 # What is 7/16 + 9/12? 7 16
+
 9 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 7 by 12, and get 84, then we multiply 16 by 12 and get 192. Do the same for the second term. We multiply 9 by 16, and get 144, then multiply 16 by 12 and get 192. So now our fractions look like this:

 84 192
+
 144 192

## Step 2

Since our denominators match, we can add the numerators.

84 + 144 = 228

 228 192

## 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:

 228 192
÷ 2 =
 114 96

So far so good... let's try to divide by that number again.

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

 114 96
÷ 2 =
 57 48

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:

 57 48
÷ 3 =
 19 16

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 16. So we're done reducing.

And we're done! Here's the final answer to 7/16 + 9/12

 7 16
+
 9 12
=
 19 16