Common denominators review

When fractions have the same denominator, we say they have common denominators.

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.

Find a common denominator for ${\displaystyle \frac{7}{8}}$‍ and ${\displaystyle \frac{3}{10}}$‍.

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.

Now, we need to rewrite ${\displaystyle \frac{7}{8}}$‍ and ${\displaystyle \frac{3}{10}}$‍ 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 ${\displaystyle \frac{7}{8}}$‍ and ${\displaystyle \frac{3}{10}}$‍ 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 try more problems like this? Check out this exercise.