MathematicsMathematics

Ronald HuiRonald Hui

Tak Sun Secondary SchoolTak Sun Secondary School

Ronald HUIRonald HUI

ReminderReminder

Review of Standard HomeworkReview of Standard Homework Today!Today!

Open Book Quiz (Chapter 0)Open Book Quiz (Chapter 0) Today!Today!

Correction of Standard Correction of Standard Homework (II) and (III)Homework (II) and (III) 21 Sep (Friday)21 Sep (Friday)

Ronald HUIRonald HUI

NumbersNumbers

Numbers (Chapter 0.1, page 2)Numbers (Chapter 0.1, page 2) Natural Number (Natural Number ( 自然數自然數 ))

1, 2, 3, 4, 5, …1, 2, 3, 4, 5, … Whole Number (Whole Number ( 完整數完整數 ))

0,0, 1,1, 2,2, 3,3, 4,4, 5,5, …… Even Number (Even Number ( 偶數，雙數偶數，雙數 ))

0, 2, 4, 6, 8, …0, 2, 4, 6, 8, … Odd Number (Odd Number ( 奇數，單數奇數，單數 ))

1, 3, 5, 7, 9, …1, 3, 5, 7, 9, …

Ronald HUIRonald HUI

CalculationCalculation

Arithmetic OperationsArithmetic Operations ““+” – Addition+” – Addition

Add… to…, Plus, SumAdd… to…, Plus, Sum “–” – “–” – SubtractionSubtraction

Subtract… from…, Minus, DifferenceSubtract… from…, Minus, Difference ““x” – Multiplicationx” – Multiplication

Multiply… by…, Times, ProductMultiply… by…, Times, Product ““” – ” – DivisionDivision

… … is divided by…, Over, Quotientis divided by…, Over, Quotient

Ronald HUIRonald HUI

Calculation orderCalculation order

Please follow the order:Please follow the order: Brackets ( ), [ ], { }Brackets ( ), [ ], { }

((小中大括號小中大括號 )) Multiplication / division first,Multiplication / division first,

then addition / subtractionthen addition / subtraction((先乘除後加減先乘除後加減 ))

From left to rightFrom left to right((由左至右由左至右 ))

Ronald HUIRonald HUI

NumbersNumbers

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

Index NotationIndex Notation

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

H.C.F.H.C.F.

Case 1Case 1 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 HCF:HCF: 6 6 = 2 x 3= 2 x 3

Case 2Case 2 700 = 2700 = 222 x 5 x 522 x 7 x 7 720720 == 2244 x 3 x 322 x 5 x 5 HCF is 20 = 2HCF is 20 = 222 x 5 x 5

Ronald HUIRonald HUI

L.C.M.L.C.M.

Case 1Case 1 44 == 22 x 2x 2 = 2 = 222

6 = 2 x 36 = 2 x 3 = 2 x 3 = 2 x 3 LCM:12 = 2 x 2 x 3 = 2LCM:12 = 2 x 2 x 3 = 222 x 3 x 3

Case 2Case 2 28 = 228 = 222 x 7 x 7 3030 == 2 x 3 x 52 x 3 x 5 LCM: 420 = 2LCM: 420 = 222 x 3 x 5 x 7 x 3 x 5 x 7

Ronald HUIRonald HUI

H.C.F. and L.C.M.H.C.F. and L.C.M.

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

Types of fractionsTypes of fractions

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 )) The following fractions are equalThe following fractions are equal

7

4

4

7

4

31

50

20

15

6

10

4

5

2

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, 4is 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

SimplestSimplestForm!Form!

21

20

42

407

4

2

5

3

2

4

7

2

12

3

2

Ronald HUIRonald HUI

Tools and unitsTools and units

Select suitable unitsSelect suitable units Length: km / m / cm / mmLength: km / m / cm / mm Time: hr / min / secTime: hr / min / sec Weight: kg / g / lbWeight: kg / g / lb Temperature: Temperature: C / C / FF Volume: L / mlVolume: L / ml

Ronald HUIRonald HUI

Revision for QuizRevision for Quiz

Textbook 1ATextbook 1A Pages 2 – 31 (Chapter 0)Pages 2 – 31 (Chapter 0)

Workbook 1AWorkbook 1A Pages 1 – 16 (Chapter 0)Pages 1 – 16 (Chapter 0)

Summer RevisionSummer Revision Pages 1 – 19 (Units 1 – 3)Pages 1 – 19 (Units 1 – 3)

My PowerPoint filesMy PowerPoint files Your own notesYour own notes

Ronald HUIRonald HUI

ReminderReminder

Correction of Standard Correction of Standard Homework (II) and (III)Homework (II) and (III) 21 Sep (Friday)21 Sep (Friday)

Dictation 2Dictation 2 24 Sep (Monday)24 Sep (Monday)

Closed Book Quiz (Chapter 0) Closed Book Quiz (Chapter 0) and Folder Checkingand Folder Checking Last week of SeptemberLast week of September

Ronald HUIRonald HUI

Dictation 2Dictation 2

Numbers in wordsNumbers in words One, Two Three, Four, Five, Six, One, Two Three, Four, Five, Six,

Seven, Eight, Nine, TenSeven, Eight, Nine, Ten Eleven, Twelve, Thirteen, Eleven, Twelve, Thirteen,

Fourteen, Fifteen, Sixteen, Fourteen, Fifteen, Sixteen, Seventeen, Eighteen, NineteenSeventeen, Eighteen, Nineteen

Twenty, Thirty, Forty, Fifty, Sixty, Twenty, Thirty, Forty, Fifty, Sixty, Seventy, Eighty, Ninety, Hundred,Seventy, Eighty, Ninety, Hundred,

Thousand, Million, Billion, …Thousand, Million, Billion, …

Ronald HUIRonald HUI

Good Luck!Good Luck!

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