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 http://mathworld.wolfram.com/ImproperFraction.html 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 (m-w.com), 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 http://mathforum.org/dr.math/
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. Richard
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.