Why is a negative times a negative positive?

+2

-(-2) = -1*-2

i'm asking you why a negative times a negative is positive.

There's a fun (but somewhat unrigorous) way to think about why a negative number times a negative number equals a positive one:

1) Take a ruler, imagine it as a number line going from the negative side on the left to the middle notch (you can designate as 0) to the positive numbers on the right side.

2)Now place your hand on the number line and imagine it being a number n on the line. This can be any number which appeals to your intuition, whether it be 1, 10, -1.5, or 0.

3)For the first part, observe how adding/subtracting a number from the number your hand is designating will transform the number line. If you add a number, you are sliding the ruler to the left, that means you are adding a number a to your number n and as such your hand is going from the number n to the number n+a. This works the same way for subtraction but instead of shifting the number line to the left it shifts to the right.

4)Final part, which is to observe how multiplication transforms the number line. To start, see how multiplying your number n by a number b will affect the ruler. If you multiply by some number b, then your hand goes from n to b*n. Now try to think of what happens when b is -1. What happens is that the ruler is FLIPPING by 180 degrees such that all positive numbers go to their equivalent negative numbers and vice versa. If you apply this same operation twice, you get one 180 degree flip from n to -n, and then ANOTHER 180 flip from -n to n. In other words, you are rotating a total of 360 degrees, which gets you back to the same number you were originally at. This means -1*n = -n, then -1*-n=n. Which answers your question.

If what I said did not make sense or the experiment I tried to lay out is not intuitive enough, try watching this video from 6:05 to about 13:00 which takes the idea of thinking about numbers as actions and actually animates them: youtu.be/mvmuCPvRoWQ

i do not have no 2 things. but you're probably trolling.

Suppose you earn M dollars a year; in N years you will have MN dollars (a positive number),
whereas if this gain had begun in the past then N years ago (i.e. " -N ") you had MN dollars less (a negative number).
If you lost M dollars a year (i.e. you earned " - M "), in N years you would have MN less, but N years ago you had more MN than you have now

you shouldn't be on your phone during 7th grade math class.

this is my favorite answer so far.

It's kind of just a definition isn't it? We define the operation of taking a negative such that if you do it again you get the original number back.

like you gain 2 dollars, = +2
you lose 2 dollars = -2
you "unlose" 2 dollars = -(-2) = +2
it's like you're "losing" your already lost money. aka you're gaining money. Weird to think about.

OP has an interesting question here.

It's simple really. Let [math] R [/math] be a ring. Then [math] \forall a,b\in R [/math], [math] (-a)(-b)+(-a)b=-a(-b+b)=-a0=0 [/math]. Therefore, [math] (-a)(-b) [/math] is the additive inverse of [math] (-a)b=-(ab) [/math], which, since inverses are unique, is [math] ab [/math].

It pretty much is a definition which (to my very legitimate knowledge) can't be "proven" rigorously so much as it can be demonstrated in an intuitive manner. Either way thank you for the complement concerning my answer

Oops, made a made in typing which made my post sound a bit pretentious. I meant to type out "limited" instead of legitimate. I should also add onto here while I can that there can *technically* be proofs of the fact that a negative times a negative equals a positive but as I already stated these are more trivial conclusions which naturally follow from other concepts. An example of this would be 's post, which uses the properties of algebraic rings to trivially show the property of negative numbers that OP was asking about in the first place.

Why are these threads allowed? Every day we get another idiot claiming some outlandish shit about how math "doesn't work" because they can't understand simple operations or negative/imaginary numbers.

You can prove these things to yourself by perusing any random textbook you used in high school. If you cared about math at all you would never ask questions like this. Take it to /x/.

I think you're over thinking it. Math is purely conceptual. You can't actually have a negative value at all. That would make something nonexistent in the physical world.

I'll try to explain logically.

The teacher asked Timmy about his age.

"Twelve", said Timmy.

"No, you're lying" - Amanda says to Timmy

"No, YOU are lying!" John says to Amanda

Considering all of those statements, Timmy is right about his age, There was a negation (Amanda) being "negated" (John). So negative times negative = positive.

Got it?

Sorry about my english btw.

>You can't actually have a negative value at all. That would make something nonexistent in the physical world.
What about electrons? They have negative charge and there's plenty of them in the physical world. I think you're being too hasty with this conclusion about negatives not existing, you just need to get a little more creative with what counts.

That's different

You never said you had an issue with
-*+ = -

In his case, he is only using -1*2 - (-1*2)
Or do you not understand how subtracting negatives makes a positive?

You can think of -3 * -2 as
0 - (-2+ -2 + -2)

Which is what you get if you look at the distances on the number line.