 # What is 9/12 + 10/11? Here's how to add

 9 12
+
 10 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 10 by 12, and get 120, then multiply 12 by 11 and get 132. The problem now has new fractions to add:

 99 132
+
 120 132

## Step 2

Since our denominators match, we can add the numerators.

99 + 120 = 219

This yields the answer

 219 132

## Step 3

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

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

Nope! So now we try the next greatest prime number, 3...

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

 219 132
÷ 3 =
 73 44

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

Nope! So now we try the next greatest prime number, 41...

Nope! So now we try the next greatest prime number, 43...

Nope! So now we try the next greatest prime number, 47...

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

There you have it! Here's the final answer to 9/12 + 10/11

 9 12
+
 10 11
=
 73 44
© 2014 Randy Tayler