 # What is 3/9 + 5/10? This is how to add

 3 9
+
 5 10

## Step 1

Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.

So, we multiply 3 by 10, and get 30, then we multiply 9 by 10 and get 90. Now for the second term. You multiply 5 by 9, and get 45, then multiply 9 by 10 and get 90. We now have a new problem, that looks like this:

 30 90
+
 45 90

## Step 2

Since our denominators match, we can add the numerators.

30 + 45 = 75

Answer:

 75 90

## Step 3

Now, do we need to simplify this fraction?

First, we attempt to divide it by 2...

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:

 75 90
÷ 3 =
 25 30

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:

 25 30
÷ 5 =
 5 6

Let's try dividing by that again...

Nope! So now we try the next greatest prime number, 7...

No good. 7 is larger than 5. So we're done reducing.

There you have it! Here's the final answer to 3/9 + 5/10

 3 9
+
 5 10
=
 5 6
© 2014 Randy Tayler