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Why negative times negative is positive

  1. Feb 24, 2012 #1
    hey friend can anybody give answer?
    why (-) * (-) = (+)
  2. jcsd
  3. Feb 24, 2012 #2


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    Science Advisor

    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?
  4. Feb 24, 2012 #3


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    Homework Helper
    Gold Member

    Re: Question

    Think of -a as a reflection of a through the origin. Reflecting twice gives you back a: -(-a) = a.
  5. Feb 25, 2012 #4
  6. Feb 25, 2012 #5

    nice link
  7. Feb 26, 2012 #6
    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.
    similar about others...
  8. Feb 26, 2012 #7
  9. Feb 29, 2012 #8
    mathforum is also not bad..
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