Adding and Subtracting Negative NumbersDate: 02/07/2002 at 20:52:15 From: Devin Myers Subject: Negative problem What is (-1) - 5 + -8 equal to? Date: 02/07/2002 at 23:14:57 From: Doctor Peterson Subject: Re: Negative problem Hi, Devin. You can picture this on a number line. You are starting at -1, which is 1 unit to the left of zero. Now you subtract 5; that takes you 5 more units to the left (to -6). Finally, you add -8. This is the same as subtracting 8: it takes you 8 units to the left. That takes you to -14. Notice that you have gone left three times, so you are 1+5+8 units to the left. This can be expressed by thinking of subtraction as addition of the negative, then thinking of a negative as multiplication by -1 and using the distributive property: -1 - 5 + -8 = -1 + -5 + -8 = (-1)(1) + (-1)(5) + (-1)(8) = (-1)(1 + 5 + 8) = -(1 + 5 + 8) = -14 This is the way I think about negative numbers, without ever having to write it out this way. When I see subtraction, I THINK addition of the negative; when I see negation, I THINK multiplication by -1. With experience, I don't have to write anything down to answer your question. But you can take your time; think it through the way you probably had to think about every step when you first learned to walk, and soon you won't be falling down so often! - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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