1. Ronald Hui Tak Sun Secondary School
Mathematics
Ronald Hui
Tak Sun Secondary School

2. Mathematics Keep silence in the class No talking when I talk
What should be ready in the next lesson?
Textbook
Erasable Pens/Pencils
Notebook & folder
Ronald HUI

3. Index Notation (p.0.10) Factors of 18: 1, 2, 3, 6, 9, 18 18 = 2 x 9
Prime factors of 18: 2, 3
18 = 2 x 9
= 2 x 3 x 3
18 = 2 x  Index Notation
32 = 3 x 3 (指數記數法)
3 is base 底
2 is index 指數
Ronald HUI

4. Index Notation (p.0.10) 32 = 3 x 3 33 = 3 x 3 x 3 34 = 3 x 3 x 3 x 3
3 to the power 2, 3 squared (平方)
33 = 3 x 3 x 3
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

5. Index Notation (p.0.10)
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 x 3 x 3 x 3 x 5 x 5
= 27 x 33 x 52
Ronald HUI

6. Time for Practice Standard Homework 0-B1 PowerPoint files Page 1
Ronald HUI

7. H.C.F. (p.0.11) Highest Common Factor (最大公因數) Factors of 18:
1, 2, 3, 6, 9, 18
Factors of 24:
1, 2, 3, 4, 6, 8, 12, 24
Common factors of 18 and 24:
2, 3, 6
H.C.F. of 18 and 24 is 6
Ronald HUI

8. H.C.F. (p.0.11) 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 = 2 x 3
Can you find the rule?
Ronald HUI

9. H.C.F. (p.0.11) Another example Can you guess the HCF? Their HCF is
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
2 x 2 x 3 = 22 x 3
= 12
Ronald HUI

10. H.C.F. (p.0.11) Another try: HCF of 700 and 720 700 = 22 x 52 x 7
Can you guess the HCF?
Their HCF is
= 22 x 5 = 20
Ronald HUI

11. H.C.F. (p.0.11)
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

12. H.C.F. (p.0.11) How about 3 or more numbers? 18 = 2 x 32 24 = 23 x 3
Their HCF is
= 2 x 3 = 6
Ronald HUI

13. L.C.M. (p.0.12) Least Common Multiple (最小公倍數) Multiples of 4:
4, 8, 12, 16, 20, 24, 28, …
Multiples of 6:
6, 12, 18, 24, 30, …
Common multiple of 4 and 6:
12, 24, …
L.C.M. of 4 and 6 is 12
Ronald HUI

14. L.C.M. (p.0.12) We can find L.C.M. from Index Notation! (用指數記數法找LCM)
6 = 2 x 3 = 2 x 3
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

15. L.C.M. (p.0.12) Another example Can you guess the LCM? Their LCM is
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 32
= 72
Ronald HUI

16. L.C.M. (p.0.12) 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

17. L.C.M. (p.0.12)
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

18. L.C.M. (p.0.12) How about 3 or more numbers? 18 = 2 x 32 24 = 23 x 3
Their LCM is
= 23 x 32 x 5 = 360
Ronald HUI

19. 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

20. Time for Practice Standard Homework 0-B1 Textbook 1A Page 0.14
4 pages (Deadline: 18 Sep, Mon)
Textbook 1A Page 0.14
Exercise II Q1-9
Textbook 1A Page 0.13
Class Practice
PowerPoint files
Ronald HUI

21. Enjoy the world of Mathematics!
Good Luck!
Enjoy the world of Mathematics!
Ronald HUI