Fraction Calculator

Fraction Calculator

This adds, subtracts, multiplies and divides two fractions, and simplifies the result automatically. Fractions cause more trouble than they should because each operation follows a different rule: multiplication is straightforward, division requires flipping the second fraction, and addition and subtraction need a common denominator before anything can happen. Getting that last step wrong — adding numerators and denominators separately — is the classic error, and it produces answers that are wrong in a way that is hard to spot. The calculator shows the simplified result along with the improper and mixed-number forms, and the sections below set out each rule with a worked example, so the page is useful for checking your method rather than only your answer. Negative numerators are accepted, and a zero denominator is rejected rather than silently producing nonsense.

How this is calculated

Multiplication: multiply the numerators and multiply the denominators. 2/3 × 3/4 = 6/12, which simplifies to 1/2.

Division: invert the second fraction and multiply. 2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9.

Addition and subtraction: convert to a common denominator first. 2/3 + 1/4 becomes 8/12 + 3/12 = 11/12. Simplification then divides both parts by their greatest common divisor, found using Euclid's algorithm.

Why you cannot just add the tops and bottoms

Adding 1/2 + 1/3 as 2/5 gives an answer smaller than the larger of the two fractions you started with, which is immediately impossible. The correct answer is 5/6.

The reason is that a fraction's denominator defines the size of the pieces being counted. Halves and thirds are different-sized pieces, so their numerators are not counting the same thing and cannot be combined directly. Converting to sixths makes the pieces the same size, at which point counting them works.

This is why the common denominator step exists, and why it has no equivalent in multiplication — multiplying fractions does not require the pieces to match, because you are scaling rather than combining.

Simplifying, improper fractions and mixed numbers

A fraction is in lowest terms when the numerator and denominator share no common factor above 1. Dividing both by their greatest common divisor gets there in one step: 6/12 has a GCD of 6, giving 1/2 directly rather than through repeated halving.

An improper fraction has a numerator at least as large as its denominator, such as 11/4. The mixed-number form is 2 3/4, obtained by dividing 11 by 4 to get 2 remainder 3. Neither form is more correct; improper fractions are easier to compute with, mixed numbers easier to picture, and this calculator shows both.

How to use the fraction calculator

Enter the first fraction. Numerator and denominator as whole numbers. Negative numerators are fine.
Choose the operation. Add, subtract, multiply or divide. Each follows a different rule — see the calculation section above.
Enter the second fraction and read the result. The answer is simplified automatically and shown in both improper and mixed-number form.

Frequently asked questions

How do you add fractions with different denominators?

Rewrite both over a common denominator, then add the numerators: 1/2 + 3/4 = 2/4 + 3/4 = 5/4 = 1¼.

How do you divide fractions?

Invert the second fraction and multiply. 2/3 ÷ 3/4 becomes 2/3 × 4/3 = 8/9. Dividing by a fraction smaller than 1 makes the result larger, which is correct even though it feels wrong.

Why can't I add the numerators and denominators separately?

Because the denominator sets the size of the pieces you are counting. Halves and thirds are different-sized pieces, so their numerators are not counting the same thing. Adding 1/2 + 1/3 as 2/5 gives an answer smaller than 1/2, which is impossible — the real answer is 5/6.

How do I convert an improper fraction to a mixed number?

Divide the numerator by the denominator. The quotient is the whole number, the remainder becomes the new numerator. 11/4 is 11 ÷ 4 = 2 remainder 3, so 2 3/4.