How do I add fractions with uncommon denominators?

First, I have to apologize for the fact that the formatting here will be hard to follow. It is not possible to set it up properly in here. I have had to show the fractions like this 1/2. I hope that isn't too confusing.

The first step in adding fractions with different denominators is to convert them to fractions with the same denominator.

Sometimes this is really easy, because one of the denominators is a multiple of the other. So, for example,

½ + ¼ is simple to do, because ½ is the same as 2/4. That's one you probably knew, but often it's hard to guess the equivalent fraction. So, just multiply both the top and bottom of the fraction by the same number.

numerator 1 x 2 = 2

denominator 2 x 2 = 4

so, the equivalent fraction is 2/4

Now the addition is straightforward:

2/4 + 1/4 = 3/4

It’s a little harder when neither number goes evenly into the other one. Then you have to find the lowest common denominator. All this means is the lowest (or smallest) number that is common to both (it is a multiple of both numbers).

Let’s look at an example:

1/3 + 2/5

We know that 3 doesn’t go evenly into 5, and 5 doesn’t go evenly into 3. So, we have to look for the smallest number that is a multiple of both 3 and 5.

The 3 table: 3 6 9 12 15 18 21 ….

The 5 table: 5 10 15 20 25 . . .

The smallest number that is a multiple of both 3 and 5 is 15.

Now to convert the fractions. The main thing to remember here is that you have to multiply top and bottom of the fraction by the same number to keep the fraction equivalent.

numerator: 1 x 5 = 5

denominator: 3 x 5 = 15

So, 1/3 is equivalent to 5/15

Now we'll do the same thing for 2/5.

numerator: 2 x 3 = 6

denominator: 5 x 3 = 15

So, 2/5 is equivalent to 6/15

Now to do the addition:

5/15 + 6/15 = 11/15