 # What is 3/4 + 2/9? Here's how we add

 3 4
+
 2 9

## 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 9, and get 27, then we multiply 4 by 9 and get 36. Do the same for the second term. We multiply 2 by 4, and get 8, then multiply 4 by 9 and get 36. The problem now has new fractions to add:

 27 36
+
 8 36

## Step 2

Since our denominators match, we can add the numerators.

27 + 8 = 35

This yields the answer

 35 36

## 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...

Nope! So now we try the next greatest prime number, 37...

No good. 37 is larger than 35. So we're done reducing.

There you have it! Here's the final answer to 3/4 + 2/9

 3 4
+
 2 9
=
 35 36
© 2014 Randy Tayler