By what percent will a fraction change if its numerator is increased by 60% and its denominator is decreased by 20%?
original value: n/d
new value: 1.60n/0.80d = 2n/d
so, it has grown by 100%
To find the percentage change in a fraction, we can use the formula:
Percentage change = ((New Value - Old Value) / Old Value) * 100
In this case, the numerator of the fraction is increased by 60% and the denominator is decreased by 20%.
Let's say the original fraction is represented as a/b.
1. The numerator is increased by 60%, so the new numerator is (a + (60% of a)) = a + 0.6a = 1.6a.
2. The denominator is decreased by 20%, so the new denominator is (b - (20% of b)) = b - 0.2b = 0.8b.
The new fraction is (1.6a)/(0.8b).
Now, we can calculate the percentage change using the formula mentioned above:
Percentage change = ((New Value - Old Value) / Old Value) * 100
= (((1.6a)/(0.8b) - a/b) / (a/b)) * 100
= (((1.6a)(b) - (0.8b)(a)) / (0.8b)(a)) * 100
= (((1.6a)(b - a)) / (0.8b)(a)) * 100
= (1.6(b - a) / 0.8a) * 100
= 2(b - a) * 100 / a
Therefore, the fraction will change by 2(b - a) * 100 / a percent.
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