Question

Why does a negative times a negative equal a positive? BTW don't use (-) x (-) in explanation

Answer 1

multiplication is a series of additions
2*4 = 2+2+2+2=8
you add 2 four times

if its -2*4, then you add -2 four times
-2 -2 -2 -2 = -8

when its -2*-4, then you add -2 (neg four) times
but that doesn't make sense , you can't add something negative times
but you can think of it as subtracting -2 four times
subtracting -2 is same as adding positive 2

-2*-4 = 2+2+2+2 = 8

Answer 2

Suppose you have
\[4\times 4\]
We know both the no.s are positive and the product will also result in a positive no.
We know by basic math that
\[\frac{1}{-1}=-1\]
Now in our multiplication We can divide and multiply by an no. and it won't affect our result
So we choose -1 . We multiply and divide by -1 and this won't change our result
so
\[\frac{-1}{-1} \times 4\times 4\]
Now \(-1 \times 4= -4\)
so we have now
\[\frac{-4}{-1} \times 4\]
We know that \[\frac{1}{-1}=-1\]
so
\[-4 \times -1 \times 4\]
so we have now
\[-4 \times - 4\]

but we know that result is 16
so this implies
\[- \times -\ is\ +\]

Answer 3

Here's explanation from Group theory.
set of real numbers is a group under operation of addition and multiplication.
if 'a' be any element of G then,
'-a' is additive inverse of 'a'.
let '-a' be represented by 'b' which is also belongs to set G (from closure property)
so 'b' in turn has additive inverse '-b'
as we know in group, an element always has unique inverse, so inverse of b is -a
or
-(-a) = a
hence we can prove that -x-=+

Answer 4

in other words, inverse of a inverse in itself. so, -x- must result to +

Answer 5

explanations given do the job of explaining but an example from real life may be good....
so
If I say "go" I am encouraging you to go (positive), but if I say "do not go" I am encouraging you to stay which is the opposite (negative).

Now if I say "Do NOT not go", I am saying I don't want you to stay, so I am back to saying "go".

So, two negatives make a positive

Answer 6

Yeah I heard that one, seems strange to use language logic in maths though.

Answer 7

The negative acts as an inverter.

Answer 8

well it depends on the person.. some people find it easier to understand language logic though...
anyway you got several ways of explanations here that can help you get the idea
hopefully you got what you needed XD