 # What is 3/10 + 10/12? Here's how to add

 3 10
+
 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 3 by 12, and get 36, then we multiply 10 by 12 and get 120. Now for the second term. You multiply 10 by 10, and get 100, then multiply 10 by 12 and get 120. We now have a new problem, that looks like this:

 36 120
+
 100 120

## Step 2

Since our denominators match, we can add the numerators.

36 + 100 = 136

Answer:

 136 120

## 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:

 136 120
÷ 2 =
 68 60

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

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

 68 60
÷ 2 =
 34 30

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

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

 34 30
÷ 2 =
 17 15

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. 17 is larger than 15. So we're done reducing.

And we're done! Here's the final answer to 3/10 + 10/12

 3 10
+
 10 12
=
 17 15
© 2014 Randy Tayler