Fraction Calculator
Add, subtract, multiply or divide two fractions — simplified automatically.
How to use the Fraction Calculator
- Enter the first fraction’s numerator and denominator.
- Choose the operation.
- Enter the second fraction and read the simplified result.
About the Fraction Calculator
Enter two fractions, choose an operation, and this calculator returns the answer in lowest terms, as a decimal, and — where it applies — as a mixed number. Multiplying and dividing are the easy cases: multiply straight across the tops and bottoms, or flip the second fraction and multiply to divide. Adding and subtracting need a common denominator, which it builds by cross-multiplying — a/b ± c/d becomes (a·d ± c·b) / (b·d) — so 1/2 + 1/3 turns into (3 + 2)/6.
Whatever the operation, that raw result is rarely in its simplest form: cross-multiplying 1/2 + 1/3 here lands on 10/12. So the tool divides the top and bottom by their greatest common divisor, which is why the reduced fraction — 5/6 — is what you see. If the answer is top-heavy it also splits off the whole part as a mixed number, and always shows the decimal for a quick sense of size.
A couple of inputs are refused on purpose: a denominator of zero is undefined, and you can’t divide by a fraction whose numerator is zero, so both raise an error rather than a nonsense answer. That reducing step is the same job done by the GCD and LCM calculator; to compare two quantities in lowest terms instead, the ratio calculator uses the very same simplification.
Frequently asked questions
How do you add two fractions with different denominators?
Give them a common denominator by cross-multiplying: for a/b + c/d the result is (a·d + c·b) over b·d. So 1/2 + 1/3 becomes (3 + 2)/6 = 5/6. Subtraction works the same way with a minus sign.
Why is the answer simplified automatically?
The raw result of cross-multiplying is usually not in lowest terms — 1/2 + 1/3 can come out as 10/12. Dividing the top and bottom by their greatest common divisor reduces it to 5/6, the standard way to write a fraction.
How do you multiply and divide fractions?
To multiply, multiply the numerators together and the denominators together. To divide, flip the second fraction and multiply. This tool does both and then simplifies the result.
What is the mixed number for?
When a fraction is top-heavy — bigger than one — it can be written as a whole number plus a proper fraction. 7/3, for example, is 2 1/3. The tool shows this whenever it applies.
Why won’t it accept a zero denominator?
A denominator of zero has no meaning — you can’t split something into zero parts — and dividing by a fraction that equals zero is undefined too. Both are rejected with an error rather than a wrong answer.