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11 February, 17:15

The numerator of a fraction is less than the denominator. If Sara adds 1 to the numerator and adds 2 to the denominator, the fraction is 1/2, when expressed in it's simplest form. FIND the original fraction.

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  1. 11 February, 17:28
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    when you multiply the numerator by 2 and add 16 to the denominator, the original fraction is reduced by 1/3.

    this means the original fraction is equal to 2/3 times what it was originally.

    your equation is:

    (x-5) * 2 divided by x + 16

    is equal to 2/3 * (x-5) / x

    this is equivalent to:

    (x-5) * 2 / (x + 16) = ((x-5) * 2) / 3x

    multiply both sides of the equation by (x+16) and by (3x) and you get:

    (x-5) * 2 * (3x) = (x-5) * 2 * (x+16)

    divide both sides of this equation by (x-5) and you get:

    2 * 3x = 2 * (x + 16)

    simplify to get:

    6x = 2x + 32

    subtract 2x from both sides of this equation to get:

    4x = 32

    divide both sides of this equation by 4 to get:

    x = 8

    that's your solution.

    your original fraction is (8-5) / 8 = 3/8

    your final fraction is (3 * 2) / (8 + 16) = 6 / 24 = 1/4

    your original fraction of 3/8 * 2/3 = 6/24 = 1/4.

    this is the same as your original fraction being reduced by 1/3.

    3/8 - 1/3 * 3/8 = 3/8 - 3/24 = 9/24 - 3/24 = 6/24 = 1/4.

    the questions was what is the original fraction.

    the answer is that the original fraction is 3/8.
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