The Missing Inverse in Percentage Calculations “An increase of 20% followed by a decrease of 20% does not bring you back to where you started.” Most students know this fact. Many teachers demonstrate it with examples. Students memorize it, use it in examinations, and then move on. But there is a more interesting question. If a 20% decrease is not the inverse of a 20% increase, then what is? Surprisingly, school mathematics rarely asks this question. Yet the answer connects percentage calculations with one of the most fundamental ideas in mathematics—the concept of an inverse . We already understand inverses When students learn algebra, they encounter two important inverses. Additive inverse A number and its additive inverse cancel each other. a+(-a)=0 For example, 8+(-8)=0. Also, if you add 8 to any number and then subtract 8 from the result you get back to the original number. That's why these two are inverse of each other. Multiplicative inverse A number and its multiplicative ...