Question

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

Answer 1

Let N be the numerator, D be the denominator 
$\frac{N}{D}$

if its numerator is decreased by 50%
$N - \frac{50}{100}N$ ==> (this will be the numerator part)

if its denominator is decreased by 25%
$D - \frac{25}{100}D$ ==> (this will be the denominator part)

I try to separate them out, so it's easier to see the problem.

$N - \frac{50}{100}N = \frac{100N}{100} - \frac{50N}{100} = \frac{50N}{100}$

$D - \frac{25}{100}D = \frac{100D}{100} - \frac{25D}{100} = \frac{75D}{100}$

$\frac{\frac{50N}{100}}{\frac{75D}{100}} = \frac{50N}{100} * \frac{100}{75D}$

$\frac{50N}{75D} = \frac{2}{3}(\frac{N}{D})$ by this, you can understand that 
$\frac{2}{3}(\frac{N}{D})$ as 66.6% of N/D because 2/3 is 0.666666.... The answer should be 66.7% if you round them up. 

Answer 2

The answer is 66.6666%