The denominator of a fraction is greater than its numerator by 9. If 7 is subtracted from both its numerator and denominator, the new fraction equals 2/3. What is the original fraction?
original numerator --- x
original denominator -- x+9
new numerator --- x-7
new denominator --- x+9-7 = x+2
(x-7)/(x+2) = 2/3
3x - 21 = 2x + 4
x = 25
original fraction = 25/34
new fraction (take 7 away from both
= 18/27
= 2/3
YEahh
Noob
To solve this problem, let's start by setting up an equation.
Let's assume that the numerator of the original fraction is "x". Therefore, the denominator would be "x + 9" since it is greater than the numerator by 9.
So the original fraction would be x / (x + 9).
Now, let's subtract 7 from both the numerator and denominator of the original fraction.
The new fraction can be written as (x - 7) / (x + 9 - 7) = (x - 7) / (x + 2).
According to the problem, this new fraction equals 2/3.
So we have the equation (x - 7) / (x + 2) = 2/3.
To solve for x, we can cross-multiply and simplify the equation:
3(x - 7) = 2(x + 2)
Now, let's distribute and simplify:
3x - 21 = 2x + 4
Subtracting 2x from both sides:
x - 21 = 4
Adding 21 to both sides:
x = 25
Therefore, the numerator of the original fraction is 25, and the denominator is 25 + 9 = 34.
So the original fraction is 25/34.