Adding Fractions Calculator

Work out adding fractions instantly with clear inputs, formula shown and shareable results.

About Adding Fractions Calculator

To add fractions you need a common denominator. Cross-multiplying gives (a·d + c·b)/(b·d), which is then reduced by dividing both parts by their greatest common divisor.

Formula

Adding fractions

a/b + c/d = (ad + cb) / bd, then divide by gcd

Worked example

With the default values below, Adding Fractions Calculator returns Sum in lowest terms of 1/2. Change any input above and every figure here is recalculated in your browser.

Inputs used

First numerator: 1
First denominator: 3
Second numerator: 1
Second denominator: 6

Results

Sum in lowest terms: 1/2
As a mixed number: 1/2
Decimal value: 0.50000000
Lowest common denominator: 6

Step by step

1Values used
2Adding fractions
3Sum in lowest terms= 1/2
4As a mixed number= 1/2
5Decimal value= 0.50000000
6Lowest common denominator= 6

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is 1/3 + 1/6?

(1×6 + 1×3)/18 = 9/18, which reduces to 1/2.

Must I use the lowest common denominator?

No. Any common denominator works; using the LCD just means less reducing at the end.