 # What is 1/10 + 3/11? Here's how we add

 1 10
+
 3 11

## Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 1 by 11, and get 11, then we multiply 10 by 11 and get 110. Now for the second term. You multiply 3 by 10, and get 30, then multiply 10 by 11 and get 110. This gives us a new problem that looks like so:

 11 110
+
 30 110

## Step 2

Since our denominators match, we can add the numerators.

11 + 30 = 41

That gives us an answer of

 41 110

## Step 3

Can this fraction be reduced?

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

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...

Nope. Try the next prime number, 41...

Nope. Try the next prime number, 43...

No good. 43 is larger than 41. So we're done reducing.

Congratulations! Here's your final answer to 1/10 + 3/11

 1 10
+
 3 11
=
 41 110
© 2014 Randy Tayler