Simple math: Obtaining a common denominator to add fractions

1/2 + 1/4

To add these two fractions, we must get a denominator that is the same. This is called the common denominator. We can get a common denominator by multiplying the two denominators, in this problem it would be 2 x 4 = 8. But that is not the lowest common denominator, which is preferred when adding and subtracting fractions. To get the lowest common denominator, let's look at all the multiples of 2 and then the multiples of 4.

Multiples of 2 are

2, 4, 6, 8, 10, 12, …...

Multiples of 4 are

4, 8, 12, 16, 20, …..

The lowest common denominator is the smallest number that is the same in both sets of multiples. Notice the 4 is bold in each set. That is the lowest common denominator.

Now that we have the common denominator, we have to make ½ into an equivalent fraction with 4 as the denominator. We learned how to do this in the previous section. If we multiply the numerator and denominator by 2, we get 2/4.. Notice ¼ already has a denominator of 4, so we don't have to change this fraction in order to add.

2/4 + 1/4 = 3/4

 

Let's now consider a little more difficult problem where we'll have to change both fractions before adding.

3/5 + 1/6

 

We need to get a common denominator, so get all the multiples of 5.

5, 10, 15, 20, 25, 30, 35, ….

Next get all the multiples of 6.

6, 12, 18, 24, 30, 36, 42, …..

Notice that 30 is the smallest of the numbers that are common to both lists, so 30 is the common denominator.

Next we get equivalent fractions with 30 in the denominator. Multiply the first fraction by 6/6 to get 18/30. Multiply the second fraction by 5/5 to get 5/30. Now we can add the fractions to get 18/30 + 5/30 = 23/30