Equations with Fractions and Decimals

Equations with fractions look scary, but there's a simple trick: multiply every term by the Least Common Denominator (LCD). This clears all fractions at once. The LCD is the smallest number that all denominators divide into evenly. Examples of LCDs: - Denominators 2 and 3 → LCD = 6 - Denominators 4 and 6 → LCD = 12 - Denominators 3, 4, and 6 → LCD = 12

Example: Solve frac{x}{3} + frac{x}{4} = 7

To clear decimals, multiply every term by 10, 100, or 1000 depending on the most decimal places in the equation. - 1 decimal place → multiply by 10 - 2 decimal places → multiply by 100 - 3 decimal places → multiply by 1000

Example: Solve 0.3x + 1.5 = 4.2