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Math Help - problem solving, which includes fractions

  1. #1
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    problem solving, which includes fractions

    okay so im having some trouble here, the problem is

    the fraction halfway between two other fractions has a decimal equivalent of 0.190476 ( which is a recurring decimal). the smaller of the two fractions is 1/7 (which is a fraction). Which is the larger fraction?


    thanks for any help
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  2. #2
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    finally understood the question

    Quote Originally Posted by coldplayroxs View Post
    okay so im having some trouble here, the problem is

    the fraction halfway between two other fractions has a decimal equivalent of 0.190476 ( which is a recurring decimal). the smaller of the two fractions is 1/7 (which is a fraction). Which is the larger fraction?


    thanks for any help
    the fraction halfway between two other fractions is the average value or mean value of two given numbers. Let x and y denote the given two numbers then the mean value is calculated by:

    m=\dfrac{x+y}2 = \dfrac x2 + \dfrac y2

    Let x < y then x = \frac17 according to your question.

    Plug in the values you already know into the formula calculating the mean value:

    0.190476 = \dfrac{\frac17}2 + \dfrac y2

    Solve this equation for y.

    EDIT: Do you mean by 0.190476 ( which is a recurring decimal) that the given value is:

    0.\overline{190476} = \dfrac{190476}{999999} = \dfrac4{21}

    If so:
    0.\overline{190476} = \dfrac4{21} = \dfrac{\frac17}2 + \dfrac y2 ~\implies~ \boxed{y = \dfrac5{21}}
    Last edited by earboth; February 4th 2009 at 11:34 PM.
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