Adding fractions is easier than you think. If you understand what improper fractions are and the lesson about comparing fractions, this lesson will be like a piece of cake. Well, almost!

There are two important things you need to know and it is very important to keep these in mind to avoid common pitfalls.

First, you cannot add the denominators; you can only add the numerators. Let's illustrate why it does not make sense to add the denominators.

 1 / 2 +   1 / 2 ≠   1 + 1 / 2 + 2
 1 / 2 +   1 / 2 ≠   1 + 1 / 2 + 2

 1 + 1 / 2 + 2 =   2 / 4

 1 + 1 / 2 + 2 =   2 / 4

However, half + half = 1 (half a pizza  +  half a pizza  = 1 pizza)

 1 / 2 +   1 / 2   =   1
 1 / 2 +   1 / 2   =   1

Second, you can only add the numerators when the denominator is the same for both fractions. Since we don't add the denominators, the denominator stays the same.

Having said that, when adding fractions and the denominators are not the same, you need to find equivalent fractions that give a common denominator for both fractions.

Let us illustrate what we just said with examples.

 What is the answer for     3 / 2 +     1 / 2

Observe that both fractions have the same denominator, which is 2. This means you can add the numerators and your denominator will stay the same. 3 + 1 = 4

4 / 2
=   2

Example #1:

 Add:    2 / 3 +     3 / 6

Notice that the denominator is not the same for both fractions, so we cannot add 2 and 3 to get 5.

Even if you did, what denominator will you choose for an answer? Is it going to be the 3 or the 6?

These questions are not meant to confuse you, but to show you the importance of making sure that both fractions have a common denominator before you add the numerators.

If you multiply the numerator and the denominator for the first fraction by 2, you will get

4 / 6

 4 / 6 is an equivalent fraction for 2 / 3 and it has the same denominator as 3 / 6

 What you are really adding is 4 / 6 +   3 / 6 (Add 4 and 3) The answer is 7 / 6

Our final example will be to add the following:

 3 / 5 +     2 / 4

Notice that it is not easy to multiply one denominator by a number to get the second denominator as we did before in example #1.

To get the same denominator, here is what you should do instead:

 Multiply the numerator and denominator for 3 / 5   by 4

 Multiply the numerator and denominator for 2 / 4   by 5

 You will get 12 / 20    + 10 / 20

10 / 20

We show the math on the same line:

 3 / 5    + 2 / 4 =   3 / 5 ×   4 / 4 +   2 / 4 ×   5 / 5 =   12 / 20 +   10 / 20 =   22 / 20

 What is the answer for     3 / 2 +     1 / 2

Observe that both fractions have the same denominator, which is 2. This means you can add the numerators and your denominator will stay the same. 3 + 1 = 4

4 / 2
=   2

Example #1:

 Add:    2 / 3 +     3 / 6

Notice that the denominator is not the same for both fractions, so we cannot add 2 and 3 to get 5.

Even if you did, what denominator will you choose for an answer? Is it going to be the 3 or the 6?

These questions are not meant to confuse you, but to show you the importance of making sure that both fractions have a common denominator before you add the numerators.

If you multiply the numerator and the denominator for the first fraction by 2, you will get

4 / 6

 4 / 6 is an equivalent fraction for 2 / 3

It has the same denominator as
3 / 6

 What you are really adding is 4 / 6 +   3 / 6

7 / 6

Our final example will be to add the following:

 3 / 5 +     2 / 4

Notice that it is not easy to multiply one denominator by a number to get the second denominator as we did before in example #1.

To get the same denominator, here is what you should do instead:

Multiply the numerator and denominator for 3/5 by 4

Multiply the numerator and denominator for 2/4 by 5

 You will get 12 / 20    + 10 / 20

10 / 20

We show the math on the same line:

 3 / 5    + 2 / 4

 =   3 / 5 ×   4 / 4 +   2 / 4 ×   5 / 5 =   12 / 20 +   10 / 20 =   22 / 20

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