Spaces and the Number LineDate: 02/26/2003 at 11:37:08 From: Holly Subject: Minus Numbers If you say, "How many degrees are there between -2 and 4?" would you count the 0 degrees and answer 7 degrees or would you not count the nought and answer 6 degrees? Date: 02/26/2003 at 12:08:24 From: Doctor Peterson Subject: Re: Minus Numbers Hi, Holly. When we subtract two numbers, we aren't counting numbers between them, but measuring the distance between. In this case, the number line (or thermometer) looks like this: |<--------------------->| -+---+---+---+---+---+---+---+---+---+---+- -5 -4 -3 -2 -1 0 1 2 3 4 5 The distance is the number of SPACES (units), like this: |<--------------------->| -+---+---+---+---+---+---+---+---+---+---+- -5 -4 -3 -2 -1 0 1 2 3 4 5 \__/\__/\__/\__/\__/\__/ 1 2 3 4 5 6 So the distance, and the difference, is 6 degrees. If you want to do it by counting, then you want to count every number after the first and including the last: |<--------------------->| -+---+---+---+---+---+---+---+---+---+---+- -5 -4 -3 -2 -1 0 1 2 3 4 5 ^ ^ ^ ^ ^ ^ 1 2 3 4 5 6 What you are really doing here is counting each space as you go past it, so it's the same as what I did above. This is like counting how far you go in your car by counting each time the odometer clicks another mile; you don't count both ends, because when you start you haven't gone anywhere yet. You only count the miles you have actually passed. Does that help answer your question? - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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