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

 1 11
+
 3 10

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 10, and get 10, then we multiply 11 by 10 and get 110. Now for the second term. You multiply 3 by 11, and get 33, then multiply 11 by 10 and get 110. This gives us a new problem that looks like so:

 10 110
+
 33 110

Step 2

Since our denominators match, we can add the numerators.

10 + 33 = 43

That gives us an answer of

 43 110

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...

Nope. Try the next prime number, 47...

No good. 47 is larger than 43. So we're done reducing.

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

 1 11
+
 3 10
=
 43 110
© 2014 Randy Tayler