Percentages (I)Form 1 MathematicsChapter 3

Reminder• Standard Homework (III), (IV) and (V)

▫ 30 Nov (Fri)• Extra Tutorial

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

on G/F• Open Book Quiz

▫ 30 Nov (Fri)• Close Book Quiz

▫ 5 Dec (Wed)

What is Percentage? (p.110)• “%” is the symbol of percentage. Per

cent means “per one hundred”.• e.g.

4

1

100

25%25

100

81%81 9.0

100

90%90

35.0%35 4567.0%67.45 0314.0%14.3

%20%5

100%100

5

1

5

1

%5.37%2

137%

2

75%

8

300%100

8

3

8

3

%7474.0 %5.12125.0

Simple Percentage Problems•P.116 Q2(c): 125% of $365.2

•P.117 Q10(c): 132 g is 88% of t g

•Remark: same units!

5.456$2

913$

4

5

10

3652$

100

125

1

2.365$%1252.365$

1502

1003

88

100132

%88132

132%88

t

t

t

t

t

Simple Percentage Problems•P.118 Q14. 1100 boys and 700 girls took an

examination. 15% of boys and 5% of girls failed. Find the total number of students passed.

•Number of boys failed = 1100 15% = 165•Number of girls failed = 700 5% = 35•Number of students failed = 165+35 = 200•Number of students = 1100+700 = 1800•Number of students passed = 1800-200 = 1600

Simple Percentage Problems•P.118 Q14. 1100 boys and 700 girls took an

examination. 15% of boys and 5% of girls failed. Find the total number of students passed.

•Number of boys passed= 1100 (1 – 15%) = 1100 (85%) = 935

•Number of girls passed= 700 (1 – 5%) = 700 (95%) = 665

•Number of students passed = 935-665 = 1600

Time for Practice•Page 117 of Textbook 1A

▫Questions 3 - 13•Pages 54 - 55 of WB 1A

▫Questions 4 - 9

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

• Last year, Andy was 150cm tall. His height is increased by 20% this year. His height now is

%100% valueOriginal

IncreaseIncrease

valueOriginalvalueNewIncrease

%1 increasevalueOriginalvalueNew

cmcmcm 1802.1150%201150

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

• The price of a car was $160,000 last month. If it is reduced by 15% this month, the new price

%100valueOriginal

DecreasedecreasePercentage

valueNewvalueOriginalDecrease

decreasePercentagevalueOriginalvalueNew 1

000,136$85.0000,160$%151000,160$

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

one and call percentage change.

• New value > Original value + (increase)• New value < Original value – (decrease)

• The temperature was dropped from 30C to 27C in the evening. The percentage change is

%100%

valueOriginal

valueOriginalvalueNewChange

%10%10030

3%100

30

3027

Percentage Change•P.130 Q19. James had $5000 in his savings

account last year. This year, he has $10000.

•Change %

•James then takes out 40% of his savings. The amount now is = $10000 (1 – 40%) = $6000

•New change %

%100%1005000

5000%100

5000

500010000

%20%1005000

1000%100

5000

50006000

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 ( 盈利 , p.131)• Selling Price (售價 ) > Cost Price (成本

價 )

%100% PriceCost

ProfitProfit

PriceCostPriceSellingProfit

%ProfitPriceCostProfit

%1 ProfitPriceCostPriceSelling

Loss ( 虧蝕 , p.134)• Selling Price (售價 ) < Cost Price (成本

價 )

%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$000,160$

%profitCostProfit

Profit and Loss•P.138 Q22. A merchant bought a chair for

$500 and a desk for $750. He sold the chair at a loss of 30% and the desk at a profit of 24%.

•Selling price of chair•Selling price of desk•Total selling prices = $350 + $930 = $1280•Total cost prices = $500 + $750 = $1250•So, the profit % is

350$%70500$%301500$ 930$%124750$%241750$

%4.2%100024.0%1001250

30%100

1250

12501280

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 (折扣 , p.138)•Western style vs. Chinese style

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

•12% discount 88折•25% discount 75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$

%1 discountMP

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

%1 discountMP

Discount•P.142 Q10. In shop A, the marked price of a

MD is $1920 and the selling price is $1248. In shop B, the prices are $1760 and $1320 respectively.

•A’s discount %

•B’s discount %

•So, B’s discount is smaller.

%35%1001920

672%100

1920

12481920

%25%1001760

440%100

1760

13201760

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

Simple Interest (單利息 , p.144)•Amount(A) = Principal(P) +

Interest(I)

•Interest(I) = Principal(P) Interest rate(r%)

Time(T)

•Formula: 100

%

TrPI

TrPI

1001

100Tr

PA

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 %

Simple Interest•P.151 Q14. Judy borrows $1000000 for 10

years. Bank A’s interest is 5% p.a. and B is 4.5% p.a.

•A’s interest

•B’s interest

•The difference is $50000.•She pays $50000 less in Bank B from in Bank A.

500000$10%51000000$

450000$10%5.41000000$

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• Term 1 Examination Syllabus (p.1-185)

▫ Chapter 0: Basic Mathematics▫ Chapter 1: Directed Numbers▫ Chapter 2: Using Algebra to Solve Problems

(I)▫ Chapter 3: Percentages (I)▫ Chapter 4: Using Algebra to Solve Problems

(II)• Date of Term 1 Examination

▫ 12-12-12 (Wed)▫ 8:30 am – 9:30 am (1 hour)▫ Room 104

Enjoy the world of Mathematics!