By what percent will a fraction increase if its numerator is decreased by 10% and its denominator is decreased by 50%?
+23252 Call the fraction x/y.
To increase x by 10% : x + 10%x = x + 0.10x = 1.00x + 0.10x = 1.10x.
To decrease y by 50%: y - 50%y = y - 0.50y = 1.00y - 0.50y = 0.50y.
The new fraction is now (1.10x) / (0.50y) = (1.10/0.50)(x/y) = (1.1/.5)(x/y = (11/5)(x/y).
11/5 = 2.2 ---> The new fraction is now 2.2 times the old fraction (x/y).
So the new fraction is 2.2 times as large as the old fraction.
2.2 times is 220%; however, to calculate the percentage of increase, you must subtract the original (which is 100%) from this 220% (which represents the original plus the increase); giving an increase of 120%.
+23252 Call the fraction x/y.
To increase x by 10% : x + 10%x = x + 0.10x = 1.00x + 0.10x = 1.10x.
To decrease y by 50%: y - 50%y = y - 0.50y = 1.00y - 0.50y = 0.50y.
The new fraction is now (1.10x) / (0.50y) = (1.10/0.50)(x/y) = (1.1/.5)(x/y = (11/5)(x/y).
11/5 = 2.2 ---> The new fraction is now 2.2 times the old fraction (x/y).
So the new fraction is 2.2 times as large as the old fraction.
2.2 times is 220%; however, to calculate the percentage of increase, you must subtract the original (which is 100%) from this 220% (which represents the original plus the increase); giving an increase of 120%.
+129849 Call the old fraction, a/b
If the numerator decreases by 10% it is now = .90a
If the denominator decreases by 50% it is now = .50b
So
.90a / .50b =
9a / [ 5b] =
(9/5) (a/b)
So....the fraction increases by 80%
Guest - it is true that both decrease, but the numerator decreases by less than the denominator.......thus........the fraction actually increases....!!!
