 # What is 4/10 + 3/12? Let's add

 4 10
+
 3 12

## Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 4 by 12, and get 48, then we multiply 10 by 12 and get 120. Now for the second term. You multiply 3 by 10, and get 30, then multiply 10 by 12 and get 120. This gives us a new problem that looks like so:

 48 120
+
 30 120

## Step 2

Since our denominators match, we can add the numerators.

48 + 30 = 78

So what's the answer so far?

 78 120

## Step 3

Can this fraction be reduced?

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

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

 78 120
÷ 2 =
 39 60

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...

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

 39 60
÷ 3 =
 13 20

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 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 13. So we're done reducing.

And we're done! Here's the final answer to 4/10 + 3/12

 4 10
+
 3 12
=
 13 20
© 2014 Randy Tayler