By what percent will the fraction increase if its numerator is decreased by 30% and denominator is decreased by 50% ?
(1-0.3)/(1-0.5) = 0.7/0.5 = 1.4
so it is increased by 40%
Thanks
To find the percentage increase in a fraction when the numerator is decreased by a certain percentage and the denominator is decreased by another percentage, follow these steps:
1. Start with the original fraction, let's call it "x/y".
2. Calculate the new numerator by applying the 30% decrease: (100% - 30%) = 70%. So the new numerator is 70% of x, which is (70/100) × x = 0.7x.
3. Calculate the new denominator by applying the 50% decrease: (100% - 50%) = 50%. So the new denominator is 50% of y, which is (50/100) × y = 0.5y.
4. Form the new fraction using the new numerator and denominator: 0.7x / 0.5y.
5. Find the increase in the fraction by subtracting the original fraction from the new fraction: (0.7x / 0.5y) - (x / y) = (0.7x - x) / (0.5y - y) = (0.7x - x) / (0.5y - y).
6. Simplify the expression: (0.7x - x) / (0.5y - y) = (0.3x) / (-0.5y) = -0.6x / y.
7. Calculate the percentage increase by multiplying the expression by 100: (-0.6x / y) × 100 = -60x / y.
Therefore, the fraction will decrease by 60% when the numerator is decreased by 30% and the denominator is decreased by 50%.
To find the percent increase in a fraction, we need to compare the difference between the new fraction and the original fraction. Let's start by considering the original fraction.
Let's assume the original fraction is represented as a/b, where a is the numerator and b is the denominator.
If the numerator is decreased by 30%, it becomes (a - (30/100) * a) = (0.7a).
Similarly, if the denominator is decreased by 50%, it becomes (b - (50/100) * b) = (0.5b).
Therefore, the new fraction is (0.7a)/(0.5b).
Now, to calculate the percent increase, we compare the difference between the new fraction and the original fraction, relative to the original fraction.
The difference between the new fraction and the original fraction is:
(0.7a)/(0.5b) - a/b
To simplify this, we need to find a common denominator for both fractions, which is 0.5b:
[(0.7a) * (0.5b)]/[(0.5b) * (0.5b)] - (a * (0.5b))/[(0.5b) * (0.5b)]
= (0.35ab)/(0.25b^2) - (0.5ab)/(0.25b^2)
= (0.35ab - 0.5ab)/(0.25b^2)
= (0.15ab)/(0.25b^2)
= (0.15a)/(0.25b)
To find the percent increase, we take the absolute value of the difference and divide it by the original fraction, then multiply by 100:
(absolute value of ((0.15a)/(0.25b))) / ((a/b)) * 100
Simplifying further, we get:
(0.15a)/(0.25b) * (b/a) * 100
= 0.15 * (b/a) * 100
= 15 * (b/a)
Therefore, the percent increase in the fraction is 15 * (b/a) percent.