What the fraction calculator does
The fraction calculator adds, subtracts, multiplies or divides two fractions and shows the answer in simplified form, as a decimal, and as a mixed number when relevant. It also walks through the steps — finding a common denominator, multiplying numerators and denominators, taking the reciprocal for division, and reducing the result using the greatest common divisor. It's a fast checker for homework and a clean explainer for anyone learning the rules from scratch.
The four operations on fractions
- Addition / subtraction. Convert to a common denominator, then add or subtract the numerators. For 1/2 + 1/3, the lowest common denominator is 6, so the sum is 3/6 + 2/6 = 5/6.
- Multiplication. Multiply across the top and across the bottom. 2/3 × 4/5 = 8/15.
- Division. Multiply by the reciprocal (flip the second fraction). 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12, which simplifies to 5/6.
- Simplification. Divide numerator and denominator by their greatest common divisor (GCD). 10/12 has GCD 2, giving 5/6.
Finding the GCD
The greatest common divisor of two integers is the largest number that divides both with no remainder. The classical Euclidean algorithm finds it in seconds: keep replacing the larger number with its remainder when divided by the smaller, until the remainder is zero. GCD(12, 8) → GCD(8, 4) → GCD(4, 0) = 4. This calculator uses that algorithm to simplify every result.
Mixed numbers and improper fractions
A mixed number like 2 1/4 means two whole units plus a quarter. To compute with it, convert to an improper fraction: 2 1/4 = (2 × 4 + 1)/4 = 9/4. After computing, the calculator reverses the conversion if the answer is improper, so 9/4 is also shown as 2 1/4. Both forms are mathematically equivalent — use whichever fits the context.
Handling negative fractions
By convention, the negative sign on a fraction sits on the numerator, so −3/4 is the canonical form. If you enter 3/−4 the calculator normalises it to −3/4. Two negatives cancel, just like in regular arithmetic: −3/4 × −2/5 is positive.
Common mistakes to avoid
- Don't add denominators directly. 1/2 + 1/3 is not 2/5 — you need a common denominator first.
- When dividing, only flip the second fraction (the divisor), not both.
- Simplify only after the whole calculation, not partway through, unless it makes the multiplication easier.
Use with the other tools
For percentages, see the percentage calculator. For decimal averages of a list, the average calculator handles mean, median and mode. For ratios and proportions, try the ratio calculator.