Respuesta :
The fraction is decreased by 85.71 %
Solution:
Let the numerator be "n" and denominator be "d"
Then the fraction is: [tex]\frac{n}{d}[/tex]
Given that numerator is decreased by 10 % and denominator is decreased by 70 %
Decreased by 10 % means = 100 % - 10 % = 90 %
Decreased by 70 % means = 100 % - 70 % = 30 %
Then the new numerator is: n - 90% of n = n - 0.9n = 0.1n
Then the new denominator is: d - 30 % of d = d - 0.3d = 0.7d
Then the new fraction is: [tex]\frac{0.1n}{0.7d}[/tex]
Percent change is given as:
[tex]\rightarrow \frac{new fraction - original fraction}{original fraction} \times 100[/tex]
[tex]\rightarrow \frac{\frac{0.1n}{0.7d} - \frac{n}{d}}{\frac{n}{d}} \times 100\\\\\rightarrow \frac{0.1}{0.7} - 1 \times 100\\\\\rightarrow -0.857 \times 100 = -85.71[/tex]
Hence the fraction is decreased by 85.71 %
Answer: by 200%
Step-by-step explanation:
given a fraction lets say a/b
the numerator is decreased by 10% = 10/100 of a = 0.1a
the new numerator is a - 0.1a = 0.9a
the denominator is decreased by 70% = 70/100 of b = 0.7b
the new denominator is b - 0.7b = 0.3b
so our new fraction is = 0.9a/0.3b
= 3(a/b)
percentage change =(the new coefficient - old coefficient)/(old coefficient) *100
percentage change = (3-1)/1 *100
percentage change = 2 * 100
percentage change = 200%
