Percentages (I)Form 1 MathematicsChapter 3

Reminder• Standard Homework (I) and (II)

▫ Today!• Standard Homework (III) and (IV)

▫ 28 Nov (Wed)• Extra Tutorial

▫ Today’s last CTP▫ MUST: 1, 10, 11, 12, 14, 16, 26, 30, 36▫ Mon & Tue after-school – Consultation on G/F

• Open Book Quiz▫ 28 Nov (Wed)

• Standard Homework (V)▫ 30 Nov (Fri)

Percentage Increase (p.119)• New value > Original value

• E.g. The Hang Seng Index increases from 11500 to 12150. We also say that the Index is increased by 5.65%.

%100valueOriginal

IncreaseincreasePercentage

valueOriginalvalueNewIncrease

increasePercentagevalueOriginalvalueNew 1

Percentage Increase•Last year, Andy was 150cm tall. His

height is increased by 20% this year. What is his height now?

•Increase or Decrease?•His height now is

cm

cm

cm

cm

180

2.1150

2.01150

%201150

Percentage Decrease (p.122)• New value < Original value

• E.g. The price of a flat decrease from $2,200,000 to $1,804,000. We always say that the price of the flat is reduced by 18%.

%100valueOriginal

DecreasedecreasePercentage

valueNewvalueOriginalDecrease

decreasePercentagevalueOriginalvalueNew 1

Percentage Decrease•The price of a car was $160,000 last

month. What is the price of the car this month if the price is decreased by 15%?

•Increase or Decrease?•The price this month is

000,136$

85.0000,160$

15.01000,160$

%151000,160$

Percentage Change (p.126)• We can summarize the two formulae into

one and call percentage change.

• If New value > Original value, then + (increase)

• If New value < Original value, then – (decrease)

%100

valueOriginal

valueOriginalvalueNewchangePercentage

Percentage Change•The temperature was 30C in the afternoon and

the temperature dropped to 27C in the evening. Find the percentage change in the temperature.

•The percentage change

•So, the percentage decrease in the temperature is 10%.

%10

%10030

3

%10030

3027

Percentage Change•The profit of a company increases from

$450,000 last year to $540,000 this year. What is the percentage change in profit?

•The percentage change

•So, the percentage increase in profit is 20%.

%20

%100450000

90000

%100450000

450000540000

Time for Practice•Page 127 of Textbook 1A

▫Class Practice•Page 129 of Textbook 1A

▫Questions 6 – 14•Pages 57 - 58 of WB 1A

▫Questions 3 - 9

Profit (p.131)• Selling Price > Cost Price

%100% PriceCost

ProfitProfit

PriceCostPriceSellingProfit

%ProfitPriceCostProfit

%1 ProfitPriceCostPriceSelling

Loss (p.134)• Selling Price < Cost Price

%100% PriceCost

LossLoss

PriceSellingPriceCostLoss

%LossPriceCostLoss

%1 LossPriceCostPriceSelling

Profit and Loss•A shop sold a car at the profit % of 20%. If

the profit was $32000, what was the cost of the car? What was the selling price?

•Profit or Loss?•Let n be the Cost Price. Then,

•So, the Selling Price is000,160$

5000,32$

000,32$5

1

000,32$%20

n

n

n

n

000,192$000,32$000,160$

Time for Practice•Pages 134 - 135 of Textbook 1A

▫Class Practice•Page 137 of Textbook 1A

▫Questions 7 – 19•Pages 61 - 62 of WB 1A

▫Questions 7 - 10

Discount (p.138)•Western style vs. Chinese style

88折 = 12% off

Discount•Western style vs. Chinese style

•10% discount 9 折•20% discount 8 折•70% discount 3 折

•12% discount 88折•33% discount 67折•5% discount 95折

Discount•Marked Price > Selling Price

%100% PriceMarked

DiscountDiscount

PriceSellingPriceMarkedDiscount

%DiscountPriceMarkedDiscount

%1 DiscountPriceMarkedPriceSelling

Discount•A pair of scorer shoes is sold at 25%

discount at a marked price of $650. Can Vincent buy the shoes if he has $500?

•Marked price = $650•Selling price of the shoes

•Since Vincent got $500, he can buy the shoes.

5.487$

%75650$

%251650$

Discount•A golden ring is sold at 30% discount with a

selling price of $441.What is the marked price?

•Selling price = $441.•Let n be Marked price. Then,

•So, the Marked price is $630.

630$7

10441$

441$10

7

441$%301

n

n

n

n

Time for Practice•Page 141 of Textbook 1A

▫Class Practice•Page 142 of Textbook 1A

▫Questions 3 – 10•Pages 65 - 66 of WB 1A

▫Questions 7 - 10

Interest (p.144)•When money is deposited in a bank, you will

receive some Interest (I, 利息 ) according to the amount of Principal (P, 本金 ). The sum of P and I is called the Amount (A, 本利和 ).

•The interest is based on a percentage (r%, 利率 ) of the principal. It is normally given in a yearly basis, e.g. 5%p.a. (p.a. = “per annum”).

•There are two methods to find the interests: simple interest or compound interest.

Simple Interest•Amount(A) = Principal(P) +

Interest(I)

•Interest(I) = Principal(P) Interest rate(r%) period of time(T)

•Formula:100

%

TrPI

TrPI

1001

%1

%

rTPA

TrPA

TrPPA

IPA

Simple Interest• If $40000 is deposited in a bank for 5 years

at 3%p.a., find the simple interest and the amount.

•P=$40000 r=3 T=5 (years)•Simple interest (I) is

•So, the amount (A) is

6000$

5100

340000$

5%340000$

46000$6000$40000$

TrPI %

Simple Interest•How long will $20000 amount to $30000 at

5%p.a. simple interest?

•P=$20000 r=5 A=30000• I = $30000-$20000=$10000•Let T be the time. Then,

•The time required is 10 years.10

5

100

2

1100

5

20000$

10000$

10000$%520000$

T

T

T

T

TrPI %

Time for Practice•Page 149 of Textbook 1A

▫Class Practice•Page 150 of Textbook 1A

▫Questions 1 – 13•Pages 69 - 70 of WB 1A

▫Questions 4 - 7

Reminder• Standard Homework (I) and (II)

▫ Today!• Extra Tutorial

▫ Today’s last CTP▫ MUST: 1, 10, 11, 12, 14, 16, 26, 30, 36▫ Mon & Tue after-school – Consultation

on G/F• Open Book Quiz

▫ 28 Nov (Wed)• Standard Homework (III), (IV) and (V)

▫ 30 Nov (Fri)

Enjoy the world of Mathematics!