Why can't you divide by zero?

@divitiae (193)
December 28, 2010 5:46am CST
When I put /0 into my laptop it says "can not divide by zero". Is there a branch of maths which tries to deal with this? In order to make somthing fit into nothing you have to make it nothing, so should n/0 be 0? Should it be the average of n divided by 1 and n/-1? If you divide a cake between no eaters doesn't the cake just remain undivided, e.g. n? As you divide by smaller fractions the answer gets bigger so is n/0 infinity? or 1/2 infinity because of negative numbers?
2 people like this
15 responses
@buwald (271)
• Netherlands
28 Dec 10
In maths, it is entirely possible to divide by zero, but since your laptop is trying to get an exact numeric answer. There is none. For example, lets look at the cake. If you want to divide it between two people, it would be in two pieces. If however, you want it to remain uncut, i.e. n, you would still have one piece. In this example, it is not possible to have the cake in zero pieces, because it would therefore not exist. In maths, however, it is possible to estimate dividing by zero. This is done by taking the equation x/0 as x/(something extremely close to, but not quite zero, for example 0,00000000000000001) If you take this fraction as so extremely small that it is irrelevant, you would get x/0. Since the fraction is so extremely small, the result will therefore be extremely large (if you divide a number by something smaller, the result will be larger.) If the divisor is extremely small, the estimate of x/0 would be infinity. Note that this is not an exact number, and that it is slightly inaccurate. I hope this hasnt confused you too much, and that this answers your question.
1 person likes this
@buwald (271)
• Netherlands
28 Dec 10
Note that when I say infinity, I mean "A number so large that it is impossible to write it down". In maths, it is sometimes necessary to speak of that, since otherwise some complex things might not be possible.
@divitiae (193)
28 Dec 10
This seems more like science, trying to obseve somthing similar, isn't the point of maths that the perfect circle can only exist as a formula and you can only "act" on the form? You wouldn't say you don't know the exact number of degrees in a circle because you can't draw one and measure them, the realer circle is the form not the particular. If there is an answer dosen't it only exist as a concept so saying you can't find any thus divided candy in the empirical world is irrelivant?
• India
28 Dec 10
Yes buwald is right when you have some fair idea at some branches like Calculus
• Canada
29 Dec 10
Basic math concepts: Multiplying is a quick way to add. 3x4 is a shortcut process for 3+3+3+3. Multiplication is simply addition, with a shortcut. Division has a similar relationship with subtraction. 12/2 is a shortcut for "subtract 2 from 12 as many times as you can, and record the number of times you subtracted it" So really the operation you are performing is 12-2-2-2-2-2-2=0, and we did the subtraction process 6 times. Now, how many times can you subtract 0 from any positive number before you get to 0? An infinite number of times. It doesn't matter how many times you subtract 0 from 12, for example, you will never get to zero. 12-0-0-0-0-0... results in an infinite number of subtractions. Your laptop cannot display infinity, so it tells you it can't divide by zero. In your cake example, it is wrong to think of it as how much cake you have left. The correct way to think of it is how many times can you give a slice to the people you are dividing it among before you have no cake left? (Infinite, because there is no one to take the first slice, so the cake will never be eaten.) The cake example is confusing because a "slice" of cake is not a concrete amount. The amount of the slice varies based on how many people you need to serve with the cake!
1 person likes this
@shattered (1728)
• Philippines
29 Dec 10
Good one Rebecca! I like this explanation easy to understand and applies basic concepts. It addresses the cake issue as well
@ndraj_2006 (1422)
• India
28 Dec 10
Hey! you cannot divide the Zero (0). i will give you some funny but, true example. dividing is nothing but, breaking into parts. unless you have an apple in your hand how can you cut it into pieces?? LOL!!! good question. i liked it!
• India
28 Dec 10
LOl! unless you have a apple how could you put that in the blender. i got at what point you are getting confused... just kidding..
@divitiae (193)
28 Dec 10
You could put it in a blender and leave the lid off?
@divitiae (193)
28 Dec 10
What if the apple hasa value of n and you want to divide the real and present apple between no apple eaters?
@jshekhar (1562)
• India
28 Dec 10
It is basic mathematics that you cannot divide by zero. coming to your question, when u divide a cake between zero people, the result expected is that "how much will each person get"? Now since there is no person, this can't be calculated. So, in my opinion, "the cake remains undivided" isn't the precise answer. and yes, n/0 can be considered as infinity for layman's use but in exact mathematics it is "cannot be determined", which is nothing but infinity.
@sid556 (30960)
• United States
28 Dec 10
It also creates a contradiction. When you divide a number then the way to check your answer is to multiply it. For example: 6 divided by 3=2. Now if you were not sure of that then a quick way to check it would be to multiply your answer by the divider. 2X3=6 so we know that the answer is correct. Now lets use 0. 6 divided by 0=6. But 6 X 0=0. It just does not work.
@divitiae (193)
28 Dec 10
If there are no eaters then dosen't each eater get zero cake - they are unable to take any with their unexistant arms?
• Romania
28 Dec 10
Yea yea yea , that's pretty much what I wanted to say but ... yea , i suck at math. xD
@dibs2010 (132)
• India
28 Dec 10
Ha Ha Ha are you joking???? you dividing zero "0". do you don't know that zero "0" can not be divided or multiplied. this is not saying by be it is written in math. i am surprised. ha ha ha sorry dude i cant help you.
