Negative numbers

[jaywhybee]

Is there a simple explanation as to why the product of two minus numbers is a positive number? Presumably -2x-3 is +6; the same as 2x3 is 6? Or am I a total idiot for not understanding the concepts involved - probably...

[landie]

Is it the same principle as a double negative in grammar?

I haven't got none !! (means you must have some).

[bernardo]

2 x 3 = 6

-2 x 3 = -1 x 2 x 3 = -6 because (-2 x 3) is (-1) x (2 x 3)

2 x -3 = 2 x -1 x 3 = -6 because (2 x -3) is (2 x 3) x (-1)

-2 x -3 = +6 because (-2 x -3) = (-1) x (2 x -3) = (-2 x 3) x (-1)

[Loosehead]

It was explained to me as a number line:

-6...-5...-4...-3...-2...-1...0...+1...+2...+3...+4...+5...+6

multiplication is just repeated addition so to multiply 2 x 3 you start at 0 and count 3 twice. (as the multiplyer is positive you start off going the positive way up the line)

The same is true with -2 x -3 you start at 0 and move up the line -3, -2 times. but because the 2 is negative you move toward the negative, subtracting -3 twice ie 0 - - 3 = +3 - - 3 = +6 .

It may appear confusing but where it not true the whole maths continuum would come crashing down!

[newtron]

http://www.aft.org/pubs-reports/american_educator/fall99/amed1.pdf  In addition to the answers already supplied,  pages 4 and 5 of this PDF give a good explanation.  I like the analogy of playing a film of a pool being drained backwards.

[Peter Pedant]

God, the pool backwards bit, I read in a science picture book in 1964!

the one I like, but no-one who i tried it on, does, is.....

2 x -3 is -6 and so if you are gonna say -2 x -3 is also    -6 then the you will be forced to conclude 2 = -2 by cancelling -3.

[jaywhybee]

Thank you all, I appreciate your efforts to enlighten me; and I do feel as if I understand it a lot more. Now I'm off to drain that pool!!

[oops!!!]

I've read all the above ... now my brain hurts!!!