MathematicsMathematics

Ronald HuiRonald Hui

Tak Sun Secondary SchoolTak Sun Secondary School

Ronald HUIRonald HUI

ReminderReminder

Standard Homework (II)Standard Homework (II) Deadline: Today!Deadline: Today!

Standard Homework (III)Standard Homework (III) Deadline: 18 Sep (Tue)Deadline: 18 Sep (Tue)

Open Book Quiz (Chapter 0)Open Book Quiz (Chapter 0) Deadline: 19 Sep (Wed)Deadline: 19 Sep (Wed)

Closed Book Quiz (Chapter 0), Closed Book Quiz (Chapter 0), Dictation 2 and Folder CheckingDictation 2 and Folder Checking Last week of SeptemberLast week of September

Ronald HUIRonald HUI

Revision for QuizRevision for Quiz

Textbook 1ATextbook 1A Pages 2 – 31Pages 2 – 31

Workbook 1AWorkbook 1A Pages 1 – 16Pages 1 – 16

Summer RevisionSummer Revision Pages 1 – 19Pages 1 – 19

My PowerPoint filesMy PowerPoint files Your own notesYour own notes

Ronald HUIRonald HUI

RevisionRevision

Prime numbers (Prime numbers ( 質數質數 )) 2,2, 3,3, 5,5, 7,7, 11,11, 13,13, 17,17, 19,19, 23,23, ……

Multiples (Multiples ( 倍數倍數 )) Multiples of 2:Multiples of 2: 2, 4, 6, 8, …2, 4, 6, 8, … Multiples of 3:Multiples of 3: 3, 6, 9, 12, …3, 6, 9, 12, …

Factors (Factors ( 因子因子 )) 2 is a factor of 2, 4, 6, 8, …2 is a factor of 2, 4, 6, 8, … 3 is a factor of 3, 6, 9, 12, …3 is a factor of 3, 6, 9, 12, …

Ronald HUIRonald HUI

RevisionRevision

Factors of 18: 1, 2, 3, 6, 9, 18Factors of 18: 1, 2, 3, 6, 9, 18 Prime factors of 18: 2, 3Prime factors of 18: 2, 3

18 = 2 x 918 = 2 x 9

= 2 x 3 x 3= 2 x 3 x 3 18 = 2 x 318 = 2 x 322 Index Notation Index Notation

3322 = 3 x 3 = 3 x 3 ((指數記數法指數記數法 )) 3 is base3 is base 底底 2 is index2 is index 指數指數

Ronald HUIRonald HUI

RevisionRevision

Index notation is very helpful in Index notation is very helpful in long expression of prime factorslong expression of prime factors

432 = 2 x 2 x 2 x 2 x 3 x 3 x 3432 = 2 x 2 x 2 x 2 x 3 x 3 x 3

= 2= 244 x 3 x 333 86400 = 2 x 2 x 2 x 2 x 2 x 2 x 286400 = 2 x 2 x 2 x 2 x 2 x 2 x 2

x 3 x 3 x 3 x 5 x 5 x 3 x 3 x 3 x 5 x 5

= 2= 277 x 3 x 333 x 5 x 522

Ronald HUIRonald HUI

RevisionRevision

We can find H.C.F. from Index We can find H.C.F. from Index Notation! (Notation! ( 用指數記數法找用指數記數法找HCF)HCF) 1818 == 22 x 3 x 3x 3 x 3 = 2 x 3= 2 x 322

24 = 2 x 2 x 2 x 324 = 2 x 2 x 2 x 3= 2= 233 x 3 x 3 We know H.C.F. of 18 and 24 is We know H.C.F. of 18 and 24 is 66 6 = 2 x 36 = 2 x 3

Can you find the rule?Can you find the rule?

Ronald HUIRonald HUI

RevisionRevision

We can find L.C.M. from Index We can find L.C.M. from Index Notation! (Notation! ( 用指數記數法找用指數記數法找LCM)LCM) 44 == 22 x 2x 2 = 2= 222

6 = 2 x 36 = 2 x 3 = 2 x 3= 2 x 3 We know L.C.M. of 4 and 6 is We know L.C.M. of 4 and 6 is 1212 12 = 2 x 2 x 312 = 2 x 2 x 3 = 2= 222 x 3 x 3

Can you find the rule?Can you find the rule?

Ronald HUIRonald HUI

RevisionRevision

If the numbers did not have If the numbers did not have common prime factors, their common prime factors, their HCF is 1 and their LCM is the HCF is 1 and their LCM is the product of themproduct of them

20 = 220 = 222 x 5 x 5 6363 == 3322 x 7 x 7 Their HCF is 1Their HCF is 1 Their LCM is 20 x 63 = 1260Their LCM is 20 x 63 = 1260

Ronald HUIRonald HUI

Fractions (p.11)Fractions (p.11)

FractionsFractions Numerator (Numerator (分子分子 ))

Fraction line (Fraction line (分數線分數線 ))

Denominator (Denominator (分母分母 )) 3 over 43 over 4 3 is divided by 43 is divided by 4 3 3 4 4 Three-quarter (quarter = ¼)Three-quarter (quarter = ¼)

4

3

Ronald HUIRonald HUI

Fractions (p.12)Fractions (p.12)

Types of FractionsTypes of Fractions Proper fraction (Proper fraction ( 真分數真分數 )) Improper fractionImproper fraction ((假分數假分數 ))

Mixed numberMixed number ((帶分數帶分數 )) http://zh.wikipedia.org/zh-hk/%E

5%88%86%E5%BC%8F#.E5.88.86.E9.A1.9E

7

4

4

7

4

31

Ronald HUIRonald HUI

Comparing FractionsComparing Fractions

The following fractions are equalThe following fractions are equal

We can then compare different We can then compare different fractionsfractions

50

20

15

6

10

4

5

2

?5

2

2

1

5

2

2

1

10

4

5

210

5

2

1

Ronald HUIRonald HUI

Addition, SubtractionAddition, Subtraction

Use improper fractionsUse improper fractions Change to same denominatorsChange to same denominators Do operations on numeratorsDo operations on numerators

LCM LCM ofof

3, 2, 43, 2, 4

is 12is 1212

1712

21

12

30

12

84

7

2

5

3

2

4

7

2

12

3

2

Ronald HUIRonald HUI

Multiplication, DivisionMultiplication, Division

Use improper fractionsUse improper fractions Use reciprocal for division Use reciprocal for division Multiply numerators and Multiply numerators and

denominators separatelydenominators separately

SimplestSimplest

Form!Form!21

20

42

407

4

2

5

3

2

4

7

2

12

3

2

Ronald HUIRonald HUI

Time for PracticeTime for Practice

Pages 21 of Textbook 1APages 21 of Textbook 1A Questions 16 – 20Questions 16 – 20

Ascending (Ascending (遞升遞升 ) ) increasing increasing Descending (Descending (遞降遞降 ) ) decreasing decreasing

Pages 10 – 12 of Workbook 1APages 10 – 12 of Workbook 1A Questions 7 – 10 Questions 7 – 10

Ronald HUIRonald HUI

ReminderReminder

BCA Online ExerciseBCA Online Exercise Deadline: 10 Sep (Mon)Deadline: 10 Sep (Mon)

Standard Homework (III)Standard Homework (III) Deadline: 18 Sep (Tue)Deadline: 18 Sep (Tue)

PowerPoint filesPowerPoint fileshttp://personal.tsss.edu.hk/roh

Ronald HUIRonald HUI

Good Luck!Good Luck!

Enjoy the world of Enjoy the world of Mathematics!Mathematics!