When adding fractions with unlike
denominators, we must change each fraction so they have the same
denominator. Here's a simple example to start with.

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. .
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. We now get...1/4 + 2/4 = 3/4

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