To add two fractions, give them the same denominator, add the numerators, and simplify the result. So 1/2 + 1/3 becomes 3/6 + 2/6 = 5/6. The fraction calculator does every step and shows the answer in lowest terms.
That is the whole method. Here it is worked through, with subtraction and mixed numbers covered too.
Why you need a common denominator
Fractions only add directly when their denominators match, because the denominator says what size the pieces are. Quarters and thirds are different-sized pieces, so you cannot add them as they stand. Rewriting both over a shared denominator turns them into pieces of the same size, which you can then count up.
The shared denominator can be any common multiple of the two denominators. The smallest one, the least common multiple, keeps the numbers tidy. For 2 and 3 the least common multiple is 6, so both fractions are rewritten over 6.
How to add fractions step by step
- Find a common denominator (the least common multiple of the two denominators).
- Rewrite each fraction over that denominator by multiplying the top and bottom by the same number.
- Add the numerators and keep the denominator.
- Simplify by dividing the top and bottom by their greatest common divisor.
Here are a few worked out:
| Sum | Common denominator | Rewritten | Added | Simplified |
|---|---|---|---|---|
| 1/2 + 1/3 | 6 | 3/6 + 2/6 | 5/6 | 5/6 |
| 1/4 + 1/4 | 4 | 1/4 + 1/4 | 2/4 | 1/2 |
| 2/3 + 1/6 | 6 | 4/6 + 1/6 | 5/6 | 5/6 |
| 3/4 + 5/6 | 12 | 9/12 + 10/12 | 19/12 | 1 7/12 |
That last one came out larger than a whole, so it is written as a mixed number. More on that below.
Subtracting fractions
Subtracting works exactly the same way, you just subtract the numerators instead of adding them. For 3/4 − 1/4 the denominators already match, so it is 2/4, which simplifies to 1/2. For 5/6 − 1/2, give them a common denominator of 6 to get 5/6 − 3/6 = 2/6, which simplifies to 1/3.
If the result comes out negative, that is fine: 1/4 − 3/4 is −2/4, or −1/2.
Simplifying the answer
Always reduce the final fraction to lowest terms by dividing the numerator and denominator by their greatest common divisor. So 6/8 becomes 3/4, and 4/2 becomes 2. If you are unsure of the greatest common divisor, the LCM and GCD calculator finds it, and the fraction calculator simplifies automatically.
Mixed numbers
A mixed number is a whole number next to a fraction, like 1 3/4. When a sum comes out as an improper fraction (top heavier than the bottom), you can write it as a mixed number by dividing. For 19/12, twelve goes into nineteen once with 7 left over, so 19/12 is 1 7/12.
To go the other way, multiply the whole number by the denominator and add the numerator: 1 7/12 is (1 × 12 + 7)/12 = 19/12. The fraction calculator shows both forms, so you can use whichever you need.