1. ## 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?

2. ## 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.

3. ## 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.

4. ## 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.