 # What is 3/12 + 5/10? This is how you add

 3 12
+
 5 10

## 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 3 by 10, and get 30, then we multiply 12 by 10 and get 120. Do the same for the second term. We multiply 5 by 12, and get 60, then multiply 12 by 10 and get 120. The problem now has new fractions to add:

 30 120
+
 60 120

## Step 2

Since our denominators match, we can add the numerators.

30 + 60 = 90

The sum we get is

 90 120

## 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:

 90 120
÷ 2 =
 45 60

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 3...

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

 45 60
÷ 3 =
 15 20

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 5...

Are both the numerator and the denominator evenly divisible by 5? Yes! So we reduce it:

 15 20
÷ 5 =
 3 4

Let's try dividing by that again...

No good. 5 is larger than 3. So we're done reducing.

There you have it! Here's the final answer to 3/12 + 5/10

 3 12
+
 5 10
=
 3 4
© 2014 Randy Tayler