 # What is 4/10 + 6/11? This is how we add

 4 10
+
 6 11

## 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 4 by 11, and get 44, then we multiply 10 by 11 and get 110. Now for the second term. You multiply 6 by 10, and get 60, then multiply 10 by 11 and get 110. We now have a new problem, that looks like this:

 44 110
+
 60 110

## Step 2

Since our denominators match, we can add the numerators.

44 + 60 = 104

That gives us the sum, which is

 104 110

## Step 3

Now, do we need to simplify this fraction?

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

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

 104 110
÷ 2 =
 52 55

Now, try the same number again.

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...

Nope. Try the next prime number, 53...

No good. 53 is larger than 52. So we're done reducing.

Congratulations! Here's your final answer to 4/10 + 6/11

 4 10
+
 6 11
=
 52 55
© 2014 Randy Tayler