# Fraction Calculator: Add and Subtract Fractions

Use this online math calculator to to add and subtract fractions.

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## What are Fractions?

In mathematical terms, a fraction is a numerical quantity that is not a whole number: 1⁄2, 1⁄4, 3⁄8 etc.

## How do I calculate Fractions?

The following examples show how to complete math with fractions.

### How to Add Fractions

The trick with adding fractions is to keep your eye on the number under the line, this number is call the Denominator. When the denominator of both fractions is the same, adding the fraction is simple. You just add the numbers above the line (this number is called the Numerator).

Fraction Calculation Example 1: 1⁄3 + 1⁄3 = 2⁄3 Easy eh?

Now, adding fractions becomes a little (but only a little) more complicated when the denominators (the number on the bottom, under the line) of the fractions that you are adding are not the same. There is a simple rule when adding fractions, the denominations must always be the same, in mathematical terms this is called a Common Denominator as all the denominators have the same 'common' value.

So, your trying to add a fraction and you need a Common Denominator, how do you get it? If you are working with 2 fractions, you can find a common denominator simply by multiplying the denominators:

Fraction Calculation Example 2a: 2⁄5 + 3⁄4 our two denominators are 5 and 4.

Fraction Calculation Example 2b: 5 x 4 = 20 We multiply them: 20 is our Common Denominator.

Got it so far? Great. Now, in order to make our original fractions Equivalent Fractions.

An Equivalent Fraction is a fraction of the same value, written in a different format, for example 1⁄2 is the same as 2⁄4 and 5⁄10.

In order to make our fractions equivalent, we must complete the same action to the top number (the numerator) as we did to the bottom number (the denominator)

Fraction Calculation Example 2c: 5 x 3 = 15 We multiply 3 by 5 as we previously multiplied 4 by 5.

Fraction Calculation Example 2d: 15⁄20 is the equivalent fraction of 3⁄4.

We then repeat the exercise for our other fraction

Fraction Calculation Example 2e: 4 x 2 = 8 We multiply 2 by 4 as we previously multiplied 5 by 4.

Fraction Calculation Example 2f: 8⁄20 is the equivalent fraction of 2⁄5.

Excellent, we now have two fractions to add that have common denominators as we made them into equivalent fractions that are easier to add together.

Fraction Calculation Example 2g: 8⁄20 + 15⁄20 = 23⁄20.

Our fraction in this case is greater than one (23 parts of a 20 piece puzzle) so we can write the fraction as 1 3⁄20

### How to Subtract Fractions

The trick with subtracting fractions is to keep your eye on the number under the line, this number is call the Denominator. When the denominator of both fractions is the same, subtracting the fraction is simple. You just add the numbers above the line (this number is called the Numerator).

Fraction Calculation Example 1: 2⁄3 - 1⁄3 = 1⁄3 Easy eh?

Now, subtracting fractions becomes a little (but only a little) more complicated when the denominators (the number on the bottom, under the line) of the fractions that you are subtracting are not the same. There is a simple rule when subtracting fractions, the denominations must always be the same, in mathematical terms this is called a Common Denominator as all the denominators have the same 'common' value.

So, your trying to add a fraction and you need a Common Denominator, how do you get it? If you are working with 2 fractions, you can find a common denominator simply by multiplying the denominators:

Fraction Calculation Example 2a: 4⁄5 + 3⁄4 our two denominators are 5 and 4.

Fraction Calculation Example 2b: 5 x 4 = 20 We multiply them: 20 is our Common Denominator.

Got it so far? Great. Now, in order to make our original fractions Equivalent Fractions.

An Equivalent Fraction is a fraction of the same value, written in a different format, for example 1⁄2 is the same as 2⁄4 and 5⁄10.

In order to make our fractions equivalent, we must complete the same action to the top number (the numerator) as we did to the bottom number (the denominator)

Fraction Calculation Example 2c: 5 x 3 = 15 We multiply 3 by 5 as we previously multiplied 4 by 5.

Fraction Calculation Example 2d: 15⁄20 is the equivalent fraction of 3⁄4.

We then repeat the exercise for our other fraction

Fraction Calculation Example 2e: 4 x 4 = 16 We multiply 4 by 4 as we previously multiplied 5 by 4.

Fraction Calculation Example 2f: 16⁄20 is the equivalent fraction of 4⁄5.

Excellent, we now have two fractions to subtract that have common denominators as we made them into equivalent fractions that are easier to subtract.

Fraction Calculation Example 2g: 16⁄20 - 15⁄20 = 1⁄20.

## A Test on Fractions

Okay, you have read the above guidance on adding and subtracing fractions, your an expert now right? Okay, whether and expert on fractions or not, try the fraction test below. Work the answers out and then use the onlie fraction calculator above to test your answers. Get them all right? Excellent, you are now ready to help your family with their maths homework and pretend that you were an ace at fractions all along.

Fraction Test 1 16⁄20 - 5⁄20 =

Fraction Test 2 12⁄13 + 5⁄20 =

Fraction Test 3 2⁄3 - 3⁄9 =

Fraction Test 4 16⁄20 + 15⁄25 =

Fraction Test 5 6⁄10 - 2⁄9 =

Fraction Test 6 5⁄7 + 9⁄11 =

Fraction Test 7 3⁄8 - 1⁄15 =

Fraction Test 8 16⁄20 + 15⁄25 =

Fraction Test 9 3⁄7 - 3⁄21 =

Fraction Test 10 27⁄35 + 15⁄20 =

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