Intermath | Workshop Support
Write-Up

 

Title

Don't Just Say It's Undefined!

 

Problem Statement
What's 0 divided by 1? What's 1 divided by 0? Give full explanations for your answers.


Problem setup

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!


Pam Joseph
prj1@aol.com