 # What is 7/10 + 8/12? This is how you add

 7 10
+
 8 12

## Step 1

We still have different denominators (bottom numbers), though, so we need to get a common denominator. This will make the bottom numbers match. Multiply the denominators together first. Now, multiply each numerator by the other term's denominator.

Now we multiply 7 by 12, and get 84, then we multiply 10 by 12 and get 120. Now for the second term. You multiply 8 by 10, and get 80, then multiply 10 by 12 and get 120. This gives us a new problem that looks like so:

 84 120
+
 80 120

## Step 2

Since our denominators match, we can add the numerators.

84 + 80 = 164

So what's the answer so far?

 164 120

## Step 3

Can this fraction be reduced?

First, we attempt to divide it by 2...

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

 164 120
÷ 2 =
 82 60

Now, try the same number again.

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

 82 60
÷ 2 =
 41 30

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...

No good. 31 is larger than 30. So we're done reducing.

Congratulations! Here's your final answer to 7/10 + 8/12

 7 10
+
 8 12
=
 41 30
© 2014 Randy Tayler