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 ...

This is a straightforward Question Answer type discussion focused on one problem related to fitness planning and some variations to it that takes deep into the concept of average and exposes some of the errors people make while using it. Question: Rohan is on a fitness drive. He has planned to burn 300 kcal in one exercise session is Gym. He has been suggested to do warmup, cardio, strength training and cooling. He divided his target kcal into 4 equal parts of 75 kcal each. His fitness tracker displays few data including calorie burnt.  Warmup burns 4 calories per minute, cardio exercise burns 8 kcal per minute, strength exercises 10 kcal per minute and cooling 2 kcal per minute.  How much time he would take in the gym to complete his exercise.  Answer: Since Rohan wants to burn 75 kcal in each of the four parts , calculate the time for each activity separately. Warm-up: Burns 4 kcal/min Time = 75 ÷ 4 = 18.75 minutes (18 min 45 sec) Cardio: Burns 8 kcal/min Time = 75 ÷...