 # What is 2/9 + 10/12? Here's how you add

 2 9
+
 10 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 2 by 12, and get 24, then we multiply 9 by 12 and get 108. Now for the second term. You multiply 10 by 9, and get 90, then multiply 9 by 12 and get 108. This gives us a new problem that looks like so:

 24 108
+
 90 108

## Step 2

Since our denominators match, we can add the numerators.

24 + 90 = 114

That gives us an answer of

 114 108

## 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:

 114 108
÷ 2 =
 57 54

Let's try dividing by that again...

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:

 57 54
÷ 3 =
 19 18

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...

No good. 19 is larger than 18. So we're done reducing.

There you have it! Here's the final answer to 2/9 + 10/12

 2 9
+
 10 12
=
 19 18
© 2014 Randy Tayler