SOLUTION: the numerator of a fraction is 1 less than the denominator. when both numerator and denominator are increased by 2, the fraction is increased 1/12`find the original fraction

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Question 1192891: the numerator of a fraction is 1 less than the denominator.
when both numerator and denominator are increased by 2,
the fraction is increased 1/12`find the original fraction
Found 3 solutions by Edwin McCravy, greenestamps, josgarithmetic:
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
You must have copied this problem wrong, or your teacher or the
the textbook writer made a mistake, for there is no solution. 
However, if 1/12 is changed to 1/9, there will be a solution.  

I will work a problem exactly like yours, changing 1/12 to 1/9. 
The problem I will work is:

The numerator of a POSITIVE PROPER FRACTION REDUCED TO
LOWEST TERMS is 1 less than the denominator. When both numerator
and denominator are increased by 2, the fraction is increased by
1/9. Find the original fraction.

Let n = the denominator

The numerator of a fraction is 1 less than the denominator.
 
Then the numerator = n-1

when both numerator and denominator are increased by 2,

the fraction is increased by 1/9.








Multiply through by the LCD = 9n(n+2)















n+5=0;   n-4=0
  n=-5;    n=4

Ignore the negative answer.

denominator = n = 4
numerator = n-1 = 4-1 = 3

original fraction = 

Checking:

The new fraction is 

 of  is 

If we add .

So the correct answer to the problem I solved is .

Be sure to inform your teacher that the problem as stated 
(with 1/12) has no solution.

Edwin
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Your statement of the problem is not clear. When the problem says the fraction is "increased by 1/12", it is not clear whether that is an increase by a FACTOR of 1/12 or an increase of an ADDED 1/12.

The other tutor interpreted the meaning to be an increase by a factor of 1/12, which makes the problem have no solution.

The problem has a solution if the increase is an added 1/12.

Let the denominator of the original fraction be x; then the two fractions are (x-1)/x and (x+1)/(x+2).

The second fraction is 1/12 MORE than the first:









or

If we choose the positive solution, then the original fraction is 3/4 and the new fraction is 5/6, and 5/6 - 3/4 = 10/12 - 9/12 = 1/12; the conditions of the problem are satisfied.

If we choose the negative solution, the the original fraction is (-7)/(-6) and the new fraction is (-5)/(-4); and (-5)/(-4) - (-7)/(-6) = 5/4 - 7/6 = 15/12 = 14/12 = 1/12; again the conditions of the problem are satisfied.

So the original fraction could be either 3/4 or (-7)/(-6). However, the format of the second "solution" is not standard, so....

ANSWER: The original fraction was 3/4
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
----------------------------------
the fraction is increased 1/12`
----------------------------------

What's that? Increased how? "1/12" assumed to be missing "by".

Original Fraction Expression, with , so fraction may start as .

When both n and d increased by 2,
.
Solve this for d.
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