 # What is 8/12 + 9/11? Here's how you add

 8 12
+
 9 11

## Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 8 by 11, and get 88, then we multiply 12 by 11 and get 132. Do the same for the second term. We multiply 9 by 12, and get 108, then multiply 12 by 11 and get 132. So now our fractions look like this:

 88 132
+
 108 132

## Step 2

Since our denominators match, we can add the numerators.

88 + 108 = 196

So the answer is:

 196 132

## Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

 196 132
÷ 2 =
 98 66

Now, try the same number again.

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

 98 66
÷ 2 =
 49 33

Now, try the same number again.

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

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 8/12 + 9/11

 8 12
+
 9 11
=
 49 33
© 2014 Randy Tayler