# What is 1/2 + 5/10?

Here's how we add

 1 2
+
 5 10

## Step 1

Now we need to make our denominators match.

Since 2 is evenly divided by 10, we can multiply just one term to get a common denominator.

Multiply 1 by 5, and get 5, then we multiply 2 by 5 and get 10.

The problem now has new fractions to add:

 5 10
+
 5 10

## Step 2

Since our denominators match, we can add the numerators.

5 + 5 = 10

This yields the answer

 10 10

## 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:

 10 10
÷ 2 =
 5 5

Let's try dividing by that again...

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

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:

 5 5
÷ 5 =
 1 1

Let's try dividing by that again...

No good. 5 is larger than 1. So we're done reducing.

There you have it! Here's the final answer to 1/2 + 5/10

 1 2
+
 5 10
=
 1 1
= 1
© 2014 Randy Tayler