 # What is 9/12 + 6/11? This is how we add

 9 12
+
 6 11

## Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 9 by 11, and get 99, then we multiply 12 by 11 and get 132. Do the same for the second term. We multiply 6 by 12, and get 72, then multiply 12 by 11 and get 132. The problem now has new fractions to add:

 99 132
+
 72 132

## Step 2

Since our denominators match, we can add the numerators.

99 + 72 = 171

The sum we get is

 171 132

## Step 3

The last step is to reduce the fraction if we can.

To find out, we try dividing it by 2...

No good. So next you try the next prime number, which is 3...

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

 171 132
÷ 3 =
 57 44

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. So next you try the next prime number, which is 37...

No good. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. So next you try the next prime number, which is 47...

No good. 47 is larger than 44. So we're done reducing.

And we're done! Here's the final answer to 9/12 + 6/11

 9 12
+
 6 11
=
 57 44
© 2014 Randy Tayler