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Course: 4th grade (Eureka Math/EngageNY)>Unit 5

Lesson 2: Topic B: Fraction equivalence using multiplication and division

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

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?
Choose all answers that apply:

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

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
(122 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 :)
(15 votes)
• How do you find a common denomenator for 2 fractions like 1/5 and 2/6?
(51 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)
• 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!!
(26 votes)
• I did help me with my own work
(0 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=
(24 votes)
• Are two fractions multiplied equals 1 called reciprocals?
(7 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)
• What's 1/4 plus 11/10?
(7 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
(28 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.
(26 votes)
• the secend last q on practice dose not work
(10 votes)
• why do we do this
(6 votes)
• to learn
(5 votes)
• I personally finding the least common denominator really confusing because the least common denominator is the one that both of them share... which defeats the entire name of " least common denominator" if it's the one that both of them share.. this probably doesn't make any sense.
(11 votes)
• just think of it being a common denominator that has a lot of numbers that can make it
(1 vote)