|Intermath | Workshop Support|
Don't Just Say It's Undefined!
First, we put the problem into words. For example, 0/1 put into words could be: How many ones are in zero? How many equal groups of 1 can 0 be broken into? You have 0 chocolate bars and you want to divide it among one friend. How much of the chocolate bar will the friend receive? Then for 1/0, these could be the words: How many zeros are in one? How many equal groups of 1 can 0 be broken into? Zero children are sharing $1.00. How much does each child get?
Plans to Solve/Investigate the Problem
We then considered fact families. If a x b = c, and c/b = a, then c/a = b. That being the case, 0 x 1=0, 0/1=0, and 0/0=1.
Investigation/Exploration of the Problem
After closer examination, we discovered that 0/0 not only equals 1, but also equals zero. Division by zero is not only undefined, it is indeterminate because 0 divided by any number also equals zero.
We had discussions about infinity, but it was decided that since infinity is only a concept, not a number, "infinity" is not a valid answer. Numbers, no matter how large or small, are the only valid answers for this indeterminate situation!