Adding and Subtracting IntegersDate: 04/17/2006 at 21:06:36 From: Constance Subject: Adding and subtracting integers I am having a hard time with integer operations. I have the most problems with subtraction when negatives are involved. Date: 04/18/2006 at 09:52:21 From: Doctor Ian Subject: Re: Adding and subtracting integers Hi Constance, Let's start with adding and subtracting integers. The basic rule is that you get partial cancellation. For example, 3 + -5 = 3 + (-3 + -2) = (3 + -3) + -2 = 0 + -2 = -2 In this case, the negative number had the larger magnitude, so we end up with some negative "left over". When the positive has the larger magnitude, the result is positive: 8 + -2 = (6 + 2) + -2 = 6 + (2 + -2) = 6 + 0 = 6 That's the basic idea. Another useful thing to know is that you can convert any subtraction into the addition of the corresponding negative, i.e., 3 - 4 = 3 + -4 What happens when you subtract a negative? 3 - -4 = ? To understand this, it's good to know that a negative number is just -1 times the corresponding positive number: -4 = -1*4 This means the negative of a negative is positive: -(-4) = -1*(-1*4) = (-1*-1)*4 = 1*4 = 4 So 3 - -4 = 3 + -(-4) = 3 + 4 Does this make sense? In practice, whenever I have both additions and subtractions, the very first thing I do is convert everything to additions, using these rules for changing signs. Why do I do that? Well, for one thing, then I just have to know how to add numbers, and I don't need extra rules for dealing with subtractions. That makes my life simpler, since I don't like to have to remember more than I absolutely have to! Second, the nice thing about additions is that addition is commutative and associative, which means I can reorder and group additions any way I want: 3 - 4 + 5 - 6 + 7 - 8 = 3 + -4 + 5 + -6 + 7 + -8 Change to additions = 3 + 5 + 7 + -4 + -6 + -8 Addition is commutative = (3 + 5 + 7) + (-4 + -6 + -8) Addition is associative = 15 + -18 = -3 But subtraction is neither commutative nor associative. So addition is much, much easier to work with. Is this clear so far? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 05/06/2006 at 10:57:11 From: constance Subject: Thank you (Adding and subtracting integers) Thank you. It was a great help. |
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