Guide
How to Add Fractions with Different Denominators
Adding fractions with unlike denominators comes down to one idea: make the bottoms match, then add the tops.
You can't add fractions directly when their denominators are different, because the pieces aren't the same size. The fix is to rewrite both fractions over a common denominator so every piece is the same size, then add the numerators.
Step by step
- 1Find the least common denominator (LCD)
The LCD is the smallest number both denominators divide into. For 1/3 and 1/4, the LCD is 12. - 2Rewrite each fraction over the LCD
Multiply the top and bottom of each fraction by whatever turns its denominator into the LCD. So 1/3 = 4/12 and 1/4 = 3/12. - 3Add the numerators
Keep the common denominator and add the tops: 4/12 + 3/12 = 7/12. - 4Simplify
Reduce the answer to lowest terms if possible. 7/12 is already in lowest terms.
Worked example
Add 1/3 + 1/4. The LCD of 3 and 4 is 12. Rewrite as 4/12 + 3/12. Add the numerators: 4 + 3 = 7. The answer is 7/12.
Common mistakes to avoid
- Adding the denominators too (1/3 + 1/4 is not 2/7).
- Forgetting to multiply the numerator when you change the denominator.
- Forgetting to simplify the final answer.
Practice this skill
Try it yourself on the Add Fractions Calculator, generate a printable worksheet, or work through it one step at a time in guided practice.
Frequently asked
What is the first step to add fractions with different denominators?
Find the least common denominator — the smallest number both denominators divide into — then rewrite each fraction over it.
Do you add the denominators when adding fractions?
No. Once both fractions share a common denominator, you add only the numerators and keep the denominator the same.
Can I use the butterfly method instead?
Yes — cross-multiplying (the butterfly method) is a shortcut that also works for two fractions, though it doesn't always give the least common denominator.