 # What is 9/12 + 7/10? This is how we add

 9 12
+
 7 10

## Step 1

Of course, you can't add two fractions if the denominators (bottom numbers) don't match. To get a common denominator, multiply the denominators together. Then we fix the numerators by multiplying each one by their other term's denominator.

Now you multiply 9 by 10, and get 90, then we multiply 12 by 10 and get 120. Do the same for the second term. We multiply 7 by 12, and get 84, then multiply 12 by 10 and get 120. The problem now has new fractions to add:

 90 120
+
 84 120

## Step 2

Since our denominators match, we can add the numerators.

90 + 84 = 174

The sum we get is

 174 120

## Step 3

The last step is to reduce the fraction if we can.

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:

 174 120
÷ 2 =
 87 60

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:

 87 60
÷ 3 =
 29 20

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. So next you try the next prime number, which is 19...

No good. So next you try the next prime number, which is 23...

No good. 23 is larger than 20. So we're done reducing.

And we're done! Here's the final answer to 9/12 + 7/10

 9 12
+
 7 10
=
 29 20
© 2014 Randy Tayler