# How to Find Common Denominators

If you are trying to add or subtract fractions with different denominators, you’ve come to the right place! In order to add or subtract fractions, we have to have common denominators. Sometimes, though, you’re given a problem that looks like this:

Those are definitely not common denominators! In order to get the denominators the same, follow these steps:

1. List multiples of both numbers. Start by listing four multiples for each number.

- 4: 4, 8, 12, 16
- 2: 2, 4, 6, 8

2. Look at the lists you’ve made. Underline any numbers that are on both lists.

- 4:
__4__,__8__, 12, 16 - 2: 2,
__4__, 6,__8__

3. Look for the smallest underlined number (known as the least common multiple, or LCM). This is your common denominator.

- Common denominator: 4

4. Multiply the numerator and denominator by the factor that it would take to get to your common denominator…like this:

and this:

For this multiplication, the first number you use is the fraction you are changing, and the second number comes from the answer to this question: “what number would I multiply the denominator by to get to the common denominator?” For the first fraction, your denominator is already your common denominator, so you simply multiply it by 1/1. We multiply by 1 (or a fraction equaling one) because this does not change the amount of the fraction, it just changes the name of the fraction. For the second fraction, you would multiply by 2/2 because your denominator (2) needs to be multiplied by 2 to reach the common denominator of 4.

Now that you have common denominators, you can simply add the fractions together. Remember, when you add fractions, the numerators (top numbers) add and the denominators (bottom numbers) stay the same!

Your new problem would look like this:

Once you add them, you should get 5/4

If you know how to simplify this (by changing it into a mixed number), please do so. If not, please review how to deal with improper fractions.

Want one more practice problem with finding common denominators? This time, we’ll do a subtraction problem. Here it is:

Follow the same steps. They are:

1. List the multiples for each number.

- 3: 3, 6, 9, 12
- 4: 4, 8, 12, 16

2. Look at the lists you’ve made. Underline any numbers that appear on both lists.

- 3: 3, 6, 9,
__12__ - 4: 4, 8,
__12__, 16

3. Look for the smallest underlined number (least common multiple, or LCM). This is your common denominator.

- Common denominator: 12.

4. Multiply the numerator and denominator of each fraction by the factor that it would take to get to your common denominator. Think about it like this:

What do you multiply by 3 to get to 12? Well, we know that 3 x 4 = 12, so we know we need to multiply by 4:

Now, we do the same thing with 1/4 to get:

What do you multiply 4 by to get to 12? Well, we know that 4 x 3 = 12, so we know we're going to multiply by 3. That looks like this:

Now we have both of our fractions with common denominators, so we can subtract! Remember, in a subtraction problem, the numerators subtract but the denominators stay the same. It looks like this:

Now see if you can fill in the answer. If you got 1/12, you're right!