# What is 4/5 + 10/12?

This is how we add

 4 5
+
 10 12

## 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 12, and get 48, then we multiply 5 by 12 and get 60.

Now for the second term. You multiply 10 by 5, and get 50, then multiply 5 by 12 and get 60.

We now have a new problem, that looks like this:

 48 60
+
 50 60

## Step 2

Since our denominators match, we can add the numerators.

48 + 50 = 98

That gives us the sum, which is

 98 60

## 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:

 98 60
÷ 2 =
 49 30

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...

No good. 31 is larger than 30. So we're done reducing.

Congratulations! Here's your final answer to 4/5 + 10/12

 4 5
+
 10 12
=
 49 30
© 2014 Randy Tayler