Division and zero can seem tricky, but its really not that bad. There are a number of ways to approach understanding this topic. Here, we will
look at division with zero as it relates to multiplication and we will also explore division with zero logically.

Remember that the answer to a division problem is one part of a multiplication problem. Example: 6 / 3 equals the other value that, when multiplied by 3, gives you 6. So when you divide 6 by 3, you say "what times 3 equals six?". 2!

What is 0 / 4? Well, what times 4 gives you 0? 0!   What is 0 / 5? What times 5 gives you 0? 0!
Zero divided by any number is 0, because 0 times any number is 0. There is only one exception to this...

What is 4 / 0? Well, what times 0 equals 4? Don't know? Well, you're in good company, because neither do I.
What is 5 / 0? What times 0 equals 5? Stumped again!
Since there is nothing, we say the answer is undefined. So, 4 / 0 is undefined. 5 / 0 is undefined.

What about 0 / 0? Well, what times 0 equals 0? EVERYTHING! So what's the answer? Undefined.
Anything divided by zero is undefined. There is no exception to this!

Let's take a look at a simple problem like 10 / 2 (ten divided by 2). What does this mean?
Most would say, "take 10 things and divide into 2 equal groups." Some might say, "Take 10 things and divide into groups of 2 things." Each is different, but produce the same result. The result of the first is how many things are in each group. The result of the second is how many groups can be made. Regardless of the logical approach, the result is the same - 5.

Let's add zero now.

What does 0 / 2 mean? Let's look at both forms of logic.
1. Divide 0 things evenly into 2 groups. How many are in each group? Well, if you have 0 things, there will be 0 things in each group.
2. Divide 0 things into groups of 2. How many groups of 2 things can you make? Well, if you have 0 things, you can't make any groups of 2, therefore, you have 0 groups.
Either way, 0 / 2 = 0. Try it with another value, it works the same way. There is only one exception...

What does 10 / 0 mean? Let's again look at both forms of logic.
1. Divide 10 things evenly into 0 groups. How many are in each group? Hmmm...tough one. Can you make 0 groups out of 10 things?
The 10 things are already in 1 group...how do I make that 0 groups? You can't! That's why its undefined.
2. Divide 10 things into groups of 0 things. How many groups of 0 things can I make? Well, as many as you want, but you'll never really get rid of those 10 things. That's why its undefined.

Here it is, in a nutshell. If nothing else, remember this...
1. Division BY zero is undefined. [When zero is in the denominator, the quotient is undefined]
2. You can divided zero by any number (except zero) - the quotient is zero. [When zero is in the numerator, but not in the denominator, the answer is 0]