Adding Fractions with Different Denominators

When dealing with two fractions that have different denominators, you must create a common denominator before adding or subtracting them. This is a two step process. First, find the least common multiple (LCM) between the denominators that you have, then change one or both fractions to have that common denominator.

Adding Fractions with Different Denominators

Adding Fractions with Different Denominators

When you’re dealing with two fractions that have different denominators, you have to create a common denominator before you can add or subtract them.

Creating a common denominator is a two-step process. First, you have to find the least common multiple between the two denominators that you have.

Then, you have to change one or both of the fractions to have that common denominator before you can proceed. Let’s look at a few examples here.

First, we have 1/3 plus 1/6. The least common multiple between 3 and 6 is 6. This one already has a denominator of six, so we just need to change this one to have a denominator of 6.

We’ll multiply the top and bottom by 2. What we get is 2 times 1 is 2 over 2 times 3 (6), plus 1/6. Then, all we have to do is add these. 2 plus 1 is 3 and we retain the 6 on the bottom.

We have 3/6, or 1/2. In this example, we have 5/9 minus 1/6. Now, the least common multiple between 9 and 6 is 18. We have to multiply both of these fractions by something to get that common denominator.

The first fraction we’ll multiply by 2/2. The second fraction we’ll multiply by 3/3. Now what we have is 2 times 5 is 10 over 2 times 9 (18) minus 1 times 3 (3). 6 times 3 is 18.

Our solution here- we’re going to retain the 18 on the bottom and on top we’ll have 10 minus 3, which is 7. In this final example, we have 3/7 plus 4/9.

In some cases, your least common multiple is just going to be one number times the other. That’s what we have here. The second fraction we’re going to multiply by 7/7.

The first fraction we’re going to multiply by 9/9. Then, that gives us 9 times 3 is 27 over 9 times 7 (63) plus 4 times 7 (28) over 9 times 7 (63). Now, we can just add these two fractions. We keep the 63 in the denominator and we add 27 and 28, which is 55.

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by Mometrix Test Preparation | Last Updated: August 15, 2019