Common denominators review

CCSS Math: 4.NF.A.2
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 78\dfrac78 and 310\dfrac3{10}.
The denominators are 88 and 1010. Let's list multiples of each:
Multiples of 88: 8,16,24,32,40,48,56,64,72,80...8, 16, 24, 32, \blueD{40}, 48, 56, 64 ,72, \blueD{80}...
Multiples of 1010: 10,20,30,40,50,60,70,80,90,100...10, 20, 30, \blueD{40}, 50, 60, 70, \blueD{80}, 90, 100...
40\blueD{40} and 80\blueD{80} are common multiples of 88 and 1010. 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\blueD{40} for our common denominator.

Rewriting fractions with a common denominator

Now, we need to rewrite 78\dfrac78 and 310\dfrac3{10} with a denominator of 40\blueD{40}.
We need to figure out what to multiply each denominator by to get 40\blueD{40}:
78×5=40\dfrac78\times\dfrac{}{5}=\dfrac{}{\blueD{40}}
310×4=40\dfrac3{10}\times\dfrac{}{4}=\dfrac{}{\blueD{40}}
Next, we multiply the numerators by the same number as their denominator:
78×55=3540\dfrac78\times\dfrac{5}{5}=\dfrac{35}{\blueD{40}}
310×44=1240\dfrac3{10}\times\dfrac{4}{4}=\dfrac{12}{\blueD{40}}
Now we have written 78\dfrac78 and 310\dfrac3{10} with a common denominator:
78=3540\dfrac78=\dfrac{35}{{40}}
310=1240\dfrac3{10}=\dfrac{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, 25\dfrac{2}{5} and 310\dfrac{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:
Choose all answers that apply:

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