Fraction Calculator
Fractions are everywhere once you start looking: half a cup of flour in a recipe, three quarters of an hour on a timesheet, two thirds of a tank of gas, or a quarter of a pizza left in the box. They are also one of the first places where school maths starts to feel tricky, because adding fractions is nothing like adding whole numbers. You cannot simply add the tops and add the bottoms — 1/2 + 1/3 is not 2/5 — and that single misunderstanding causes a surprising number of wrong answers. This free fraction calculator does the work properly for you. Enter two fractions, choose whether to add, subtract, multiply or divide them, and it gives you the answer as a simplified fraction and as a decimal, with the working shown so you can follow each step. It runs entirely in your browser, with nothing to install and no account to create, and it is just as useful for checking homework as it is for scaling a recipe or splitting a bill.
Your Fraction Result
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How to Use This Calculator
- Enter the first fraction. Type its numerator (the top number) and its denominator (the bottom number). The denominator cannot be zero.
- Enter the second fraction in the same way, using a minus sign in a numerator for a negative fraction.
- Choose the operation: add, subtract, multiply or divide.
- Tap Calculate. Read the simplified fraction, the decimal, the mixed number and the step-by-step working below.
Understanding Fractions
A fraction has two parts: the numerator on top tells you how many pieces you have, and the denominator on the bottom tells you how many equal pieces make a whole. So 3/4 means three pieces out of four, and 1/2 means one piece out of two. Two fractions can look different but have exactly the same value — 1/2, 2/4 and 3/6 are all the same amount — and that idea is the key to every fraction calculation. Simplifying a fraction means dividing the top and bottom by their greatest common divisor, the largest number that divides both evenly, until nothing except 1 divides both. For 6/12 the greatest common divisor is 6, so dividing both parts by 6 gives 1/2.
Adding and subtracting need a common denominator, because you can only add pieces of the same size. To add 1/2 and 1/3, rewrite them with the denominator 6: 1/2 becomes 3/6 and 1/3 becomes 2/6, and then 3/6 + 2/6 = 5/6. Subtraction works the same way, with the numerators subtracted instead. Multiplication is simpler: multiply the numerators together and the denominators together, then simplify — 3/4 × 2/3 = 6/12 = 1/2. Division has a neat trick: flip the second fraction upside down (its reciprocal) and multiply. So 1/2 ÷ 1/4 is 1/2 × 4/1 = 2.
Watch out for the classic mistakes. Never add or subtract the denominators: 1/2 + 1/3 is 5/6, not 2/5. Never divide by zero, and remember that a fraction with a zero numerator, such as 0/5, is simply zero. If an answer is larger than one, you can write it as a mixed number — 5/4 is 1 1/4. Converting a fraction to a decimal is just division: divide the numerator by the denominator, so 5/6 is about 0.8333 and 1/2 is exactly 0.5.
Worked Example
Example 1 — addition: Work out 1/2 + 1/3. The denominators are 2 and 3, so the common denominator is 6. Rewrite: 1/2 = 3/6 and 1/3 = 2/6. Add the numerators: 3 + 2 = 5, giving 5/6, which is about 0.8333 as a decimal. It cannot be simplified further, because 5 and 6 share no common divisor except 1.
Example 2 — multiplication: Work out 3/4 × 2/3. Multiply the numerators: 3 × 2 = 6. Multiply the denominators: 4 × 3 = 12. That gives 6/12, and dividing the top and bottom by 6 simplifies it to 1/2, or 0.5. You can see the same answer faster by cancelling first: the 3 on top cancels with the 3 below, and the 2 on top cancels with half of the 4 below.
Example 3 — division: Work out 2/3 ÷ 1/6. Flip the second fraction and multiply: 2/3 × 6/1 = 12/3 = 4.
Frequently Asked Questions
How do I add fractions with different denominators?
Find a common denominator, rewrite each fraction with that denominator, add the numerators, and simplify. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6, because 6 is the smallest number both 2 and 3 divide into.
How do I multiply fractions?
Multiply the numerators together and multiply the denominators together, then simplify. For example, 3/4 x 2/3 = 6/12 = 1/2. You can cancel common factors before multiplying to keep the numbers small.
How do I divide fractions?
Flip the second fraction upside down and multiply instead. For example, 1/2 divided by 1/4 = 1/2 x 4/1 = 4/2 = 2. This works because dividing by a fraction is the same as multiplying by its reciprocal.
What does it mean to simplify a fraction?
Simplifying means dividing the numerator and the denominator by their greatest common divisor until no number except 1 divides both. For example, 6/12 simplifies to 1/2 because 6 divides both 6 and 12. The value stays the same; only the numbers get smaller.
Can this calculator handle negative fractions?
Yes. Put a minus sign in front of a numerator to make a fraction negative, for example -1/2. The calculator keeps the sign on the numerator and simplifies the answer in the usual way.