 # What is 3/10 + 2/3? Here's how we add

 3 10
+
 2 3

## 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 3 by 3, and get 9, then we multiply 10 by 3 and get 30. Do the same for the second term. We multiply 2 by 10, and get 20, then multiply 10 by 3 and get 30. The problem now has new fractions to add:

 9 30
+
 20 30

## Step 2

Since our denominators match, we can add the numerators.

9 + 20 = 29

This yields the answer

 29 30

## Step 3

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

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

Nope! So now we try the next greatest prime number, 3...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

Nope! So now we try the next greatest prime number, 11...

Nope! So now we try the next greatest prime number, 13...

Nope! So now we try the next greatest prime number, 17...

Nope! So now we try the next greatest prime number, 19...

Nope! So now we try the next greatest prime number, 23...

Nope! So now we try the next greatest prime number, 29...

Nope! So now we try the next greatest prime number, 31...

No good. 31 is larger than 29. So we're done reducing.

There you have it! Here's the final answer to 3/10 + 2/3

 3 10
+
 2 3
=
 29 30
© 2014 Randy Tayler