 # What is 3/4 + 5/10? Let's add

 3 4
+
 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 4 by 10 and get 40. Do the same for the second term. We multiply 5 by 4, and get 20, then multiply 4 by 10 and get 40. The problem now has new fractions to add:

 30 40
+
 20 40

## Step 2

Since our denominators match, we can add the numerators.

30 + 20 = 50

The sum we get is

 50 40

## 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:

 50 40
÷ 2 =
 25 20

Now, try the same number again.

Nope. Try the next prime number, 3...

Nope. Try the next prime number, 5...

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

 25 20
÷ 5 =
 5 4

Now, try the same number again.

No good. 5 is larger than 4. So we're done reducing.

Congratulations! Here's your final answer to 3/4 + 5/10

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