 What is 1/11 + 3/5? This is how to add

 1 11
+
 3 5

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 1 by 5, and get 5, then we multiply 11 by 5 and get 55. Do the same for the second term. We multiply 3 by 11, and get 33, then multiply 11 by 5 and get 55. So now our fractions look like this:

 5 55
+
 33 55

Step 2

Since our denominators match, we can add the numerators.

5 + 33 = 38

Now we have an answer.

 38 55

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...

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. 41 is larger than 38. So we're done reducing.

And we're done! Here's the final answer to 1/11 + 3/5

 1 11
+
 3 5
=
 38 55
© 2014 Randy Tayler