# 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 $\dfrac78$ and $\dfrac3{10}$.
The denominators are $8$ and $10$. Let's list multiples of each:
Multiples of $8$: $8, 16, 24, 32, \blueD{40}, 48, 56, 64 ,72, \blueD{80}...$
Multiples of $10$: $10, 20, 30, \blueD{40}, 50, 60, 70, \blueD{80}, 90, 100...$
$\blueD{40}$ and $\blueD{80}$ 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 $\blueD{40}$ for our common denominator.

## Rewriting fractions with a common denominator

Now, we need to rewrite $\dfrac78$ and $\dfrac3{10}$ with a denominator of $\blueD{40}$.
We need to figure out what to multiply each denominator by to get $\blueD{40}$:
$\dfrac78\times\dfrac{}{5}=\dfrac{}{\blueD{40}}$
$\dfrac3{10}\times\dfrac{}{4}=\dfrac{}{\blueD{40}}$
Next, we multiply the numerators by the same number as their denominator:
$\dfrac78\times\dfrac{5}{5}=\dfrac{35}{\blueD{40}}$
$\dfrac3{10}\times\dfrac{4}{4}=\dfrac{12}{\blueD{40}}$
Now we have written $\dfrac78$ and $\dfrac3{10}$ with a common denominator:
$\dfrac78=\dfrac{35}{{40}}$
$\dfrac3{10}=\dfrac{12}{{40}}$
Note: The new fractions are equal to their original form, however they are often easier to work with when the denominators are the same.
You have two fractions, $\dfrac{2}{5}$ and $\dfrac{3}{10}$, and you want to rewrite them so that they have the same denominator (and whole number numerators).