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What is the fraction if the denominator is three times its numerator?

A fraction will be one-half if one is added to the numerator and subtracted from the denominator.

Numerator—n:
(n + 1)/(3n – 1) = 1/2
3n – 1 = 2(n + 1)
3n – 1 = 2n + 2
n = 3

Denominator:
= 3(3)
= 9

Answer: 3/9 is the fraction.

This entry was posted on Saturday, January 2nd, 2010 at 5:12 pm and is filed under fraction. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

6 Responses to “What is the fraction if the denominator is three times its numerator?”

  1. Jun Agruda Says:
    January 2nd, 2010 at 10:33 pm

    Numerator—n:
    (n + 1)/(3n – 1) = 1/2
    3n – 1 = 2(n + 1)
    3n – 1 = 2n + 2
    n = 3

    Denominator:
    = 3(3)
    = 9

    Answer: 3/9 is the fraction.
    References :

  2. Miss Molly Marjorie Says:
    January 2nd, 2010 at 11:19 pm

    That would make it either 0/3 or 1/3. Since 0/3 is mathematically impossible, I would go with 1/3
    References :

  3. railbuff Says:
    January 2nd, 2010 at 11:52 pm

    first question: 1/3

    6/13
    (6+1)/(13-1) = 7/12 not one half.
    Your premise as stated is incorrect
    References :
    retired math teacher

  4. AudioPhilia Says:
    January 3rd, 2010 at 12:28 am

    Please clarify, are those two different questions? Or is that the explanation of your main question? And shouldn’t this be in math??
    References :

  5. Erik Says:
    January 3rd, 2010 at 1:03 am

    first question: 1/3
    second: 0/3
    References :
    math

  6. MathBioMajor Says:
    January 3rd, 2010 at 1:50 am

    Let the numerator be x. Then the denominator is 3x. So the original fraction is x/3x. Now, if the new fraction is equivalent to ½ when 1 is added to x and 1 is subtracted from 3x, we can express the new fraction as this:

    ½ = (x + 1)/(3x - 1)

    Now we can cross-multiply the fraction above to get this:

    1 (3x - 1) = 2 (x + 1).

    Now we distribute the multipliers and move variable terms to one side of the equation, and constant terms to the other side of the equation to solve for x:

    3x -1 = 2x + 2
    3x - 2x = 2 + 1
    x = 3.

    If x = 3 is the original numerator, then the original denominator is 3x = 3 (3) = 9. If we add 1 to 3 and subtract 1 from 9, we get this:

    (3 + 1)/(9 - 1) = 4/8 = ½.

    So the original fraction is (3/9). Notice that the given operation will not work if we use the fraction (1/3), because 1 + 1 = 2 and 3 - 1 = 2. Their quotient then is (2/2) = 1, not ½.
    References :

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