In math WHY is a negative multiplied by another negative positive?

Question

Everyone knows the saying 'Two wrongs don't make a right', yet in mathematics, the product of two negative values equals a postive value. I would really like to know if anyone knows the theory/concept behind this. Please explain as detailed as possible.

Alot of you are only reiterating what you've been programmed to know. You are using the concept to prove it's theory, as if someone asked you to tell them the definition of 'perfect' and you told them it was when someone accomplishes 'perfection'. Can't do that. Only one person has the best possible answer so far...

Answer 1

Mathematicians aren't always correct.

On a Y,X axis plane the the rectangles formed would all be in different quadrants.

(-5 x 4) / (5 x 4)
----------/----------
(-5 x -4)/ (5 x -4)

But in simple math, they cancel each other out.

[edit] Multiplication
Multiplication of a negative number by a positive number yields a negative result: −2 × 3 = −6. Multiplication of two negative numbers yields a positive result: −4 × −3 = 12.

One way of understanding this is to regard multiplication by a positive number as repeated addition. Think of 3 x 2 as 3 groups, with 2 in each group. Thus, 3 × 2 = 2 + 2 + 2 = 6 and so naturally −2 × 3 = (−2) + (−2) + (−2) = −6.

Multiplication by a negative number can be regarded as repeated addition as well. For instance, 3 × -2 can be thought of as 3 groups, with -2 in each group. 3 × −2 = (-2) + (−2) + (-2) = −6. Notice that this keeps multiplication commutative: 3 × −2 = −2 × 3 = −6.

Applying the same interpretation of "multiplication by a negative number" for a value that is also negative, we have:

−4 × −3 = − (−4) − (−4) − (−4)
= 4 + 4 + 4
= 12

However, from a formal viewpoint, multiplication between two negative numbers is directly received by means of the distributivity of multiplication over addition:

−1 × −1
= (−1) × (−1) + (−2) + 2
= (−1) × (−1) + (−1) × 2 + 2
= (−1) × (−1 + 2) + 2
= (−1) × 1 + 2
= (−1) + 2
= 1

Answer 2

Let's start by trying to work out the answer to 5 × (-4).
First of all, think about the sum 5 × 4. The answer is 20.
This is the same as 4 + 4 + 4 + 4 + 4, which gives 20.
In the same way, the sum 5 × (-4) can be written (-4) + (-4) + (-4) + (-4) + (-4), which gives -20.
Now, the -5 x -4 is the same as (-1) x (5) x (-4), which is (-1) x (-20) = 20

To think of it another way, if you multiply a negative number by a positive number, you get a negative number. Obviously, if you multiply a negative number by a negative number, you couldn't also have a negative number, otherwise, you would come up with the contradiction, in the above example, that -20 = 20. If that were true, then that would be the end of the universe as we know it!

Answer 3

Math is a set of postulates, definitions and theories based on those postulates and definitions.

The product of two negative numbers has no real analog in the real world (where as the addition of integers clearly does. If you add an apple to another apple, you have 2 apples).

Therefore, it is "defined" to be a positive value. WIth that definition, all sorts of other math becomes possible.

In any case, comparing the mathematical properties of negative numbers and the social properties of negative actions is really misleading. Why did you choose multiplication and not, say, addition?

One wrong plus another wrong makes a right? If "wrong" is negative, two wrongs is MORE negative.

Answer 4

If you take Abstract Algebra in college, you will have your explination.
here's the best I can do without my textbook in front of me.

given, a,b in
a=b>0 (a and b are both positive)
-a=-1a
-a*-b = -a*-a
(-1*-1)(ab) = (-1*-1)(aa)
divide by -1
-ab=-aa
as diviging by -1 changes the sign, and a number is either negative or positive, as (-1)ab is negative, (-1*-1)ab MUST be positive.

boy did I botch that one. For now, that'll do.

I think I forgot something, like the foundation of abstract algebra in general.
It is a difficult proof for something I've known since the early 1990s.
Number theory is a *****.

Answer 5

Because the two negatives cancel each other out. You have to look at it from an abstract angle and really think about it for it to make any sense.

Answer 6

If you think of positive and negative numbers as moving either forward or backward. Moving forward is positive, moving backward is negative. So, moving backward from moving backward would be the same as moving forward.

I know that seems lame, but it's not any more complicated than that.

Answer 7

Only in morality and bad English (I don't got no milk) does that "Two wrongs don't make a right," saying take effect. But think of it this way if you have a monthly bill (1*(-x)) the your more in debt next month. But if you take away a bill
((-1)(-X)) then you have that much more money next month.

Answer 8

Sure:

if you have -2 of something and you double it, you get -4
if you take the -(-4) you get +4

its just distribution of the negative sign:

its really (-1)(2)(-2) = 4!

Answer 9

Because. -2 *-2 = 4 BECAUSE NEGATIVE NEGATIVE 2 IS POSITIVEM BECAUSE THERE'S A NEGITIVE NEGATIVE 2 ITS A POSITIVE TWO.

Its hard too explain

also i accidently left caps lock on, sorry to lazy to fix it

Answer 10

i ask myself that and think i dont care all i see is that the two -'s make a + joined together HEhehe