Why can't you divide by zero? Wouldn't zero divided by zero, be one, theoretically?

Answer 1

Nope, 0/0 could be 1 but it could also be anything else. Division is the opposite of multiplication and 0 times anything at all, even infinity, is still zero.

Answer 2

We cannot divide zero by zero because there is no unique answer and it can be anything. Therefore 0/0 is stated as UNDEFINED.

For example, the following equations are true:

0 x 1 = 0
0 x 2 = 0
0 x 3 = 0
0 x 4 = 0
0 x 5 = 0
...
0 x n = 0

However, if 0/0 is allowed, then our equation above becomes,

0 x 1 = 0 imples 1 = 0/0

Doing the same to the other numbers,

1 = 0/0
2 = 0/0
3 = 0/0
4 = 0/0
5 = 0/0
...
n = 0/0

This means that every number is equal to every other number.

1=2=3=4=5=...=n= 0/0

You see the problem.

Hence 0/0 is left as UNDEFINED.

Answer 3

Dividing something by zero is not "allowed" because we cannot make sense of the operation.

A simple way to understand this is to look at the operation:

10 / 2 = 5

What that means is that if you have 10 blocks and divide it into 2 groups, you have 5 blocks in each group. Conversely:

2 x 5 = 10

This means 2 groups of 5 blocks equal 10.

Now apply this to zero:

10 / 0 = ??? and

??? x 0 = 10

Reading the first equation: Dividing 10 blocks into nothing (zero groups) equals... ??? You can't figure it out, because you obviously have 10 blocks to begin with. What does it mean to divide something into nothing?

Reading the second equation: How many groups of zeros equals 10. This obviously makes no sense. You can have a billion groups of zero, but they will never make 10.

Hence, division by zero does not make sense.

Answer 4

Ok, I'm going to answer this question b/c I don't like anyone's answer. You can't divide by zero b/c there are infinite numbers of solutions when you divide by zero whereas when you divide by any other number there is one and only one answer.

Zero divided by zero could be anything. Want a light proof?

Let k be any number, and assume that zero actually does divide zero. So:

0/0=k

multiply both sides by zero we get:

0=k*0

Now what value/s can k take on? ANY VALUE. Hence 0/0 is undefined becuase it can take on multiple values.

Answer 5

Zero divided by zero is undefined. However, an equation may (or may not) approach a real value as a limit as the value of the equation approaches 0/0. For example, sin(x)/x approaches 1. But x^2/x approaches 0 and x/x^2 approaches infinity as the value of x approaches 0.

Answer 6

Division is breaking objects in to groups and finding the number of groups needed. The divisor is the amount each group can hold the dividend is the amount needed to be placed into groups and the quotient is the number of groups needed, (dividend /divisor =quotient) If you have groups that hold zero objects there is no way of knowing how many groups are needed. That is the easiest way I can think of explaining it.

There is a proof that I can't remember right now that shows that you can't divide by zero. So it's not just a bunch of bull, it's true.

Answer 7

Welllll...no. Think of it in real terms. If you have no M&M's, and you then divide by no M&M's, you still have no M&M's. Or another way: When you divide by something you are breaking it into equal parts. Four divided by two is two, meaning, if I have four things and break them into two equal groups each group will have two parts. So using that reasoning, four divided by zero means take a group of four (like 4 M&M's) and try to break them into no (zero) groups. You aren't talking about your original ONE group of four, you are trying to create no groups at all. Doesn't work. You can either have four M&M's, or no M&M's, but not both at the same time. See? ( Mmmmm, M&M's....)

Answer 8

No. Zero divided by zero would not be one. Zero is a number just like any other number, therefore you would not say it is "undefined" either, unless ANOTHER number is divided by zero (i.e. 5/0) it is undefined, because the number "blows up". So zero divided by zero is just zero.

Answer 9

Let's do symbols:^_^

Let
z = x/y where x, y and z are real numbers

If z = x/y then x = yz

Let y = 0 (from your problem) and x (is not equal to) 0
so,
z = x/0 and
x = (0)(z)
x = 0
but
x is not equal to 0, so you cannot divide a nonzero real number by 0.

Let y = 0 and x = 0, so
z = x/y
z = 0/0
therefore
0 = z(0)

From this equation you can see that any real number z can satisfy the condition, so z, or 0/0 can be any real number, and that is why the expression 0/0 is indeterminate

^_^

Answer 10

zero is an absolute number. It is the existance of nothing. If nothing exists to divide by or from, then how can it be divided, and how can it equal to one? Other whole numbers divided by themselves is obviously one because it is the absolute whole number divided by itself. Zero is the absolute absence of a whole number while anything above zero is the absolute presence of a number.

Answer 11

You can once you get to Calculus. The answer is not always infinity, though. When you divide, you're breaking things into smaller, equal groups. it's impossible to divide four quarters into groups of zero and not have anything left over.