By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?
original fraction : x/y
new fraction : (.5x)/(.75y) = (2/3) (x/y)
so the new fraction is 2/3 of the old one, thus it was decreased by 1/3
To find the percentage decrease of a fraction, we need to compare the original value to the decreased value and calculate the difference as a percentage of the original value.
Let's assume the fraction is represented as numerator/denominator.
First, let's calculate the decreased numerator. If the numerator is decreased by 50%, it means we are left with 50% of the original value. We can calculate this by multiplying the original numerator by 0.50.
Next, let's calculate the decreased denominator. If the denominator is decreased by 25%, it means we are left with 75% of the original value. We can calculate this by multiplying the original denominator by 0.75.
Now we have the original fraction numerator/denominator and the decreased fraction (0.50 * numerator)/(0.75 * denominator).
To find the percentage decrease, we need to calculate the difference between the original and decreased fractions and express it as a percentage of the original fraction.
The percentage decrease can be calculated using the following formula:
(Original Value - Decreased Value) / Original Value * 100
Let's plug in the values and calculate the percentage decrease:
Percentage decrease = ((numerator/denominator) - ((0.50 * numerator)/(0.75 * denominator))) / (numerator/denominator) * 100
Simplifying this expression will give us the exact percentage decrease.