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### Working with negative numbers – Part II

July31

– (-16) = +16

“How do you go from ‘ – (–16)’ to ‘ + 16‘ in your first step?” This is actually a fairly important concept and 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 some 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 happen to good people: a good thing  (+) x (+) = +ve answer

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