Rules for Subtracting IntegersDate: 10/31/2001 at 10:41:08 From: Julie Subject: Rules for subtracting integers For my assignment I need to write rules for subtrating integers. I don`t know where to get this information. Date: 10/31/2001 at 16:58:52 From: Doctor Peterson Subject: Re: Rules for subtracting integers Hi, Julie. I don't tend to use "rules"; it works better to base what I do on an understanding of how things work. Let's look at how things work, and then you can see if you can express that in a simple set of rules. If we put two numbers on the number line, then when we subtract A from B, we get the "directed distance" from A to B: B-A +-----------------> <------------o-----------------o-------------------------> A B That is, B-A is the number you have to add to A in order to get B: A + (B-A) = B If B > (is greater than) A, as shown, then B-A is a positive number (the arrow goes to the right). But if B < (is less than) A, then the difference will be negative: B-A <-----------------+ <------------o-----------------o-------------------------> B A In fact, B-A is exactly the opposite of A-B: B-A = -(A-B) So you can subtract a larger number from a smaller one by subtracting the other way around and sticking a negative sign on the answer. That's a rule you can use. Another fact you may want to use is that if you have a number in between, the difference is the sum of the two intermediate differences: B-A C-B +----------------->---------> <------------o-----------------o---------o---------------> A B C +---------------------------> C-A C-A = (B-A) + (C-B) Notice that I deliberately didn't indicate on the number line whether A and B are positive or negative; I didn't show where zero is. That's because this definition of subtraction doesn't care about that. But when you actually try to subtract two numbers, it will matter. And 0 may play the role of A, B, or C in this picture. For example, if B is zero, since 0-A is -A, and C-0 is just C, this says that C-A = -A + C Since A is a negative number, -A is positive, and this gives a way to subtract a negative number from a positive by just adding two positive numbers, something you already know how to do. There are three places where I could have put the zero, and each corresponds to a different case you may want to consider when you write your rules. Try writing a rule to find B-A in each of these cases: 1. A and B are both positive: A B-A +----------------->---------> <------------o-----------------o---------o---------------> 0 A B +---------------------------> B 2. A is negative and B is positive: -A C +----------------->---------> <------------o-----------------o---------o---------------> A 0 B +---------------------------> B-A 3. A and B are both negative: B-A -B +----------------->---------> <------------o-----------------o---------o---------------> A B 0 +---------------------------> -A In each case, you will want to consider which number is larger (and in case 2, that means which of the two is positive); I've only shown B larger. This will give you six cases; you may find a way to simplify your rules by combining related cases. Have fun finding a way to say all this neatly! Really, it can all be done with those two little "rules" I gave above: B-A = -(A-B) and B - A = B + -A Just put these together a little differently in each case. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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