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Math Help - Subtracting from a negative fraction. (Signs in cross multiplication)

  1. #1
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    Subtracting from a negative fraction. (Signs in cross multiplication)

    -1 - \frac{1}{3}

    - \frac{1 * 3}{1 * 3} - \frac{1}{3} = - \frac{3}{3} - \frac{1}{3} = - \frac{-3 - 1}{3} = - \frac{-4}{3} = ??

    does the negative sign on the faction mean that both the numerator and the denomanator shoud be treated as negative numbers when used in cross multiplication?
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  2. #2
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    -\frac{-4}{3}=(-1)\frac{-4}{3}=\frac{4}{3}
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  3. #3
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    -1-1/3 = -(1 + 1/3) = ?

    Sometimes easier I find:
    8 - 2/3 - 3/5 ; multiply by -1:
    = -8 + 2/3 + 3/5
    = -8 + 10/15 + 9/15
    = -8 + 19/15
    = -120/15 + 19/15 ; multiply by -1:
    = 120/15 - 19/15
    = 101/15
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  4. #4
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    Quote Originally Posted by DrSteve View Post
    -\frac{-4}{3}=(-1)\frac{-4}{3}=\frac{4}{3}
    so

     -1 - \frac{1}{3} = \frac{4}{3} !?!
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  5. #5
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    - 1 - \frac{1}{3} = - \frac{1}{1} - \frac{1}{3} = - ( \frac{-1 * 3 - 1 * - 1}{ -1 * 3}) = -(\frac{(-3) - (-1)}{-3}) = -(\frac{-2}{-3}) = -(\frac{2}{3})=  - \frac{2}{3} ???
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  6. #6
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    Quote Originally Posted by alyosha2 View Post
    -1 - \frac{1}{3}

    - \frac{1 * 3}{1 * 3} - \frac{1}{3} = - \frac{3}{3} - \frac{1}{3} = - \frac{-3 - 1}{3} = - \frac{-4}{3} = ??

    does the negative sign on the faction mean that both the numerator and the denomanator shoud be treated as negative numbers when used in cross multiplication?
    -\frac{-4}{3}= \frac{4}{3}

    But " - \frac{3}{3} - \frac{1}{3} = - \frac{-3 - 1}{3}" is wrong.

    You should have either -\frac{3}{3}- \frac{1}{3}= \frac{-3- 1}{3}= \frac{-4}{3} or
    -\frac{3}{3}- \frac{1}{3}= -\frac{3+ 1}{3}= -\frac{4}{3}
    but not both!

    And, of course, -\frac{4}{3}= \frac{-4}{3}.
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  7. #7
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    Quote Originally Posted by alyosha2 View Post
    so

     -1 - \frac{1}{3} = \frac{4}{3} !?!
    No. I was just simplifying -\frac{-4}{3} for you. There are errors in your computation as other posters have already explained.
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  8. #8
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    Quote Originally Posted by HallsofIvy View Post
    -\frac{-4}{3}= \frac{4}{3}

    But " - \frac{3}{3} - \frac{1}{3} = - \frac{-3 - 1}{3}" is wrong.

    You should have either -\frac{3}{3}- \frac{1}{3}= \frac{-3- 1}{3}= \frac{-4}{3} or
    -\frac{3}{3}- \frac{1}{3}= -\frac{3+ 1}{3}= -\frac{4}{3}
    but not both!

    And, of course, -\frac{4}{3}= \frac{-4}{3}.

    But I still don't understand how we are supposed to understand the negative sign in front of the fraction.

    I understand what I'm supposed to have. I just don't understand why.
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  9. #9
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    Quote Originally Posted by alyosha2 View Post
    But I still don't understand how we are supposed to understand the negative sign in front of the fraction
    -\dfrac{a}{b}=\dfrac{-a}{b}=\dfrac{a}{-b}

    -\dfrac{3}{4}=\dfrac{-3}{4}=\dfrac{3}{-4}

    Does that help?
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