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.

Lesson 2: 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 $\frac{7}{8}$ and $\frac{3}{10}$.
The denominators are $8$ and $10$. Let's list multiples of each:
Multiples of $8$: $8,16,24,32,40,48,56,64,72,80\text{…}$
Multiples of $10$: $10,20,30,40,50,60,70,80,90,100\text{…}$
$40$ and $80$ 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 $40$ for our common denominator.

## Rewriting fractions with a common denominator

Now, we need to rewrite $\frac{7}{8}$ and $\frac{3}{10}$ with a denominator of $40$.
We need to figure out what to multiply each denominator by to get $40$:
$\frac{7}{8}×\frac{}{5}=\frac{}{40}$
$\frac{3}{10}×\frac{}{4}=\frac{}{40}$
Next, we multiply the numerators by the same number as their denominator:
$\frac{7}{8}×\frac{5}{5}=\frac{35}{40}$
$\frac{3}{10}×\frac{4}{4}=\frac{12}{40}$
Now we have written $\frac{7}{8}$ and $\frac{3}{10}$ with a common denominator:
$\frac{7}{8}=\frac{35}{40}$
$\frac{3}{10}=\frac{12}{40}$
Note: The new fractions are equal to their original form, however they are often easier to work with when the denominators are the same.

## Practice

Problem 1
You have two fractions, $\frac{2}{5}$ and $\frac{3}{10}$, and you want to rewrite them so that they have the same denominator (and whole number numerators).
What number(s) could you use for the denominator?

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• I get it. If a anyone is do this right now, click the upvote.
• If I don't get it than do I click downvot?
• At first I was really confused with the least common denominator Q's. Then i realised that I had to find the number which was in both multiples. Some questions can be answered like this:

Oh, 3 times 5 is 15! yas

But can you do it another way? (not for the one which you have to times the denominators, but like, the other types of questions)
?/6 and ?/4, something like that. Hope you understand me XD :3
• At first i was confused by the option 15 because i wasn't thinking straight and thought that 15 was 10 times five instead of 10 plus five :)
• How do you find a common denomenator for 2 fractions like 1/5 and 2/6?
• You would just keep listing all the multiples until you find a common one, so both 5 and 6 are multiples of 30, so the common denominator would be 30
• That was sorta hard but fun
• Can you up vote this
• the lowest common denominater of 1/6 and 3/6 is 12 right?
• No, in this case 1/6 and 3/6 already have a common denominator of 6.
• If you don't understand just ask the teacher! 😘
• I don't have a teacher I have a tutor
• Are two fractions multiplied equals 1 called reciprocals?
• Reciprocals are fractions turned upside down and have the numerator in the denominator area with the denominator in the numerator area. For example, reciprocal of 5/8 is 8/5
• What's 1/4 plus 11/10?
• 1∕4 + 11∕10

First, let's find the least common denominator.
One way of doing this is to write down multiples of the smaller denominator until we get a number that is also a multiple of the larger denominator.
1 × 4 = 4 (not a multiple of 10)
2 × 4 = 8 (not a multiple of 10)
3 × 4 = 12 (not a multiple of 10)
4 × 4 = 16 (not a multiple of 10)
5 × 4 = 20 = 2 × 10

This tells us that if we multiply 1∕4 by 5∕5 and 11∕10 by 2∕2,
the resulting fractions will have the same denominator.

1∕4 + 11∕10
= 5∕5 × 1∕4 + 2∕2 × 11∕10
= (5 × 1)∕(5 × 4) + (2 × 11)∕(2 × 10)
= 5∕20 + 22∕20

Now that the two fractions have the same denominator we can simply add the numerators.

5∕20 + 22∕20
= (5 + 22)∕20
= 27∕20