two negatives equal a positive?

Question

Many times i do my math and come across two integers that are multiplied. I know they are supposed to become positive, but is there a particular reason why? Is i just a rule or is there a reason behind it? help!

Answer 1

Here is what i found :

proofs, multiplying integers

Well, when we say -1 we mean the additive inverse of 1 so we have:

1 + -1 = 0 (since they are inverses)

1 + (1)*-1 = 0 (1 multiplied by anything is that thing)

1 = -(1)*-1 (subtract (1)*-1 from both sides)

1 = -1*-1 (the parenthesis don't mean anything)

So a negative times a negative means a positive.

Hope this helps.

-Doctor Steven, The Math Forum

Answer 2

Basically it is a mathematical rule that when you multiply 2 negatives you get a positive and when you divide two negatives you get a positive. If you divide an odd number of integers and multiply an odd number of integers you get a positive
but as long you understand how to get the right don't worry about it

Answer 3

Not a simple explanation but here it is:
(1) Zero times anything equals zero.

(2) Every number has exactly one additive inverse. This means if N
is a positive number, then -N is its additive inverse, so that
N + (-N) = 0. Likewise, the additive inverse of -N is N.

(3) We want negative numbers to obey the distributive law. This
says that

a*(b+c) = a*b + a*c.

(4) Now, we are forced to accept a new law, that negative times
positive equals negative. This is because we can use the
distributive law on an expression like

2*(3 + (-3)).

This equals 2*(0), which is zero. But by the distributive law,
it also equals

2*3 + 2*(-3).

So 2*(-3) does the job of the additive inverse of 2*3, and
therefore 2*(-3) is the additive inverse of 2*3. But the
additive inverse of 6 is just -6. So 2 times -3 equals -6.

(5) Next, we are forced to accept another new law, that negative
times negative equals positive. It's a lot like the example
in (4). We use the distributive law on, say,

-3*(5 + (-5)).

This is again equal to zero. But by the distributive law, it
also equals

-3*5 + (-3)*(-5).

We know the first thing, (-3*5) equals -15 because of the law
in (4). So (-3)*(-5) is doing the job of the additive inverse
of -15. We know -15 has exactly one additive inverse, namely 15.
Therefore,

(-3)*(-5) = 15.

Answer 4

No two positives equal a positive. To negatives equal a positive in multiplication

Answer 5

Basically it is a mathematical rule that when you multiply 2 negatives you get a positive and when you divide two negatives you get a positive. If you divide an odd number of integers and multiply an odd number of integers you get a positive

Answer 6

Will you accept that a negative times a positive is a negative? For example, 3 x (-4) = (-4) + (-4) + (-4)+ (-4) = -16.

Then, would it seem reasonable that a negative times a negative should be different than a negative times a positive?

Answer 7

usually, when you get more familiar with things then you'll be able to understand the "why" but if you don't know it so well then the "why" will just confuse you. when in math, for me, i don't question why because that just gets me confused so you should think of it as a rule.

Answer 8

if you count up the negatives in the equation and it turns out to be even, the answer is positive, but if it's odd, then the answer is negative

i think it's just a rule

Answer 9

It is kind of like speaking, a double negative makes a positive.

I am NOT INconsiderate.
I am considerate.

Get it?

Answer 10

use :

Signs
Unlike
Negative
Signs
Alike
Positive

SUNSAP

For example : -4 x -6 = +24 (signs are alike)

-4 x 6 = -24 (signs are different)