 # What is 1/6 + 6/7? 1 6
+
 6 7

## 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 1 by 7, and get 7, then we multiply 6 by 7 and get 42. Do the same for the second term. We multiply 6 by 6, and get 36, then multiply 6 by 7 and get 42. So now our fractions look like this:

 7 42
+
 36 42

## Step 2

Since our denominators match, we can add the numerators.

7 + 36 = 43

 43 42

## 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...

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. So next you try the next prime number, which is 41...

No good. So next you try the next prime number, which is 43...

No good. 43 is larger than 42. So we're done reducing.

And we're done! Here's the final answer to 1/6 + 6/7

 1 6
+
 6 7
=
 43 42