Fraction Calculator

Work with fractions exactly

Enter two fractions, choose an operation, and the answer appears in lowest terms, as a mixed number where one exists, and as a decimal. Each fraction has a whole-number box, so mixed numbers like 2½ can be typed directly — leave it empty for an ordinary fraction.

The calculation runs in your browser. Values can be included in the page address so you can share a particular calculation, but they are not sent away for the calculation itself.

Adding and subtracting

Fractions can only be added when they are counted in the same size of piece, which is what a common denominator provides. Rewrite both fractions over that denominator, combine the numerators, and reduce:

a/b + c/d = (a×d + c×b) ÷ (b×d)

For 1/2 + 1/3, the smallest common denominator is 6. One half is three sixths, one third is two sixths, and together they make five sixths:

1/2 + 1/3 = 3/6 + 2/6 = 5/6

Subtraction works the same way, and the answer is allowed to go below zero: 1/3 − 1/2 = −1/6.

Multiplying and dividing

Multiplication needs no common denominator at all — multiply across the top and across the bottom:

a/b × c/d = (a×c) ÷ (b×d)

Division is multiplication by the reciprocal: flip the second fraction over and multiply.

1/2 ÷ 1/3 = 1/2 × 3/1 = 3/2 = 1½

This is the step that produces the result people find counterintuitive — dividing by a fraction smaller than one makes the answer larger. That is correct, and it is easier to see if you read the question as “how many thirds fit into a half?” The answer is one and a half of them.

Mixed numbers and negative signs

A mixed number is combined into a single improper fraction before any arithmetic happens: 2½ becomes 5/2, because two wholes are four halves and one more half makes five.

A minus sign in front of a mixed number applies to the whole quantity. −2½ means −(2 + ½) = −5/2, not −2 + ½ = −1½. This trips up hand calculations often enough that it is worth stating plainly; the calculator follows the standard reading.

Lowest terms

A fraction is in lowest terms when its numerator and denominator have no common factor except 1. Dividing both by their greatest common divisor gets there in one step: 6/8 shares a factor of 2, so it reduces to 3/4.

Answers here are always reduced. That is why 2/4 + 2/4 comes back as 1 rather than 4/4, and why 2/6 × 3/2 is shown as 1/2 rather than 6/12.

Why this is not done in decimals

Most fractions have no exact decimal form. One third is 0.333… with no end, so any decimal version is already an approximation before the arithmetic starts. Add three of them and you get 0.999999…, which is not 1 — a small error, but a visible one in a tool whose entire purpose is exactness.

This calculator keeps everything in whole numbers from beginning to end and only divides once, at the very end, to show you a decimal. So 1/3 + 1/3 + 1/3 is exactly 1, and 63/8 is exactly 7.875 rather than something ending in stray digits.

What has no answer

A denominator of zero does not describe a fraction: it asks how large each piece is when something is cut into no pieces, which has no value. Dividing by a fraction that equals zero fails for the same reason. In both cases the calculator says the answer is undefined rather than showing infinity, which tends to get copied into a spreadsheet and cause trouble later.

Frequently asked questions

How do I add fractions with different denominators?

Rewrite both over a common denominator, add the numerators, then reduce. For 1/2 + 1/3, the common denominator is 6: 1/2 becomes 3/6 and 1/3 becomes 2/6, so the sum is 5/6. The calculator does this for you and always reduces the answer.

How do I divide one fraction by another?

Multiply by its reciprocal — flip the second fraction and multiply. 1/2 ÷ 1/3 becomes 1/2 × 3/1 = 3/2, or 1½. Dividing by a fraction that equals zero has no answer, and the calculator says so rather than showing infinity.

How do I enter a mixed number like 2½?

Put 2 in the Whole box, 1 in Numerator and 2 in Denominator. Leave the whole box empty for an ordinary fraction. A negative whole number applies to the entire quantity, so −2 with 1/2 means −2½, not −2 + ½.

What does "lowest terms" mean?

A fraction is in lowest terms when its numerator and denominator share no common factor other than 1. 6/8 reduces to 3/4 because both divide by 2. The calculator always reduces, so 2/4 + 2/4 is shown as 1 rather than 4/4.

Why not just use decimals?

Many fractions have no exact decimal form. One third is 0.333… forever, so adding three of them in decimal gives 0.999999…, not 1. This calculator works in whole numbers throughout and only converts to a decimal at the end, so 1/3 + 1/3 + 1/3 is exactly 1.

What is the difference between an improper fraction and a mixed number?

An improper fraction has a numerator at least as large as its denominator, like 7/4. The same value as a mixed number is 1¾. Neither is more correct; improper fractions are easier to calculate with, mixed numbers are easier to picture. The calculator shows both.