Adding Fractions | How To add fractions

There are Three Steps you need to take when Adding Fractions:

How To add fractions with the same denominator

  • Step 1: Ensure that the bottom number on the fraction (called the denominator) you are adding are the same.

Example:  1/ 3 + 1 / 3. The denominator in these two fractions are the same. The common denominator is the number 3.

 

  • Step 2: Next simply add the top numbers of the two fractions (called the numerators) together, and put that number over the common denominator. 
  • Step 3: And lastly, you can simplify the resulting fraction if you can

 

For Example:

 

    1 / 3 + 1 / 3

 

Since the bottom numbers (the denominators) are the same, all we have to do is just add the top numbers of each fraction together, and put the answer over the denominator. 

So, by following the above rule,   1 / 3 + 1 / 3 becomes 2 / 3.

Example 2: How to Add Fractions with different denominators?

1 / 2  + 1 / 6 

 

Step 1: How do you add fractions which has a different denominators?

 

Make the denominators the same in each fraction. 

We cannot add them in their present form. They must first have their denominators made the same before they can be added. 

The easy way to do this is simply multiply the top and bottom numbers in the first fraction by the denominator of the second fraction. The first fraction is 1 / 2. And the denominator of the second fraction is the number 6. 

 

This then works out to be: 

1 x 6 = 6

2 x 6 = 12

 

 

So the first fraction, 1 /2, now becomes 6 / 12

 

And to make the denominator of the second fraction the same as the first fraction, just do the opposite. Just multiply the second fraction 1 / 6, by the denominator of the first fraction. The denominator of the first fraction 1 / 2 is the number 2. So, you are multiplying the top and bottom numbers of the second fraction, 1 / 6,  by the number 2.

This becomes:

1 x 2 = 2

2 x 6 = 12

The second fraction now becomes 2 / 12

Now that you have both of the fractions with the same denominator, the denominator 12, you can now add them as follows.

2 / 12 + 6 / 12

Because the above fraction both have the same bottom numbers (the denominator) all you have to do to add them now is to add only the top numbers of the fractions and put them over the common denominator, 12.

You add this as follows:

6 + 2 = 8

This then becomes   8 / 12

This can be simplified further by finding the factors of the fraction 8 / 12, like this: 

8 = 4 x 2

12 = 4 x 3

 

We now have:

 

4 x 2             2
_______   =   __

4 x 3             3

 

The answer for adding 1 / 2 + 1 / 6 is 2 / 3. 

 

Click Here for the Lesson How To Multiply Fractions

 

Note: 

 

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