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Q&A #3893

Teachers' Lounge Discussion: Dividing by zero

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From: Loyd 
To: Teacher2Teacher Public Discussion
Date: 2002121020:24:43
Subject: Re: Division by Zero; my approach for K-12

Lets look at division by zero in another way.  If we have a length of
candy say, 27 inches (or we can just as well say, 27 cm).  If this
candy is to be divided by the number of kids who are to eat it, we
would divide 27 by the number of kids.  This would give the serving
size:

If there are nine kids, the each kid would get 27/9 = 3 inches of
candy. 

We could also say if the serving size is to be 3 inches then this
would feed 9 kids.

27 / 3 = 9 kids will get 3 inches each.  

So, lets divide the total length of candy by various serving sizes of
27, 9, 3, 1,  and finally lets look at zero.

27/27 = 1 kid will get 27 inches of candy

27/9 = 3 kids will get 9 inches of candy

27/3 = 9 kids will get 3 inches of candy

27/1 = 27 kids will get 1 inch of candy

27/.5 = 54 kids will get   inch of candy

finally,

27/0 = infinite number of kids will get zero inches.  That is they
will get nothing. 

If we make the serving size equal to zero, each kid would gets
nothing.  Thus division by zero is undefined as is division by
infinity.  

I never had any trouble with this concept.  I think the one I have
given is good enough for high school down to the elementary grades. 
Most kids can understand this; it is just that most kids have not
thought about it.

We can, however, divide by a number approaching zero. 

27/.000000000000000000001 is defined and that equals   27 x 10^20 or
2,700,000,000,000,000,000,000.  That would feed a lot of kids, but
they wouldn't get very much.  In fact, the piece would probably be
smaller than an atom.  An atom is a lot larger than nothing.

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