By what percent will a fraction change if its numerator is decreased by 10% and its denominator is decreased by 50%?
Fraction = n.
n*0.9/0.5 = 1.8n.
1.8n/n = 1.8 = 180%,
Change = 180% - 100% = 80%.
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%
To calculate the percentage change of a fraction, we need to find the difference between the original fraction and the new fraction, and then express it as a percentage relative to the original fraction.
Let's say the original fraction is A/B, where A is the numerator and B is the denominator.
If the numerator is decreased by 10%, the new numerator becomes A - (A * 10/100) = 0.9A.
Similarly, if the denominator is decreased by 50%, the new denominator becomes B - (B * 50/100) = 0.5B.
The new fraction is (0.9A)/(0.5B) = 1.8A/B.
To calculate the percentage change, we need to find the difference between the original fraction and the new fraction, divide it by the original fraction, and then multiply by 100 to express it as a percentage.
Percentage change = ((1.8A/B) - (A/B)) / (A/B) * 100
Simplifying this expression gives us:
Percentage change = 1.8 - 1 * (B/A) * 100
Since the numerator is decreased by 10%, the fraction A/B changed by -10%.
Therefore, the percentage change is:
Percentage change = 1.8 - 1 * (-10)
Percentage change = 1.8 + 10
Percentage change = 11.8%
So, the fraction will change by 11.8%.