1. 1MPES2 Percentages Ecole Supérieure de Commerce de Neuchâtel Pierre Marchal 22.10.2015 http://creativecommons.org/licences/by/3.0/ Attribute to: Pierre Marchal (Lycée Jean-Piaget)

2. Objectives of the course By the end of the course, you should be able to: – Define the percentage – Calculate a percentage – Evaluate a percentage

3. Percentages - Definition A with a denominator is called a fraction equals to 100 percentage

4. Difference in percentage To calculate a, simply divide the by the To get the proper sign: A price goes from 150.- to 165.- The percentage of increase is: difference initial value difference in percentage difference = final value – initial value

5. Evaluating a percentage To evaluate a percentage simply the 2 numbers, then Find the percentage of 5 with respect to 35: divide amplify by 100

6. Word problems Translate: – Is / were / was / will be: – After: – Before: – Discount: – Increase: = × ÷ − discount% + increase%

7. For instance Price after a discount: – Final Price = initial Price × (100% - discount%) Price after increase: – Final Price = initial Price × (100% + increase%) Price before discount: – Initial Price = final Price ÷ (100% - discount%) Price before increase: – Initial Price = final Price ÷ (100% + increase%)

8. EXAMPLES OF APPLICATION

9. Exercise n° 1 The price for pants is 53 CHF. What is the price after a 20% discount? – The price for pants is 53 CHF. – - discount% = 20% What is the price after a 20% discount – Price after a discount: Init. P. = 53.- CHF Fin. P. = init. P. × (100% - 20%) Fin. P. = 53 × 80% = 42.40 CHF Final price, after discount, is 42.40 CHF Fin. Price = init. Price × (100% - discount%)

10. Exercise n° 2 73.10 CHF is the price after a 15% discount. What was the original price? – 73.10 CHF is the price after a 15% discount. – - discount% = 15% What was the original price? – Price before discount: Fin. Price = 73.10 CHF Init. P. = fin. P. ÷ (100% - 15%) Init. P. = 73.10 ÷ 85% = 86 CHF The initial price was 86 CHF Init. Price = fin. Price ÷ (100% - discount%)

11. Exercise n° 3 An item is sold 1’200 CHF. What is the price after an 13% increase? – An item is sold 1’200 CHF. – - increase% = 13% What is the price after an 13% increase? – Price after increase: Init. P. = 1’200 CHF Fin. P. = init. P. × (100% + 13%) Fin. P. = 1’200 ×(113%) Fin. P. = 1’356.- CHF Fin. Price = init. Price × (100% + increase%)

12. Exercise n° 4 After an 8% increase, an item was sold for 1’350 CHF. What was the original price ? – After an 8% increase, an item was sold for 1’350 CH – - increase% = 8% What was the original price ? – Price before increase: Fin. P. = 1’350 CHF Init. P. = fin. P. ÷ (100% + 8%) Init. P. = 1’350 ÷ (108%) Init. P. = 1’250 CHF Init. Price = fin. Price ÷ (100% + increase%)

13. Any question ?

14. THANK YOU FOR YOUR ATTENTION See you on Thursday and please learn your lessons !