 # What is 3/9 + 4/12? Here's how to add

 3 9
+
 4 12

## 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 3 by 12, and get 36, then we multiply 9 by 12 and get 108. Do the same for the second term. We multiply 4 by 9, and get 36, then multiply 9 by 12 and get 108. So now our fractions look like this:

 36 108
+
 36 108

## Step 2

Since our denominators match, we can add the numerators.

36 + 36 = 72

Now we have an answer.

 72 108

## 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...

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

 72 108
÷ 2 =
 36 54

Now, try the same number again.

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

 36 54
÷ 2 =
 18 27

Now, try the same number again.

Nope. Try the next prime number, 3...

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

 18 27
÷ 3 =
 6 9

Now, try the same number again.

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

 6 9
÷ 3 =
 2 3

Now, try the same number again.

No good. 3 is larger than 2. So we're done reducing.

Congratulations! Here's your final answer to 3/9 + 4/12

 3 9
+
 4 12
=
 2 3
© 2014 Randy Tayler