Definition of Mixed Number

Date: 11/22/2004 at 17:20:43
From: Brian
Subject: Is 5 a mixed number?  If so, why?

Is 5 a mixed number?  Why or why not?  I think it is, because you can
write 5 0/3, can't you?

Date: 11/22/2004 at 18:02:37
From: Doctor Rick
Subject: Re: Is 5 a mixed number?  If so, why?

Hi, Brian.

I think it's important, when considering this question, to keep in 
mind the difference between a number and a numeral.  A number is more 
of an idea, while a numeral is a name for a number--a way of telling 
others what number you're thinking of.  For instance, 1.5, 3/2, and 1 
1/2 are three different numerals that all represent the same number.

A mixed number would be better called a mixed numeral, because it is 
a way of writing a number.  When you ask if the number 5 is a mixed 
number, you're really asking about this particular way of writing it: 
is the *numeral* 5 a mixed number?

You *can* represent the number 5 by a mixed number 5 0/3, though I 
wouldn't do so except while working a problem with mixed numbers (even 
then I'll probably only "write" it this way in my head), or because I 
was asked to do it.  But the numeral 5 is not a mixed number because 
it doesn't have a fraction part.

If a mixed number meant a number that *could* be written with a whole 
number and a fraction, then *every* number would be a mixed number. 
For instance, 0.5 would be a mixed number because it can be written 0 
1/2.  There would be no reason to call anything "mixed number", 
because it wouldn't tell you anything about the number!

That's my opinion.  I haven't checked to see whether everyone agrees 
with me.  If you find out that someone disagrees, I'd like to see 
their reasons.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/