Fraction calculator
Enter two fractions and pick an operation. The calculator combines them, reduces the result to its simplest form, and shows the decimal and mixed-number equivalents.
Use it to add, subtract, multiply, or divide fractions and see the answer fully simplified.
Result
5/6
- Decimal
- 0.8333
- Mixed number
- 5/6
The result updates as you type. The headline is the simplified fraction; the others give the decimal value and the mixed-number form.
How does it work?
Add and subtract over a common denominator; multiply across; divide by flipping the second fraction. The result is reduced with the greatest common divisor.
Fraction operations
- a, c
- The numerators of the two fractions.
- b, d
- The denominators of the two fractions.
1/2 + 1/3 = (1×3 + 1×2) / (2×3) = 5/6 ≈ 0.833. To divide, multiply by the reciprocal of the second fraction.
Method & sources
Numerators are integers; denominators are positive integers. Add and subtract use a common denominator; multiply and divide go across. The result is reduced with the greatest common divisor.
Sources
Where this method comes from — use these references to understand the formula, assumptions, and limits.
- Fractions — mathematical operations — National Institute of Standards and Technology, verified 2026-06-10
How we calculate
- Numerators are integers; denominators are positive integers.
- Add and subtract use a common denominator; multiply and divide go across.
- The result is reduced with the greatest common divisor.
- Dividing by a zero fraction is undefined.
Rounding
The fraction result is exact; the decimal is shown to four places. The calculation uses full precision.
What this calculator does
Fraction arithmetic has different rules for each operation. This calculator handles them all: a common denominator for adding and subtracting, multiplying across for products, and flipping the second fraction for division — then it reduces the answer.
How to use it
- Enter the first numerator and denominator.
- Pick an operation: add, subtract, multiply, or divide.
- Enter the second numerator and denominator.
- Read the simplified fraction, decimal, and mixed number.
A worked example
1/2 + 1/3 uses a common denominator of 6: 3/6 + 2/6 = 5/6, which is about 0.833 and stays as 5/6 since it's already in lowest terms.
Reducing and mixed numbers
The result is always reduced using the greatest common divisor, so 4/8 becomes 1/2. If the fraction is top-heavy, the mixed-number form shows it as a whole number plus a fraction, like 7/3 = 2 1/3.
Common mistakes
- Adding numerators and denominators directly without a common denominator.
- Entering a denominator of zero, which has no value.
- Forgetting that dividing flips the second fraction.
When it's useful
For homework, cooking and recipe scaling, measurements, or any time you need an exact fraction rather than a rounded decimal.
FAQ
- How do you add two fractions?
- Put them over a common denominator, add the numerators, then reduce. 1/2 + 1/3 = 3/6 + 2/6 = 5/6.
- How do you divide fractions?
- Multiply the first fraction by the reciprocal (flip) of the second. Dividing by 2/3 is the same as multiplying by 3/2.
- What does 'simplified' mean?
- The fraction is divided by the greatest common divisor of its numerator and denominator, so 6/8 becomes 3/4.
- What is a mixed number?
- A whole number plus a proper fraction. An improper fraction like 7/3 becomes the mixed number 2 1/3.
- Can the result be negative?
- Yes. Enter a negative numerator, or subtract a larger fraction, and the result carries the sign.
- Can I share a calculation?
- Yes. Use Share to copy a link that reopens the calculator with the same fractions and operation.
Related calculators
Embed this calculator
Add this calculator to your own site. The snippet includes the calculator iframe and a small attribution link:
<iframe src="https://wisecalcs.com/embed/en/fraction-calculator" width="100%" height="520" style="border:0" loading="lazy"></iframe>
<p>Calculator from <a href="https://wisecalcs.com/en/math/fraction-calculator">WiseCalcs</a></p>