 # What is 5/12 + 7/9? Here's how you add

 5 12
+
 7 9

## 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 5 by 9, and get 45, then we multiply 12 by 9 and get 108. Now for the second term. You multiply 7 by 12, and get 84, then multiply 12 by 9 and get 108. This gives us a new problem that looks like so:

 45 108
+
 84 108

## Step 2

Since our denominators match, we can add the numerators.

45 + 84 = 129

That gives us an answer of

 129 108

## Step 3

Can this fraction be reduced?

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

Nope! So now we try the next greatest prime number, 3...

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

 129 108
÷ 3 =
 43 36

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

Nope! So now we try the next greatest prime number, 37...

No good. 37 is larger than 36. So we're done reducing.

There you have it! Here's the final answer to 5/12 + 7/9

 5 12
+
 7 9
=
 43 36
© 2014 Randy Tayler