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### Course: 4th grade > Unit 7

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 $8$ : $8,16,24,32,{40},48,56,64,72,{80}\text{\u2026}$

Multiples of $10$ : $10,20,30,{40},50,60,70,{80},90,100\text{\u2026}$

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 ${40}$ :

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

Now we have written $\frac{7}{8}$ and $\frac{3}{10}$ 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.(455 votes)
- What are u talking about(7 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(111 votes)- 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 :)(10 votes)

- That was sorta hard but fun(44 votes)
- Can you up vote this(47 votes)

- How do you find a common denomenator for 2 fractions like 1/5 and 2/6?(48 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(25 votes)

- If you don't understand just ask the teacher! 😘(23 votes)
- I don't have a teacher I have a tutor(0 votes)

- here is a trick i learnd:

if your having trouble remembering witch is witch think of the denomanator as the de-bottom-nator! hope that helped! upvote if it did!!(22 votes) - Are two fractions multiplied equals 1 called reciprocals?(6 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(18 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.(22 votes)

- 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=(22 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(25 votes)