Question

use properties of equal fractions to find numerical values of variables.
a. \\(\frac{1}{2} = \frac{x}{100}\\)
b. \\(\frac{1}{5} = \frac{x}{100}\\)
c. \\(\frac{7}{2x} = \frac{1}{6}\\)
d. \\(\frac{x}{10} = 0.6\\)
e. \\(\frac{3}{5} = \frac{12}{x}\\)
reminder:
if \\(\frac{a}{b} = \frac{k}{m}\\)
then \\(a \times m = b \times k\\)
\\(0.6 = \frac{6}{10}\\)
\\(0.06 = \frac{6}{100}\\)
\\(0.006 = \frac{6}{1000}\\)
\\(0.0006 = \frac{6}{10000}\\)

Explanation:

Step1: Solve Part A

Given \(\frac{1}{2}=\frac{x}{100}\), using the property \(a\times m = b\times k\) (where \(a = 1\), \(b = 2\), \(k = x\), \(m = 100\)), we get \(1\times100=2\times x\).
Simplify: \(100 = 2x\), then \(x=\frac{100}{2}=50\).

Step2: Solve Part B

For \(\frac{1}{5}=\frac{x}{100}\), apply the property: \(1\times100 = 5\times x\).
Simplify: \(100 = 5x\), so \(x=\frac{100}{5}=20\).

Step3: Solve Part C

Given \(\frac{7}{2x}=\frac{1}{6}\), use the property: \(7\times6=2x\times1\).
Simplify: \(42 = 2x\), then \(x=\frac{42}{2}=21\).

Step4: Solve Part D

For \(\frac{x}{10}=0.6\), rewrite \(0.6=\frac{6}{10}\), so \(\frac{x}{10}=\frac{6}{10}\). By equality of fractions, \(x = 6\).

Step5: Solve Part E

Given \(\frac{3}{5}=\frac{12}{x}\), apply the property: \(3\times x=5\times12\).
Simplify: \(3x = 60\), then \(x=\frac{60}{3}=20\).

Answer:

A. \(x = 50\)
B. \(x = 20\)
C. \(x = 21\)
D. \(x = 6\)
E. \(x = 20\)