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Math Help - Factors and Simplest Form: Concept Check

  1. #1
    Junior Member Euclid Alexandria's Avatar
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    Question Factors and Simplest Form: Concept Check

    From the book
    "Why is the following way to simplify the fraction 17/75 incorrect?"

    \frac{1\not7}{\not75}=\frac{1}{5}

    My answer
    This is an incorrect way to simplify the fraction because 17/75 cannot be simplified any further by dividing out digits within whole numbers in the numerator and denominator.

    Do you think this clear and correct?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Euclid Alexandria View Post
    From the book
    "Why is the following way to simplify the fraction 17/75 incorrect?"

    \frac{1\not7}{\not75}=\frac{1}{5}

    My answer
    This is an incorrect way to simplify the fraction because 17/75 cannot be simplified any further by dividing out digits within whole numbers in the numerator and denominator.

    Do you think this clear and correct?
    Perhaps something like:

    When cancelling you are removing common factors of the numerator and
    the denominator. In this case the 7's are not factors of the 17 or 75 but
    are digits in their decimal representation. As 7 is not a common factor of
    17 and 75 the 7's cannot be cancelled

    RonL.
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  3. #3
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    Hello, Euclid Alexandria!

    Why is the following way to simplify the fraction \frac{17}{75} incorrect?

    \frac{1\!\!\!\not7} {\not75}=\frac{1}{5}

    But it works for these . . . LOL!

    . . \frac{16}{64}\;=\;\frac{1\!\!\!\not6}{\not64}\;=\;  \frac{1}{4}

    . . \frac{19}{95}\;=\;\frac{1\!\!\!\not9}{\not95} \;=\;\frac{1}{5}

    . . \frac{26}{65}\;=\;\frac{2\!\!\!\not6}{\not65} \;=\;\frac{2}{5}

    . . \frac{49}{98}\;=\;\frac{4\!\!\!\not9}{\not98} \;=\;\frac{4}{8}\:=\:\frac{1}{2}

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  4. #4
    Junior Member Euclid Alexandria's Avatar
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    Thumbs up

    Thanks Captain, that explanation is right on the mark (well, except for the first sentence, if you consider Soroban's reply).
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  5. #5
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    Quote Originally Posted by Euclid Alexandria View Post
    From the book
    "Why is the following way to simplify the fraction 17/75 incorrect?"

    \frac{1\not7}{\not75}=\frac{1}{5}

    My answer
    This is an incorrect way to simplify the fraction because 17/75 cannot be simplified any further by dividing out digits within whole numbers in the numerator and denominator.

    Do you think this clear and correct?
    No, you are wrong

    in numerater 7 is in unit place(value is 7), in denominator 7 in tenth place
    (value is 70), hence we can't cancel 7 and 70.
    - R.Mangalesh
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