How to Add Fractions With Unlike Denominators
Pennpaper Team
Adding fractions is one of the first math skills that feels different from whole-number arithmetic. The key is simple: fractions must describe equal-sized pieces before you can combine them.
Quick idea
A denominator names the size of the pieces. You can only add the numerators after both fractions use the same denominator.
Steps
- Find a common denominator. The least common denominator is best, but any shared multiple works.
- Rewrite each fraction as an equivalent fraction with that denominator.
- Add the numerators and keep the denominator the same.
- Simplify the answer if the numerator and denominator share a factor.
Worked example
Add one third and one fourth.
Full solution
Step-by-step walkthrough
Step 1
The denominators are 3 and 4, so use 12 as the common denominator.
Step 2
One third becomes four twelfths, and one fourth becomes three twelfths.
Step 3
Add 4 plus 3 to get 7 twelfths.
Common mistake
Do not add the denominators. One third plus one fourth is not two sevenths because thirds and fourths are different-sized pieces.
Practice problems
- Add 1/2 + 1/3.
- Add 2/5 + 1/10.
- Add 3/4 + 2/3.
Answers
- 5/6
- 1/2
- 17/12 or 1 5/12
Ask Pennpaper to explain it live
If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.