How to use the Fraction Calculator
- Choose the operation you need.
- Enter the numerator and denominator of each fraction.
- Read the simplified result, mixed number and decimal together.
- For negative fractions, put the minus sign on the numerator.
How the calculation works
Addition and subtraction require a common denominator. The safe general method multiplies crosswise — a/b ± c/d = (a·d ± c·b)/(b·d) — which always works even though it can produce larger numbers than strictly necessary. Simplifying afterwards by the greatest common divisor gets you back to lowest terms, so the result is identical to the one you would reach using the least common denominator.
Multiplication is the straightforward case: numerators multiply, denominators multiply. Division is multiplication by the reciprocal, which is why dividing by 1/2 doubles a quantity rather than halving it — a result that reliably surprises people the first time they meet it in a recipe.
The final simplification divides both parts by their greatest common divisor, found with the Euclidean algorithm. A mixed number is then read off by integer division: the quotient is the whole part and the remainder stays over the denominator.
a/b + c/d = (ad + cb)/(bd) ; a/b ÷ c/d = (a·d)/(b·c) ; simplify by dividing both terms by gcdSource: Standard rational-number arithmetic; Euclidean algorithm for the greatest common divisor.
Worked example
A recipe needs 3/4 cup of flour and you are making one and a half batches.
- Set the operation to multiply.
- Enter 3/4 and 3/2.
- Numerators: 3 × 3 = 9. Denominators: 4 × 2 = 8.
- 9/8 simplifies no further; gcd is 1.
9/8 cups, which is 1 1/8 cups or 1.125 cups.
Frequently asked questions
Why is my answer already in lowest terms?+
The result is divided by the greatest common divisor automatically, so it is always fully simplified.
Can I enter mixed numbers?+
Convert them first with the mixed number calculator, or enter the improper form directly.
What happens if a denominator is zero?+
The result is undefined — division by zero has no value, and the decimal shows as a non-number.
How do I handle negatives?+
Enter the minus sign on the numerator. A negative denominator gives the same value but a confusing display.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.