Adding Fractions

1	+	1
4		4

1	+	1	=	1 + 1	=	2
4		4		4		4

 

Step 3. Simplify the fraction:

2	=	1
4		2

 

(If you are unsure of the last step see the equivalent fractions page)

 

Example 2:

1	+	1
3		6

Step 1: The bottom numbers are different. We can't add them like this:

	1/3	+	1/6	=	?

So we need to do something to make them have the same denominator.

In this case we can multiply the top and bottom of the first fraction (¹/₃) by 2, like this:

× 2

1	=	2
3		6

× 2

And now our question looks like this:

Step 2: Add the top numbers (the numerators) and put them over the same denominator:

	2/6	+	1/6	=	3/6

Step 3: Simplify the fraction:

³/₆ is the same as ¹/₂:

	2/6	+	1/6	=	3/6	=	1/2

And we have the answer!

Example 3:

1	+	1
3		5

Again, they are different sizes!

	1/3	+	1/5	=	?

But let us try dividing them into smaller sizes that will be the same:

	5/15	+	3/15

By multiplying the top and bottom of the first fraction by 5 we ended up with ⁵/₁₅ :

× 5

1	=	5
3		15

× 5

And by multiplying the top and bottom of the first fraction by 3 we ended up with ³/₁₅ :

× 3

1	=	3
5		15

× 3

The denominators are now the same, so we can go ahead and add them:

	5/15	+	3/15	=	8/15

 

Making the Denominators the Same

In the previous example how did I know to cut them into ¹/₁₅ths to make the denominators the same? You can read how to do this using either one of these methods:

• Common Denominator Method, or the
• Least Common Denominator Method

They both work, use whichever you prefer!