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 Equivalent Fractions.)

 

Example 2:

1	+	1
3		6

Step 1: The bottom numbers are different. See how the slices are different sizes? We need to make them the same before we can continue, because we can't add them like this:

	1/3	+	1/6	=	?

 

To make the bottom numbers the same, 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 and put them over the same denominator:

2	+	1	=	2 + 1	=	3
6		6		6		6

In picture form it looks like this:

	2/6	+	1/6	=	3/6

Step 3: Simplify the fraction:

3	=	1
6		2

 

In picture form the whole answer looks like this:

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

 

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

Example 3:

1	+	1
3		5

Again, the bottom numbers are different (the slices are different sizes)!

	1/3	+	1/5	=	?

But let us try dividing them into smaller sizes that will each 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 second fraction by 3 we ended up with ³/₁₅ :

× 3

1	=	3
5		15

× 3

The bottom numbers are now the same, so we can go ahead and add the top numbers:

	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!

Adding Mixed Fractions

I have a special page on Adding Mixed Fractions.