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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!