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## 5th grade

# 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:

Next, we multiply the numerators by the same number as their denominator:

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:

**Note:**The new fractions are equal to their original form, however they are often easier to work with when the denominators are the same.

*Want to learn more about common denominators? Check out this video.*

## Want to join the conversation?

- I get it. If a anyone is do this right now, click the upvote.(296 votes)
- If I don't get it than do I click downvot?(28 votes)

- 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(88 votes) - How do you find a common denomenator for 2 fractions like 1/5 and 2/6?(40 votes)
- 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(18 votes)

- That was sorta hard but fun(27 votes)
- Can you up vote this(14 votes)

- :3 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⠶⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⢋⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠉⠓⠦⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⡄⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀ ⠀⠀⣠⠞⠁⠀⠀⣀⣠⣏⡀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⡃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆ ⢀⡞⠁⠀⣠⠶⠛⠉⠉⠉⠙⢦⡸⣿⡿⠀⠀⠀⡄⢀⣀⣀⡶⠀⠀⠀⢀⡄⣀⠀⣢⠟⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃ ⡞⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⢳⢀⣠⠀⠀⠀⠉⠉⠀⠀⣀⠀⠀⠀⢀⣠⡴⠞⠁⠀⠀⠈⠓⠦⣄⣀⠀⠀⠀⠀⣀⣤⠞⠁⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠁⠀⢀⣀⣀⡴⠋⢻⡉⠙⠾⡟⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠉⠀⠀⠀⠀ ⠘⣦⡀⠀⠀⠀⠀⠀⠀⣀⣤⠞⢉⣹⣯⣍⣿⠉⠟⠀⠀⣸⠳⣄⡀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠙⠒⠒⠒⠒⠚⠋⠁⠀⡴⠋⢀⡀⢠(28 votes)
- Cinnamoroll! I LOVE CINNAMOROLL!(1 vote)

- how do you find the common denominators?(6 votes)
- Usually multiple the denominators then cross multiply the denominators by the numerators.So if you have 4/6 x 5/8=

what you would do is do 8 x 6 and get 48 thats you products denominator. Then 8 x 4= 32 and 6 x 5= 30. now you have 30/48x32/48=(20 votes)

- If you don't understand just ask the teacher! 😘(17 votes)
- I don't have a teacher I have a tutor(0 votes)

- the lowest common denominater of 1/6 and 3/6 is 12 right?(8 votes)
- No, in this case 1/6 and 3/6 already have a common denominator of 6.(17 votes)

- Are two fractions multiplied equals 1 called reciprocals?(2 votes)
- 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(15 votes)

- What's 1/4 plus 11/10?(5 votes)
- 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(16 votes)