About this calculator
Fractions are where school math meets real life: halving a recipe that calls for 3/4 of a cup, combining offcut boards in a workshop, splitting a bill three ways. The arithmetic is simple once the rules click — addition and subtraction need a common denominator, multiplication and division do not — but it is fiddly enough that everyone reaches for a calculator. This one also simplifies every answer and converts between mixed numbers, improper fractions and decimals.
Tip for whole numbers and mixed numbers: enter a whole number as a fraction over 1 (3 = 3/1), and a mixed number like 2 1/2 as 5/2 — multiply the whole part by the denominator and add the numerator.
How to use it
- Enter the numerator and denominator of the first fraction.
- Choose the operation.
- Enter the second fraction and read the result in three forms.
The formula
Adding and subtracting first rewrite both fractions over the shared denominator bd, then combine the numerators. Multiplication is straight across. Division flips the second fraction and multiplies ("invert and multiply"). Every result is then reduced by dividing top and bottom by their greatest common divisor.
Worked example
2/3 + 3/4: the common denominator is 12, so 8/12 + 9/12 = 17/12, written as the mixed number 1 5/12, or 1.4167 as a decimal. Simplifying works the same way in reverse: 36/48 divides top and bottom by 12 to become 3/4.
Frequently asked questions
How do I convert a mixed number to an improper fraction?
Multiply the whole number by the denominator and add the numerator: 2 3/4 = (2×4 + 3)/4 = 11/4. To go back, divide: 11 ÷ 4 is 2 remainder 3, so 2 3/4. This calculator shows both forms of every result automatically.
Why do fractions need a common denominator to add?
Because the pieces must be the same size before they can be counted together — thirds and quarters are different-sized slices. Converting to twelfths makes both fractions count the same slice size. Multiplication needs no such step because it works on the counts directly: "half of a third" is naturally a sixth.
How do I turn a fraction into a percentage?
Divide the numerator by the denominator, then multiply by 100: 3/4 = 0.75 = 75%. The decimal shown for every result here is exactly that intermediate step. Our Percentage Calculator can take it from there.
Can a denominator be zero?
No — division by zero is undefined, because no number multiplied by zero gives back the numerator. If a calculation seems to produce a zero denominator, the original problem has no numerical answer (this calculator will refuse it rather than invent one).