Subtracting Positive and Negative NumbersDate: 5/21/96 at 10:51:32 From: Anonymous Subject: Subtracting positive and negative numbers How would you figure out the answer to -13 - 6= ? How can you subtract a negative number from a positive number? And how do you subtract a positive number from a negative number? From, Lucie and Maite Date: 6/15/96 at 9:13:21 From: Doctor Chaos Subject: Re: Subtracting positive and negative numbers To answer your first question: Subtracting a number from a negative number is like starting below zero on a thermometer and removing more heat. It sounds wierd but if the temperature is -13, not only is it cold, but it is BELOW ZERO. If we remove 6 more degrees of heat, it gets colder and the mercury moves down the scale 6 more degrees to -19. Make sense? So subtracting a number is like moving down the thermometer. The other part of your question is trickier. Subtracting a NEGATIVE number is like REMOVING a debt. Let's think in terms of money. If I owe you 5 dollars, it could be written as -5 in my book, to remind me that I must remove 5 dollars from my account. But if you say "Oh forget it. You don't owe me any more.", then I need to subtract the debt from my books. It's like saying -(-5), which to ME is like adding the money back into my account. What we say is that subtracting a negative is JUST LIKE adding a positive. So let's get specific. If I SUBTRACT -5 from 12, I can write it as 12-(-5) which is JUST LIKE 12+5 which is 17. You might also want to think about how we can show this on a number line. A thermometer is a vertical number line. Discuss this with your teacher and other students. If you want to get back in touch with us, please do so. -Doctor Chaos, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 7/19/96 at 19:8:59 From: Doctor Jodi Subject: Re: Subtracting positive and negative numbers The way I think of negative numbers has to do with direction. On a number line, for example, if I want to show 3 + 2, I can do this by starting at the number three and moving 2 spaces to the right. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 * + + * means start here + means spaces moved to the right Since I end up at 5, 2 +3 =5 Think of subtracting as moving to the left. 8 - 3, for example, starts at 8 and moves three spaces to the left. -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 - - - * * means start here - means spaces moved to the right Now, if I want to add 4 + -2, I start at 4 and move -2 spaces to the right, or 2 spaces to the left: -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 - - * I end up at 2. So 4 + -2 is the same as 4 - 2, which equals 2. Does this make sense? What if I want to add negative numbers? Let's try -3 + -4. We'll start at -3 and move -4 spaces to the right (or 4 spaces to the left). -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 - - - - * So -3 + -4 = -7 Does that make sense? Here are a few problems for you to try: -9 + -3 2 - 5 -3 + 4 Here's another question for you: does it matter which number you use first? (Is -9 + -3 the same as -3 + -9?) I hope this helps. Let us know if we can help again. We'll look forward to hearing from you. -Doctor Jodi, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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