any theory behind this?

Question

+ X + = +
and
- X - = +
and
- X + = -

i dont need your own theories man

Answer 1

It is not a therory, it is a consequence. It is the definition of positive and negative numbers, and the rule that govern tem. It is just plain math.

Take a positive number a positive number of times, and the result is positive.

Take a negative number a negative number of times (like taking away a debt) and you have a positive.

Take a positive number a negative number of times (or a negative value a positive number of times) and you have a negative.

Answer 2

Not really theory, it's just the way numbers (and language) works.

Think about this pattern:

2 x 2 = 4
1 x 2 = 2
0 x 2 = 0
-1 x 2 = ???

Well, the left side numbers go down by ones, the right side by twos! So the ??? answer is -2! Compare 1 x 2 with -1 x 2.

How about the other way around?

2 x -3 = -6
1 x -3 = -3
0 x -3 = 0
-1 x -3 = ???

Compare the left side (going down by ones) to the right side (going UP by threes!). Following the pattern, the ??? answer is equal to Positive 3.

When you multiply one negative with one positive, it's like changing a statement with a "Not", like saying "This question will NOT end."

But when you multiply two negatives together, it's a double negative, like saying "There's NO way that this question does NOT end somewhere!" That means that the question has an end, which is a positive statement.

And that's the end of the question. See? I told ya'!

Answer 3

Math must be consistent. We assume that a positive time a negative gives a positive{+2 times +3 we want to give the same answer as 2 times 3 so we assume it to be true and look for contradictions}
(1) +2*+3 = +6 assumption then
(2) +2*-3 = -6 or +2* -3 = +6 we have a contradiction if we choose the 2nd +2*-3=+6 and +2*+3 = +6 can not both be true. this would give you two answers to
+2times ? = +6
(3) -2*-3 = +6 or -2*-3 = -6NO BECAUSE THIS CONTRADICTS NUMBER 2 ABOVE

Answer 4

This is really a result of axioms governing what are known as ordered fields. These following result from those axioms

If x+y=x+z, then y=z (1)

So simply let z = -x in (1) and you get

If x+y=x+-x, then y=-x (2)

but in (2) we knpw x+-x = 0, so we get

If x+y=0, then y=-x (3)

Now, if you replace x with -x in (3) you get

If -x+y=0, then y=x (4).

These then imply that -(-x) = x.

Now, for the rules concerning multiplication we have

(-x)*y = -(x*y) = x*(-y) (5)

This follows from

(-x)y+xy = (-x+x)*y = 0*y = 0, or (-x)y+xy = 0, or (-x)y = (-x*y) and

x(-y) + xy = (-y+y)*x = 0*x = 0, or x(-y) + xy =0, or x(-y) =-(xy)

Thus proving (5). Now take

(-x)(-y) = x*y (6)

(-x)(-y) = -[x(-y)] = -[-(xy)] = xy, from (4)

Answer 5

I actually have four very different answers to the same question. The first is cute and easy to follow, but it may leave you unconvinced. The second is my favorite: not hard to follow, very convincing, and (best of all) very concrete. The third one demonstrates a good way of dealing with negative numbers in general, which is to start with positive numbers and work down. And the fourth is for people who like to "prove" things.

The First Answer: Grammatical Analogy
Some people think of negative as meaning "not." So if I say "I am not going to the store," that is sort of the negative version of "I am going to the store."
So what do two "nots" mean? Consider this sentence: "You may tell me NOT to go to the store, but I'm NOT going to do what you say!" By negating your negation, I am insisting that I WILL go to the store.

OK, you get the idea? Two "nots" cancel each other out, just like two negatives. That was the appetizer: here comes the main course...

