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### Course: Arithmetic > Unit 13

Lesson 3: 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?

- 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(128 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 :)(18 votes)

- How do you find a common denomenator for 2 fractions like 1/5 and 2/6?(52 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(28 votes)

- Are two fractions multiplied equals 1 called reciprocals?(9 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(21 votes)

- how do you find the common denominators?(7 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=(26 votes)

- the lowest common denominater of 1/6 and 3/6 is 12 right?(9 votes)
- No, in this case 1/6 and 3/6 already have a common denominator of 6.(28 votes)

- its too hard for me i need help.(7 votes)
- If you need help,read this excerpt.

When fractions have the same denominator, we say they have common denominators. (e.g. 1/6 has a common denominator with 2/6.)

Having common denominators makes things like comparing, adding, and subtracting fractions easier.

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.

(e.g 1/4 2/5

4,8,12,16,20

5,10,15,20

Twenty appears in both tables so, 1/10 is the same as 2/20)

Get it?(9 votes)

- 2 x 9 = 18.

2,000 has three zeros at the end, and 900 has two zeros at the end. This is a total of five zeros at the end.

So 2,000 x 900 = 1,800,000.

Have a blessed, wonderful day!(8 votes)

- how doses 1/3= 3,6,9,12,15

and 6/5=5,10,15,20,25

= 15(5 votes) - what is 7/6 i want to know what it is(5 votes)
- can get help with fractions?(4 votes)