 # What is 5/11 + 6/9? This is how we add

 5 11
+
 6 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 11 by 9 and get 99. Now for the second term. You multiply 6 by 11, and get 66, then multiply 11 by 9 and get 99. We now have a new problem, that looks like this:

 45 99
+
 66 99

## Step 2

Since our denominators match, we can add the numerators.

45 + 66 = 111

That gives us the sum, which is

 111 99

## 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:

 111 99
÷ 3 =
 37 33

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 33. So we're done reducing.

Congratulations! Here's your final answer to 5/11 + 6/9

 5 11
+
 6 9
=
 37 33
© 2014 Randy Tayler