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Mathematics

Mathematics. Ronald Hui Tak Sun Secondary School. Reminder. Corrections of Dictation 1 and Standard Homework (I) Deadline: 14 Sep (Fri) Standard Homework (II) Deadline: 17 Sep (Mon) Standard Homework (III) Deadline: 18 Sep (Tue). Reminder. Corrections of Standard Homework (II) and (III)

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Mathematics

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  1. Mathematics Ronald Hui Tak Sun Secondary School

  2. Reminder • Corrections of Dictation 1 and Standard Homework (I) • Deadline: 14 Sep (Fri) • Standard Homework (II) • Deadline: 17 Sep (Mon) • Standard Homework (III) • Deadline: 18 Sep (Tue) Ronald HUI

  3. Reminder • Corrections of Standard Homework (II) and (III) • Deadline: 19 Sep (Wed) • Open Book Quiz (Chapter 0) • Deadline: 19 Sep (Wed) • Closed Book Quiz (Chapter 0), Dictation 2 and Folder Checking • Last week of September Ronald HUI

  4. Revision for Quiz • Textbook 1A • Pages 2 – 31 • Workbook 1A • Pages 1 – 16 • Summer Revision • Pages 1 – 19 • My PowerPoint files • Your own notes Ronald HUI

  5. Mathematics • How to get better results? • Understand first! • Do correction! • Dictation: 10 times • Test/Homework: Other colour pens • Revise! • Try more (workbook) Ronald HUI

  6. Revision • Prime numbers (質數) • 2,3,5,7,11,13,17,19,23,… • Multiples (倍數) • Multiples of 2: 2, 4, 6, 8, … • Multiples of 3: 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, … Ronald HUI

  7. 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 Ronald HUI

  8. Prime Factors (p.9) • Prime factors (質因子) • Afactor which is prime • Factors of 18: 1, 2, 3, 6, 9, 18 • Prime factors of 18: 2, 3 • All numbers can be expressed as a product of prime factors only – How? Ronald HUI

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

  10. Index Notation (p.9) • 32 = 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

  11. 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 x 3 x 3 x 3 x 5 x 5 = 27 x 33x 52 Ronald HUI

  12. Time for Practice • Pages 10 – 11 of Textbook 1A • Class Practice • Questions 6 – 9 • Pages 6 – 7 of Workbook 1A • Questions 5 – 9 Ronald HUI

  13. Mathematics nearby • What is Google? • http://zh.wikipedia.org/zh-hk/Google#.E5.BB.BA.E7.AB.8B • Google was mis-spelt from googol! • Googol = 10100 = 1000000…00000 (100 zeros!) Ronald HUI

  14. H.C.F. • 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

  15. H.C.F. • We can find H.C.F. from Index Notation! (用指數記數法找HCF) • 18=2x 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

  16. H.C.F. • Another example • 24 = 2 x 2 x 2 x 3 = 23 x 3 • 36=2x 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

  17. 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 Ronald HUI

  18. 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 Ronald HUI

  19. 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 = 2 x 3 = 6 Ronald HUI

  20. L.C.M. • 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

  21. L.C.M. • We can find L.C.M. from Index Notation! (用指數記數法找LCM) • 4=2x 2 = 22 • 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

  22. L.C.M. • Another example • 24 = 2 x 2 x 2 x 3 = 23 x 3 • 36=2x 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

  23. 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 Ronald HUI

  24. 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 Ronald HUI

  25. 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 Ronald HUI

  26. 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

  27. Reminder • BCA Online Exercise • Deadline: 10 Sep (Mon) • Standard Homework (II) • Deadline: 17 Sep (Mon) • PowerPoint files • http://personal.tsss.edu.hk/roh Ronald HUI

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

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