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# why does negative*negative=positive?

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1. I thought it's because two negatives cancel each other out to make a positive as nothing is left over, so it would make 0. While if it was - * +, it would be negative. If you try examples, you can see this happening. Math is stupid
2. I like to think of it in terms of rotations.Think of some 2D plane (that would contain the complex numbers) with the negative line at 180 degrees and the positive line at 0 degrees. When multiplying numbers together, it's the same as adding their angles together mod 360. EDIT: technically it would be in radians but degrees are a more accessible concept
3. -2(6+-6)=0 Hence negative multiplied by negative = positive.

EDIT: RDKGAMES got to it before me , so never mind.
4. I'll throw yet another justification into the mix:

Take a look at the attached picture.

1) Region A has area 2 since 1 x 2 = 2 (since multiplication by 1 leaves the number unchanged)

2) Region B has area -2 since 1 x -2 = -2 (since multiplication by 1 leaves the number unchanged)

3) Region D has area -2 since 2 x -1 = -1 + -1 = -2 (since multiplication by an integer is equivalent to repeated addition)

What is the area of region C then? Well, note that the total area of regions A and B = 0, and that regions C and D are congruent to regions A and B (i.e. we've just shifted the shape 1 unit to the left). So the total area of regions C and D must be 0 (since surely we cant change the area of a region just by translating it a bit) so we must have:

4) Region C has area 2 = -1 x -2.
5. (Original post by atsruser)
I'll throw yet another justification into the mix:

Take a look at the attached picture.

1) Region A has area 2 since 1 x 2 = 2 (since multiplication by 1 leaves the number unchanged)

2) Region B has area -2 since 1 x -2 = -2 (since multiplication by 1 leaves the number unchanged)

3) Region D has area -2 since 2 x -1 = -1 + -1 = -2 (since multiplication by an integer is equivalent to repeated addition)

What is the area of region C then? Well, note that the total area of regions A and B = 0, and that regions C and D are congruent to regions A and B (i.e. we've just shifted the shape 1 unit to the left). So the total area of regions C and D must be 0 (since surely we cant change the area of a region just by translating it a bit) so we must have:

4) Region C has area 2 = -1 x -2.
Areas are always non-negative - at best you mean signed area. Region B clearly has area 2.
6. (Original post by RichE)
Areas are always non-negative - at best you mean signed area. Region B clearly has area 2.
Well, yes, it's certainly signed area that I'm referring to, and mutatis mutandis, I don't think that it's too bad a hand-waving justification for the OP's question, unless you can see a more fundamental problem.
7. (Original post by atsruser)
Well, yes, it's certainly signed area that I'm referring to, and mutatis mutandis, I don't think that it's too bad a hand-waving justification for the OP's question, unless you can see a more fundamental problem.
Translating A and B one unit up changes the 'area' the way you've calculated it, so you can't claim their congruency means they have the same 'area' without already understanding that neg*neg=pos so that horizontal shifts won't change it the way you've calculated it.
8. (Original post by atsruser)
Well, yes, it's certainly signed area that I'm referring to, and mutatis mutandis, I don't think that it's too bad a hand-waving justification for the OP's question, unless you can see a more fundamental problem.
Well amongst other things you selectively use congruence in your argument to make a case for C and D having the same overall area as A and B. But D is congruent to A and yet has different "area" in your argument.
9. Most of the posts here provide intuition as a reason, which isn't very precise.
The intuition is what made mathematicians decide that . They define it like that; it's axiomatic.
10. (Original post by p29)
maths=english??
Well, yes, actually, or rather the other way round. English, and all other languages, incorporate mathematical ideas. Our mathematical notation might be quite different if it were devised by mathematicians from other parts of the world, with different number systems to ours, and indeed whole different ways of concieving of numbers. Some languages don't have a number system at all.

Maths is a description of a real phenomenon, or rather a range of phenomena which are defined by the laws of physics, but there is more than one way of describing it. Before the modern period, there were different 'mathses' the same as there were different languages.
11. (Original post by IrrationalRoot)
Most of the posts here provide intuition as a reason, which isn't very precise.
The intuition is what made mathematicians decide that . They define it like that; it's axiomatic.
That's rarely taken as an axiom. It follows from more fundamental rules about addition and multiplication relating to 0, 1 and distributivity.
12. The negative "-" reverses the sign of whatever it's multiplied by. So when a negative is multiplied by a negative, the negative is reversed and becomes a positive.
13. im learning so much
14. (Original post by p29)
im learning so much
have you had a response that leaves you comfortable with (-2) x (-3) equalling 6?

How does that now make sense to you?
15. (Original post by RichE)
have you had a response that leaves you comfortable with (-2) x (-3) equalling 6?

How does that now make sense to you?
16. Multiplication is addition sped up.*

If you can get your head around the fact a negative added to a negative is a positive, then just imagine that negative numbers multiplied is the same thing.*

Other than that, I have nothing. We were just expected to learn it and deal with it. Never had it explained to us. Never had to think about it until reading this thread so that's how little I need to know. Unless you're taking A level maths I think you can do without it too!*
17. (Original post by RichE)
have you had a response that leaves you comfortable with (-2) x (-3) equalling 6?

How does that now make sense to you?
I'd just leave it. The fact that this thread has 4 pages and the OP is still doesn't understand it make it clear that he is trolling. Otherwise I'm concerned for his common sense.
18. (Original post by p29)
I'm surprised no-one's made more of the debt metaphor - though some did point out that debt is a good use for negative numbers.

So if someone asked why -2 x -10 = 20 then treat -10 as a debt.

So 2 x -10 = -20 as you're in twice as much debt.

However -2 x -10 would be the amount needed to get you out of that debt. So it's 20.
19. (Original post by RDKGames)
I'd just leave it. The fact that this thread has 4 pages and the OP is still doesn't understand it make it clear that he is trolling. Otherwise I'm concerned for his common sense.
I'm half of that mind and half of a mind that most of the explanations in this thread are unduly formal or over-complicated.

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