 # What is 8/10 + 9/11? This is how we add

 8 10
+
 9 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 8 by 11, and get 88, then we multiply 10 by 11 and get 110. Do the same for the second term. We multiply 9 by 10, and get 90, then multiply 10 by 11 and get 110. The problem now has new fractions to add:

 88 110
+
 90 110

## Step 2

Since our denominators match, we can add the numerators.

88 + 90 = 178

The sum we get is

 178 110

## Step 3

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

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:

 178 110
÷ 2 =
 89 55

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 3...

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. So next you try the next prime number, which is 53...

No good. So next you try the next prime number, which is 59...

No good. 59 is larger than 55. So we're done reducing.

And we're done! Here's the final answer to 8/10 + 9/11

 8 10
+
 9 11
=
 89 55
© 2014 Randy Tayler