How To Add Fractions

First of all, it is really easy if the bottom numbers of the fractions are the same (the technical term for this is the 'denominator' - why do they always have to complicate things with nasty long words?)

If the bottom numbers are the same, like this; 2/5 + 1/5

then all you have to do is add the two top numbers (numerators) together
2 + 1 = 3
and leave the bottom number the same, that's 5
so the answer is 3/5

Here's another example, what is 5/17 + 8/17
the two botton numbers are the same, 17
so you just add the top numbers, 5 + 8 = 13

therefore the answer is 13/17

What happens when the bottom numbers are not equal I here you ask? This is where I got stuck when I was in school. There is more than one way of doing this, which doesn't help.

The rule is; you have to find the smallest number that both bottom numbers can divide into exactly - the 'lowest common denominator'. Is your head starting to hurt yet? Don't worry, this is where you have to think and make a decision.

Question. Does the lowest of the two bottom numbers divide into the highest number exactly?

For example, 2/3 + 1/6
Does 3 go into 6? Yes, there are two 3's in 6.

so, multiplying the top and bottom by 2 gives 4/6

4/6 is now the first fraction, so the sum now becomes, 4/6 + 1/6
The bottom numbers are now the same so you just add the top numbers to get, 5/6

Going back to the Question - Does the lowest of the two bottom numbers divide into the highest number exactly? If the answer is NO then you do the following:-

For example, 1/3 + 2/5
Now here, 3 does not go into 5 exactly, so you need to follow the next few steps.

Step 1, multiply the first top number with the second bottom number, 1 x 5 = 5

Step 2, multiply the second top number with the first bottom number, 2 x 3 = 6

Step 3, add these two numbers together, 5 + 6 = 11

11 now becomes the resulting top number.

Step 4, multiply the two bottom numbers, 3 x 5 = 15

15 now becomes the resulting bottom number.

Answer 11/15

Now let's try one using a whole number and fractions.

what is, 1 3/8 + 1/2

ignore the whole number 1 for now, and just add the fractions.

3/8 + 1/2

the bottom numbers are different, so you have to ask the question - Does the lowest of the two bottom numbers divide into the highest number exactly?

So does 2 divide into 8 exactly?

Yes, 2 into 8 is 4

so, multiplying the top and bottom of the second fraction by 4 gives 4/8

4/8 is now the new second fraction, so the sum is now, 3/8 + 4/8

The denominators are now the same, so you can just add the numerators,

3 + 4 = 7

therefore the result of adding the fractions is 7/8

Now just add the whole number 1 to get 1 7/8

Any clearer? If you copy these steps and follow them every time you add a fraction, I'm sure you will pick it up fairly quickly. Eventually you will be able to do the working out in your head, and just write the answer down.

I wish now that someone could have explained how to add fractions like this when I was at school.