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Q&A #9415


Integers

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From: Suzanne A. (for Teacher2Teacher Service)
Date: Sep 21, 2002 at 22:20:03
Subject: Re: Integers

Hi Ellie, I'll see if I can explain subtracting a negative number using a number line. Here's our number line with "|" representing 0 and each dash representing one unit, some going to the left of "|" representing "negative" and others going to the right representing "positive". - - - - - - - - - - -|- - - - - - - - - - Let's just try 3 - 4 for starters. |- - - x I start at zero and "positive" three means that I go 3 spaces to the right. I mark the 3 by putting an x below it. Now I want to subtract 4. When I subtract I go in the OPPOSITE direction. If I move 4 spaces to the left, I end up at one space to the left of 0. -| x My answer to 3 - 4 is -1 (1 space to the left of 0 on the number line.) Now let's try -4 - 4 (similar to your original problem) - - - -| x I start at 0 but because the first number is "negative" I go to the left four spaces and I mark it with an x. I'm standing on -4 and when I subtract 4 I have to move to the left 4 more spaces. - - - - - - - -| x My answer this time is -8 (8 spaces to the left of 0 on the number line) Now let's try your problem, -4 - -4 If you start at -4 on the number line, it would be here: - - - -| x If I subtract it means I'm going to continue moving to the left BUT I have to also think what -4 means. That second negative makes me change direction and now I'm going to the right and I end up at 0! | x Here's another way to think about it. What if I owe you 4 dollars? I can represent that as -4 (4 dollars in the red). If I subtract that amount that I owe you then it would be the same as paying you back. The amount I owe is 0 dollars. The only way that I could owe you a total of 8 dollars would be if I added -4 and -4. So, -4 + -4 = -8 -4 + 4 = 0 4 + -4 = 0 -4 - -4 = 0 4 - -4 = 8 4 - 4 = 0 I hope that helps. -Suzanne A., for the T2T service Thanks for visiting our on-line community. Visit Teacher2Teacher again at http://mathforum.org/t2t/

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