How do you add Fractions?
Support Page

Welcome to our How do you Add Fractions support page.

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

Adding Fractions Calculator

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.

How do you add fractions Support

Here are 3 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.

Step 3: Simplify the answer if needed.

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.

Step 3: Simplify the answer if needed.

One you have an answer, you might need to simplify it, or convert improper fractions into mixed numbers.


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

How do you Add Fractions - Examples

Example 1) Work out \[{3 \over 11} + {5 \over 11} \]

Step 1)

You will notice that the two denominators are identical (they are both 11), so we can move straight on to step 2).

Step 2)

With equal denominators, we can just add the numerators together.

This gives us: \[{3 \over 11} + {5 \over 11} = {3 + 5 \over 11} = {8 \over 11} \]

Step 3)

This fraction is already in simplest form so we have our answer.

Final answer: \[{3 \over 11} + {5 \over 11} \; = \; {8 \over 11} \]


Example 2) Work out \[{2 \over 5} + {4 \over 15} \]

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.

\[{2 \over 5} = {2 \times 3 \over 5 \times 3} = {6 \over 15} \]

So we now have: \[{2 \over 5} + {4 \over 15} \; = \; {6 \over 15} + {4 \over 15} \]

Step 2)

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

This gives us: \[{6 \over 15} + {4 \over 15} = {6 + 4 \over 15} = {10 \over 15} \]

Step 3)

We need to write this answer in simplest form, so divide the numerator and denominator by a common factor of 5!

\[{10 \over 15} \; = \; {10 ÷ 5 \over 15 ÷ 5} \; = \; {2 \over 3}\]

Final answer: \[{2 \over 5} + {4 \over 15} \; = \; {2 \over 3} \]


Example 3) Work out this fraction sum, giving your answer as a mixed number. \[{2 \over 7} + {3 \over 4} \]

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 gives us: \[{2 \over 7} = {2 \times 4 \over 7 \times 4} = {8 \over 28} \]

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

This gives us: \[{3 \over 4} = {3 \times 7 \over 4 \times 7} = {21 \over 28}\]

We have now converted the two fractions into fractions with like denominators, and changed our sum to: \[{2 \over 7} + {3 \over 4} = {8 \over 28} + {21 \over 28}\]

Step 2)

Now we have converted the two fractions into fractions with equal denominators, all we need to do now is to add the numerators together.

This gives us: \[{8 \over 28} + {21 \over 28} = {8 + 21 \over 28} = {29 \over 28}\]

Step 3)

This fraction is already in simplest form.

Now we need to convert the answer into a mixed number: \[{29 \over 28} = 1 {1 \over 28}\]

Final answer: \[{2 \over 7} + {3 \over 4} \; = \; 1 {1 \over 28}\]


Example 4) Work out this fraction sum, giving your answer as an improper fraction. \[{5 \over 3} + {7 \over 8} \]

Step 1)

The denominator of the first fraction is 3. The denominator of the second fraction is 8. These numbers are not multiples of one another so we need to use Step 1a)

So we need to multiply the numerator and denominator of the 1st fraction by 8 and the numerator and denominator of the 2nd fraction by 3..

This gives us: \[{5 \over 3} + {7 \over 8} = {5 \times 8 \over 3 \times 8} + {7 \times 3 \over 8 \times 3} = {40 \over 24} \; + \; {21 \over 24} \]

Step 2)

Now we have converted the two fractions into fractions with equal denominators, all we need to do now is to add the numerators together.

This gives us: \[{40 \over 24} + {21 \over 24} = {40 + 21 \over 24} = {61 \over 24}\]

Step 3)

This fraction is already in simplest form.

Final answer: \[ {5 \over 3} + {7 \over 8} = {61 \over 24} \]

How do you add fractions - the algebra...

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

To add 2 fractions: \[{a \over b} + {c \over d} \]

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 : \[{a \over b} + {c \over d} = {a \times d \over b \times d} \; + \; {c \times b \over d \times b}\]

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: \[{ad \over bd} \; + \; {cb \over bd} \; = \; {ad + bc \over bd}\]

Adding and Subtracting Fractions Video

This video clip shows you how to add and subtract fractions.

There are several different examples including adding and subtracting fractions with both like and unlike denominators, and also examples where one denominator is a multiple of the other.

How do you add fractions printable support sheets

Print out our printable support sheet for step-by-step instructions to add two fractions together.

More Recommended Math Resources

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

Adding Fractions Worksheets

The sheets in this section will help you practice adding fractions.

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

Learning Fractions Math Help Page

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.
 

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