Calculators

Fraction Calculator

Add, subtract, multiply and divide fractions, with the answer reduced to lowest terms and shown as a decimal.

First fractionFirst fraction
+
Second fractionSecond fraction
OperationOperation
Result in lowest terms5/61/2 + 1/3
As a mixed number5/6
As a decimal0.833333

How it works

Adding and subtracting needs a common denominator, which multiplying the two denominators always provides. Multiplying is simply across the top and across the bottom. Dividing is multiplying by the reciprocal — flip the second fraction and multiply. Every result is then reduced by dividing both parts by their greatest common divisor.

a/b + c/d = (ad + cb) / bd · a/b × c/d = ac / bd · a/b ÷ c/d = ad / bc
a/b
The first fraction — a is the numerator, b the denominator
c/d
The second fraction
bd
The common denominator formed by multiplying the two
GCD
Greatest common divisor, used to reduce the answer

Worked example

Adding 1/2 and 1/3.

  1. 1Multiply the denominators for a common one: 2 × 3 = 6
  2. 2Scale each numerator: 1 × 3 = 3 and 1 × 2 = 2
  3. 3Add them: 3 + 2 = 5, over 6
  4. 4Check for common factors: 5 and 6 share none, so it is already reduced

1/2 + 1/3 = 5/6, or about 0.833.

Frequently asked questions

Why do fractions need a common denominator to add?

Because the denominator defines the size of the pieces, and you can only count pieces of the same size. Halves and thirds are different-sized pieces, so 1/2 + 1/3 is not 2/5. Rewriting both as sixths makes the pieces comparable, and then the numerators can simply be added.

How do I reduce a fraction to lowest terms?

Divide the numerator and denominator by their greatest common divisor. For 18/24 the GCD is 6, giving 3/4. Repeatedly dividing by any shared factor you spot gets you there too, just in more steps. A fraction is in lowest terms when the only number dividing both parts is 1.

What is a mixed number?

A whole number alongside a proper fraction, such as 2 1/3 instead of 7/3. Mixed numbers read more naturally when describing quantities, while improper fractions are easier to compute with. This calculator shows both so you can use whichever suits.

Why does dividing by a fraction make the answer bigger?

Dividing asks how many of the second thing fit inside the first. Four divided by one-half asks how many halves fit into four, and the answer is eight. Whenever you divide by a number smaller than one, the result grows — which is exactly what flipping and multiplying produces.

Can the denominator be negative?

It can be written that way, but the convention is to keep the sign on top: −1/4 rather than 1/−4. They are the same value, and this calculator always moves the sign to the numerator so results are easy to compare at a glance.

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