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Multiplying signed negatives

  1. Aug 30, 2006 #1
    I'm looking for a good/simple explanation for why the rules for multiplying signed numbers are the way they are.

    i.e. why does (-)*(-)= (+); (-)*(+)=(-); etc.

    Also, I'm looking for some good real world examples to where these situations apply.

    Thanks for you help.
     
  2. jcsd
  3. Aug 30, 2006 #2

    berkeman

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    One good real world example is modulation. Modulation is multiplying two signals together for some purpose, like shifting a data waveform up to RF waveform frequencies for transmission.

    So the modulated waveform looks like M(t) = A sin(w1 * t) * B sin(w2 * t)

    Draw out the waveforms and see how the sign convention represents reality in the modulation process. Does that help?
     
  4. Aug 31, 2006 #3
    Sorry, but not really.

    I should clarify. I'm looking for an example that I can share with my 9th grade students. :smile:
     
  5. Aug 31, 2006 #4

    berkeman

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    Doh! :rofl: Well, bright 9th graders would probably understand modulation -- just make some pretty slides up with colored sine waves...

    Multiplication is a non-linear process, so your examples are going to have to involve non-linear phenomena (like modulation). Let's see, what else is an example of non-linear stuff....

    Boy, that's a toughie. I'd stick with modulation and try to introduce it gently to them. :blushing:
     
  6. Aug 31, 2006 #5

    Hurkyl

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    0 * (-1) = 0
    (1 + (-1)) * (-1) = 0
    1 * (-1) + (-1) * (-1) = 0
    (-1) + (-1) * (-1) = 0
    1 + ((-1) + (-1) * (-1)) = 0 + 1
    (1 + (-1)) + (-1) * (-1) = 1
    0 + (-1) * (-1) = 1
    (-1) * (-1) = 1

    There's a proof in excruciating detail. :smile: Well, it takes a little bit more to prove (-1) * x = (-x), but this might be enough for them.
     
  7. Aug 31, 2006 #6

    Hurkyl

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    You might be able to concoct a "real world" example from the notion of a "signed distance". I.e. that (-3) meters to the right is the same thing as (+3) meters to the left.
     
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