Subtracting Negative NumbersDate: 12/06/2005 at 14:49:15 From: Rashi Subject: How do you subtract negative numbers Why do we have to change a subtraction problem to an addition problem and change the second term to the opposite sign? For example, -9 - (-3) = -9 + (3) = -6 My teacher made me memorize the rule but I want to fully understand why it works. I don't just want a rule, I want an example that I can understand and use. Date: 12/06/2005 at 20:15:53 From: Doctor Rick Subject: Re: How do you subtract negative numbers Hi, Rashi. I like it when students want to UNDERSTAND math! Memorizing rules is OK sometimes, but it's much better to understand the reasoning behind them, because you can do a lot more with reasoning than with rules. Let's start by understanding what subtraction means. To do that, I'll start with addition. Consider the addition 6 + 3 = 9 on a number line. You start at the 6 and go 3 units to the right: 6 +3 =9 O=============>O --+----+----+----+----+----+----+----+----+----+----+----+-- 0 1 2 3 4 5 6 7 8 9 10 11 Now, what does the subtraction 9 - 3 = 6 mean? It is the answer to the problem ___ + 3 = 9 In other words, the subtraction is "undoing" the addition above: we start at the 9 and back up three spaces. (Read backwards: 9 - 3 = 6) =6 -3 9 O<=============O --+----+----+----+----+----+----+----+----+----+----+----+-- 0 1 2 3 4 5 6 7 8 9 10 11 Now what about negative numbers? To add 9 + -3, I start at 9 on the number line and move LEFT 3 spaces: =6 + -3 9 O<=============O --+----+----+----+----+----+----+----+----+----+----+----+-- 0 1 2 3 4 5 6 7 8 9 10 11 That's 9 + -3 = 6. Notice that it's the same as 9 - 3 = 6: adding a negative is the same as subtracting the opposite of the negative (which is positive). Finally, we can subtract -3 from 6: the result is the answer to the problem ___ + -3 = 6 As before, I work backward: I start at the 6 and "undo" the addition of -3. I reverse the arrow I drew above, going 3 spaces to the right instead of left. 6 - -3 =9 O=============>O --+----+----+----+----+----+----+----+----+----+----+----+-- 0 1 2 3 4 5 6 7 8 9 10 11 What do you notice this time? I do exactly the same thing that I did for 6 + 3. 6 - (-3) is the same as 6 + 3 Does this help? - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ Date: 12/07/2005 at 08:10:01 From: Rashi Subject: Thank you (How do you subtract negative numbers) Yes, that helped a lot. Thank you. |
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