What it does
Add, subtract, multiply or divide two fractions. Enter each fraction as a numerator and a denominator (with an optional whole part for mixed numbers), pick an operator, and you will see the answer as a simplified fraction, a mixed number where one exists, and a decimal.
How it works
Every result is a pair of whole numbers — a numerator over a denominator — then simplified by dividing both by their greatest common divisor. The sign lives on the numerator; the denominator is kept positive.
Every result is then reduced by the greatest common divisor (GCD) of the numerator and denominator, computed with the Euclidean algorithm. So 6/12 comes back as 1/2, not 6/12.
Worked example — adding
2/3 + 1/6: put both over a common denominator of 18, giving 12/18 + 3/18. Add the numerators: 15/18. Simplify by the GCD to 5/6.
Worked example — multiplying
2/3 × 3/4: multiply straight across — 6/12 — then simplify to 1/2.
Worked example — dividing
1/2 ÷ 1/4: flip the second fraction and multiply, giving 1/2 × 4/1 = 2/1.
Common uses
- Recipes. Halving 3/4 cup, or trebling 1/3 teaspoon — fractional arithmetic without decimal drift.
- DIY measurements. Working in imperial units where lengths are quoted as fractions of an inch.
- Teaching. Show pupils each simplification step alongside the mental method.
- Quick maths. Anywhere a decimal answer isn't what you want.
Frequently asked
How do you add fractions with different denominators?
Put them over a common denominator first — the product of the two denominators is always safe. Then add the numerators, keep the denominator, and simplify at the end.
What is a mixed number?
A whole number written next to a proper fraction, like 1 3/4, meaning "one and three-quarters". Any improper fraction (numerator bigger than denominator) can be written as a mixed number: 7/4 = 1 3/4. This tool accepts a whole part on either fraction, and shows a mixed-number form of the answer when one exists.
Can I use negatives?
Yes. Put the minus sign on the whole part (for a mixed number like -1 3/4) or on the numerator directly. The tool keeps the denominator positive and shows the sign on the numerator.
Improper or mixed — which is right?
Both are correct; they are the same number written two ways. Improper fractions are easier to work with; mixed numbers are easier to read. This tool shows both, so you can pick.
See how we build and verify our tools.