About this tool
This calculator performs the four basic fraction operations and always reduces the result to its simplest form using the greatest common divisor. Everything runs locally in your browser.
How to use the Fraction Calculator
- Enter the first fraction in the left pair of boxes: numerator in the first box, denominator in the second. The page opens with 1/2 + 3/4 filled in.
- Choose an operation from the middle menu: +, −, × or ÷.
- Enter the second fraction in the right pair of boxes the same way.
- Read the Result: the answer in lowest terms, with its decimal value on the line below. It updates as you type.
How each operation works
Adding and subtracting fractions requires a common denominator first. This tool uses the product of the two denominators as that common denominator, cross-multiplies the numerators (a/b + c/d = (a×d + c×b) / (b×d)), and then reduces the answer. Multiplying fractions is the simplest operation: multiply the numerators together and the denominators together. Dividing by a fraction is the same as multiplying by its reciprocal (flipping the numerator and denominator) — this tool handles that flip automatically.
Worked example
Adding 1/2 and 3/4, the default on this page: the calculator cross-multiplies to get (1 × 4 + 3 × 2) / (2 × 4) = 10/8, then divides top and bottom by their greatest common divisor, 2, to show 5/4 with Decimal: 1.25 underneath. By hand you would more likely use the least common denominator, 4, turning 1/2 into 2/4 so that 2/4 + 3/4 = 5/4; both routes give the same answer. As a mixed number, 5/4 is 1¼.
Things to watch out for
A denominator of zero isn't a valid fraction, since division by zero is undefined — the calculator won't produce a result if either denominator is set to zero. For a negative fraction, put the minus sign on the numerator (like -1/2), which is the standard convention. A negative denominator also works: the result always moves the sign to the top, so 1/-2 is shown as -1/2. Dividing by a fraction whose numerator is 0 shows "Undefined".
Simplify fractions
To simplify fractions, divide the numerator and denominator by their greatest common divisor. For example, 18/24 simplifies to 3/4 because both numbers divide by 6.
Fraction rules at a glance
| Operation | Rule |
|---|---|
| Add or subtract | Make the denominators equal, then add or subtract the numerators |
| Multiply | Multiply tops, multiply bottoms |
| Divide | Flip the second fraction and multiply |
| Simplify | Divide top and bottom by their greatest common divisor |
| Mixed number to improper | Whole x denominator + numerator, over the denominator |
For example, 2/3 + 1/4 = 8/12 + 3/12 = 11/12, and 3/4 divided by 1/2 is 3/4 x 2/1 = 6/4, which simplifies to 3/2 or 1 1/2.
Frequently asked questions
The result is automatically simplified to its lowest terms — for example, 4/8 is simplified to 1/2, since both represent the same value. This matches standard math convention for a final answer.
Enter a whole number as itself over 1 (like 5 as "5/1"), or as just the numerator with the denominator left at 1. Mixed numbers (like 2½) should be converted to an improper fraction first (2½ becomes 5/2) before entering them.
A fraction represents division, and dividing by zero is undefined in standard arithmetic — there's no number that answers "how many zeros fit into this amount." A denominator of zero isn't a valid fraction.
No. Each box takes a whole number, and a decimal is cut to its whole part, so 1.5 is read as 1 and 0.5 as 0. Write the decimal as a fraction instead: 0.5 is 1/2 and 1.5 is 3/2. The decimal line under the result is rounded to four places.