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