How to Add and Subtract Fractions: Common Denominator, Combine, Simplify
Published 12/15/2025 · 3 min read · Everyday calculators
To add or subtract fractions, give them a common denominator, then add or subtract the numerators while keeping that denominator, and simplify. For 1/3 + 1/4, the common denominator is 12: rewrite as 4/12 + 3/12 = 7/12, which is already in lowest terms. For 5/6 − 1/4, use 12 again: 10/12 − 3/12 = 7/12. If the result shares a common factor with its denominator, divide both by it to simplify.
You can only add or subtract fractions that share a denominator. Learn to find a common denominator, combine the numerators, and simplify the result, with a worked example.
Why you need a common denominator
A fraction's denominator names the size of each piece, and the numerator counts how many pieces you have. You can only add counts of the same-size piece — thirds and quarters are different sizes, so 1/3 + 1/4 is not 2/7. First both fractions must be re-cut into pieces of one common size.
The common denominator is that shared piece size. The least common multiple of 3 and 4 is 12, so twelfths work for both: a third is 4 twelfths and a quarter is 3 twelfths. Any common multiple works, but the smallest keeps the numbers manageable.
Worked example: 1/3 + 1/4
The denominators are 3 and 4, whose least common multiple is 12. Rewrite each fraction over 12: multiply 1/3 by 4/4 to get 4/12, and multiply 1/4 by 3/3 to get 3/12. Now both are twelfths, so you can combine them.
Add the numerators and keep the denominator: 4/12 + 3/12 = 7/12. Check whether it simplifies — 7 is prime and does not divide 12, so 7/12 is already in lowest terms. That is the final answer.
Subtracting and simplifying
Subtraction works the same way. For 5/6 − 1/4, the least common multiple of 6 and 4 is 12. Rewrite 5/6 as 10/12 and 1/4 as 3/12, then subtract: 10/12 − 3/12 = 7/12. Again 7/12 is already simplified.
When a result does need reducing, divide top and bottom by their greatest common factor. For example 8/12 shares a factor of 4, so 8/12 = 2/3. Always finish by checking whether the numerator and denominator have a common factor greater than 1.
Worked with our own calculator
Fraction Calculator
Given
- First numerator
- 2
- First denominator
- 4
- Operation
- Subtract (−)
- Second numerator
- 2
- Second denominator
- 6
Result
- Result numerator
- 1
- Result denominator
- 6
- Decimal value
- 0.167
These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.
Run it on your own figures →Frequently asked questions
- Do I always need the least common multiple?
- No. Multiplying the two denominators together always gives a valid common denominator. The least common multiple just keeps the numbers smaller and reduces later simplifying.
- How do I add a whole number to a fraction?
- Write the whole number as a fraction over the same denominator. To add 2 + 1/4, write 2 as 8/4, then 8/4 + 1/4 = 9/4.
- What if the answer is bigger than 1?
- That is fine — it is an improper fraction like 9/4. You can leave it that way or convert it to a mixed number: 9/4 = 2 and 1/4.
- Can I subtract a larger fraction from a smaller one?
- Yes — the result is simply negative. For 1/4 − 5/6 use twelfths: 3/12 − 10/12 = −7/12. The method is identical; only the sign changes.
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