# Why negative times negative is positive

1. Feb 24, 2012

### gurudon

hey friend can anybody give answer?
why (-) * (-) = (+)

2. Feb 24, 2012

### HallsofIvy

Re: Question

Its impossible to give an explanation that you would accept without knowing what kind of explanation you would accept!

For example, one can show that a(b+ c)= ab+ ac (the "distributive law"). In particular, if we take a=-x, b=y, c= -y, that says -x(y+ (-y))= -x(y)+ (-x)(-y). But y+(-y)= 0 and -x(0)= 0 so that tells us that -x(y)+ (-x)(-y)= 0. Adding x(y) to both sides, -x(-y)= x(y).

Is that acceptable?

3. Feb 24, 2012

### dx

Re: Question

Think of -a as a reflection of a through the origin. Reflecting twice gives you back a: -(-a) = a.

4. Feb 25, 2012

### gurudon

5. Feb 25, 2012

### daveyinaz

:rofl:

6. Feb 26, 2012

### vkash

I have a simple explanation if u confined to Integers only
first of u need to know why - * + = -
multiplication is seemed to be derived from addition. Like2*3=2+2+2. and 3+4=3+3+3+3..
So when u write (-3)*4= (-3)+ (-3)+ (-3)+ (-3)=- (-12)
hence it is proved that (-)* (+)= (-)

Now come to (-)* (-)= (+)
Let me say u want to solve the question something like this. (-1)/1. you must have done divisions in primary classes where you make make a pie ∏ shape. write denominator part inside and numerator part outside etc,..
when u do such ting with (-1)/1. then u have two choices for quotient 1 or (-1). If u put 1 then using quotient rule. 1*(-1)+0=1 . But it's wrong so -1 is only answer u can think of..

All this is poor explanation since real numbers and complex number are not taken.
these all are based on logics and data.2+(3+5)=2*8=2*3+2*5 after many tries it was found that is applicable everywhere so it's made as property of numbers.