Why can't you divide by zero? – TED-Ed

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In the world of math, many strange results are possible when we change the rules. But there’s one rule that most of us have been warned not to break: don’t divide by zero. How can the simple combination of an everyday number and a basic operation cause such problems?

Lesson by TED-Ed, animation by Nick Hilditch.

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41 COMMENTS

  1. Thank you so much to everyone who has joined us over on patreon.com/teded! Your support is helping bring free educational materials to curious, life-long learners around the world!
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  2. anyone: you can't divide by zero!
    russian deputy: but you can always make corrections to arithmetic textbooks…

  3. 10/0 = Infinity……0 isn't the smallest number, we can go back the number line to -1 then -2 then -3 and on to infinity.
    So the equation should actually be let 10 or any number = x
    x/infinity=infinity …….and from this word i can't stresss my mind any more.

  4. If you have one thing, and you multiply it by nothing, you still have that one thing. So one times zero is one.

  5. i'd like to say this: try 3/0. imagine writing a 2D graph of 3/x. you'll find 2 curves that are opposite to each other, and the y coordinate higher as the x coordinate goes all the way to 0. what happens at 0 is that it is at (0, ∞). but also, 0 is both a positive AND a negative number. so, you also get (0, -∞). and this literally goes for all the graphs for n/0 (in this case n was 3). so the solution, in the end, is both +∞ and -∞. me 1, you 0. haha.

  6. I believe in the order of operations that divide by any zero should be first, because 1/0 *0/1 is 1 (where the zeros cancel each other), and this is non-sense, because infinity is incomprehensible and undefined as a number.

  7. I had to learn this the hard way when I kept dividing by zero on a calculator and it was saying "ERROR ERROR ERROR!"

  8. The square root of 9 is 3 and -3. Why do we accept this possibility in that case but not when dividing by zero? Couldn't we just say that infinity times 1/0 is every number?

  9. No. You're doing it wrong. 10/2 = 5 with no remainder. 10-2-2-2-2-2=0. 0 goes in to 10 an infinite number of times with a remainder of 10. All those other rules discussed only hold for finite numbers.

  10. The reason why we can't ÷0 because the results is going to be more than infinity let's say 1÷0.infinity 0and 1 the answer should be infinity right so that mean the answer of 1÷0 should be more than infinity because [0.infinity 0and1]is bigger than 0 (maybe I'm wrong)

  11. 10 Facts
    .

    1) Your reading this.

    2) You can't say the letter M without without both of your lips touching each other.

    3) You just tried it.

    4) Your smiling.

    6) You didn't notice I said "without without" in fact number two.

    7) You didn't notice that I missed fact five.

    8) You just checked it.

    9) You are either smiling or giggling.

    10) You are going to like or comment.

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