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?
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?
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.
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.