 # What is 10/12 + 6/10? 10 12
+
 6 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 10 by 10, and get 100, then we multiply 12 by 10 and get 120. Do the same for the second term. We multiply 6 by 12, and get 72, then multiply 12 by 10 and get 120. The problem now has new fractions to add:

 100 120
+
 72 120

## Step 2

Since our denominators match, we can add the numerators.

100 + 72 = 172

The sum we get is

 172 120

## 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:

 172 120
÷ 2 =
 86 60

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:

 86 60
÷ 2 =
 43 30

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...

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. So next you try the next prime number, which is 29...

No good. So next you try the next prime number, which is 31...

No good. 31 is larger than 30. So we're done reducing.

And we're done! Here's the final answer to 10/12 + 6/10

 10 12
+
 6 10
=
 43 30