 What is 6/11 + 3/12? 6 11
+
 3 12

Step 1

We can't add two fractions with different denominators (the bottom number). So you need to get a common denominator - both bottom numbers need to match. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 6 by 12, and get 72, then we multiply 11 by 12 and get 132. Do the same for the second term. We multiply 3 by 11, and get 33, then multiply 11 by 12 and get 132. So now our fractions look like this:

 72 132
+
 33 132

Step 2

Since our denominators match, we can add the numerators.

72 + 33 = 105

 105 132

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

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

No good. So next you try the next prime number, which is 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

 105 132
÷ 3 =
 35 44

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 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. So next you try the next prime number, which is 37...

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

And we're done! Here's the final answer to 6/11 + 3/12

 6 11
+
 3 12
=
 35 44