Subjects algebra

Percents Proportions Ce9Aed

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. The problem is to understand how to work with percents and proportional fractions. 2. Percent means "per hundred," so $x\%$ means $\frac{x}{100}$. 3. Proportional fractions mean two ratios or fractions are equal, for example, $\frac{a}{b} = \frac{c}{d}$. 4. To solve problems with percents, convert the percent to a fraction or decimal first. 5. For example, to find 25% of 80, write $25\% = \frac{25}{100} = 0.25$. 6. Then multiply: $0.25 \times 80 = 20$. 7. For proportional fractions, if $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$. 8. Example: If $\frac{3}{x} = \frac{6}{8}$, cross multiply: $3 \times 8 = 6 \times x$. 9. Simplify: $24 = 6x$. 10. Divide both sides by 6: $$\frac{\cancel{24}}{\cancel{6}} = \frac{6x}{6} \Rightarrow 4 = x$$. 11. So, $x = 4$. This shows how to convert percents to fractions and solve proportional fraction problems step-by-step.