Why is it not allowed?

Question

In mathematics its said that dividing some thing with 0 (zero) is not allowed. What is the logic behind it? On the face of it if I divide some thing with 0, the answer remains the same like 5/0 = 5. Why they dont allow such calculations?

Answer 1

Division of some thing by 0 is not allowed because its equations returns to a wrong answer. For exampe: -
if we say
x/0 = y,
x = 0 x y
and it will return the value of y to 0 which is mathematically wrong.

Thats the reason division of a number by 0 is not allowed.

Answer 2

"Not allowed" isn't the correct way to put it. It isn't some arbitrary rule, like "driving on the left side of the road is not allowed." "Not allowed" applies to something that we could do, but for some reason we do not do.

Division by zero is "not defined," which is a very different thing. It is not defined because it does not make sense. You would not ask, "Why does a loud tree sleep fortunately?" The sentence is grammatical but nonsensical. In the same way, 5/0 looks formally like a fraction, but it is nonsensical.

What does "divide" mean? It means, if I took the numerator and created as many equal pieces out of it as the denominator says, what is the size of each piece? So 5 split into 1 piece has the same size: 5. 5 split into 8 pieces has the size 0.625. With some imagination, we can say that if splitting in 2 means halving the numerator, then splitting by 1/2 must mean doubling the numerator, so we get 5 / 0.5 = 10. But what can it mean to take zero pieces and ask what is the size? It is a nonsensical concept. That is why 5/0 is not defined.

Answer 3

Then what would 5/1 be? The same as 5/0?

Answer 4

Because division and multiplication are interchangable.

Example.
I divide 6 by 3. I get 2. Multiply the latter: 3x2=6. There's my 6 again.

This is true for ALL numbers:
18/3 = 6 and 6x3=18.
A/B=C and C x B = A.

The only time it doesn't work is when B is 0.
Example:
A/0 = C.
Now you have to find a C that, multiplied by 0, gives A.
So for example 6/0 = C.
0 x C = 6. There is NO number that, if you take it 0 times, gives you 6.

That's why division by 0 is prohibited by law, and you can be fined up to $50 if you attempt it :)

Answer 5

Mathematical calculations have to be CONSISTENT. If you define something, and the definition turns out to create inconsistency, then you have defined it wrongly.

Mathematicians have found no consistent way to define the result of dividing by zero. Maybe you can't find the inconsistencies, but they have, every time. So, it is undefined.

Answer 6

Think of kindergarten teachers asking "If 5 apples are shared among zero people, how many apples does each person get?"

Well... doesn't really make sense.

Answer 7

u must divide in something n not in nothing,so it's nonsense to divide something by nothing(zero).