Dividing by zero

[Surgenator]

I like the sandwich idea. Why would you try to divide a sandwich between zero people and how would you know when you were through?

I see, but why is it ok to multiply by zero? I'm not being obtuse, I seriously don't know. lol

This is the simpliest example I know.

x*0 = 0
x can be any number for this equation to be true.
Now I re-arrange my equation to
x = 0/0.
X can be any number.
Hence, 0/0 is not defined because it can be anything.

[Jenny A]

I like the sandwich idea. Why would you try to divide a sandwich between zero people and how would you know when you were through?

I see, but why is it ok to multiply by zero? I'm not being obtuse, I seriously don't know. lol

Multiplication is really just a kind of addition. When you multiply 4 x 5 you are saying add four 5s together: 5 + 5 + 5 +5 = 20.

Reverse the numbers to get 5 x 4 and you are saying add five to 4s together: 4 + 4 + 4+ 4 + 4 = 20.

Notice that regardless of the order of the numbers in the question, the answer is the same: 4 x 5 and 5 x 4 both equal 20.

Now try it with zero. When you multiply 0 x 4 you are saying add zero fours together. Well if you don't have any fours, what do you have? Nothing. Zero

Try it the other way: 4 x 0. Now you are saying add four zeros together: 0 + 0 + 0 + 0 = nothing, nada, zip. Zero.

The answer isn't undefined, it's zero.

[Magilla]

I think of division as follows. Division may be expressed in various ways. For example: (24 ÷ 6) OR (24/6) OR (24 x 6E-1)
In these very simple example formats, what we are saying is: If we have 24 items and split them into 6 equal groups, how many items in each group?
The answer is of course 4 items in each group.
In more abstract terms, we might think of it as: If we begin with the number 24, and rip it apart into 6 equal portions, then what is the number which resides in each of those portions?
Again the answer is of course, 4 items in each portion.

We can divide "distribute" items into equally, 1 group, and the result will the total number of items in the resultant group, (dividing by 1).
We can divide "disperse" a number equally, into 1 portion, and the result will the number itself, (again division by 1).

It makes no sense to divide items or a number into zero groups or portions. It just does not compute. So division by zero is undefined.
Any equation we might formulate which implies a division by zero contains an undefined process, and is flawed because of it.

x = 0/0 cannot result in any number at all, because /0 is undefined from the get-go. You can't divide a number zero ways, even when it's zero at the outset.

[*Deidre*]

I see, but why is it ok to multiply by zero? I'm not being obtuse, I seriously don't know. lol

Multiplication is really just a kind of addition. When you multiply 4 x 5 you are saying add four 5s together: 5 + 5 + 5 +5 = 20.

Reverse the numbers to get 5 x 4 and you are saying add five to 4s together: 4 + 4 + 4+ 4 + 4 = 20.

Notice that regardless of the order of the numbers in the question, the answer is the same: 4 x 5 and 5 x 4 both equal 20.

Now try it with zero. When you multiply 0 x 4 you are saying add zero fours together. Well if you don't have any fours, what do you have? Nothing. Zero

Try it the other way: 4 x 0. Now you are saying add four zeros together: 0 + 0 + 0 + 0 = nothing, nada, zip. Zero.

The answer isn't undefined, it's zero.

Thank you! THIS...makes perfect sense to me, now.

[Smaug]

Multiplying by zero equals zero.

It's true for real numbers algebra.

It's interesting, however, that you could come up with a set and with a binary operation (multiplication) where a, b are not zero yet a*b = 0. For example, in a ring of residues modulo 6: [2]*[3]=[0] (while [2] =/= [0], and [3] =/= [0]). Not going into much details I'd point out that zero here is an additively-neutral element: [a] + [0] = [a] just like a+0=a in case of real numbers.

[Mental Outlaw]

I'm not a math wiz. Why is it you can multiply by zero and get zero but you can't divide by zero?

Why doesn't 1/0 equal 0 but 1*0 does? Is there a reason or is it arbitrary?

If you have 1 apple 0 times then you have 0 apples, thus 1*0 = 0 however if you tried to divide 1 apple between 0 people that would be impossible since you can't split something by nothing.

[bennyboy]

I'm not a math wiz. Why is it you can multiply by zero and get zero but you can't divide by zero?

Why doesn't 1/0 equal 0 but 1*0 does? Is there a reason or is it arbitrary?

If you have 1 apple 0 times then you have 0 apples, thus 1*0 = 0 however if you tried to divide 1 apple between 0 people that would be impossible since you can't split something by nothing.

[GrandizerII]

I can imagine splitting nothing by nothing but not something by nothing. Splitting nothing by nothing leads to infinite numerical answers while splitting something by nothing makes no sense. Either way, both lead to undefined answers.