Fraction Calculator
Add, subtract, multiply or divide two fractions.
Results update as you type.
How it works
A fraction represents a part of a whole as one number divided by another, a numerator over a denominator, and combining two fractions means finding the single fraction equal to their sum, difference, product or quotient. The challenge is that fractions can only be added or subtracted once they share a denominator, while multiplication and division follow different rules again. The fraction calculator handles all four operations and then reduces the outcome, so the answer arrives in its simplest form rather than an awkward, oversized ratio. To add or subtract, the tool rewrites both fractions over a common denominator, most simply the product of the two denominators, then works on the numerators; adding 1/2 and 1/3 becomes the numerator 1 times 3 plus 1 times 2 over 2 times 3, which is 5/6. To divide, it multiplies by the reciprocal of the second fraction. Every result is then divided top and bottom by the greatest common divisor, because a fraction calculator should present a value like 5/6 in lowest terms and its decimal, roughly 0.833333, alongside it. Students learning arithmetic, cooks scaling recipes, carpenters working in inches and anyone splitting quantities rely on this fraction calculator to combine fractions accurately without slips in the cross-multiplication.
a/b + c/d = (a·d + c·b) / (b·d), then simplify by the GCD
Adding fractions requires a shared denominator, so multiplying each numerator by the other fraction's denominator, a times d and c times b, rewrites both over the common base b times d without changing their values. The rewritten numerators can then be added directly. Dividing the final numerator and denominator by their greatest common divisor removes the shared factor, so 1/2 plus 1/3 lands as 5/6 in lowest terms.
Source:Standard arithmetic
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter numerator 1, denominator 1, operation, numerator 2 and denominator 2.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Result updates instantly as you type — no button to press.
Frequently asked questions
How do I add fractions with different denominators?
Give them a common denominator first. The simplest shared denominator is the product of the two, so for 1/2 and 1/3 you use sixths: 1/2 becomes 3/6 and 1/3 becomes 2/6. Add the numerators to get 5/6, then reduce if the result shares a common factor. Multiplication and division do not need a common denominator, but addition and subtraction always do.
Does the calculator simplify the answer?
Yes, every result is reduced to lowest terms. After performing your chosen operation, the tool finds the greatest common divisor of the numerator and denominator and divides both by it, so nothing is left with a shared factor. That is why 1/2 plus 1/3 is reported as 5/6 rather than an unreduced equivalent. The decimal form, about 0.833333, is shown too for quick reference.
How do I divide by a fraction?
Multiply by its reciprocal, flipping the second fraction upside down and multiplying. Dividing by 1/3 is the same as multiplying by 3/1, because division asks how many of the divisor fit into the dividend. The calculator applies this automatically when you choose the divide operation, then simplifies the product, so you never have to invert the fraction or reduce the result yourself.
How do I multiply fractions?
Multiply the numerators together and the denominators together, with no common denominator needed. For 1/2 times 1/3 the numerators give 1 and the denominators give 6, so the product is 1/6. Multiplication is the most direct fraction operation because it works straight across. The calculator then reduces the result to lowest terms, cancelling any factor the top and bottom share.
What is a fraction as a decimal?
It is the value you get by dividing the numerator by the denominator. Splitting 5 by 6 gives about 0.833333, which is why the calculator shows that alongside the fraction 5/6. Some fractions produce terminating decimals, like 1/2 equalling 0.5, while others repeat forever. The decimal form is handy for comparing fractions or plugging a result into further calculations that expect a plain number.