Q&A #6433

Subtracting integers

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From: Ralph (for Teacher2Teacher Service)
Date: May 31, 2001 at 15:36:17
Subject: Re: Subtracting integers

Dear Jackie,

The "rules" for adding and subtracting integers can certainly be challenging 
and confusing. In your previous question on adding integers, Roya gave you 
some sources in the "Ask Dr. Math" archives that will likely prove helpful, 
particularly in understanding the idea that "subtracting a number" and 
"adding the opposite" of that number gives the same result.  This is the 
basis behind the rule that suggests that you can solve  -10 - -7  by 
rewriting it as -10 + +7 and following the "addition rules". In the case of 
the integers, "the rules" your son has been given are designed to give a 
"consistent procedure" that will yield the correct answer each time its 
applied correctly. But be aware that there's certainly more than one way to 
SOLVE such problems. So, for example, when your son decided to look at
-10 - -7, determined that since both numbers had the same sign he could "just 
subtract", and arrived at -3 as the answer, that's a perfectly legitimate way 
to solve that question. BUT, if he chooses to apply that method, he has to 
be sure to keep straight what he's subtracting from what--in this instance, 
taking -7 from -10 leaves -3, as he concluded, BUT your last question then 
said, so why wouldn't +11 - + 12 be +1?  If you/your son chooses to do this 
as subtraction, that's fine, but then it has to be realized that you are 
STARTING with 11, and SUBTRACTING 12, resulting in -1, not +1. I have a 
slightly different approach to using the number line with integers than that 
suggested in the Dr. Math answers you were referred to, but explaining that 
might add more confusion at this point.  If your son continues to experience 
difficulties when adding/subtracting integers, write back and I'd be glad to 
provide more details about the way I have my students apply the number line 
to such questions.

 -Ralph, for the T2T service

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