Mathematics
Ronald Hui
Tak Sun Secondary School
Reminder
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Corrections of Dictation 1 and
Standard Homework (I)
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Standard Homework (II)
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Deadline: 14 Sep (Fri)
Deadline: 17 Sep (Mon)
Standard Homework (III)
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Deadline: 18 Sep (Tue)
Ronald HUI
Reminder
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Corrections of Standard
Homework (II) and (III)
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Open Book Quiz (Chapter 0)
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Deadline: 19 Sep (Wed)
Deadline: 19 Sep (Wed)
Closed Book Quiz (Chapter 0),
Dictation 2 and Folder Checking
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Last week of September
Ronald HUI
Revision for Quiz
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Textbook 1A
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Workbook 1A
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Pages 1 – 16
Summer Revision
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Pages 2 – 31
Pages 1 – 19
My PowerPoint files
Your own notes
Ronald HUI
Mathematics
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How to get better results?
Understand first!
 Do correction!
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Dictation: 10 times
 Test/Homework: Other colour pens
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Revise!
 Try more (workbook)
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Ronald HUI
Revision
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Prime numbers (質數)
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2, 3, 5, 7, 11, 13, 17, 19, 23, …
Multiples (倍數)
Multiples of 2:
 Multiples of 3:
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2, 4, 6, 8, …
3, 6, 9, 12, …
Factors (因子)
2 is a factor of 2, 4, 6, 8, …
 3 is a factor of 3, 6, 9, 12, …
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Ronald HUI
Revision
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Find all factors of 18.
18 = 1 x 18
 18 = 2 x 9
 18 = 3 x 6
 18 = 6 x 3
 18 = 9 x 2
 18 = 18 x 1
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Factors of 18: 1, 2, 3, 6, 9, 18
Ronald HUI
Prime Factors (p.9)
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Prime factors (質因子)
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Factors of 18: 1, 2, 3, 6, 9, 18
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A factor which is prime
Prime factors of 18: 2, 3
All numbers can be expressed
as a product of prime factors
only – How?
Ronald HUI
Index Notation (p.9)
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Factors of 18: 1, 2, 3, 6, 9, 18
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Prime factors of 18: 2, 3
18 = 2 x 9
=2x3x3
18 = 2 x 32
 Index Notation
32 = 3 x 3
 3 is base 底
 2 is index 指數
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Ronald HUI
(指數記數法)
Index Notation (p.9)
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32 = 3 x 3
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33 = 3 x 3 x 3
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3 to the power 2, 3 squared (平方)
3 to the power 3, 3 cubed (立方)
34 = 3 x 3 x 3 x 3
35 = 3 x 3 x 3 x 3 x 3
What is 31 ?
31 = 3
Ronald HUI
Index Notation (p.9)
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Index notation is very helpful in
long expression of prime factors
432 = 2 x 2 x 2 x 2 x 3 x 3 x 3
= 24 x 33
86400 = 2 x 2 x 2 x 2 x 2 x 2 x 2
x3x3x3x5x5
= 27 x 33 x 52
Ronald HUI
Time for Practice
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Pages 10 – 11 of Textbook 1A
Class Practice
 Questions 6 – 9
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Pages 6 – 7 of Workbook 1A
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Questions 5 – 9
Ronald HUI
Mathematics nearby
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What is Google?
http://zh.wikipedia.org/zhhk/Google#.E5.BB.BA.E7.AB.8B
Google was mis-spelt from
googol!
Googol = 10100
= 1000000…00000
(100 zeros!)
Ronald HUI
H.C.F.
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Highest Common Factor
(最大公因數)
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Factors of 18:
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Factors of 24:
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1, 2, 3, 4, 6, 8, 12, 24
Common factors of 18 and 24:
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1, 2, 3, 6, 9, 18
2, 3, 6
H.C.F. of 18 and 24 is 6
Ronald HUI
H.C.F.
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We can find H.C.F. from Index
Notation! (用指數記數法找HCF)
18 = 2 x 3 x 3
= 2 x 32
 24 = 2 x 2 x 2 x 3 = 23 x 3
 We know H.C.F. of 18 and 24 is 6
 6= 2x3
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Can you find the rule?
Ronald HUI
H.C.F.
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Another example
24 = 2 x 2 x 2 x 3 = 23 x 3
 36 = 2 x 2 x 3 x 3 = 22 x 32
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Can you guess the HCF?
Their HCF is
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2x2x3
Ronald HUI
= 22 x 3
= 12
H.C.F.
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Another try: HCF of 700 and 720
700 = 22 x 52 x 7
720 = 24 x 32 x 5
Can you guess the HCF?
Their HCF is
= 22 x 5 = 20
Ronald HUI
H.C.F.
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If the numbers did not have
common prime factors, their
HCF is 1
49 = 72
36 = 22 x 32
Their HCF is 1
Ronald HUI
H.C.F.
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How about 3 or more numbers?
18 = 2 x 32
24 = 23 x 3
30 = 2 x 3 x 5
Their HCF is
=2x3 =6
Ronald HUI
L.C.M.
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Least Common Multiple
(最小公倍數)
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Multiples of 4:
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Multiples of 6:
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6, 12, 18, 24, 30, …
Common multiple of 4 and 6:
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4, 8, 12, 16, 20, 24, 28, …
12, 24, …
L.C.M. of 4 and 6 is 12
Ronald HUI
L.C.M.
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We can find L.C.M. from Index
Notation! (用指數記數法找LCM)
4 =2x2
= 22
 6 =2x3
=2x3
 We know L.C.M. of 4 and 6 is 12
 12 = 2 x 2 x 3
= 22 x 3
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Can you find the rule?
Ronald HUI
L.C.M.
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Another example
24 = 2 x 2 x 2 x 3 = 23 x 3
 36 = 2 x 2 x 3 x 3 = 22 x 32
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Can you guess the LCM?
Their LCM is
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2 x 2 x 2 x 3 x 3 = 23 x 3 2
= 72
Ronald HUI
L.C.M.
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Another try: LCM of 28 and 30
28 = 22 x 7
30 = 2 x 3 x 5
Can you guess the HCF?
Their LCM is
= 22 x 3 x 5 x 7 = 420
Ronald HUI
L.C.M.
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If the numbers did not have
common prime factors, their
LCM is the product of them
20 = 22 x 5
63 = 32 x 7
Their HCF is 1
Their LCM is 20 x 63 = 1260
Ronald HUI
L.C.M.
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How about 3 or more numbers?
18 = 2 x 32
24 = 23 x 3
30 = 2 x 3 x 5
Their LCM is
= 23 x 32 x 5 = 360
Ronald HUI
Time for Practice
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Find H.C.F. and L.C.M. of the
following pairs
10, 15
 26, 39
 36, 54
 56, 98
 91, 117
 24, 36, 60
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Ronald HUI
Reminder
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BCA Online Exercise
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Standard Homework (II)
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Deadline: 10 Sep (Mon)
Deadline: 17 Sep (Mon)
PowerPoint files
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http://personal.tsss.edu.hk/roh
Ronald HUI
Good Luck!
Enjoy the world of
Mathematics!
Ronald HUI