1 MPES 2 Percentages Ecole Suprieure de Commerce

1 MPES 2 Percentages Ecole Supérieure de Commerce de Neuchâtel Pierre Marchal http: //creativecommons. org/licences/by/3. 0/ Attribute to: Pierre Marchal (Lycée Jean-Piaget)

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

Percentages - Definition • A fraction with a denominator equal to 100 is called a percentage

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

Evaluating a percentage • To evaluate a percentage simply divide the 2 numbers, then amplify by 100 and express it as percentage (i. e. fraction “over 100”) • Find the percentage of 5 with respect to 35:

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

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%)

EXAMPLES OF APPLICATION

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. – Init. P. = 53. - CHF - discount% = 20% • What is the price after a 20% discount – Price after a discount: Fin. Price = init. Price × (100% - discount%) Fin. P. = init. P. × (100% - 20%) Fin. P. = 53 × 80% = 42. 40 CHF Final price, after discount, is 42. 40 CHF

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. – Fin. Price = 73. 10 CHF - discount% = 15% • What was the original price? – Price before discount: Init. Price = fin. Price ÷ (100% - discount%) Init. P. = fin. P. ÷ (100% - 15%) Init. P. = 73. 10 ÷ 85% = 86 CHF The initial price was 86 CHF

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. – Init. P. = 1’ 200 CHF - increase% = 13% • What is the price after an 13% increase? – Price after increase: Fin. Price = init. Price × (100% + increase%) Fin. P. = init. P. × (100% + 13%) Fin. P. = 1’ 200 ×(113%) Fin. P. = 1’ 356. - CHF

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 – Fin. P. = 1’ 350 CHF - increase% = 8% • What was the original price ? – Price before increase: Init. Price = fin. Price ÷ (100% + increase%) Init. P. = fin. P. ÷ (100% + 8%) Init. P. = 1’ 350 ÷ (108%) Init. P. = 1’ 250 CHF

Any question ?

See you at the next course, please learn your lessons ! THANK YOU FOR YOUR ATTENTION