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- 1. And its applications in real life!
- 2. ? What is percentage? ? Percentages, fractions and decimal fractions ? Real life ? Percentage increase and percentage decrease ? Percentage increase ? Percentage decrease ? Repeated increase and decrease ? Reverse modelling
- 3. ? Percent means out of 100, for example 3% means 3out of 100, 30 percent means 30 out of 100, 50% humidity means 50% of the air around us, which is 100%, is made up of water molecules and ..... ? 100 is the total amount and every percentage is calculated out of 100 ? Percentage calculation: ? Example: What is the percentage of boys and girls in your class? ? Answer: Use the number line modelling (The total number of the students is 27) 0% 0 100% 27
- 4. ? Converting fractions to percentages - Write the fraction - Multiply by 100% - Cancel or simplify as appropriate - Example: write 8/40,5/10 and 27/100 as a percentage. ? Converting decimal fractions to percentages - A decimal fraction can be converted to a percentage by multiplying by 100 - Example: Write 0.5, 0.065 and 0.3 as a percentage ? Converting a percentage to a fraction or a decimal fraction - Example : Write 72% and 45% as a fraction and as a decimal fraction
- 5. ? Definitions - Discounts = ? - Mark ¨C ups = ? - GST = ? - Profit and loss = ? ? Discount = money saved = (Percentage discount) total price , Money to pay = Total money ¨C discount Example: K Mart has a 15% discount storewide on all items. How much would I save on a pair of shoes which normally costs $ 45? Page 160 of text book 0% 0 15% ? 100% $45
- 6. ? GST= 10% Price ? Total price = GST + price ? Example: Price of a pair of pants, excluding GST is $40. How much should I pay to buy the pants?
- 7. ? Mark ¨C up price = Mark- up percentage price ? Total price = Mark ¨C up price + initial price ? Example: Sam operates a fruit shop. He marks all his fruit up by 40%. How much would a customer pay for a punnets of strawberries that cost Sam 60 cents?
- 8. ? Income ¨C expenditure= profit or loss ? Sales ¨C costs= profit or loss - Profit if the result is positive - Loss if the result is negative ? Example: Joshi¡¯s tile shop made a profit of 5.8% on total costs last year. If the actual profit was $83 000, what were the total costs, and what were the total sales?
- 9. ? You can solve most of the percentage problems in one step using percentage increase or percentage decrease ? Discounts and Loss are percentage decrease problems ? GSTs, Mark- ups and profits are percentage increase problems
- 10. ? Percentage increase: (100 + a)% total= total increased 0% 0 100% total 100%+a% Total increased
- 11. ? Example: 1. Increase the prices below by 20%. a) $ 20 b) $30 c) $ 60 d) $ 75 2. The number of patient admissions at a certain hospital last year was 890 and increased by 23% this year. How many admissions are there this year?
- 12. ? Percentage decrease: (100% ¨C a%) total= total decreased 00% 0 100%-a% Total decreased 100% Total
- 13. ? Examples: 1. Decrease the prices below by 15%. a) $ 30 b) $ 45 c) $ 50 d) $15 2. A government department was ordered to decrease its $2 000 000 budget by 3% in the coming year. How much did they have for their budget?
- 14. 1. I paid $77 for an item recently. What was the price before adding GST, and what tax was paid to the Government? 2. The Elegant Shirt Shop is closing down and has discounted all its prices by 35%. What was the original price of a shirt whose discounted price is $92.30? 3. Shares in a particular stock fell 34% to $5.30. What was the price before the fall? 4. Sam operates a fruit shop. He marks- up all his fruit by 30% of their cost. A customer pays 75 cents for a punnet of strawberries. What was the original price of the strawberries? 5. A discount of 8% was made on a product costing $550. A further discount of 5% on the new price was then made. What is the cost now? Using the discounts in the above exercise, we find that an item costs $56 after the two discounts. What was the original price?