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