Ronald Hui Tak Sun Secondary School Mathematics Ronald Hui Tak Sun Secondary School

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

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 32  Index Notation 32 = 3 x 3 (指數記數法) 3 is base 底 2 is index 指數 Ronald HUI

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

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

Time for Practice Standard Homework 0-B1 PowerPoint files Page 1 http://personal.tsss.edu.hk/roh Ronald HUI

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

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

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

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

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

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

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

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

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

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

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

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

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

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 http://personal.tsss.edu.hk/roh Ronald HUI

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