The Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

Is the Fraction N/N Considered Proper or Improper?

Date: 10/31/2003 at 09:22:47
From: Richard Menor
Subject: Fraction terminology

I am developing a technical math review program for adults and have a
question regarding the correct term to use when attempting to identify
the fraction n/n when n is greater than 0.  It does not seem to fit
into any of the common fraction categories, (ie, proper, improper,
mixed).  I understand that it can be identified as "1", but was
wondering if n/n is just a unique situation that does not fit into any
of the fraction groups.  It would seem that it could be identified as
a mixed number, (n/n = 1 0/n but that seems too obvious).  Any
comments would be appreciated.

Date: 10/31/2003 at 10:30:56
From: Doctor Peterson
Subject: Re: Fraction terminology

Hi, Richard.

It certainly is not "mixed", since it has only a fractional part, and 
no whole part.  The numerator of a "proper" fraction is less than the 
denominator, so I would call this an improper fraction.  You can find 
definitions of "improper" that say the numerator has to be greater,
not just equal; but I think that is wrong.  See this page, which is a
little ambivalent:

  Improper Fraction 

  A fraction p/q > 1. A fraction with p/q < 1 is called a proper
  fraction. Therefore, the special cases 1/1, 2/2, 3/3, etc. are
  generally considered to be improper.

According to Merriam-Webster (, an improper fraction is

  a fraction whose numerator is equal to, larger than, or of equal
  or higher degree than the denominator.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum 

Date: 10/31/2003 at 13:02:17
From: Richard Menor
Subject: Thank you (Fraction terminology)

Thanks for quick response.  The books that I referenced indicated that
improper fractions had numerators larger than denominators.

Thanks again.

Associated Topics:
Middle School Definitions
Middle School Fractions

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.