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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
Percent means out of 100, for example 3% means 3out of100, 30 percent means 30 out of 100, 50% humidity means50% of the air around us, which is 100%, is made up of watermolecules and ..... 100 is the total amount and every percentage is calculatedout of 100 Percentage calculation: Example: What is the percentage of boys and girls in yourclass? Answer: Use the number line modelling (The total number ofthe students is 27)0% 0100% 27
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 bymultiplying by 100- Example: Write 0.5, 0.065 and 0.3 as a percentage Converting a percentage to a fraction or a decimalfraction- Example : Write 72% and 45% as a fraction and as a decimalfraction
Definitions- Discounts = ?- Mark – ups = ?- GST = ?- Profit and loss = ? Discount = money saved = (Percentage discount) total price, Money to pay = Total money – discountExample: K Mart has a 15% discount storewide on all items.How much would I save on a pair of shoes which normallycosts $ 45?Page 160 of text book0% 015% ?100% $45
GST= 10% Price Total price = GST + price Example: Price of a pair of pants, excluding GST is $40. How muchshould I pay to buy the pants?
Mark – up price = Mark- up percentage price Total price = Mark – up price + initial price Example: Sam operates a fruit shop. He marks all hisfruit up by 40%. How much would a customer pay for apunnets of strawberries that cost Sam 60 cents?
Income – expenditure= profit or loss Sales – 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 totalcosts last year. If the actual profit was $83 000, whatwere the total costs, and what were the total sales?
You can solve most of the percentage problems in onestep using percentage increase or percentage decrease Discounts and Loss are percentage decrease problems GSTs, Mark- ups and profits are percentage increaseproblems
Percentage increase:(100 + a)% total= total increased0% 0100% total100%+a% Total increased
Example:1. Increase the prices below by 20%.a) $ 20 b) $30 c) $ 60 d) $ 752. The number of patient admissions at a certain hospitallast year was 890 and increased by 23% this year. Howmany admissions are there this year?
Percentage decrease:(100% – a%) total= total decreased00% 0100%-a% Total decreased100% Total
Examples:1. Decrease the prices below by 15%.a) $ 30 b) $ 45 c) $ 50 d) $152. A government department was ordered to decrease its$2 000 000 budget by 3% in the coming year. How muchdid they have for their budget?
1. I paid $77 for an item recently. What was the price before addingGST, and what tax was paid to the Government?2. The Elegant Shirt Shop is closing down and has discounted all itsprices by 35%. What was the original price of a shirt whosediscounted price is $92.30?3. Shares in a particular stock fell 34% to $5.30. What was the pricebefore the fall?4. Sam operates a fruit shop. He marks- up all his fruit by 30% of theircost. A customer pays 75 cents for a punnet of strawberries. Whatwas the original price of the strawberries?5. A discount of 8% was made on a product costing $550. A furtherdiscount of 5% on the new price was then made. What is the costnow? Using the discounts in the above exercise, we find that anitem costs $56 after the two discounts. What was the original price?