 # What is 2/3 + 2/7? Here's how to add

 2 3
+
 2 7

## 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 2 by 7, and get 14, then we multiply 3 by 7 and get 21. Do the same for the second term. We multiply 2 by 3, and get 6, then multiply 3 by 7 and get 21. The problem now has new fractions to add:

 14 21
+
 6 21

## Step 2

Since our denominators match, we can add the numerators.

14 + 6 = 20

The sum we get is

 20 21

## Step 3

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

To find out, we try dividing it by 2...

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. 23 is larger than 20. So we're done reducing.

And we're done! Here's the final answer to 2/3 + 2/7

 2 3
+
 2 7
=
 20 21
© 2014 Randy Tayler