 # What is 3/12 + 7/10? Here's how we add

 3 12
+
 7 10

## 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 3 by 10, and get 30, then we multiply 12 by 10 and get 120. Do the same for the second term. We multiply 7 by 12, and get 84, then multiply 12 by 10 and get 120. So now our fractions look like this:

 30 120
+
 84 120

## Step 2

Since our denominators match, we can add the numerators.

30 + 84 = 114

So the answer is:

 114 120

## 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:

 114 120
÷ 2 =
 57 60

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...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

 57 60
÷ 3 =
 19 20

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. 23 is larger than 19. So we're done reducing.

And we're done! Here's the final answer to 3/12 + 7/10

 3 12
+
 7 10
=
 19 20
© 2014 Randy Tayler