Why does multiplying by 0 equal 0?

[Tedjn]

I have only one thing to say about this discussion: I opened it up, read the problem, thought of my answer, then looked at the first post and realized I just thought of the same response I posted two years ago. Obviously, little progress has been made on the math front ;)

 

[jquark]

adding, you add 100 to zero. that's 100 * 1. one instance of 100. zero instances of 100 is none.

 

[shinkyo00]

One possible conceptual way to think about it is to say, multiplying 2 * 100 is like having 2 groups of 100 cookies on the table. Multiplying 1 * 100 is like having 1 group of 100 cookies on the table. Multiplying 0 * 100 is like having no groups of 100 cookies on the table, hence no cookies at all.

However, I agree that this is may not be very intuitive. When dealing with 0, it is sometimes more difficult to match mathematical situations to real life situations. It is probably better to understand 0 * any number = 0 just as a consequence of several properties of numbers that we take for granted.

as a perhaps redundant addition:

0 * 100 is 0 groups of 100, or 100 groups of 0

if you take 0 to mean nothing, then you end up with 0

otherwise, if you don't assign a meaning to 0, then you end up with:

0 * 100 = 0 groups of 100 = 0 groups of 100 = ... ad infinitum

so the only sensible thing to do is assign it with a meaning (nothing)

also, this helps explain why you can't divide by 0

this is really a physical "proof" of the idea though

 

[asdfghjklqqww]

EDIT: I think the French don't have this problem …
they distinguish between (pardon my French! ) …
"multiplier par rien" and "ne multiplier par rien"[/QUOTE]

very true :)

 

[asdfghjklqqww]

oops i failed with the quote thing :(
but you get the idea!
:)

 

[netslider]

This is far too natural to be confusing. Remember that multiplication is repeated addition. If you add 100, ZERO times, you have ZERO. If you want 100 as result, then you must add 100 ONE time.

Hi all.
Just saw this post and wanted to follow up with a question that will address this point: the issue is in the order, if you think about it. What if one sees the issue as not adding 100 zeros, but as adding 100 zero times (read this carefully, as it confuses people even if I speak it in person). Basically the statement that if you have 100 already and you don't add anything to it (as you add 100 zero times, thus add nothing or anything really). So the order of numbers comes to play, in a way, and so when let's say 8*5 is the same as 5*8, when it come to zero it's not interchangeable (or at least one can argue that perception may be argued). It is partially a language issue, I def agree with that. But it also seems to be the issue of view point and perception of the order in the world.
I’m not a mathematician by trade at all but whole zero concept always got to me. I should say that I was always somewhat bright when it came to math and I liked to think deeply about it when I was in high school. Comes from having a grandfather physicist I guess and ironically this issue was actually seeded in me by the same grandfather (though I think he only wanted to mass with me at the time and make me think). In reality I understand that the concept works and all, but it still bugs me that in practical applications there is certain way of perceiving multiplication by zero that does create some confusion.
In any event, if someone looking for some helpful links, I found these very straight forward:
http://mathforum.org/library/drmath/view/61435.html
http://www.math.utah.edu/~pa/math/0by0.html