Question

Explain why a change from 20 to 40 is a 100% increase, but a change from 40 to 20 is a 50% decrease. Increasing 20 to 40 is the same as increasing 20 by a . So, it is a 100% increase. Decreasing 40 to 20 is the same as decreasing 40 by one-half of . So, it is a 50% decrease.

Answer 1

To find increase/decrease, divide the starting number by the ending number.

40 to 20

20 ÷ 40 = 0.5

0.5 can be represented by 50%.

20 to 40

40 ÷ 20 = 2

2 can be represented by 200%. This is why decreasing 40 to 20 is a 200% increase. In the wording, it says it's a 100% increase. That would be 20 plus 20 times 1 (which is the same as 100%) which is 40.