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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