 # What is 1/4 + 5/10? This is how to add

 1 4
+
 5 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 1 by 10, and get 10, 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. So now our fractions look like this:

 10 40
+
 20 40

## Step 2

Since our denominators match, we can add the numerators.

10 + 20 = 30

Now we have an answer.

 30 40

## 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:

 30 40
÷ 2 =
 15 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 3...

No good. So next you try the next prime number, which is 5...

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

 15 20
÷ 5 =
 3 4

So far so good... let's try to divide by that number again.

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

And we're done! Here's the final answer to 1/4 + 5/10

 1 4
+
 5 10
=
 3 4
© 2014 Randy Tayler