|
|
|
|
|
|
|
||
|
|
|
|
|
Adding and Subtracting Negative Numbers (page 2 of 4) Sections: Introduction, Adding and subtracting, Multiplying and dividing, Negatives and exponents How do you deal with adding and subtracting negatives? It works similarly to adding and subtracting positive numbers. If you are adding a negative, this is pretty much the same as subtracting a positive, if you view "adding a negative" as adding to the left. Let's return to the first example from above: "9 – 5" can also be written as "9 + (–5)". Graphically, it would be drawn as "an arrow from zero to nine, and then a 'negative' arrow five units long":
...and you get "9 + (–5) = 4". Now look back at that subtraction you couldn't do: 5 – 9. Because you now have negatives off to the left of zero, you have the "space" to complete this subtraction. View the subtraction as adding a negative 9; that is, draw an arrow from zero to five, and then a "negative" arrow nine units long:
...or, which is the same thing:
Then 5 – 9 = 5 + (–9) = –4. Of course, this method of counting off your answer on a number line won't work so well if you're dealing with larger numbers. For instance, think about doing "465 – 739". You certainly don't want to use a number line for this. You know that the answer to "465 – 739" has to be negative, (because "minus 739" will take you somewhere to the left of zero), but how do you figure out which negative number is the answer? Copyright © Elizabeth Stapel 2006-2008 All Rights Reserved Look again at "5 – 9". You know now that the answer will be negative, because you're subtracting a bigger number than you started with (nine is bigger than five). The easiest way of dealing with this is to do the subtraction "normally" (with the smaller number subtracted from the larger number), and then put a "minus" sign on the answer: 9 – 5 = 4, so 5 – 9 = –4. This works the same way (and is simpler) for bigger numbers: 739 – 465 = 274, so 465 – 739 = –274. Adding two negative numbers is easy: you're just adding two "negative" arrows, so it's just the backwards of "regular" addition. For instance, 4 + 6 = 10, and –4 – 6 = –4 + (–6) = –10. But what about when you have lots of both positive and negative numbers? For instance:
Probably the simplest thing to do is convert everything to addition, group the positives together and the negatives together, combine, and simplify. It looks like this: 18 – (–16) – 3 – (–5) + 2
"Whoa! Wait a minute!" you say. "How do you go from ' – (–16)' to ' + 16' in your first step?" This is actually a fairly important concept, and, if you're asking, I'm assuming that your teacher's explanation didn't make much sense to you. So I won't give you a "proper" mathematical explanation of this "the minus of a minus is a plus" rule. Instead, here's a mental picture that I ran across in an algebra newsgroup: Imagine that you're cooking some kind of stew, but not on a stove. You control the temperature of the stew with magic cubes. These cubes come in two types: hot cubes and cold cubes. If you add a hot cube (add a positive number), the temperature goes up. If you add a cold cube (add a negative number), the temperature goes down. If you remove a hot cube (subtract a positive number), the temperature goes down. And if you remove a cold cube (subtract a negative number), the temperature goes UP! That is, subtracting a negative is the same as adding a positive. Now suppose you have some double cubes and triple cubes. If you add three double-hot cubes (add three-times-positive-two), the temperature goes up by six. And if you remove two triple-cold cubes (subtract two-times-negative-three), you get the same result. That is, –2(–3) = + 6. There's another analogy that I've been seeing recently. Letting "good" be "positive" and "bad" be "negative", you could say: good things happening to good people: a good thing The above isn't a technical explanation or proof, but I hope it makes the "minus of a minus is a plus" and "minus times minus is plus" rules seem a bit more reasonable. Let's look at a few more examples:
–43 – (–19) – 21 + 25
You can only move stuff around like this after you have converted everything to addition. You cannot reverse a subtraction, only an addition. In shorthand, you can only move the numbers around if you move their signs with them. If you move only the numbers and not their signs, you will have changed the problem. Continuing... 44 + (–64) = 44 – 64 Since 64 – 44 = 20, then 44 – 64 = –20. Here's another example:
84 + (–99) + 44 – (–18) – 43
<< Previous Top | 1 | 2 | 3 | 4 | Return to Index Next >>
|
|
|
|
Copyright © 2006-2008 Elizabeth Stapel | About | Terms of Use |
|
|
|
|
|
|
