 # What is 8/10 + 5/9? Here's how we add

 8 10
+
 5 9

## 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 8 by 9, and get 72, then we multiply 10 by 9 and get 90. Do the same for the second term. We multiply 5 by 10, and get 50, then multiply 10 by 9 and get 90. So now our fractions look like this:

 72 90
+
 50 90

## Step 2

Since our denominators match, we can add the numerators.

72 + 50 = 122

So the answer is:

 122 90

## 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...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

 122 90
÷ 2 =
 61 45

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 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. So next you try the next prime number, which is 47...

No good. 47 is larger than 45. So we're done reducing.

And we're done! Here's the final answer to 8/10 + 5/9

 8 10
+
 5 9
=
 61 45
© 2014 Randy Tayler