• Switzerland
28 Dec 10
You can multiply something by 0. The result would be always 0.
@Vaultar (95)
• Romania
28 Dec 10
I'm not really a pro at this but dividing by zero is impossible because you can't divide a stack of candy ( as an example ) to 0 kids , you can give them all to 1 kid , or you can give 0.823784952837489 of them to 1 kid . I don't think anyone is really dealing with this right now , It's just impossible. There's probably a somewhat more logical explanation for this but judging the mark i got at my math exam , you'll never get anything from me . :D I'll keep watching this discussion and maybe I'll find something out :) Good luck !
@divitiae (193)
28 Dec 10
what about giving no candy to anyone? what about theiving candy back of the kids?
• Romania
28 Dec 10
Giving no candy to anyone ? Well , GIVING candy to SOMEONE is the purpose of dividing. Thieving would be subtracting . The only way you could give no candy to anyone would be dividing 0 to other numbers. Like giving 0 candy to 5 kids . 0/5 = 0 since you got no candy , no matter how many kids there are , the answer will still be 0 ... I'm really lost ... xD
@divitiae (193)
28 Dec 10
coundn't theving be dividing a negative number if you wanted a specific amount of candy and as a fair person you don't see why any one child should have to be mugged more than any other?
@lingli_78 (12822)
• Australia
29 Dec 10
i don't know why... all i can say is that is what i learn in mathematics... :-) i just know that anything that is divided with 0 will give the result of infinity... take care and have a nice day...
@sid556 (30960)
• United States
28 Dec 10
It's probably just the calculator on your computer. It probably just feels it would be a waste to try to divide anything by zero because you just end up with the same number you are trying not to divide. Seriously...it's not really dividing anything at all. Why would even want to divide anything by zero...just to see what the computer would answer?
• United States
28 Dec 10
Partly because you can't make a zero. What I mean is that you cannot show me zero pieces of pie. I see there is nothing there, but I cannot show you zero literally. You cannot divide something into zero groups.
@shattered (1728)
• Philippines
29 Dec 10
This is a good one divitae, never though a math problem would get this much response! Didn't realize there were so many mathematicians in myLot. Computers generally "compute" inputs that are within the range of their programming. As such a computer cannot compute an equation that was not included in its programing. Dividing a number (x) by 0 would lead to mathematical dilemma as pointed out earlier, the exact opposite of division is multiplication but why can you multiply by 0 and get 0 but if you divide by 0 you get no answer? I am actually dumbfounded by this. 6 x 0 = 0 in order to check this you divide 0/6 = ? But then again what would be the reason why one would want to divide a number by 0?
• India
28 Dec 10
First of all let me answer your question in parts Q:n/0 becomes infinity A:infinity as you know is not any spefic number. So you cannot possibly arrive as that number which is not specific and definite. Q:If you divide a cake between no eaters does not the cake just remain undivided? A:This point seems more valid. Yes it is undivided but mathematically if you see 6/2 = 3 because when the denominator 2 is cross multiplied to the answer ie 3 you should arrive at the numerator. ie 6 = (3*2) - 6 = 6. So correct Simlarly 15/3 = 5 - 15 = (5*3) - 15 = 15 So correct. But when you divide a number with 0, on the similar grounds as stated above the answer can be any number as upon cross multiplication any number multiplied to 0 is 0 itself which might not be equal to the numerator. ie for example 2/0 = 1 - 2 = (1*0) - 2 = 0. (not coreect) Simarly for any answer on the number scale. 2/0 can also be 2 as - 2 = (0*2) - 2 = 0. I hope I am clear.
@divitiae (193)
28 Dec 10
"you can not possibly arrive at a no. which is not specific and definite" This seems to contradict the previous post, maybe it is the arriving bit which is unclear, but then isn't the answer just to reask the question?
@yumcookie (146)
• United States
28 Dec 10
You can't divide by zero because you are dividing nothing. If you had a million dollars and zero people to give it to then no one gets a million dollars. But if you had one person to divide the million dollars than they would get all of the million dollars. I know it doesn't seem to make sense now but as you progress in math you'll begin to understand why nothing can divided by zero.
@meuji100 (198)
• Philippines
29 Dec 10
This problem is really impossible to solve. You can not divide something to nothing. You cannot give a chocolate bar to no one. The answer would be undefined. You can give it to a person and you get an answer of one. This problem is very hard to solve and is for mathematicians who know this and can explain this thoroughly.
• Indonesia
28 Dec 10
why cannot divide by zero? because it is illegal. Why it is illegal? because you cannot find the answer by these reasons. first, suppose you have 12/6 then the answer is 2 because 2*6 = 12. but if you have 12/0 = Y, it is false to say 0*Y = 12. second, suppose you have 10/5 then the answer is 2, means that if you have 10 brics you can divide them into 5 groups of 2 bricks. but if you have 8/0, you cannot divide the bricks because no group will collect the bricks. try to ask Dr. Math, they have the answers and some really funny to scrutinize.
@zaga_cleuth (1407)
• Philippines
28 Dec 10
Because zero is considered as non value number.