 # What is 5/12 + 5/9? 5 12
+
 5 9

## Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 5 by 9, and get 45, then we multiply 12 by 9 and get 108. Now for the second term. You multiply 5 by 12, and get 60, then multiply 12 by 9 and get 108. We now have a new problem, that looks like this:

 45 108
+
 60 108

## Step 2

Since our denominators match, we can add the numerators.

45 + 60 = 105

That gives us the sum, which is

 105 108

## Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

Nope. Try the next prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

 105 108
÷ 3 =
 35 36

Now, try the same number again.

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

No good. 37 is larger than 35. So we're done reducing. 