Fraction Calculator · Practical guide
How to Add Fractions with Different Denominators
Convert both fractions to a shared denominator, add the numerators, then simplify — with worked examples below.
At a glance
The Short Answer
To add fractions with different denominators, rewrite both fractions over a common denominator, add the new numerators, and simplify. For example, 3/4 + 2/3 becomes 9/12 + 8/12 = 17/12, or 1 5/12 (about 1.416667). The calculator above does all of this and shows each step.
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Enter your own values, then compare the result with the examples below.
Result
The Formula
For fractions a/b and c/d, addition is:
a/b + c/d = (a·d + b·c) / (b·d)
You multiply each fraction's numerator by the other fraction's denominator, add the results, and place the sum over the product of the denominators.
Worked Example: 3/4 + 2/3
- Common denominator: 4 × 3 = 12
- Convert: 3/4 = 9/12 and 2/3 = 8/12
- Add numerators: 9 + 8 = 17, giving 17/12
- 17 and 12 share no common factor, so 17/12 is already in lowest terms
Using the Least Common Denominator
The product of the denominators always works, but the least common denominator (the LCM of the two denominators) keeps numbers small. For 1/6 + 3/4, the LCD is 12 instead of 24: 2/12 + 9/12 = 11/12 ≈ 0.916667. Using the product (24) gives 10/24 + 18/24 = 28/24, which simplifies to the same 11/12 — so either route lands on the identical answer.
Common Mistakes to Avoid
- Adding numerators and denominators straight across (1/2 + 1/3 is not 2/5).
- Forgetting to multiply the numerator when you scale the denominator.
- Skipping the final simplification step — always divide by the greatest common divisor.
Frequently Asked Questions
What if the denominators are already the same?
Just add the numerators and keep the denominator, then simplify. For example, 2/7 + 3/7 = 5/7, no conversion needed.
Can I add more than two fractions at once?
Yes. Convert all of them to one common denominator, add all the numerators, and simplify. With this calculator, add two at a time and feed each result into the next addition.
How do I add a fraction and a whole number?
Treat the whole number as a fraction over 1. For example, 2 + 3/4 = 8/4 + 3/4 = 11/4 = 2 3/4.
What about adding negative fractions?
The rules are identical — a negative fraction simply subtracts. The calculator accepts negative numerators and denominators and handles the signs automatically.