By what percent will a fraction change if its numerator is decreased by 10% and its denominator is decreased by 50%?

Answer 1

Fraction = n.
n*0.9/0.5 = 1.8n.
1.8n/n = 1.8 = 180%,
Change = 180% - 100% = 80%.

Answer 2

let the original fraction be n/d
new fraction is .9n/.5d or 9n/5d

change = 9n/5d - n/d
= 9n/5d - 5m/5d
= 4n/5d

percentage change = (4n/5d) / n/d
= 4/5 = 80%

illustration:
suppose our original fraction was 5/8
new fraction = .9(5)/4 = 45/40 or 9/8
change = 9/8-5/8 = 1/2
percentage change = (1/2) / (5/8) = 4/5 = .8 = 80%