Fractions, Decimals, Percents, and Ratios

Fractions, Decimals, Percents, and Ratios

Number sense and proportional reasoning form approximately 45% of the quantitative questions on the GED Mathematical Reasoning test.

Key Concepts & Conversion Rules

1. Converting Between Forms

• Fraction to Decimal: Divide numerator by denominator ($$\frac{3}{4} = 3 \div 4 = 0.75$$).
• Decimal to Percent: Multiply by 100 and add the % symbol ($$0.75 \times 100 = 75\%$$).
• Percent to Decimal: Divide by 100 and remove the % symbol ($$45\% = 0.45$$).

2. The Percent Equation

$$\text{Part} = \text{Percent (in decimal form)} \times \text{Whole}$$

3. Ratio and Proportion

A proportion states that two ratios are equal: $$\frac{a}{b} = \frac{c}{d} \implies a \cdot d = b \cdot c$$

Worked Example:

A worker earning $24.00 per hour receives an 8% pay raise. What is their new hourly wage?

1. Calculate raise amount: $$24.00 \times 0.08 = 1.92$$
2. Add to base wage: $$24.00 + 1.92 = \$25.92$$ per hour.