The numerator of a fraction is 8 less than the denominator. If 1 is added to each of the numerator and the denominator, the fraction becomes equal to 1/2. What is the original fraction?
Answers
Answer:
Step-by-step explanation:
Let, the denominator be x.
Numerator is 8 less than the denominator = x-8
Original Fraction would be = x-8/x
If 1 is added to both the numerator and denominator fraction becomes equal to 1/2.
New fraction = x-8+1/x+1
=> x-8+1/x+1 = 1/2
=> x-7/x+1 = 1/2
=> 2(x-7) = 1(x+1)
=> 2x-14 = x+1
=> 2x-x = 1+14
=> x = 15
Original Fraction = 15-8/15 = 7/15
Fraction = Numerator / Denominator
Let the numerator = x
Now, According to question,
= x - 8 / x
New fraction according to question,
= x - 8 + 1 / x + 1
= x - 7 / x + 1
In question it is given that the latest fraction = 1/2.
= x - 7 / x + 1 = 1/2
= 2x - 14 = x + 1 ( BY CROSS MULTIPLICATION )
= 2x - x = 1 + 14
= x = 15
Now,
At first we assumed that numerator = x - 8
and denominator = x.
Therefore, Original fraction = 15 - 8 / 15
= 7 / 15 ANSWER.
PLEASE MARK IT AS BRAINLIEST.