If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Arithmetic (all content)

### Course: Arithmetic (all content)>Unit 5

Lesson 9: Common denominators

# Common denominators review

Review finding common denominators, and try some practice problems.

## Common denominators

When fractions have the same denominator, we say they have common denominators.
Having common denominators makes things like comparing, adding, and subtracting fractions easier.

## Finding a common denominator

One way to find a common denominator for two (or more!) fractions is to list the multiples of each denominator until we find the smallest multiple they have in common.
Example
Find a common denominator for start fraction, 7, divided by, 8, end fraction and start fraction, 3, divided by, 10, end fraction.
The denominators are 8 and 10. Let's list multiples of each:
Multiples of 8: 8, comma, 16, comma, 24, comma, 32, comma, start color #11accd, 40, end color #11accd, comma, 48, comma, 56, comma, 64, comma, 72, comma, start color #11accd, 80, end color #11accd, point, point, point
Multiples of 10: 10, comma, 20, comma, 30, comma, start color #11accd, 40, end color #11accd, comma, 50, comma, 60, comma, 70, comma, start color #11accd, 80, end color #11accd, comma, 90, comma, 100, point, point, point
start color #11accd, 40, end color #11accd and start color #11accd, 80, end color #11accd are common multiples of 8 and 10. So, we can use either of these for a common denominator. Most often, we will use the smallest common denominator, so we can work with smaller numbers.
Let's use start color #11accd, 40, end color #11accd for our common denominator.

## Rewriting fractions with a common denominator

Now, we need to rewrite start fraction, 7, divided by, 8, end fraction and start fraction, 3, divided by, 10, end fraction with a denominator of start color #11accd, 40, end color #11accd.
We need to figure out what to multiply each denominator by to get start color #11accd, 40, end color #11accd:
start fraction, 7, divided by, 8, end fraction, times, start fraction, divided by, 5, end fraction, equals, start fraction, divided by, start color #11accd, 40, end color #11accd, end fraction
start fraction, 3, divided by, 10, end fraction, times, start fraction, divided by, 4, end fraction, equals, start fraction, divided by, start color #11accd, 40, end color #11accd, end fraction
Next, we multiply the numerators by the same number as their denominator:
start fraction, 7, divided by, 8, end fraction, times, start fraction, 5, divided by, 5, end fraction, equals, start fraction, 35, divided by, start color #11accd, 40, end color #11accd, end fraction
start fraction, 3, divided by, 10, end fraction, times, start fraction, 4, divided by, 4, end fraction, equals, start fraction, 12, divided by, start color #11accd, 40, end color #11accd, end fraction
Now we have written start fraction, 7, divided by, 8, end fraction and start fraction, 3, divided by, 10, end fraction with a common denominator:
start fraction, 7, divided by, 8, end fraction, equals, start fraction, 35, divided by, 40, end fraction
start fraction, 3, divided by, 10, end fraction, equals, start fraction, 12, divided by, 40, end fraction
Note: The new fractions are equal to their original form, however they are often easier to work with when the denominators are the same.