How do you do add fractions

To add fractions, you have to convert the fractions into the same family.  This is also called ‘finding the common denominator’ – the denominator is the bottom number (or family) and ‘common’ means they are the same.   If you have

½ + ¼   

it is easy to convert, because ½ is the same as 2/4.  So, you get

2/4 + ¼

Now just add the numerators – you have 2 of something and add another 1 of the same thing, you have 3 of them all together.

2/4 + ¼ = ¾

What if you can’t change one of them to be the same as the other?  For example,

1/3 + ¼

You have to find a third number that they both CAN go into – this is called finding the ‘lowest common multiple’.  The new number has to be a multiple of both 3 and 4.  You want the smallest number that works. 

3 x 1 = 3 no

3 x 2 = 6 no

3 x 3 = 9 no

3 x 4 = 12 yes!  4 goes into 12 evenly too

To convert 1/3, multiply TOP AND BOTTOM by how many times 3 goes into 12 -- which is 4.  You get 4/12.  

To convert 1/4, multiply TOP AND BOTTOM by how many times 4 goes into 12 -- which is 3.  You get 3/12. 

4/12 + 3/12 = 7/12 

The key thing to remember is to multiply top and bottom by the same thing.