the difference between the numerator and denominator of a fraction is 5. if 5 is added to its denominator then the fraction is decreased by one of its one fourth 1(1/4). find the value of fraction
what does "decreased by one of its one fourth" mean?
decreased by 1/4, or decreased by 1/4 of its value?
either
n = d+5
or n = d-5
so, the new value is either
(d+5)/(d+10) or (d-5)/(d+5)
now equate that to whatever your weird statement implies.
The difference between the numerator and the denominator of a fraction
is 5. If 5 is added to the denominator, the fraction is decreased by 1 1/4
Find the fraction.
if the difference is 5 between the numerator and denominator, that means that the numerator is 5 more than the denominator. So it would be x+5/x. When you add 5 to the denominator it would be x+5/x+5 which would cancel out to be one. Now if the fraction got decreased by 1 1/4, then it is 1 1/4 + 1 which equals 2 1/4.
To find the value of the fraction, let's first assign variables to the numerator and denominator of the fraction.
Let's say the numerator is represented by "x" and the denominator is represented by "x + 5".
According to the given information, if 5 is added to the denominator, the fraction is decreased by one-fourth. This can be written as:
x / (x + 5) = (x / (x + 5 + 5)) - 1/4
Now, let's simplify the equation:
x / (x + 5) = x / (x + 10) - 1/4
To simplify further, let's get rid of the fractions by multiplying both sides of the equation by the common denominator (4 * (x + 5) * (x + 10)):
4 * (x + 5) * (x + 10) * (x / (x + 5)) = 4 * (x + 5) * (x + 10) * (x / (x + 10)) - (x + 5)(x + 10)
Now, eliminate the denominators:
4x(x + 10) = 4x(x + 5) - (x + 5)(x + 10)
Expand and simplify both sides of the equation:
4x^2 + 40x = 4x^2 + 20x - x^2 - 15x - 50
Combine like terms:
4x^2 + 40x = 4x^2 + 20x - x^2 - 15x - 50
0 = -21x - 50
Rearrange the equation:
21x = -50
Divide both sides by 21:
x = -50/21
Therefore, the value of the fraction is "-50/21".