Multiply by zero and Divide by Zero
Any number multiplied by zero is great mistake if takes
'zero' seriously. Means takes 'nothing' seriously, and argued
upon 'nothing' seriously.
We defined multiply by zero and divide by zero, considering one side of coin only.
Lets see :
The product of zero and a negative is zero, 0 x -4 =0 (it is correct only if considered one side on coin)
The product of zero and a positive is zero, 0 x -3 =0 (it is correct also, only if considered one side on coin)
The product of two zeros is zero. (it is always correct)
* If told to any one that, take nothing, three times and add
such nothing three times, then absolutely one get nothing in answer,
i.e. 0+0+0=0. (one side of coin)
** But it is told to any one that, takes 3 mangoes, and add
zero/nothing in it, then absolutely one get three mangoes, i.e. 3+0=3.
Because mangoes remain intact. (another side of coin).
Which side is correct?
Basically numbers are only representative of real things.
Don’t let them ride upon us.
If we teach 2 or 3 years old babies only numbers without
representing real things. Then they never consider what numbers are
1 represents one real thing.
2 represent two real things.
3 represent three real things… and so on.
0 represent nothing, no real things, it is only place holder. (Great concept, great miss understood by us.)
Then what is solution?
If we give weightage to nothing (0+0+0=0) then answer is nothing or zero.
so 0 x 3 = 0 Correct!
But we give weightage to something (3+0+0=3) then answer is 3.
so 3 x 0 = 0 is incorrect
and 3 x 0 = 3 is CORRECT!
Because if there are something and one say multiply it by nothing then there are no ambiguity.
Cause there are something which we never do vanish/disappear. It
is not possible for human being, then how we do it in mathematics,
because of nothing represent by 0. Zero is only representative of
nothing but we gave presence to nothing by forcing to zero as a value,
it is not correct at all.
We gave weightage to one side of coin only. We gives importance
to zero base multiply and zero base divide operations. Means we gave
importance to take nothing/zero three times and add it. Answer is
always nothing or zero. (0 multiply 3 times).
Bramhagupta says that nothing added by nothing is always nothing (0+0=0)
Multiplication means addition represented by short cut.
3x4 means 3+3+3+3 and
3x20 means 3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3+3 add three twenty times.
3x0 means 3+0 or 3+nothing (consider three is intact don’t think
that it will vanish automatically by multiplying it with 0. As we are
real thing want to add or subtract real things, and only saying add
zero in 3 mangoes not vanish mangoes.)
Multiplication is not new operation. It is only shortcut method
to write long addition operations. So why different rule for same
3+3+3 = 9 and how 3x3=0 ?
Why we do so. Because we gave importance to representative of nothing
(zero). Because we are so impressed by invent of zero. “why
mathematics and mathematical expressions required?”
Why mathematics required?
To represent real things on paper and makes calculations of real things on paper easily.
It is not for unreal things.
So we have to give importance to real things and so we should give answer
3 x 0 = 3
But if you want to give importance to nothing then you can write
0 x 3 = 0 but it is meaningless in real world. Why anyone want to add,
subtract, multiply or divide nothing with anything. He must be crazy.
Conclusion: 3 multiply by 0 (zero) is always 3 or vice versa.
Same rule applicable for divide operation.
Because division is subtraction of number, given times, from given number, above conclusion is also applicable to it.
20/4=5 means subtract 4 from 20 till get 0 (zero) or smaller value than 4.
20-4-4-4-4-4=0 here we subtract 4 from 20 by 5 times to get 0 or smaller value than 4.
Means there are 20 mangoes in basket we should make a bunch of 4
mangoes and put it on floor till basket remain no mangoes. We get 5
groups of 4 mangoes.
Means there are 20 mangoes in basket we should make a bunch of
no mangoes (0 mangoes) and put it on floor till basket remain no
mangoes. We get no groups of 0 mangoes. It is not practically possible
to take 0 mangoes from basket and put it on floor. So we get no (0)
groups. But we has 20 mangoes in basket intact.
So again 2 sides of coins.
If we gave importance to group of mangoes on floor, than answer is 0 (zero) groups we has.
So 20/0=0 groups on floor.
But if we gave importance to mangoes in basket then we has group of 20 mangoes in basket.
So 20/0=0 groups in basket.
Again rule of subtract zero from value, break by expression 20/0=0.
- a positive number minus zero = positive number
20-0=20 means remove nothing from 20 mangoes, so 20 mangoes remain intact.
Then how we defined that 20/0=0?
20 mangoes in basket and we want to subtract no/zero mangoes
from basket till basket has no or zero mangoes, how it is possible.
It is unreal thing so we have to false act (actually not taking
any mango) to takes mangoes from basket and put on floor. (Isn’t it
childish thing or foolish thing). We have to do it infinite time, but
we never succeed to empty basket. (So isn’t 20/0=0 is foolish answer)
In real world we have to translate it as ‘takes no mangoes from
basket’ so ‘put it on floor’ is meaningless. So we don’t have to do it.
If we think, we make it 0 (zero) time. Then answer of making group 0 times, is correct.
If we ask how many mangoes are there in basket, then
answer is 20. So we get 1 group of 20 mangoes. We don’t make group on
floor but they are there. It is not important that they are on floor or
in basket. Mangoes have importance.
So 20/0=20, because they are there. Or 20/0=20x1, because 1 group of 20 mangoes
If we said don’t make group of 20 mangoes then is it possible they 20 mangoes goes disappear or vanish?
So be practical and accept it.
So 20/0=20, because they are there. Or 20/0=20x1, because 1 group of 20 mangoes.
And what about 0/0=?
Simple answer is : 0 (zero)
Because nothing is nothing, you cannot take nothing and another nothing
to add or subtract, because it is not possible to human being to take
Yogesh C. Ugale,
Nasik Road, Tal. Dist. Nasik,
State Maharashtra, India