By what percent will a fraction change if its numerator is decreased by 50% and its denominator is decreased by 25%?
n/d becomes .5n/.75d = (.5/.75)(n/d) = (2/3)(n/d)
So, it will decrease by 33 1/3 %
To find the percentage change in a fraction when its numerator and denominator are changed, we can follow these steps:
Step 1: Find the original value of the fraction.
Step 2: Find the new value of the fraction after the changes.
Step 3: Calculate the percentage change using the formula: (New Value - Original Value) / Original Value * 100.
Let's apply these steps to the given fraction:
Step 1: Original value of the fraction.
Let's assume the original fraction is represented as "a/b," where 'a' is the numerator and 'b' is the denominator. So the original fraction can be written as a/b.
Step 2: New value of the fraction after changes.
If the numerator is decreased by 50%, it would become (1 - 50/100) * a = 0.5a.
If the denominator is decreased by 25%, it would become (1 - 25/100) * b = 0.75b.
So the new fraction can be represented as 0.5a/0.75b.
Step 3: Calculate the percentage change.
The percentage change will be (New Value - Original Value) / Original Value * 100.
Substituting the values, we get ((0.5a/0.75b) - (a/b)) / (a/b) * 100.
Simplifying further, we have:
((0.5a - 0.75b) / 0.75b) / (a/b) * 100
Now, if we simplify this expression, we can calculate the percentage change in the fraction.
33 and 1/3
n/d becomes .5n/.75d = (.5/.75)(n/d) = (2/3)(n/d)
So, it will decrease by 33 1/3 %