Percentages (I)Form 1 MathematicsChapter 3

Reminder• Folder Checking

▫ 26 Nov (Mon) – All Chapters 0, 1, 2 and 4!• ALL Corrections

▫ 26 Nov (Mon) – All Chapters 0, 1, 2 and 4!▫ Close Book Quiz with Parent’s signature!

• Extra Tutorial▫ 27 Nov (Tue) – based on Close Book Quiz

result▫ Mon & Tue after-school – Consultation on

G/F• Open Book Quiz

▫ 28 Nov (Wed)

Reminder• Term 1 Examination Syllabus

▫ 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

• Result of Close Book Quiz▫ Full mark: 40 and 10 bonus▫ Highest: 41▫ Lowest: 6▫ Average: 28.6 (Open Book: 21.1)▫ Number of students between 10 - 19: 3▫ Number of students between 0 - 9: 1

• Major Problems▫ Don’t understand well the question!

Result of Close Book Quiz

• Result of Close Book Quiz• 5th place(5): CHAN Tsz Long, Sam

FU Ling YinKO Ka Chung BostonTANG Yiu Cheung HaraldYUEN Tin Wai, Timmy

• 4th place: LI Ming Chun Edward • 2nd place(2): WU SHAN Hao Yi

LI Sai Kong• 1st place: CHOI King Shing, Walker

Congratulations!!!!!! Well done!!!!!!

Result of Close Book Quiz

Mathematics nearby•Mr. Hui bought a new car with $100,000•He makes up the car well and then try to

sell it at a better price. So, he marked up 50% (half).

•His friend wants to buy a car also and then he approached Mr. Hui.

•Mr. Hui decided to sell it to his friend at a “friendship price” of 50% (half) of the marked price.

•Did Mr. Hui gain, lose or no gain no loss?

What is Percentage?• Percentage is a fraction with the

denominator equal to 100.• “%” is the symbol of percentage and

often is called “Per cent”. Per cent means “per one hundred”.

• Percentages can be presented in decimals.

• 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

What is Percentage?• In other words, a fraction or decimal can

be converted to percentage.• e.g.

%20%5

100%100

5

1

5

1

%5.37%2

137%

2

75%

8

300%100

8

3

8

3

%74%10074.074.0

%5.12%100125.0125.0

Simple Percentage Problems•“What is 25% of $800?” •“What percentage of 24 apples is 6?”•“15% of the number of staff of a company

is 24. What is the number of staff of that company?”

•These are the examples of simple percentage problems. By using some simple calculation, we can find the answers..

Simple Percentage Problems•What is 25% of $800?

•What percentage of 24 apples is 6?

200$258$100

25800$%25800$

%25%1004

1%100

24

6

Simple Percentage Problems• Jacky participates in a 5-km race. He has

finished 1800m already. What percentage of the whole race does Jacky not finish?

•The remaining distance that Jacky needs to run = 5km – 1800m = 5000m – 1800m = 3200m

•The percentage Jacky does not finish is

•Remark: same units!%64%

50

3200%100

5000

3200

m

m

Simple Percentage Problems• In a concert held in the Hong Kong Stadium,

there were 8344 female persons, which was 28% of the total persons. Given that there were 40000 seats, find the percentage of seats occupied.

•Let n be total number of persons in the concert.

•Percentage of seats occupied %5.74%10040000

29800

?298008344%28 whynn

Time for Practice•Page 117 of Textbook 1A

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

▫Questions 4 - 9

Percentage Increase• 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 Decrease• 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 Increase & Decrease•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 Increase & 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• We can summarize the two formulae into

one and call percentage change.

• If New value > Original value, then +

• If New value < Original value, then –

%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

Percentage Change• If the length and the width of a picture

increased by 30% and 40% respectively, find the percentage change in the area of the picture.

•Let x and y be the length and the width of the picture respectively.

•The original area of the picture = xy

Percentage Change•The new area of the picture

•The percentage change

•So, the percentage increase in the area is 82%.%82

%10082.0

%10082.1

xy

xy

xy

xyxy

xy

yx

yx

82.1

4.13.1

%401%301

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

Reminder• Folder Checking

▫ 26 Nov (Mon) – All Chapters 0, 1, 2 and 4!▫ ALL Corrections are needed!▫ Close Book Quiz with Parent’s signature!

• Standard Homework (I) and (II)▫ 27 Nov (Tue)

• Extra Tutorial▫ 27 Nov (Tue) – based on Close Book Quiz

result▫ Mon & Tue after-school – Consultation on G/F

• Open Book Quiz▫ 28 Nov (Wed)

Enjoy the world of Mathematics!

Ronald HUI