How to Add and Subtract Fractions (Common Denominators Made Easy)
Adding and subtracting fractions is easy once you understand common denominators. Learn what a common denominator is, how to find one, and how to simplify — with worked examples.
The most common stumbling block when adding or subtracting fractions is finding a common denominator. The good news: once the idea clicks, fraction arithmetic gets much simpler. In this guide we walk through why common denominators matter and how to find them, step by step.
Why do we need a common denominator?
A fraction tells you how many equal parts of a whole you have. For example, 1/2 means one part out of two, and 1/3 means one part out of three. When the denominators (the bottom numbers) are different, the parts are different sizes, so you cannot simply add or subtract them. It is like trying to add lengths measured on rulers with different-sized marks.
To fix this, we rewrite the fractions so they share the same denominator. This is called finding a common denominator. Once the denominators match, you are counting parts of the same size.
The steps
First, find the least common multiple of the two denominators. That becomes your common denominator. Then rewrite each fraction by multiplying its numerator and denominator by the same number so the denominator matches.
Let's try 1/2 + 1/3. The least common multiple of 2 and 3 is 6. Multiply 1/2 by 3/3 to get 3/6, and multiply 1/3 by 2/2 to get 2/6. Now both fractions share the denominator 6.
Finally, add the numerators: 3/6 + 2/6 = 5/6. Subtraction works the same way — find a common denominator first, then subtract the numerators.
Don't forget to simplify
After calculating, check whether the answer can be simplified. Simplifying means dividing the numerator and denominator by their greatest common divisor to reach the smallest possible form. For instance, 4/6 simplifies to 2/3 by dividing both by 2.
Common denominators use the least common multiple, and simplifying uses the greatest common divisor. These two ideas are the foundation of fraction arithmetic, so it helps to learn them together.
Check your work
Once you know the steps, practice by working problems out by hand and then checking your answers. Our fraction calculator shows not only the answer but also the common-denominator and simplification steps, so you can see exactly where a mistake happened.