Comments on: What is the fraction if the denominator is three times its numerator?

By: MathBioMajor

MathBioMajor — Sun, 03 Jan 2010 06:50:59 +0000

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.
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By: Erik

Erik — Sun, 03 Jan 2010 06:03:59 +0000

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

By: AudioPhilia

AudioPhilia — Sun, 03 Jan 2010 05:28:59 +0000

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

railbuff — Sun, 03 Jan 2010 04:52:59 +0000

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

By: Miss Molly Marjorie

Miss Molly Marjorie — Sun, 03 Jan 2010 04:19:59 +0000

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

Jun Agruda — Sun, 03 Jan 2010 03:33:59 +0000

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.
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