# Why negative times negative is positive

by gurudon
Tags: negative, positive, times
 P: 8 hey friend can anybody give answer? why (-) * (-) = (+)
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 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?
 HW Helper PF Gold P: 1,961 Think of -a as a reflection of a through the origin. Reflecting twice gives you back a: -(-a) = a.
 P: 8 Why negative times negative is positive i was cleared after going through this. http://www.mathsisfun.com/multiplying-negatives.html
P: 318
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.
 Quote by Hallsoflvy 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?
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.