 What is 1/11 + 2/9? This is how you add

 1 11
+
 2 9

Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 1 by 9, and get 9, then we multiply 11 by 9 and get 99. Now for the second term. You multiply 2 by 11, and get 22, then multiply 11 by 9 and get 99. We now have a new problem, that looks like this:

 9 99
+
 22 99

Step 2

Since our denominators match, we can add the numerators.

9 + 22 = 31

That gives us the sum, which is

 31 99

Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

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. 37 is larger than 31. So we're done reducing.

And we're done! Here's the final answer to 1/11 + 2/9

 1 11
+
 2 9
=
 31 99
© 2014 Randy Tayler