# What is 3/10 + 4/6?

This is how you add

 3 10
+
 4 6

## 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 6, and get 18, then we multiply 10 by 6 and get 60.

Now for the second term. You multiply 4 by 10, and get 40, then multiply 10 by 6 and get 60.

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

 18 60
+
 40 60

## Step 2

Since our denominators match, we can add the numerators.

18 + 40 = 58

That gives us the sum, which is

 58 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:

 58 60
÷ 2 =
 29 30

So far so good... let's try to divide by that number again.

No good. So next you try the next prime number, which is 3...

No good. So next you try the next prime number, which is 5...

No good. So next you try the next prime number, which is 7...

No good. So next you try the next prime number, which is 11...

No good. So next you try the next prime number, which is 13...

No good. So next you try the next prime number, which is 17...

No good. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. 31 is larger than 29. So we're done reducing.

And we're done! Here's the final answer to 3/10 + 4/6

 3 10
+
 4 6
=
 29 30
© 2014 Randy Tayler