 # What is 3/12 + 6/10? This is how we add

 3 12
+
 6 10

## 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 3 by 10, and get 30, then we multiply 12 by 10 and get 120. Now for the second term. You multiply 6 by 12, and get 72, then multiply 12 by 10 and get 120. We now have a new problem, that looks like this:

 30 120
+
 72 120

## Step 2

Since our denominators match, we can add the numerators.

30 + 72 = 102

That gives us the sum, which is

 102 120

## 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:

 102 120
÷ 2 =
 51 60

Now, try the same number again.

Nope. Try the next prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

 51 60
÷ 3 =
 17 20

Now, try the same number again.

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...

No good. 19 is larger than 17. So we're done reducing.

Congratulations! Here's your final answer to 3/12 + 6/10

 3 12
+
 6 10
=
 17 20
© 2014 Randy Tayler