By what percent will a fraction decrease if its numerator is decreased by 50% and its denominator is decreased by 25%?

Question

I can't seem to figure this problem out, can someone help me? (percentage form)

Answer 1

The fraction is n/d

Since ALL OF IT is 100$, "Decreased by 50%" means 100%-50%= 50% = 0.5 = 1/2 or HALF OF IT

LIkewise, decreased by 25% means 100% - 25% = 75% = 0.75 = 3/4

The new fraction is

0.5*N / 0.75 D = (0.5/0.75)(N/D)

So the new fraction obeys the ration 0.5/0.75 = 50/75 = 2/3

So the new fraction is 2/3 of the old fraction

That's a decrease of

1 - 2/3 = 1/3 = 0.3 = 33 and 1/3 %

Answer 2

Let x/y be the original fraction.

After decreasing the numerator by 50% and decreasing the denominator by 25%, the fraction is:

(x - 0.5x) / (y - 0.25y) = (0.5x) / (0.75y)

= (2/3)(x/y) = 66 2/3% of x/y

So, the fraction decreased by 33 1/3%.