Add, subtract, multiply and divide fractions and get the answer fully simplified, as a mixed number and as a decimal. No common-denominator headaches required.
Fraction Calculator
How the Fraction Calculator Works
Fractions turn up everywhere once you start looking: halving or doubling a recipe, cutting materials to length in a DIY project, splitting a quantity fairly, and of course school maths. This calculator adds, subtracts, multiplies and divides two fractions for you and — the part people find fiddly by hand — always cancels the answer down to its simplest form. It also shows the result as a mixed number and as a decimal, so you can read it whichever way suits the job.
Each operation follows the standard rule. To add or subtract, both fractions are first put over a common denominator: a/b ± c/d becomes (a×d ± c×b) over (b×d), so the pieces are the same size before they are combined. To multiply, the numerators are multiplied straight across and so are the denominators: (a×c) over (b×d). To divide, the second fraction is flipped upside down and the sum becomes a multiplication: a/b ÷ c/d = (a×d) over (b×c). Whichever operation you choose, the raw answer is then simplified by dividing the top and bottom by their greatest common divisor (GCD) — the largest whole number that divides into both exactly — and repeating until no common factor remains. That is how an answer like 18/30 becomes 3/5.
A few rules are built in for correctness. The denominator of the answer is always kept positive, with any minus sign carried on the numerator instead, so results are written the standard way. A fraction with a zero denominator is refused, because dividing by zero has no meaning, and you cannot divide by a fraction whose numerator is zero, for the same reason. Because every step uses whole-number arithmetic, the fraction answer is exact — nothing is rounded — while the decimal shown alongside it is there for quick size comparisons.
How to Use This Calculator
- Enter the numerator (top number) and denominator (bottom number) of your first fraction.
- Enter the numerator and denominator of your second fraction.
- Choose the operation: add, subtract, multiply or divide.
- Press Calculate.
- Read the answer three ways: the simplified fraction, the mixed number if it is bigger than one, and the decimal.
Example
Example 1. Add 1/2 + 1/3. Put both over the common denominator 6: 1/2 becomes 3/6 and 1/3 becomes 2/6. Add the tops: 3 + 2 = 5. The answer is 5/6, which is already in its simplest form and equals about 0.833 as a decimal.
Example 2. Multiply 2/3 × 9/10. Multiply straight across: 2 × 9 = 18 on top and 3 × 10 = 30 on the bottom, giving 18/30. The GCD of 18 and 30 is 6, so divide both by 6. The answer is 3/5, or 0.6 as a decimal.
Understanding Your Result
The three forms shown are the same value wearing different clothes, and each has its moment. The simplified fraction is the exact answer, best for further maths. The mixed number — a whole part plus a fraction, like 2 1/3 — is usually easiest to picture in real life, such as cups of flour or lengths of timber. The decimal is best when you need to compare sizes quickly or feed the number into another calculation. If your result is a whole number, that is because the fraction cancelled all the way down (6/3 becomes simply 2). A negative answer just means the subtraction or division took the value below zero; the minus sign is shown on the numerator.
A practical way to choose between the forms: keep the fraction while you are still calculating, because decimals round and fractions do not — chaining 0.833 into a second sum quietly loses a little accuracy each time, while 5/6 stays exact. Switch to the mixed number when the answer leaves the page and becomes a measurement, an ingredient or a length, since “2 1/3 cups” is far easier to act on than “7/3 cups”. And when two fractions need comparing at a glance — which is bigger, 5/6 or 7/9? — the decimals (0.833 against 0.778) settle it instantly.
Fraction Calculator FAQs
Why did the calculator change my answer’s numbers?
It simplified it. Answers are divided top and bottom by their greatest common divisor so the fraction is in its lowest terms — 18/30 and 3/5 are the same amount, but 3/5 is the standard way to write it.
Can I enter a mixed number like 2 1/3?
Not directly — each fraction is one numerator over one denominator. Convert a mixed number first by multiplying the whole part by the denominator and adding the numerator: 2 1/3 becomes 7/3, which you can enter as it is.
What happens if I enter a denominator of zero?
The calculation is refused. A denominator of zero would mean dividing something into zero parts, which is undefined in maths, so no fraction — and no answer — can be built from it.
Can the calculator handle negative fractions?
Yes. Enter the minus sign on a numerator and the arithmetic, including the simplifying and the final sign of the answer, is handled for you. The denominator of any result is always shown as positive.
How is the decimal version worked out?
By dividing the numerator by the denominator. Some decimals stop neatly, like 3/5 = 0.6; others repeat forever, like 5/6 = 0.8333…, and are shown rounded — one more reason the exact fraction is the main result.
Related calculators: Percentage Calculator, Scientific Calculator, Standard Deviation Calculator.