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Math & Statisticsfractions

Fraction Calculator

Add, subtract, multiply or divide two fractions, with the result simplified. Division inverts the second fraction, which is the step that turns a hard operation into an easy one.

Also called: add fractions, fraction arithmetic.

Result
11/12

11/12, which is 0.92 as a decimal. It is already a proper fraction. The unsimplified answer was 22/24.

As a decimal
0.92
Before simplifying
22/24
As a mixed number
It is already a proper fraction.
Numerator
11
Denominator
12
How this is calculated
Method and background

How this is calculated

Addition and subtraction need a common denominator, taken here as the product of the two. Multiplication goes straight across. Division multiplies by the reciprocal, which is why dividing by a half is the same as multiplying by two. The result is then reduced by the greatest common divisor, and both the raw and simplified forms are shown so the reduction is visible rather than assumed.

add over a common denominator; multiply straight across; divide by inverting the second fraction
a/b, c/d
The two fractions

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

three quarters plus a sixth

First numerator
3
First denominator
4
Operation
Add
Second numerator
1
Second denominator
6

Result11/12

Common denominator 24, then reduced by 2

Open this example

dividing by a half doubles

First numerator
6
First denominator
1
Operation
Divide
Second numerator
1
Second denominator
2

Result12

boundary: the reciprocal rule

Open this example

Method and limits

What it assumes

  • Integer numerators and denominators.

What it deliberately does not model

  • A zero denominator is undefined and declines, as does dividing by a zero fraction.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

Why does dividing by a fraction make the number bigger?
Because dividing by a number less than one is multiplying by its reciprocal, which is greater than one. Six divided by a half is twelve: it asks how many halves fit in six.