### Free Educational Resources

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##### Description:

Learn how to add fractions with different denominators and why you have to have those common denominators to make it all work.

Check out how to add any fractions together, then apply your knowledge with five questions to see if you understand how it all works.

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Tutorial

## How to Add Any Fractions

When you add fractions you are putting things together.  By combining two amounts you find the total amount you have.  For example, when you add 3 + 7 you put all the one's together and in this case you have 10 ones.  It could be anything though, marbels, cookies, plates, pizzas.

For fractions you are doing the samething.  Let's say you have  and  and you add them up.  What you are looking for are how many fifths you have in total.  In this case you have 8 fifths or , which can be changed to  .

What happens though when you take fifths and you try to put it together with a half?  You can't just combine them because they are different parts.  If you take  and add it  to , you don't know how much the total is unless you make the parts (denominators) the same.

Let's start with .  If you take each of the two pieces the whole is make up of and divide each into 2 peieces, you end of up with 4 total parts (denominator)  and 2 pieces (numerator) or .  Still you can't combine the two fractions.  So we try again...

Take each half and divide it into three peices, you end up with 6 total parts (denominator) and 3 pieces (numerator)  or

We can keep doing this to  and continue to get equal fractions.  They are equal because they still show the same amount everytime.

With  you can do the same.  Take each part (fifths) and divide them into two.  We would then have 10 total parts (denominators) and 6 peices (numerator); or .

can equal 5 pieces (numerator) over 10 parts (denominator).  So we have found our match!

+  can be rewritten as  +

Now you can combine the amount of tenths you have to find you have 11 tenths or .  Or rewrite is as .

See the pictures below to help you unerstand how this worked :)