Why minus times minus equals plus?
Mike Savage gives a brilliant explanation on the excellent British website of mathtutor. I can't but recommend this website heartily.
So, why "minus times minus equals plus"?
We have to remember two arithmetics rules:
Then we can now prove that minus x minus = plus.
(read "negative one"," times", *two plus one")
Now, for rule 2 (above) the operation can be rewritten as
= (-1)x2 + (-1)x(1)
so, similarly, we can take another operation such as
and by expanding the brackets (rule 2) we obtain
But (-1)x(-1+1) can also be formulated with the rule 1 above (the precedence law, brackets first) as
Which simply gives
Now, we combine the two
(-1)x(-1) -1 = 0
which is the same to say
(-1)x(-1) = 0 +1
(-1)x(-1) = 1
Source, Mike Savage, Mathtutor website
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