why negative*negative=positive??

Answer 1

By definition, the additive inverse of a real number x (its negative), denoted -x, is the unique number which satisfies

x + (-x) = 0.

In addition to that, the operation of subtraction is in fact defined by the following rule

x - y = x + (-y).

(So when we say 'x minus y', we actually mean 'x plus the additive inverse of minus y'.)

Now, we'll show that (-x)y = - xy:

xy + (-x)y = (x + (-x))y = (x - x)y = 0y = 0

Thus x y + (-x)y = xy + (-xy), and cancelling xy from both sides yields (-x)y = - xy. Now,

-xy + (-x)(-y) = (-x)y + (-x)(-y) = (-x){ y + (-y)}

=(-x){ y -y} = (-x)0 = 0.

Thus -xy + (-x)(-y) = -xy + xy, and cancelling -xy from both sides yields

(-x)(-y) = xy. QED

(If you want a more intuitive explanation, the link to mathforum provided below might help.)

Answer 2

Well, when we say -1 we mean the additive inverse of 1.if u haven't leaned abt inverses, don't worry abt it it isn't important ...

we know;
1 + -1 = 0 (since they are inverses)

1 + (1)*-1 = 0 (1 multiplied by anything is that thing)

1 = -(1)*-1 (subtract (1)*-1 from both sides)

1 = -1*-1 (the parenthesis don't mean anything)

So a negative times a negative means a positive.

Answer 3

Let's look at the following problem first:

Suppose that I regularly save 100 dollars per month. What will the change in my money be 10 months from now?

This is easy; over the next 10 months, at 100 dollars per month, I'll have 10 x 100 = 1000 dollars more than I do now.

Now, a slightly different problem: Suppose instead that I've fallen on hard times, and I regularly lose 100 dollars per month. How much will the change in my money be 10 months from now?

Well, if I'm losing 100 dollars per month, the change in my money will be -100 dollars per month. Over 10 months, this means that the change will be 10 x -100 = -1000 dollars. I'll lose 1000 dollars over the next 10 months.

Now, one more problem: Suppose I'm losing 100 dollars a month, and I want to know how much money I had 10 months ago.

Well, the answer is clearly $1000. How should we relate this to multiplication of negative numbers?

We can think of "10 months ago" as "-10 months in the future." As I move into the future, my money is changing by -100 dollars per month. So to make multiplication work correctly, we'd expect -100 x -10 = 1000.

Answer 4

Consider (-8) * (-3) as an example.
Split each number into a positive value and a sign:
8 * 3 * (-1) * (-1)
= 24 * (-1) * (-1)
When you multiply a number by -1, you change the sign.
Here, you are multiplying by -1 twice; so you change the sign twice.

Answer 5

ill tell u the aswer to that question once u answer me this....

why is negative * positive = negative!?????

Answer 6

bcoze if it was not so positive numbers cannot exist