). Левая часть равна \(\frac{102}{19}\), поэтому \(0.8x=\frac{5/2}{102/19}=\frac{95}{204}\).

\(x=\frac{95}{204}\cdot\frac{5}{4}=\frac{475}{816}\).

Ответ: 1) \(x=8\); 2) \(x=3.9\); 3) \(x=0.16\); 4) \(x=\frac{475}{816}\).