 # What is 1/11 + 3/7? Let's add

 1 11
+
 3 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 1 by 7, and get 7, then we multiply 11 by 7 and get 77. Do the same for the second term. We multiply 3 by 11, and get 33, then multiply 11 by 7 and get 77. The problem now has new fractions to add:

 7 77
+
 33 77

## Step 2

Since our denominators match, we can add the numerators.

7 + 33 = 40

The sum we get is

 40 77

## Step 3

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

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

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

Nope. Try the next prime number, 7...

Nope. Try the next prime number, 11...

Nope. Try the next prime number, 13...

Nope. Try the next prime number, 17...

Nope. Try the next prime number, 19...

Nope. Try the next prime number, 23...

Nope. Try the next prime number, 29...

Nope. Try the next prime number, 31...

Nope. Try the next prime number, 37...

Nope. Try the next prime number, 41...

No good. 41 is larger than 40. So we're done reducing.

Congratulations! Here's your final answer to 1/11 + 3/7

 1 11
+
 3 7
=
 40 77
© 2014 Randy Tayler