Why two negatives equal a positive
In: 3
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.
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?
Definitly an ELi5 explanation, but if 2 – 1 is being two steps forward and taking 1 step backward, than 2 – (-1) would be like being two steps forward and turning around and taking a step backward which puts you…3 steps forward.
Me: You are **negative.**
You: **Negative!**
This means that you are **positive**. You disagree with the fact that you are negative.
Me: Are you **negative?**
You: **Positive!**
This means you are **negative**. You agree with the fact that you are negative.
Me: Are you **positive?**
You: **Positive!**
This means you are **positive**. You agree with the fact that you are posititive.
Because you are taking away a negative number. Its like saying I’m not going to not do it. That means I am going to do it. You got 5 beans I take away -5, so you got 10 beans.
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