Who is asking: Teacher
Level: Middle
Question:
Please advise how best to explain the distinction between the solution
to 'zero divided by one' and 'one divided by zero'. I remember being
told in school that one of them is undefined and the other is zero
but I'm having difficulty with calculating and explaining it to some
highly curious 10 year olds! HELP!!!
Katrina,
twelve divided by three:
You have twelve cookies to share equally among three children, how many cookies does each child get?
eight divided by two:
You have eight cookies to share equally among two children, how many cookies does each child get?
five divided by one:
You have five cookies to share equally among one child, how many cookies does that child get?
zero divided by one:
You have zero cookies to share equally among one child, how many cookies does that child get?
Now comes the philosophical part:
one divided by zero:
You have one cookie to share equally among zero children, how many cookies does each child get?
Claude
It is good to 'make sense' out of the choices so that you don't have to rely on memory. It is even better if the kids can make sense out of it!
Consider the questions:
1
x ? = 0
0
If we play around, we can find that:
1
This tells us what the first ? could be. So 0/1 = 0.
In the end, what makes something 'an answer; is that it checks when you multiply.
We have trouble finding anything which makes:
0
Play as you like, 0 N = 0, for all the numbers the kids (and you) can think of.
So we don't have an answer to the question: 1/0 = ?
Well, later on, they will learn about more types of numbers, and more possibilities. They can keep looking and asking - are we there yet? After some years, they may find something to fill in there and 'make sense' out of the process. [There are ways, with infinity, and process of change - i.e. calculus - to develop some answers, in some situations. Different situations, different infinities, give different answers. It is just not grade 4 stuff!]
Walter