 # What is 8/10 + 7/9? This is how to add

 8 10
+
 7 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 8 by 9, and get 72, then we multiply 10 by 9 and get 90. Do the same for the second term. We multiply 7 by 10, and get 70, then multiply 10 by 9 and get 90. The problem now has new fractions to add:

 72 90
+
 70 90

## Step 2

Since our denominators match, we can add the numerators.

72 + 70 = 142

This yields the answer

 142 90

## Step 3

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

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:

 142 90
÷ 2 =
 71 45

Now, try the same number again.

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...

Nope. Try the next prime number, 43...

Nope. Try the next prime number, 47...

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

Congratulations! Here's your final answer to 8/10 + 7/9

 8 10
+
 7 9
=
 71 45
© 2014 Randy Tayler