(Friday) - Index Notation - Tak Sun Secondary School Personal Web
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Transcript (Friday) - Index Notation - Tak Sun Secondary School Personal Web
Mathematics
Ronald Hui
Tak Sun Secondary School
Reminder
Corrections of Dictation 1 and
Standard Homework (I)
Standard Homework (II)
Deadline: 14 Sep (Fri)
Deadline: 17 Sep (Mon)
Standard Homework (III)
Deadline: 18 Sep (Tue)
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Reminder
Corrections of Standard
Homework (II) and (III)
Open Book Quiz (Chapter 0)
Deadline: 19 Sep (Wed)
Deadline: 19 Sep (Wed)
Closed Book Quiz (Chapter 0),
Dictation 2 and Folder Checking
Last week of September
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Revision for Quiz
Textbook 1A
Workbook 1A
Pages 1 – 16
Summer Revision
Pages 2 – 31
Pages 1 – 19
My PowerPoint files
Your own notes
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Mathematics
How to get better results?
Understand first!
Do correction!
Dictation: 10 times
Test/Homework: Other colour pens
Revise!
Try more (workbook)
Ronald HUI
Revision
Prime numbers (質數)
2, 3, 5, 7, 11, 13, 17, 19, 23, …
Multiples (倍數)
Multiples of 2:
Multiples of 3:
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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Revision
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
Factors of 18: 1, 2, 3, 6, 9, 18
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Prime Factors (p.9)
Prime factors (質因子)
Factors of 18: 1, 2, 3, 6, 9, 18
A factor which is prime
Prime factors of 18: 2, 3
All numbers can be expressed
as a product of prime factors
only – How?
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Index Notation (p.9)
Factors of 18: 1, 2, 3, 6, 9, 18
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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(指數記數法)
Index Notation (p.9)
32 = 3 x 3
33 = 3 x 3 x 3
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
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Index Notation (p.9)
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
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Time for Practice
Pages 10 – 11 of Textbook 1A
Class Practice
Questions 6 – 9
Pages 6 – 7 of Workbook 1A
Questions 5 – 9
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Mathematics nearby
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.
Highest Common Factor
(最大公因數)
Factors of 18:
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
Common factors of 18 and 24:
1, 2, 3, 6, 9, 18
2, 3, 6
H.C.F. of 18 and 24 is 6
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H.C.F.
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
Can you find the rule?
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H.C.F.
Another example
24 = 2 x 2 x 2 x 3 = 23 x 3
36 = 2 x 2 x 3 x 3 = 22 x 32
Can you guess the HCF?
Their HCF is
2x2x3
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= 22 x 3
= 12
H.C.F.
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
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H.C.F.
If the numbers did not have
common prime factors, their
HCF is 1
49 = 72
36 = 22 x 32
Their HCF is 1
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H.C.F.
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
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L.C.M.
Least Common Multiple
(最小公倍數)
Multiples of 4:
Multiples of 6:
6, 12, 18, 24, 30, …
Common multiple of 4 and 6:
4, 8, 12, 16, 20, 24, 28, …
12, 24, …
L.C.M. of 4 and 6 is 12
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L.C.M.
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
Can you find the rule?
Ronald HUI
L.C.M.
Another example
24 = 2 x 2 x 2 x 3 = 23 x 3
36 = 2 x 2 x 3 x 3 = 22 x 32
Can you guess the LCM?
Their LCM is
2 x 2 x 2 x 3 x 3 = 23 x 3 2
= 72
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L.C.M.
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
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L.C.M.
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
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L.C.M.
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
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Time for Practice
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
Ronald HUI
Reminder
BCA Online Exercise
Standard Homework (II)
Deadline: 10 Sep (Mon)
Deadline: 17 Sep (Mon)
PowerPoint files
http://personal.tsss.edu.hk/roh
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Good Luck!
Enjoy the world of
Mathematics!
Ronald HUI