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.

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Here you will find some simple advice and support to help you learn to add two fractions together.

At the bottom of this page, there are also three printable resource sheets which explain about adding fractions in a little more detail.

Before you start learning to add fractions with different denominators, you should be confident using equivalent fractions.

If you want to add two fractions together, please use the calculator below.

To enter a fraction, you have to enter the numerator followed by '/' followed by the denominator. E.g. 4/5 or 23/7

To enter a mixed fraction, first type the whole number followed by space followed by the numerator followed by '/' followed by the denominator. E.g. 3 1/4 (3 and a quarter).

If you need help to find out how to add fractions, there is more help further down this page!

Find out how to add fractions using the video below.

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.

Here you will find a selection of Fraction worksheets designed to help your child understand and practice how to add and subtract 2 fractions.

Before your child tackles adding and subtracting fractions, they should be confident with equivalent fractions.

Using these sheets will help your child to:

- apply their understanding of equivalent fractions;
- add 2 fractions with different denominators;
- subtract 2 fractions with different denominators.

All the Adding Subtracting Fractions sheets in this section support the Elementary Math Benchmarks for Fifth Grade.

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.

Return to Free Math Help Online

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