As shown is the typical fraction.
But one day, a student asked a question to our teacher, "Why can't you represent a fraction with a Zero in the denominator (sometimes called 'dividing by zero')?" 
The teacher's answer was a bit harsh, straight forward, and authoritative: "You can't divide by Zero because it is not defined!"
That was it, no explanation, no sympathy for an inquisitive student. Done!

Years later, this subject was reapproached from a different perspective and there is a much simpler and intuitive answer that the teacher could have provided: 

"It's because Zero is NOT A NUMBER"


Epilogue:
Little did the Math Teacher realize what a great opportunity for 'getting off task' this question provided.
The gradual acceptance of Zero and its subsequent use spanned the globe: Ancient Mayan, Eqyptian, China, India, Persia, Greco-Roman, and finally in the 12th century to European mathematics.
The mystery of Zero includes religion, history, practicality, positional numbering systems, and disputes and discussions of how to represent NOTHING, which in times past, had a god-like, invisible quality. (And when god was involved you had some very polarized opinions!) 


So if you are not overloaded on math at this point, I suggest you continue with the audio podcast link below.


Enjoy the Podcast!
Sincerely
Virtual Saguaro

Following are some internet links to articles on this topic of Zero. 
Keep in mind that these scholars have perhaps not had the opportunity to listen to this podcast. It seems they quickly place Zero into the number system as a number without regard to its 'nothingness'. :)

The History of Zero, by the Yale Center
The Origin of Zero, by Scientific American
“Zero, The Biography of a Dangerous Idea”, by Charles Seife, Book Available at Amazon
Representations of Numbers, Encyclopedia of Mathematics
0 (Number), Wikipedia
"Numbers Song in French"  Written and performed by A.J. Jenkins - Audio Segment used in Podcast

"Increasing America’s debt weakens us domestically and internationally. Leadership means that ‘‘the buck stops here.’’ Instead, Washington is shifting the burden of bad choices today onto the backs of our children and grandchildren. America has a debt problem and a failure of leadership. Americans deserve better."

I therefore intend to oppose the effort to increase America’s debt limit.

It appears that once you get elected president, that your beliefs of what is detrimental to the USA society can change - drastically.

Listen to an impassioned speech delivered in 2006 by the current president insisting that increasing the federal deficit was a drastic and irresponsible mistake.

You may READ the entire text of the Congressional Record by clicking this link 
S2238 CONGRESSIONAL RECORD — SENATE March 16, 2006

Intro:
You've seen this line a hundred million times, snaking its way along the roof line of your math class. Long, detailed fractions occassionaly interspersed with some positions for prime numbers. Enchanting color coordinated paper strips to complement the room's theme: MATHS (as some of the world calls it)

Background:
Having asked the following question many times and not receiving a sufficiently simple answer, I always wondered why teachers were so defensive when asked, "Since we are allowed to ask how parts of something are there in another something (allowed to divide any number by any other number) , "Why can't we divide any number by ZERO?"
"Just because you can't - it's undefined!" was the retort. What did I know, I was a just an inquiriing student asking a question.....

Let's digress for a minute. The concept of nothingness, emptiness, invisibility has been looked at by cultures in very different ways. If you can't see something it was relegated to the domain of the gods many years ago. Bacteria, electrons, magnetic fields, TV signals, practically the entire electromagnetic spectrum was invisible and unknown for most of human history. The very idea of having a symbol to represent NOTHINGNESS was tinkering with the realms of mystery and religion.
Yet, as the world of maths evolved and we bumped into the need for a place marker to satisfy our position number system, voila the ZERO appeared. It was a brilliant solution. No longer was a Nine only a Nine. If it was to the left of a zero, it was Nine units of ten, and no units of ones, resulting in 90. We leapt from hash marks on endless streams of paper, crossing every fourth mark to make an easy counting by fives, it was obvious looking at an abacus that something was needed to represent a positional nothing. 
Slowly, this symbol, not really a number, began to have equality to a number. We recited and placed it in the lowest integer position. We were taught that any number multiplied by zero equaled zero. (At least they didn't teach us that it was undefined)
I just wish they had insisted in our learning that multiplying by zero is a fantastic journey of imagination, stating the process a little differently: 3 times 2 would be stated "What is the total of 2 sets of 3?"
Then when asked, 3 times 0 would turn out to be "What is the total of ZERO sets of 3? -- No need to make a didactic rule stating that all numbers multiplied by zero would be zero, the question doesn't even deserve an answer.