Distributive Property with Negatives
Date: 10/13/2004 at 21:26:37 From: Albert Subject: Distributive property with negatives I am a grade eight student enrolled into a grade nine math program. When using the distributive property with negative numbers, I don't understand when, why, and how the operator changes (from addition to subtraction, or the other way). Sometimes it changes, sometimes it doesn't. It gets me extremly frustrated. I never get it. Can you please explain it when to change it and why?
Date: 10/14/2004 at 12:50:47 From: Doctor Ian Subject: Re: Distributive property with negatives Hi Albert, Here's the thing. If you try to learn a lot of rules for what to do, you're going to get them mixed up, and forget them when you're under pressure (e.g., during a test). I suggest that you start by always converting subtractions to equivalent additions: For example, suppose I have (-3 + 4) - (7 - 2) = (-3 + 4) - (7 + -2) Change to addition = (-3 + 4) + -1(7 + -2) Change to addition = (-3 + 4) + (-1*7 + -1*-2) Distribute the -1 = (-3 + 4) + (-7 + 2) and now all I have are additions. So I can use the associative and commutative properties to do them in any order I want: = -3 + 4 + -7 + 2 = -3 + -7 + 4 + 2 = -10 + 6 = -4 The same thing works with variables: (-3 + x) - (2x - 2) = (-3 + x) - (2x + -2) Change to addition = (-3 + x) + -1(2x + -2) Change to addition = (-3 + x) + (-1*2x + -1*-2) Distribute the -1 = (-3 + x) + (-2x + 2) = -3 + x + -2x + 2 = -3 + 2 + x + -2x = -1 + -x Does this make sense? This might seem like a lot of extra trouble to go through, but if you do the extra steps, you'll get the right answers slowly, which is better than getting the wrong answers quickly. And as you get practice, you'll start forming your own set of rules for shortcuts, which will make sense to YOU--and that's better than trying to learn a set of rules that someone else made up, because they made sense to HIM. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 10/14/2004 at 16:46:21 From: Albert Subject: Thank you (Distributive property with negatives) Thank you very much. It absolutely works! I dunno if I passed the test, but if I do, it's thanks to you!
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.