How to add, subtract, multiply and divide fractions
Fractions follow four simple rules. To add or subtract, put both fractions over a common denominator, then add or subtract the numerators. To multiply, go straight across, top by top and bottom by bottom. To divide, flip the second fraction and multiply. This calculator does all four and reduces the answer to its lowest terms.
The formulas
Add or subtract: a/b then c/d = (a×d combined with c×b) / (b×d). Multiply: a/b × c/d = (a×c) / (b×d). Divide: a/b ÷ c/d = (a×d) / (b×c).
Two examples
1/2 + 1/3: the common denominator is 6, so it becomes 3/6 + 2/6 = 5/6.
2/3 ÷ 4/5: flip the second fraction and multiply, 2/3 × 5/4 = 10/12, which reduces to 5/6.
Common mistakes
The most common slip is adding the denominators, writing 1/2 + 1/3 as 2/5. You only add numerators, and only after finding a common denominator, never the denominators themselves. The other frequent miss is forgetting to reduce the final answer, for example leaving 10/12 instead of 5/6.
Frequently asked questions
How do I find a common denominator?
Multiply the two denominators together, or use their lowest common multiple for smaller numbers, then convert each fraction before adding or subtracting.
Does it simplify the answer?
Yes. The result is automatically reduced to lowest terms, so 10/12 is shown as 5/6.
Can I use negative fractions?
Yes. Enter a negative numerator for a negative fraction.
What about mixed numbers?
Convert a mixed number to an improper fraction first, for example 1 1/2 becomes 3/2.