number divided by zero?

Question

I know that people claim that any number (besides zero) divided by zero equals to infinity. but if you multiply infinity and zero, you will get zero.

So my question is, shouldn't a number (besides zero) divides by zero become quotient 0 and remainder is the number ( eg. 1/0=0 Remainder 1 ). because when you use the basic,classic method to divide (like a square root sign) you will get the answer 0 remainder 1.


( correct me if I am wrong )

Answer 1

I actually believe you are correct on this matter as divide means how many of a specific number are in another number.



So we can use this statement to solve it, which is how many 0's are in 1 which equals 0 remainder 1.



As there is a remainder of 1, there is still a 1 in the equation which leads me to believe that the answer is in fact 1. As the only whole number that remains in the equation is 1.

Your also able to express this in words (nothing remainder something) is something.



Also an infinity amount of numbers can also be expressed as on (in computer terminology) and something. Which is therefore expressed as 1.



The answer of 'Mathnasium of South Tulsa' and second answer of 'Awms A' is wrong because how many 0's you may have, it still equals 0.

Answer 2

"I know that people claim that any number (besides zero) divided by zero equals to infinity but if you multiply infinity and zero, you will get zero"



These people are wrong. In standard arithmetic (field arithmetic of the real number line), division by zero is undefined. Always.



You _can_ divide by 0 in the arithmetic of the real projective line, and it's true the result of dividing any number by 0 is infinity. So in that context, yeah, 1/0 = ∞. However: in that same context, the product of ∞ and 0 is undefined.



"So my question is, shouldn't a number (besides zero) divides by zero become quotient 0 and remainder is the number ( eg. 1/0=0 Remainder 1 )."



No. Look at how integer quotients are defined.

a / b = c remainder d

where c is the _largest_ integer such that bc ≤ a.



Now, you want to say that if a=1 and b=0 then c=0 and d=1, but ask yourself: can you find a c greater than 0 such that bc ≤ a? Well, how about c=1?

bc = 0*1 = 0 ≤ a



How about c=2?

bc = 0*2 = 0 ≤a



How about c=3?

bc = 0*3 = 0 ≤a



You see where this is going. There is no largest integer c such that bc ≤ a, since that inequality holds for _all_ integers.

Answer 3

Hope you don't mind, but I'm ignoring your post until "So my question is". I have two things to say about that:



First:



Let's work by analogy. Suppose we divide 100 by 3, with remainder. Then we get

100 / 3 = 33 remainder 1.

In other words,

100 / 3 = 33 + 1/3

(this is exactly what division with remainder means)



In your situation,

1/0 = 0 remainder 1

is re-written as

1/0 = 0 + 1/0.

(can you see why it's not helpful?)



---------------



Second:

You shouldn't mistake an algorithm used to divide for actual division. Suppose we tried using this algorithm here:



How many times does 0 go into 1? Well, 700 * 0 = 0, so write down 7 in the hundreds place and subtract 0 from 1 to get 1.

How many times does 0 to into 1? Well, 5000 * 0 = 0, so write down 5 in the thousands place and subtract 0 from 1 to get 1.

etc.



Do you see the problem with this algorithm when attempting to divide by 0? For instance, from the above, I would be able to write

1/0 = 5700 + 1/0

which doesn't even "feel" right. Also, why did I choose 7 and 5? There's no reason I couldn't choose any other number, so the algorithm just fails when you try to divide by 0.

Answer 4

You have several errors in your question:



1) Infinity is not a number. It is a concept that numbers go on forever. Since infinity is not a number, you cannot multiply it by zero and get zero.



2) Think of division as asking - "how many complete sets of this fit inside that - and how much is left over?" In a normal case of division such as 7 divided by 2, we say that 3 complete 2s fit inside 7, with 1 left over, so 7 divided by 2 equals 3 remainder 1. However, this breaks down when you try to divide by zero. It is true that one answer to 1 divided by 1 could be zero zeros with one left over. But you could also say the answer is 2 zeros, with one left over, or three zeros with one left over, or 1,000,000 zeros with one left over. This is why you cannot divide by zero!

Answer 5

If you divided 1 by 0.1 you get 10 if you divide 1 by 0.01 you get 100 if you divide 1 by 0.001 you get 1000. etc



Therefore as the divisor tends to 0 the quotient tends to infinity. Therefore it is reasonable to state a number divided by 0 is infinity but it is a bit of an over simplification.

Answer 6

u r right , remainder is the number itself but quotient is not always 0 , it can be anything from -infinity to +infinity, that's the reason why division by 0 is considered not defined and not infinity

Answer 7

if you take any number (besides 0) and divide it by zero... you will not be able to divide it

Because, in reverse, any number that is multiplied by zero... is zero



X / 0 = answer

X = answer * 0 = 0

X = 0



the only number that can be divided by zero is zero...

0/0=0



therefore... any number you try to divide by zero would be logically impossible to divide by 0



also:

0/0 = practically infinite number of answers

Answer 8

People who claim that any number divided by zero is infinity, are poorly mistaken.

When zero is the denominator of anything (Except zero), it is undefined.

Answer 9

It will remain 0.

Answer 10

Any number divided by zero is undefined..