How to Add Fractions with Different Denominators
Adding fractions with different denominators involves a few clear steps. Here's a simple guide to help you:
Step 1: Find the Least Common Denominator (LCD)
- The denominator is the bottom number of a fraction.
- To add fractions, their denominators must be the same.
- Find the least common denominator, which is the smallest number that both denominators can divide into evenly.
Step 2: Convert Fractions to Equivalent Fractions
- Change each fraction to an equivalent fraction with the LCD as the new denominator.
- To do this, multiply both the numerator (top number) and denominator of each fraction by the number needed to get the LCD.
Step 3: Add the Numerators
- Now that the denominators are the same, add the numerators together.
- Keep the denominator the same.
Step 4: Simplify the Fraction
- If possible, simplify the resulting fraction by dividing the numerator and denominator by their greatest common divisor (GCD).
Example
Add 23\frac{2}{3}32 and 14\frac{1}{4}41:
- Find the LCD of 3 and 4, which is 12.
- Convert fractions:
- 23=2×43×4=812\frac{2}{3}=\frac{2\times 4}{3\times 4}=\frac{8}{12}32=3×42×4=128
- 14=1×34×3=312\frac{1}{4}=\frac{1\times 3}{4\times 3}=\frac{3}{12}41=4×31×3=123
- Add numerators:
- 8+3=118+3=118+3=11
- Result:
- 1112\frac{11}{12}1211 (already simplified)
If you want, I can provide more examples or practice problems!
