Also see if you can explain unary minus. .... e.g. -2^3 This always causes grief. Excel evaluates it to -8 and so does Wolfram Alpha.
Assuming we're
not considering it's usage in computer programming languages:
Graham,
The "-" sign can have several meanings, two of which are:
1. "Minus"
2. "Negative".
In the following simple formula, both meanings are displayed:
[LATEX=]8 - 10 = -2[/LATEX]
i.e., we would
say the formula as: "eight
minus ten is equal to
negative two (and I suppose you could say "minus two, as well, but for the sake of the argument, let's stick with "negative" two).
Now, of course, a number that is being
multiplied by a - (use "minus" in ths case) obviously has a different connotation.
Let's start by stating a simple math assumption: ANY number, when multiplied by 1, is essentially
unchanged. OK?
If, however, we were to
multiply a number by -1, it does what?
It changes the "sign" of the value, making a
considerable change to its value, right?
So, take, for instance as KISS offered in the quote above:
-2^3, which could (and
should) be read as "negative two raised to the third power"
OR [LATEX=]-2^{3}[/LATEX] OR [LATEX=]-(2)^{3}[/LATEX].
OR, read as "negative one
times the
quantity two cubed, then [LATEX=](-1)(2)^{3}[/LATEX] OR [LATEX=](-1)*(2)^{3}[/LATEX].
One last example (YEAH!!!)
It can also be written as -2 times -2 times -2 = -8: (-2 *-2 = 4, then, -2 * 4 = -8).
These are all
identical in their solution.
I know. lotta verbiage for what is trully a simple concept, but with a slew of options in how to write or express it - welcome to mathematics. Being able to wade through the myriad variations is no small task and only becomes "bike riding" (you never forget how) with practice.