 # What is 9/12 + 6/9? Let's add

 9 12
+
 6 9

## Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 9 by 9, and get 81, then we multiply 12 by 9 and get 108. Do the same for the second term. We multiply 6 by 12, and get 72, then multiply 12 by 9 and get 108. So now our fractions look like this:

 81 108
+
 72 108

## Step 2

Since our denominators match, we can add the numerators.

81 + 72 = 153

Now we have an answer.

 153 108

## Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing 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:

 153 108
÷ 3 =
 51 36

Let's try dividing by that again...

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

 51 36
÷ 3 =
 17 12

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...

No good. 13 is larger than 12. So we're done reducing.

There you have it! Here's the final answer to 9/12 + 6/9

 9 12
+
 6 9
=
 17 12
© 2014 Randy Tayler