Definition of Quotient

Date: 11/13/2008 at 01:54:38
From: Khalid
Subject: Definition of Quotient

I always thought that if we divide 15 by 2, then 2 is the divisor, 15 
is the dividend, 1 is the remainder, and 7 is the quotient.  But I
read in a book that 15/2 is also a quotient for that problem.

We also represent rational numbers (a/b) by Q (Quotient).  The
quotient rule is used to take the derivative of such numbers.  We also
use the quotient rule with powers where (a/b)^r = a^r /b^r.  

How can "quotient" mean so many different things? 

Date: 11/13/2008 at 09:18:32
From: Doctor Peterson
Subject: Re: Definition of Quotient

Hi, Khalid.

Like many definitions, this one varies somewhat with context.
Everything you have quoted is true, in its own place.

In the context of whole numbers (or integers), where fractional 
answers can't be accepted, the quotient is the whole number result, 
and there may be a remainder.  This is how the word is used in early 
grades in school, and also in number theory and similar fields, such 
as division of polynomials in algebra.

In the context of real numbers (or rational numbers, including 
fractions and decimals), we can get a single number when we divide, 
so that is what we call the quotient.  This is the usual meaning when 
there is no reason to restrict answers to integers.

So, the general meaning of "quotient" is "the result of a division"; 
but that may be either the integer part of that result, or the entire 
number.

See the following page from MathWorld:

  Mathworld: Quotient
    http://mathworld.wolfram.com/Quotient.html 

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


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