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Compensatory Number

Date: 01/29/2002 at 08:20:38
From: Kris Marshall
Subject: Math term: compensatory number

Is there a math definition for the term "Compensatory number"? In the 
English dictionary compensation can mean an equivalent or balancing 
number. I was asked this question by our Gifted Services Coordinator 
but I'm not sure of the context.

She also wanted the definition of compatible number and I found 
several references in the archives. 

Thanks in advance.

Date: 01/29/2002 at 09:57:56
From: Doctor Sarah
Subject: Re: Math term: compensatory number

Hi Kris - thanks for writing to Dr. Math.


   Mathematics Glossary, Ohio Draft Education Standards   

   Compensatory numbers are used to adjust numbers in a computation 
   after use of compatible numbers.

   Example 1: 25 / 6 =~ (equals approximately) 24 / 6 = 4 is an 
   approximate answer using compatible numbers. The exact answer is 
   given as 4 + 1/6, where 1/6 is the compensatory number.

   Example 2: 32 - 17 becomes 32 - 20 using compatible numbers. The 
   exact answer is 15, so the compensatory number allowing someone to 
   adjust the estimated difference is 3.

   Example 3: 23 + 18  =~ 23 + 20 = 43. Since two was added to 
   increase 18 to 20 as compatible numbers, two will be subtracted 
   from 43 to compensate for the change. Thus, two is the compensatory 

   Example 4: 32 - 17 = 35 - 20. This is the equal adding method 
   (three was added to both numbers in the subtraction problem), which 
   is not the same thing as compensatory numbers.

- Doctor Sarah, The Math Forum   

Date: 01/29/2002 at 11:10:09
From: Kris Marshall
Subject: Math term: compensatory number

Thank you very much for your repid and helpful reply!
Associated Topics:
Elementary Number Sense/About Numbers
Middle School Number Sense/About Numbers

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