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Thread: Division By Zero

  1. #1
    Super Member harpazo's Avatar
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    Division By Zero

    How would you explain to a student in grades 6 to 8 that division by zero is not possible? Middle school students struggle with this math fact. If x is a number, then x/0 is undefined. What is the best way to make this clear to a child?
    Last edited by harpazo; Mar 12th 2019 at 04:19 PM.
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  2. #2
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    Re: Division By Zero

    I'd start by looking at patterns

    $\displaystyle 1 \div \frac{1}{10} = 10 $

    $\displaystyle 1 \div \frac{1}{100} = 100 $

    $\displaystyle 1 \div \frac{1}{1000} = 1000 $

    $\displaystyle 1 \div \frac{1}{10 000} = 10 000 $


    As the divisor gets closer and closer to zero the quotient just keeps increasing.
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  3. #3
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    Re: Division By Zero

    When I was in middle school (grade 7-9), my home tutor explained to me with the example 5 0. He said, so... Because there's no number which if multiplied by 0 becomes 5, the result is undefined.
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  4. #4
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    Re: Division By Zero

    The point Monoxdifly makes is the one I would use: x= a/b means bx= a. If b= 0, then bx= 0x= 0 which is NOT equal to non-zero a.

    Many texts make a distinction between "a/0" where a is non-zero and "0/0", calling the first "undefined", for the reason above, and the second "undetermined" or "indeterminate", since "0/0= x" would mean 0x= 0 which is true but for all x so that "0/0" does not determine a specific value for x.
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