How does 2 negatives make a positive?

Keep in mind that the negative sign indicates the number is the additive inverse of what it's applied to. There are only two real number operations: addition and multiplication. Subtraction is the addition of the additive inverse, and division is multiplication by the multiplicative inverse. That may seem like it's over-complicating things, but it's really just getting back to the basic definition of the operations.

Looking at it this way also allows us to prove that the product of two negatives is a positive. It's not good enough to just say it's the way it is, or it's a rule or law of math. We need to demonstrate why this "rule" is consistent with the other definitions governing the number system.

First let's think about a negative times a positive.

Suppose you have (-2)(3). Why is this -6?

Well, if you take (2)(3) + (-2)(3) = 6 + (-2)(3), by the distributive property that's equal to

(2 + (-2))(3) = 0(3) = 0

So (-2)(3) is additive inverse of 6, or -6

Similarly, (2)(-3) works out to be the same thing, -6.

Now suppose you have (-2)(-3)

Consider (-2)(-3) + (2)(-3), which is equal to (-2 + 2)(-3) = 0

So (-2)(-3) must be the additive inverse of (2)(-3), which is -6.

So (-2)(-3) = +6

I hope this was helpful.

Thank you all great answers😊

It happens only in multiplication.

K = {ab + a(-b)} + (-a)(-b) = ab + {a(-b)} + (-a)(-b)}

= ab + {a + (-a)}(-b) = ab + 0(-b) = ab + 0 = ab

K = {ab + a(-b)} + (-a)(-b) = a{b + (-b)} + (-a)(-b)

= a(0) + (-a)(-b) = 0 + (-a)(-b) = (-a)(-b)

(-a)(-b) = ab.

The facts are :-

(+ ve) x (+ ve) = + ve

(+ ve) x (- ve) = - ve

(-ve) x (-ve) = + ve

(-ve) x (+ve) = - ve

2×(-10) = 2×(-1)×10 = (-1)×20 = -20

The principle is -1 x -1 = +1, -1 x (+1) = -1. Generally, the '+' sign is not written on the left side of the number. When no sign is mentioned on the left side of the number it is understood to be '+' sign, a positive number only.

-2 * -10 = 20 not 10 as mentioned by you. however, 2 * -10 = -20 is correct.

The justification for why the product of two negative numbers is a positive number can be observed in the analysis of complex numbers.

(Ans.)

That's like asking why 1+1 is 2. It just is, there's not an explanation

Might be something you'll just have to accept.

-a * b = -ab

a * -b = -ab

-a * -b = ab

Also: -2 * -10 = 20 not 10

think of -2 * -10 as - (2 *-10) = - ( -20) as the opposite of -20......

The two negatives cancel each other out and make the positive. It's just one of the laws of math.