Question

By what percent will a fraction change if its numerator is decreased by 10% and its denominator is decreased by 70%?

Answer 1

The fraction is decreased by 85.71 %

Solution:

Let the numerator be "n" and denominator be "d"

Then the fraction is:
`(n)/(d)`

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:
`(0.1n)/(0.7d)`

Percent change is given as:

`\rightarrow (new fraction - original fraction)/(original fraction) * 100`

`\rightarrow ((0.1n)/(0.7d) - (n)/(d))/((n)/(d)) * 100\\\\\rightarrow (0.1)/(0.7) - 1 * 100\\\\\rightarrow -0.857 * 100 = -85.71`

Hence the fraction is decreased by 85.71 %

Answer 2

Answer: by 200%

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%