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### Undefined Fractions

```
Date: 02/19/2002 at 01:47:35
From: Sandy Morris
Subject: Undefined numbers

My students always ask, Why is a fraction with a denominator of
zero called "undefined"?

None of my explanations seem to satisfy the kids.  Any ideas?
```

```
Date: 02/19/2002 at 02:39:12
From: Doctor Jeremiah
Subject: Re: Undefined numbers

Hi Sandy,

A fraction bar is a division symbol, so you are really dividing the
top number by the bottom number. But you can't divide by zero, so zero
cannot be the bottom number.

The reason you can't divide by zero is that no one has bothered to
define what it means (thats why it undefined). There is no definition,
so dividing by zero has no answer.

We could define it to mean something, but we would have to be very
careful not to contradict any other math laws along the way.

If you define division by zero to mean the same thing as division by
any other number, then you can do things like making the number 2
equal to the number 1:

False Proofs, Classic Fallacies
http://www.mathforum.org/dr.math/faq/faq.false.proof.html

So we need to come up with a definition of what it means to divide by
zero that is not the same as what division means for every other
number. And it would be confusing if division meant two different
things (especially in algebra where you have a variable that you don't
know the value of!).

So to avoid the confusion of having division mean two things, we just
don't have a definition for division by zero at all.

See the Dr. Math FAQ:

Dividing by 0
http://mathforum.org/dr.math/faq/faq.divideby0.html

Does that help?

- Doctor Jeremiah, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Number Theory
Middle School Fractions

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