Results 1 to 8 of 8

Math Help - Why do two likes give a positive, and two unlikes give a negative

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    8

    Why do two likes give a positive, and two unlikes give a negative

    The rule i learned is:

    For multiplication or division two likes give a positive answer, two unlikes give a negative answer.

    E.g.
    -2 * -2 = 4

    -2 * 2 = -4

    BUT look at this...

    2 * 2 = 4 is the same as saying 2 + 2 = 4. Right?So....

    -2 * -2 = 4 should be the same as saying -2 + -2 = x

    But... -2 + -2 = -2 - 2 = -4 ..... so it isn't the same pattern as above.

    Can anyone shed some light?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    Quote Originally Posted by Kick View Post
    The rule i learned is:

    For multiplication or division two likes give a positive answer, two unlikes give a negative answer.

    E.g.
    -2 * -2 = 4

    -2 * 2 = -4

    BUT look at this...

    2 * 2 = 4 is the same as saying 2 + 2 = 4. Right?So....

    -2 * -2 = 4 should be the same as saying -2 + -2 = x

    But... -2 + -2 = -2 - 2 = -4 ..... so it isn't the same pattern as above.

    Can anyone shed some light?

    A mistake here:

    -2 * -2 = 4 should be the same as saying -2 + -2 = x
    Think more...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,974
    Thanks
    1121
    What kind of answer do you want? You can show from the "field axioms" that the product of two negative numbers is positive. That's very simple, completely correct and very technical- requiring that you know a lot of definitions and abstract concepts you probably don't.

    Or you can argue that, just as if you have, say, 5 boxes, each containing 10 dollars, then you have 5*10= 50 dollars, that if you owe $10 to each of 5 people (so - $10), and each of the 5 people cancels ("negates") the debt, you no longer owe any thing- its just as if you had suddenly gained $50 to pay off your debts: (-$10)(-5)= +$50. That's very basic, very simple, and very "hand-waving".

    But that's the way mathematics is- you can have technical and precise or non-technical and vague.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2010
    Posts
    8
    Quote Originally Posted by Also sprach Zarathustra View Post
    A mistake here:



    Think more...
    I have thought. Where is the mistake.

    If 2 * 2 = 4 is the same as saying 2 + 2 = 4 then...

    -2 * -2 = 4 is the same as saying -2 + -2 = 4. But the last equation does not equal 4, it equals -4. -2 + -2 = -4.

    So what is going on?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Pim
    Pim is offline
    Member
    Joined
    Dec 2008
    From
    The Netherlands
    Posts
    91
    The flaw is in that the rule a*b = a+a+a+a+... (and that b times) can't be a applied to negative numbers.
    You can't say: I'll add -2 to itself -2 times. You can't do something a negative amount of times.

    How HallsofIvy explained it is a better way to think about it.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2010
    Posts
    23
    Imagine Do is +, Don't is -
    Imagine Win is +, lose is -
    Imagine we a gambling - so we either win or lose.

    2 times I do(+) win(+) 10 : so I win(+) 20 : so +x+ = +

    2 times I dont(-) win(+) 10: so I lose(-) 20: so -x+ = -

    2 times I do(+) lose(-) 10 : so I lose(-) 20: so +x- = -

    Here is you tricky bit.

    2 times I dont(-) lose(-) 10 : so I win(+) 20: so -x- = +
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    Quote Originally Posted by Kick View Post
    I have thought. Where is the mistake.

    If 2 * 2 = 4 is the same as saying 2 + 2 = 4 then...

    -2 * -2 = 4 is the same as saying -2 + -2 = 4. But the last equation does not equal 4, it equals -4. -2 + -2 = -4.

    So what is going on?
    You are using the * operator as an addition operation.

    "2 times 2" maybe ordinarily worded as 2 "two times with a plus between".

    2(2) or 2*2 is 2+2.
    3(2) or 3*2 is 2+2+2 or 3+3
    4(2) or 4*2 is 2+2+2+2 or 4+4


    -2*2 is a symbolic way to represent a "double subtraction of 2"
    -2-2=2(-2)=2(-1)2=(-1)4
    Basically it is "subtract 2 twice" in common language (just one way to describe it).

    -2*3=-2-2-2
    -2*4=-2-2-2-2

    (-2)*(-2)=-[2(-2)]=-(-2-2)=-(-4)

    "-" is the opposite of, if you'd like to think of it that way.

    So you have the "opposite of subtract 2 twice" which is....
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Banned
    Joined
    Oct 2009
    Posts
    769

    Pattern answer

    Quote Originally Posted by Kick View Post
    The rule i learned is:

    For multiplication or division two likes give a positive answer, two unlikes give a negative answer.

    E.g.
    -2 * -2 = 4

    -2 * 2 = -4

    BUT look at this...

    2 * 2 = 4 is the same as saying 2 + 2 = 4. Right?So....

    -2 * -2 = 4 should be the same as saying -2 + -2 = x

    But... -2 + -2 = -2 - 2 = -4 ..... so it isn't the same pattern as above.

    Can anyone shed some light?
    What you're really asking is why is the product of a negative and a positive number defined to be a negative number and why is the product of two negative numbers defined to be a positive number?

    Let's do a pattern:

    4 x 4 = 16
    4 x 3 = 16 - 4 = 12
    4 x 2 = 12 - 4 = 8
    4 x 1 = 8 - 4 = 4
    4 x 0 = 4 - 4 = 0
    4 x -1 = 0 - 4 = -4...

    let's do another pattern:

    -4 x 4 = -16
    -4 x 3 = -16 + 4 = -12
    -4 x 2 = -12 + 4 = -8
    -4 x 1 = -8 + 4 = -4
    -4 x 0 = -4 + 4 = 0
    -4 x -1 = 0 + 4 = 4...

    If you see the patterns and you know a little algebra to generalize the results, then you have your answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. give an example
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 16th 2010, 09:44 AM
  2. Calculations give me a negative relative entropy
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: November 11th 2009, 08:37 PM
  3. Give an example
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 5th 2009, 03:37 AM
  4. Give an example...
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 11th 2009, 07:35 PM
  5. Give an example..
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: September 5th 2009, 09:32 PM

Search Tags


/mathhelpforum @mathhelpforum