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Math Help - reduced fraction

  1. #1
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    reduced fraction

    Give the sum p+q where p/q is the reduced fraction represented by the repeating decimal 1.36

    Choices

    a. 13
    b. 19
    c. 26
    d. 28

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  2. #2
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    Hint: 1.363636... = 1+36/99
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  3. #3
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    Hello, ccdalamp!

    Give the sum p+q where \frac{p}{q} is the reduced fraction

    represented by the repeating decimal 1.\overline{36}

    Choices: . a)\;13\qquad b)\;19 \qquad c)\;26\qquad d)\; 28
    Here's an algebraic solution . . .


    Let N \:=\:1.363636...

    Multiply 100: . 100N \;=\;136.363636...
    . Subtract N\!:\quad\;\;\;N \;=\quad\; 1.363636...

    And we have:. 99N \;=\;135\quad\Rightarrow\quad N \:=\:\frac{135}{99} \:=\:\frac{15}{11}


    Therefore: . p + q\:=\:15 + 11\:=\:26

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