Welcome to the Math Salamanders How do you Add Fractions support page.

Here you will find some helpful support to help you learn how to add fractions.

If you just want a calculator to do the hard work for you, then try our Adding Fractions Calculator.

The calculator will add any two fractions or mixed numbers.

The great thing is that it will also show you all the working out - job done!

If you would rather learn how to do this for yourself, then ignore this part and keep reading.

Here are 2 easy steps to help you add two fractions together.

Step 1: Convert the fractions to the same denominator.

If the fractions already have the same denominator, you do not need to do anything!

Step 2: Add the two numerators together (and keep the denominator the same) to get the answer.

You should now have the answer to your fraction sum!

See below for a step-by-step breakdown of how to add fractions.

Step 1: Convert the fractions to the same denominator.

If the fractions already have the same denominator, skip the rest of this part.

If the fractions have different denominators, keep reading!

We can only add fractions together if they have the same denominator.

It is a bit like when you are adding inches and centimetres together - you need to convert both measures to the same units - either centimetres or inches!

There are two different possibilities for the this step:

Step 1a) If one of the denominators is a multiple of the other denominator.

If this is the case, you just need to multiply the numerator and denominator of the fraction with the lower denominator so that the two denominators are the same.

Step 1b) If one of the denominators is not a multiple of the other denominator.

The easiest and simplest way to convert the two fractions to equivalent fractions with the same denominators is to multiply the numerator and denominator of each fraction by the other fraction's denominator.

Step 2: Add the two numerators together

Once the two fractions have the same denominator, we can add the numerators together.

This will give us the answer we are looking for.

Have a look at the examples below to see how it all works!

How do you Add Fractions - Examples

*
Example 1)
3
5
+
4
15
*

Step 1)

You will notice that the second denominator (15) is a multiple of the first denominator (5) so we need to follow Step 1a)

So we need to multiply the numerator and denominator of the first fraction by 3.

This give us:

3 5 = 3x3 5x3 = 9 15

So we now have:

3 5 + 4 15 = 9 15 + 4 15

Step 2)

Now the denominators are equal, all we need to do now is to add the numerators together.

9 15 + 4 15 = 9+4 15 = 13 15

*
Example 2)
2
7
+
3
4
*

Step 1)

The denominator of the first fraction is 7. The denominator of the second fraction is 4. These numbers are not multiples of one another.

We need to use Step 1b)

So we multiply the numerator and denominator of the first fraction by the second fraction's denominator (4).

This give us:

2 7 = 2x4 7x4 = 8 28

Next we multiply the second fraction's numerator and denominator by the first fraction's denominator (7).

This give us:

3 4 = 3x7 4x7 = 21 28

Step 2)

Now the denominators are equal, all we need to do now is to add the numerators together.

2 7 + 3 4 = 8 28 + 21 28 = 29 28 or 1 1 28

So let's remember the two important steps:

Step 1: convert both fractions to fractions with the same denominator

Step 2: add the two numerators and keep the denominator the same!

For those of you who like to see things in Algebra...this is what it looks like

To add 2 fractions a b + c d

First we convert the two fractions to the same denominator by multiplying the numerator and denominator of the first fraction by d, and the numerator and denominator of the second fraction by b.

This gives us equivalent fractions of:

a x d b x d and c x b d x b

Since b x d is the same as d x b, we now have two fractions that are equivalent to the fractions we started with, and have the same denominator!

The last step is to add up the numerators, this gives us:

a b + c d = a x d b x d + c x b d x b = (a x d) + (c x b) d x b

If you would like to see this all in a little more detail, please print out the three sheets below which will tell you all you need about adding two fractions.

Take a look at some more of our resources similar to these.

The sheets in this section will help you learn to add improper fractions.

Some of the sheets also involve simplifying the fractions and converting the answers to mixed fractions.

Here you will find the Math Salamanders free online Math help pages about Fractions.

There is a wide range of help pages including help with:

- fraction definitions;
- equivalent fractions;
- converting improper fractions;
- how to add and subtract fractions;
- how to convert fractions to decimals and percentages;
- how to simplify fractions.

How to Print or Save these sheets

Need help with printing or saving?

Follow these 3 easy steps to get your worksheets printed out perfectly!

How to Print or Save these sheets

Need help with printing or saving?

Follow these 3 easy steps to get your worksheets printed out perfectly!

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