The numerator and the denominator of a fraction are in a ratio 3:2.If 3 is added to the numerator and 2 is subtracted from the denominator,a new fraction is formed whose value is 9/4 . Find the original fraction.
let the original fraction be 3x/(2x)
(3x+3)/(2x-2) = 9/4 , where x ≠ 1
18x-18 = 12x + 12
6x = 30
x = 5
the original fraction is 15/10
A poorly thought-out question.
Fractions should be reduced to their lowest terms.
We would of course reduce our fraction 15/10 to 3/2. In that case the suggested operation results in 6/0, which is undefined
only if we leave the fraction in its incomplete form is the result valid.
(15+3)/(10-2) = 18/8 = 9/4
Let's solve this step-by-step.
Step 1: Let's assume the numerator of the original fraction is 3x and the denominator is 2x, where x is a common factor.
Step 2: According to the given condition, we can write the fraction as (3x)/(2x).
Step 3: Adding 3 to the numerator gives us (3x + 3), and subtracting 2 from the denominator gives us (2x - 2).
Step 4: The new fraction formed is given as (3x + 3)/(2x - 2), and its value is 9/4.
Step 5: Equating the two fractions, we have (3x + 3)/(2x - 2) = 9/4.
Step 6: To simplify the equation, we cross-multiply, giving us (3x + 3) * 4 = 9 * (2x - 2).
Step 7: Expanding both sides of the equation, we have 12x + 12 = 18x - 18.
Step 8: Rearranging the equation, we have 18x - 12x = 12 + 18.
Step 9: Simplifying further, we have 6x = 30.
Step 10: Dividing both sides of the equation by 6, we find x = 5.
Step 11: Now that we have the value of x, we can find the original fraction.
Step 12: The numerator of the original fraction is 3x = 3 * 5 = 15.
Step 13: The denominator of the original fraction is 2x = 2 * 5 = 10.
Step 14: Therefore, the original fraction is 15/10, which can be simplified to 3/2.
So, the original fraction is 3/2.
To find the original fraction, we can first set up a system of equations based on the given information.
Let's represent the numerator and the denominator of the original fraction as 3x and 2x, respectively, where x is a common factor. Therefore, the original fraction can be written as (3x)/(2x).
According to the given conditions, when 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed with the value 9/4. So we can set up the equation:
(3x + 3)/(2x - 2) = 9/4
To solve for x, we can cross-multiply:
4(3x + 3) = 9(2x - 2)
12x + 12 = 18x - 18
Collect like terms:
6x = 30
Divide both sides by 6:
x = 5
Now that we know the value of x, we can substitute it back into the original fraction:
Original numerator = 3x = 3 * 5 = 15
Original denominator = 2x = 2 * 5 = 10
Therefore, the original fraction is 15/10, which can be simplified to 3/2.