Adding and Subtracting Fractions

Accompanying Resources: Study Guide, Boom Cards, Activity, Task Cards

Same Denominators
Different Denominators
Video
Practice

Adding/Subtracting Fractions with Common Denominators

If you're new to adding and subtracting fractions or just want a refresher, make sure to check out the lesson on adding fractions with a common denominator first. The basic idea is that fractions must have the same denominator (bottom number) in order to combine them with addition or subtraction. When the denominators are the same, the whole has been split into equal pieces that are the same size. If the denominators are not the same, the pieces are not the same size and the two fractions cannot be combined as they are.

$When fractions have a common denominator, the whole has been split into equal pieces that are the same size. When the denominators are different, the pieces are different sizes.$

If the denominators are the same, you can combine two fractions together with addition or subtraction. Just count up the pieces using the numerators. The size of the pieces does not change, so the denominator stays the same.

$When fractions have a common denominator, you can combine the two together. The denominator does not change.$

Here's the general rule for adding/subtracting fractions with the same denominator:

$Rule for adding and subtracting fractions with a common denominator.$

Here are a few examples.

$How to add or subtract fractions with a common denominator.$

Check out the lesson on adding fractions with a common denominator for more examples. Open the next tab to see what to do when the denominators are not the same.

How to Add/Subtract Fractions with Different Denominators

When two fractions have different denominators, that means the pieces that the wholes have been split into are not the same size. We cannot combine them with addition or subtraction until we "fix" them by finding a common denominator.

There's more than one way to find a common denominator. We usually want the smallest number possible to use to make things easier, so we're looking for what's called the lowest common denominator (LCD). This is also called finding the least common multiple (LCM). One way is to list the multiples of each denominator and look for the smallest number they have in common.

Multiples of 5: 5, 10, 15, 20 . . . .
Multiplies of 2: 2, 4, 6, 8, 10 . . . .

The smallest multiple that the two denominators have in common is 10, so we can rewrite the two fractions using 10 as the common denominator. To do this, we need to multiply both fractions by a "fancy form of 1." Make sure to multiply the numerator and denominator of the fraction by the same number.

$Multiplying by a fancy form of 1 to rewrite fractions with a common denominator.$

Once your fractions are rewritten with the same denominator, you can combine them together with addition or subtraction.

$Adding fractions with a common denominator.$

So here's the general rule when it comes to adding fractions with different denominators:

$Rule for adding or subtracting fractions with different denominators. Rewrite using a common denominator, then add or subtract. Simplify if needed.$

Here are a few examples:

$Adding fractions with unlike denominators example.$

In the problem above, 18 is the smallest possible number you could have used as the common denominator. You could have used a larger number that is also a multiple of 6 and 9, such as 36 or 54. If you used a larger number you would just need to make sure to simplify the fraction in the end.

$Subtracting fractions with unlike denominators example.$

In the problem above, 20 is the smallest possible number you could have used as the common denominator.You could have used a larger number that is also a multiple of 10 and 4, such as 40. If you used a larger number you would just need to make sure to simplify the fraction in the end.

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