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 – ups = ?
- GST = ?
- Profit and loss = ?
Discount = money saved = (Percentage discount) total price
, Money to pay = Total money – 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 – up price = Mark- up percentage price
Total price = Mark – 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 – 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 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
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?
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?
