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why does a negative number multiplied by another negative number equal a positive number like how can u even multiply something negatively lmao idg anything

In: Mathematics

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Double negative. “Two negatives make a positive” & whatnot. That’s the best I can explain it.

negatives can be thought of as direction. let’s look at this in terms of money. a common example of a negative amount of money is dept. you don’t have it, you owe it to someone else. multiplying by a positive can be seen as getting something and a negative can be seen as sending something. So combining these two metaphors, we get sending/receiving checks/bills.

A negative times a positive is like getting a bill. You end up having to send money (a negative). But a negative times a negative is like **sending** someone a bill. In this case, you end up receiving money from them.

Think of a collection of positive and negative blocks. The total number is the sum of all blocks, which can be positive or negative.

+ + + – – = 3 – 2 = 1

+ – – – = 1 – 3 = -2

Zero is when you have an equal amount of positive and negative blocks. 2 – 2 = 10 – 10 = 0.

Multiplication is adding or removing multiple blocks at once.

* Positive * Positive means **adding** *positive* blocks. 2*3 means adding 6 (+).

1 + (2*3) = + [add +++ +++] = +++++++ = 7

* Positive * negative means **adding** *negative* blocks. 2*(-3) means adding 6 (-).

1 + (2*-3) = + [add – – – – – -] = + – – – – – – = -5

* Negative * positive means **removing** *positive* blocks. -2 * 3 means removing 6 (+).

7 + (-2*3) = +++++++ [remove +++ +++] = + = 1.

* Negative * negative means **removing** *negative* blocks. -2 * -3 means removing 6 (-).

-7 + (-2*-3) = – – – – – – – [remove – – – – – -] = – = -1. It’s the same as if you did -7 + 6.

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Another way of thinking about it is as a direction on a number line: … -3, -2, -1, 0, 1, 2, 3 …

A*B comes down to stepping forwards (positive B) or backwards (negative B) while facing right (positive A) or left (negative A). Negative*negative then means looking left and stepping back, which has the same effect as positive*positive.

So the previous statements are nice explanations but they are not right. Actually, this is an example of an axiom, or a fundamental rule that is accepted as true, but cannot be logically shown why. Most “meaningful” (loaaded) math is based on axioms. Certainly all the math you know is. Like for any two points there is a line that intersects them. You learned that in school and it is an axiom. You cannot prove it via logic, but also no one has disproved it and it is really, really useful if you treat it as a building block for logic. Very important to point out again, an axiom only remains as long as no one finds a contradiction so they aren’t just accepted without vetting. The number of axioms different fields and ‘modes’ of mathematics are generally few. Theorems are born from combining these axioms, axioms and theorems, and theorems with theorems.The rules of -/+ multiplication do not have proofs or logically mathematical explanations: many of mathematics brightest have tried to make a proof for why 1x-1=-1 is logically resultant from other axioms, and they all failed (including Euler!) But doing 1x-1=-1 is waaaaaaaaay more useful than 1x-1=1. Why this is so gets far beyond ELI5.Maybe someday someone will do it, like find the proof with new math, but for other more exciting reasons, not being able to “prove something” can be a serious argument for it being true, because of Godel’s Incompleteness Theoroms. So humanity has probably not wildly messed up ;POther comments here about arithmetic are great for just giving yourself your own logic, or explaining to someone learning this for the first time, like they are good!

Think of multiplication as asking “How many of something do I have?” This way, 3 * -5 means you have three times the number -5. So you get -5, -5, and -5. Or -15.

Similarly, if you multiple two negative numbers, you’re basically asking yourself how many negatives of something you have. If you have -3 * -5, you are telling yourself you have the negative of that, which is positive 15.

I apologize to any mathematicians if I just slaughtered that.