 # What is 9/12 + 8/9? 9 12
+
 8 9

## 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 9, and get 81, then we multiply 12 by 9 and get 108. Do the same for the second term. We multiply 8 by 12, and get 96, then multiply 12 by 9 and get 108. The problem now has new fractions to add:

 81 108
+
 96 108

## Step 2

Since our denominators match, we can add the numerators.

81 + 96 = 177

The sum we get is

 177 108

## 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:

 177 108
÷ 3 =
 59 36

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. 37 is larger than 36. So we're done reducing.

And we're done! Here's the final answer to 9/12 + 8/9

 9 12
+
 8 9
=
 59 36