Why two negatives equal a positive

In: 3

A good example is in a physics model: in motion, a negative value means movement in an opposing direction, so if you go opposite of an opposite, you’re back moving in the same direction.

Your premise is a bit flawed. It’s two negatives multiplied that equal a positive.

Let’s map it out:

-2 x -2 = 4

Why? Treat the negative sign as “opposite”. So

2 x 2 = 4, right?

So, changing one of them to be opposite would look like:

-2 x 2 = -4

Both sides of the equal sign have to balance out with negatives or positives. The opposites of opposite (total of two opposites) would equal positive.

-2 x -2 = 4

Thought of another way, if you have negative 2 apples (you owe two apples) and I multiply your debt by 2, you now owe 4 apples. But what if I multiply your debt by -2, logic would follow that the opposite of that would be you now own/have 4 apples.

Imagine yourself on a number line facing the positive numbers. When you take a step back that is like subtracting a number. When you are multiplied by a negative 1, that is like turning 180 degrees. So say I’m at 5 on the number line and I’m subtracting by negative 3, I turn 180 degrees to face the decreasing numbers on the number line and then take 3 steps backwards and end up at 8.

Better question: why do two positives not equal a negative?

Think of negative as “inverse” or “opposite”. If the opposite of yes is no, then it follows that the opposite of the opposite of yes is still yes.