The Second Answer: Money Analogy
One way to think of numbers is in terms of money. Let's say you and I are playing poker. To make life convenient, we use chips instead of real money. A green chip is worth $5. A red chip means that you owe $5. So if you lose $5, you can represent that by giving up a green chip, or (if you're out) by picking up a red chip. Of course, you are always allowed to pick up a green chip and a red chip at the same time, because that doesn't change your total sum. (At the end, presumably, we'll cash in all our chips and see who gains or loses what money.)
I hope you see the mathematical analogy I'm drawing here: A green chip represents +$5, and a red chip represents -$5. Make sense? If so, here comes multiplication in terms of chips.

If you gain three green chips, what happens? Intuitively, you know that you gain $15. Mathematically, we take the +$5 that one chip is worth, and multiply it by +3, to indicate that you are gaining three chips. 3 x $5 = $15; positive times positive is positive.

If you gain three red chips, what happens? If you think about it, I think you'll agree that you just lost $15. Mathematically, this looks the same as the previous example, except that the +$5 that represents a green chip, is replaced by -$5 to represent a red chip. 3 x -$5 = -$15; positive times negative is negative.

Now, what if you lose three green chips? Once again, you have lost $15. We represent this "loss" mathematically by changing the 3 into a -3, so our equation is: -3 x $5 = -$15. Negative times positive is negative.

And finally, what if you lose three red chips? Hooray! This is happy news, it means you have actually gained money. Mathematically, this is -3 (since you lost) times -$5 (since they were red chips). -3 x -$5 = +$15. Negative times negative is positive.

The Third Answer: Progress from the Positive Numbers
This is a little more abstract and mathematical.
Another way to think about negative numbers is that they "continue the sequence" as positive numbers go down. In other words, if I go from 4 to 3 to 2 to 1 to 0 and then keep going, I get into the negative numbers. Nothing should change drastically when I make that switch.

So, consider what happens when I take all the numbers in that sequence, and multiply them by 5:

4 x 5 = 20
3 x 5 = 15
2 x 5 = 10
1 x 5 = 5
0 x 5 = 0

What's happening on the left is that the numbers are going down by one. What's happening on the right is that the numbers are going down by 5.

If we keep dropping the left-hand column by one, we expect the trend to continue. Hence, the next few terms are...

-1 x 5 = -5
-2 x 5 = -10
-3 x 5 = -15

...and so on. So this tells us that a negative times a positive is a negative.

Now, let's do the same thing with the multiples of -5 instead of 5.

4 x -5 = -20
3 x -5 = -15
2 x -5 = -10
1 x -5 = -5
0 x -5 = 0

Once again, on the left, our terms are going down by 1. But what's happening on the right? The terms are going up by 5 each time. (If you don't believe this, think of them as temperatures. When you go from -20 to -15, the temperature has gone up by 5.) So if that sequence continues, we will see...

-1 x -5 = 5
-2 x -5 = 10
-3 x -5 = 15

Once again, a negative times a negative is a positive.

The Fourth Answer: A Proof of Sorts
Finally, for people who like algebraic sorts of proofs, consider this. A and B are both positive numbers.
A + (-A) = 0
(A)(B) + (-A)(B) = 0

Since the term on the left is positive, the term on the right must be negative. (I'm assuming here that if two non-zero numbers add up to zero, then one of them is negative and one is positive—I think that is too obvious to require a proof.) This proves that negative times positive is negative. Now:

A + (-A) = 0
(A)(-B) + (-A)(-B) = 0

Since the term on the left is negative (as we just proved!), the term on the right must be positive.

Answer 6

It is often answerer to the most easiest questions have the most hardest answerer.
In math, everything is expected after a concise proof is given. As in your case, the proof goes deep, I mean deep in the heart of number theory and only senior mathematicians can provide the proof.

Answer 7

Two wrongs make a right?

You missed out + X - = -. So there are just as many minus outcomes as plus outcomes. No big deal there.

Answer 8

Yeah dude, a positive number times a positive number is a positive number. Now, you figure out the rest!

Answer 9

if u r a positive minded n u r friend is a positive minded then both of u discuss about the positive things
if u r a negitive minded n u r friend is a positive minded then u will discuss about the -ve things n ur friend with +ve things.

Answer 10

42 but what is the ?