
Percentage increase.
Consider the following simple multiplication:
2 x 3 = 6
Now consider that the first term is increased by 50% to 3 and the second term is decreased by 67% to 1:
3 x 1 = 3
The total has decreased by 3, or 50%. To what extent does the increase of 2 to 3 account for this change and to what extent does the decrease from 3 to 1 account for the change?

(ax)(by)= (ab)(xy)
"Increased by 50%" is the same as itself plus 1/2 iteself or (1+ 1/2) itself = (3/2) itself.
"Decreased by 67%" (you really mean 2/3) is the same as itself minus 2/3 itself or (1 2/3) itself= (1/3) itself.
You multiplied the first number by 3/2 and multiplied the second number by 1/3. That is the same as multiplying the product by (3/2)(1/3)= 1/2.