The Math Forum

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

Opposite of Percentage

Date: 07/31/2001 at 20:45:01
From: Marty Ryerson
Subject: Term for the "opposite" of percentage


I am beginning to wonder if there *is* an answer to this.

I am trying to write a document explaining a common procedure, namely, 
calculating a discounted price. To calculate the discount, you 
multiply the "base" by the "percent discount" to yield "percentage."  
At least, these were the terms I was taught.

So, if the price is $32 and the discount is 15%, then you multiply 32 
times .15 to get the amount that is to be subtracted from the initial 
price ($4.80) to yield the discounted price ($27.20). I have been 
taught that the "initial price" ($32) is the "base," the .15 is the 
"percent" or "discount rate," and the resulting discount amount 
($4.80), is the "percentage."

Another way to calculate the final price would be to subtract the 
percentage from 100 (100% - 15% = 85%) and then multiply that result 
by the original price (.85 times $32 = 27.20).  Or, as it appears in 
many computer programs, net = price * (1-discount_rate), where it is 
understood that discount_rate is a decimal fraction.

My question is one of terminology. What is the name given to the term 
"(1-discount_rate)" in this example? I have looked up reciprocal, 
complement, inverse, etc., but none of those fits. I need to be able 
to define this word once and then use it repeatedly in my document, 
rather that explaining it every time I use it, which will be many 

Thanks for any help.


Date: 07/31/2001 at 22:39:23
From: Doctor Peterson
Subject: Re: Term for the "opposite" of percentage

Hi, Marty.

What you want is "the complement of the discount rate." Here is one 
site I've found that defines it:

   Trade Discounts - Business Mathematics, Confederation College   

   Trade discounts are used in the retail sector. They are used to 
   calculate how much a retailer will pay a manufacturer for a given 

   Complement of a Trade Discount: This is the difference between the 
   discount rate and 100%. The complement can be any percent that 
   results when you subtract the trade discount rate from 100%.

In general mathematicians use the word "complement" to mean "all 
except ..." or "the whole minus a given part"; here it means 1 minus a 
fraction - though I haven't found any dictionary that gives this 

- Doctor Peterson, The Math Forum   
Associated Topics:
High School Definitions
High School Interest

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.