 # What is 1/10 + 6/9? Here's how you add

 1 10
+
 6 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 1 by 9, and get 9, then we multiply 10 by 9 and get 90. Do the same for the second term. We multiply 6 by 10, and get 60, then multiply 10 by 9 and get 90. The problem now has new fractions to add:

 9 90
+
 60 90

## Step 2

Since our denominators match, we can add the numerators.

9 + 60 = 69

This yields the answer

 69 90

## Step 3

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

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:

 69 90
÷ 3 =
 23 30

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. 29 is larger than 23. So we're done reducing.

And we're done! Here's the final answer to 1/10 + 6/9

 1 10
+
 6 9
=
 23 30
© 2014 Randy Tayler