➗ Math
How to Add, Subtract, Multiply and Divide Fractions
A clear, worked guide to the four fraction operations — common denominators, cross-multiplying, flipping to divide — plus how to simplify and convert to mixed numbers.
Updated 14 September 2026 · 2 min read
Fractions have a reputation for being harder than they are. Each of the four operations follows one fixed rule, and once you've matched the rule to the operation there's nothing to guess. Here's each one, with a worked example, followed by the two finishing steps — simplifying and writing the answer as a mixed number — that most people forget.
Adding and subtracting: match the denominators first
You can only add or subtract fractions when their denominators (the bottom numbers) are the same. If they differ, rewrite each fraction over a common denominator, then add or subtract the numerators and keep the denominator unchanged.
A reliable shortcut is to use the product of the two denominators as the common denominator, as above — it always works, though it can leave you with larger numbers to simplify at the end. Subtraction is identical, just with a minus sign: 3/4 − 1/6 = (18 − 4)/24 = 14/24, which reduces to 7/12.
Multiplying: straight across
Multiplication is the easy one — no common denominator needed. Multiply the numerators together and the denominators together:
Notice that the answer often simplifies neatly, because factors on the top and bottom cancel. Multiplying a fraction by a whole number works the same way if you treat the whole number as itself over one — 5 is 5/1.
Dividing: flip and multiply
To divide by a fraction, turn it upside down (take its reciprocal) and multiply instead. Nothing else changes:
The rule feels like a trick, but it follows from what division means: dividing by 3/4 asks "how many three-quarters fit in?", and that's the same as multiplying by four-thirds. You can't divide by a fraction equal to zero, just as you can't divide by zero itself.
The two finishing steps
An answer isn't really done until you've tidied it up:
- Simplify to lowest terms. Divide the top and bottom by their greatest common factor. 6/12 becomes 1/2; 14/24 becomes 7/12. A GCF & LCM calculator finds that common factor for you.
- Convert top-heavy fractions to mixed numbers. If the numerator is bigger than the denominator, divide to pull out the whole part: 7/4 = 1 3/4.
The fraction calculator does all of this at once — it applies the right rule for your operation, reduces the result to its lowest terms, and shows it as both a decimal and a mixed number. It's the fastest way to check homework or a measurement. For the closely related world of percentages, our guide to percentages made simple uses the same divide-and-multiply thinking.
Frequently asked questions
- Why do you need a common denominator to add fractions but not to multiply them?
- Adding counts how many equal-sized pieces you have, so the pieces must be the same size — that's what a common denominator guarantees. Multiplying scales one fraction by another, which works piece-for-piece regardless of size, so you can just multiply straight across.
- How do you simplify a fraction?
- Find the greatest common factor of the numerator and denominator, then divide both by it. For example, 8/12 has a greatest common factor of 4, so it simplifies to 2/3. The fraction calculator does this automatically for every answer.