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Math Help - How to change a proper, negative fraction to an improper fraction

  1. #1
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    How to change a proper, negative fraction to an improper fraction

    How would you write -1 13/56 as an improper fraction? If it wasn't negative, the answer would be 69/56. Since it is negative, is the answer -69/56? OR is the answer -43/56, which a colleague says; his reasoning being, to find the numerator: -1 x 56 = - 56; then add 13 to get -43. So his answer is -43/56. Which is correct?
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  2. #2
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    Re: How to change a proper, negative fraction to an improper fraction

    -43/56 is greater than -1, but the mixed number is actually less than -1, therefore your colleague's answer is not correct; -69/56 is the answer. I always used to solve these by ignoring the negative sign, solving as if the mixed number was positive, then tacking the negative sign back onto the improper fraction.
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  3. #3
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    Re: How to change a proper, negative fraction to an improper fraction

    Hello, jacklogan!

    \text{How would you write }\text{-}1\tfrac{13}{56}\text{ as an improper fraction?}
    \text{If it wasn't negative, the answer would be }\tfrac{69}{56}.
    \text{Since it is negative, is the answer }\text{-}\tfrac{69}{56}\,?
    \text{Or is the answer }\text{-}\tfrac{43}{56}\text{ which a colleague claims.}

    Your colleague is dangerously wrong.
    I hope he doesn't apply that to Real Life.

    Suppose he had $5.75 and he spent $2.25.
    . . How much would he have left?
    His answer would be $4.00.

    How would he get that awful answer?
    . . Like this . . .

    . . \begin{array}{c}\$5.75\, = \,5\tfrac{3}{4}\text{ dollars} \\ \\[-3mm] \$2.25 \,=\,2\tfrac{1}{4}\text{ dollars} \end{array}

    \begin{array}{ccccccccc}\$5.75 - 2.25 &=& 5\frac{3}{4} - 2\frac{1}{4} \\ \\[-3mm] & = & 5 + \frac{3}{4} - 2 \;{\color{red}+\;\frac{1}{4}} \\ \\[-3mm] &=& (5-2) + (\frac{3}{4} + \frac{1}{4}) \\ \\[-3mm] &=& 3 + \frac{4}{4}\\ \\[-3mm] &=& \$4 \end{array}


    Ask him to consider this . . .

    What is \text{-}1\tfrac{1}{4} ?

    He believes it means: . \text{-}1 \:{\color{red}+\: \tfrac{1}{4}} \:=\:\text{-}\tfrac{3}{4}

    If that is true, why didn't they write \text{-}\tfrac{3}{4} in the first place?
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  4. #4
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    Re: How to change a proper, negative fraction to an improper fraction

    Quote Originally Posted by jacklogan View Post
    How would you write -1 13/56 as an improper fraction? If it wasn't negative, the answer would be 69/56. Since it is negative, is the answer -69/56? OR is the answer -43/56, which a colleague says; his reasoning being, to find the numerator: -1 x 56 = - 56; then add 13 to get -43. So his answer is -43/56. Which is correct?
    This whole thread is result of just out-of-date group of people.
    The truth is there is absolutely no reason to use so-called improper fractions.

    Given the wide use of calculators and computer algebra systems in which improper fractions have no place, what good are they? Let's drop their use!
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