The Denominator Of A Fraction Is 7 More Than Its Numerator. If 5 Is Added To Each, The Value Of The Resulting Fraction Is 1/2. Find The Original Fract

The denominator of a fraction is 7 more than its numerator. If 5 is added to each, the value of the resulting fraction is 1/2. Find the original fraction

 

Answer:

The value of the original fraction is 2/9.

Step-by-step explanation:

Step 1: Let the denominator be d and the numerator as n.

Step 2: Interpret the first statement "The denominator of a fraction is 7 more than its numerator."

  1. denominator = 7 + numerator (since the denominator is more than its numerator)
  2. With basis to step 1, the equation one is now: d=7+n

Step 3: Interpret the second statement "If 5 is added to each, the value of the resulting fraction is 1/2."

  1. To make the interpretation easier then we will use the format of a fraction (numerator/denominator)
  2. Add 5 to each: \frac{numerator + 5}{denominator + 5}
  3. The resulting fraction is equal to 1/2: \frac{numerator + 5}{denominator +5} = \frac{1}{2}
  4. With basis to step 1, the equation two is now: \frac{n+5}{d+5} =\frac{1}{2}

Step 4: Rearrange equation two in order for it to be in terms of d

  1. \frac{n +5}{d+5} = \frac{1}{2}
  2. (2)(\frac{n+5}{d+5})=1
  3. 2(n+5)=d+5
  4. 2n+10=d+5
  5. 2n+10-5=d
  6. d=2n+5

Step 5: Equate equation 1 and 2

  1. 2n + 5= 7+n

Step 6: Solve for n

  1. 2n+5=7+n
  2. 2n-n=7-5
  3. n=2

Step 7: Since we already know the value of n, then we could now compute for d using equation one.

  1. d=n+7; where n is 2
  2. d=9

The value of denominator is 9 while that of numerator is 2. Therefore, the original fraction is 2/9.


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