 What is 1/11 + 5/9? Here's how you add

 1 11
+
 5 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 1 by 9, and get 9, then we multiply 11 by 9 and get 99. Do the same for the second term. We multiply 5 by 11, and get 55, then multiply 11 by 9 and get 99. The problem now has new fractions to add:

 9 99
+
 55 99

Step 2

Since our denominators match, we can add the numerators.

9 + 55 = 64

This yields the answer

 64 99

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...

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. So next you try the next prime number, which is 61...

No good. So next you try the next prime number, which is 67...

No good. 67 is larger than 64. So we're done reducing.

And we're done! Here's the final answer to 1/11 + 5/9

 1 11
+
 5 9
=
 64 99
© 2014 Randy Tayler