Why are percentage increases and decreases not equal?

Question

E.g. 2/3 and 3/2 is 66% and 150%. Why is there a 16% difference between the 2 (34% and and 50%) and why does the direction of the percentage change (positive or negative change things). I can do the calculation but don't get the logic. This is probably Mathematical logic I believe?

Answer 1

$2/3$ is dividing the whole (eg $100\%$) into 3 equal parts, while $3/2$ is dividing it into 2 equal parts. Since the size of the whole is the same for both fractions, whatever quantity $1/3$ is, it must be smaller than the $1/2$ quantity. Hence, for the decrease you are subtracting less than you are adding for the increase.

Answer 2

The starting number is not the same.

On one, you start with 2 and divide that 2 into 3 equal parts, which is 66%.

On the second one you start off with 3 (rather than 2) and you divide that 3 into 2 equal parts, which is 150%.

The key to percentages is the starting number, it becomes much simpler when you look at it that way.