1. Mathematics Ronald Hui Tak Sun Secondary School

2. Ronald HUI Reminder Standard Homework (II) Standard Homework (II) Deadline: Today! Deadline: Today! Standard Homework (III) Standard Homework (III) Deadline: 18 Sep (Tue) Deadline: 18 Sep (Tue) Open Book Quiz (Chapter 0) Open Book Quiz (Chapter 0) Deadline: 19 Sep (Wed) Deadline: 19 Sep (Wed) Closed Book Quiz (Chapter 0), Dictation 2 and Folder Checking Closed Book Quiz (Chapter 0), Dictation 2 and Folder Checking Last week of September Last week of September

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

4. Ronald HUI Revision Prime numbers ( 質數 ) Prime numbers ( 質數 ) 2, 3, 5, 7, 11, 13, 17, 19, 23, … 2, 3, 5, 7, 11, 13, 17, 19, 23, … Multiples ( 倍數 ) Multiples ( 倍數 ) Multiples of 2:2, 4, 6, 8, … Multiples of 2:2, 4, 6, 8, … Multiples of 3:3, 6, 9, 12, … Multiples of 3:3, 6, 9, 12, … Factors ( 因子 ) Factors ( 因子 ) 2 is a factor of 2, 4, 6, 8, … 2 is a factor of 2, 4, 6, 8, … 3 is a factor of 3, 6, 9, 12, … 3 is a factor of 3, 6, 9, 12, …

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

6. Ronald HUI Revision Index notation is very helpful in long expression of prime factors Index notation is very helpful in long expression of prime factors 432 = 2 x 2 x 2 x 2 x 3 x 3 x 3 432 = 2 x 2 x 2 x 2 x 3 x 3 x 3 = 2 4 x 3 3 = 2 4 x 3 3 86400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 86400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 = 2 7 x 3 3 x 5 2 = 2 7 x 3 3 x 5 2

7. Ronald HUI Revision We can find H.C.F. from Index Notation! ( 用指數記數法找 HCF) 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 3 2 18 = 2 x 3 x 3= 2 x 3 2 24 = 2 x 2 x 2 x 3= 2 3 x 3 24 = 2 x 2 x 2 x 3= 2 3 x 3 We know H.C.F. of 18 and 24 is 6 We know H.C.F. of 18 and 24 is 6 6 = 2 x 3 6 = 2 x 3 Can you find the rule? Can you find the rule?

8. Ronald HUI Revision We can find L.C.M. from Index Notation! ( 用指數記數法找 LCM) We can find L.C.M. from Index Notation! ( 用指數記數法找 LCM) 4 = 2 x 2= 2 2 4 = 2 x 2= 2 2 6 = 2 x 3= 2 x 3 6 = 2 x 3= 2 x 3 We know L.C.M. of 4 and 6 is 12 We know L.C.M. of 4 and 6 is 12 12 = 2 x 2 x 3= 2 2 x 3 12 = 2 x 2 x 3= 2 2 x 3 Can you find the rule? Can you find the rule?

9. Ronald HUI Revision If the numbers did not have common prime factors, their HCF is 1 and their LCM is the product of them If the numbers did not have common prime factors, their HCF is 1 and their LCM is the product of them 20 = 2 2 x 5 20 = 2 2 x 5 63 = 3 2 x 7 63 = 3 2 x 7 Their HCF is 1 Their HCF is 1 Their LCM is 20 x 63 = 1260 Their LCM is 20 x 63 = 1260

10. Ronald HUI Fractions (p.11) Fractions Fractions  Numerator ( 分子 )  Fraction line ( 分數線 )  Denominator ( 分母 ) 3 over 4 3 over 4 3 is divided by 4 3 is divided by 4 3  4 3  4 Three-quarter (quarter = ¼) Three-quarter (quarter = ¼)

11. Ronald HUI Fractions (p.12) Types of Fractions Types of Fractions Proper fraction ( 真分數 ) Proper fraction ( 真分數 ) Improper fraction ( 假分數 ) Improper fraction ( 假分數 ) Mixed number ( 帶分數 ) Mixed number ( 帶分數 ) http://zh.wikipedia.org/zh- hk/%E5%88%86%E5%BC%8F#.E5.88.86.E9.A1.9E http://zh.wikipedia.org/zh- hk/%E5%88%86%E5%BC%8F#.E5.88.86.E9.A1.9E http://zh.wikipedia.org/zh- hk/%E5%88%86%E5%BC%8F#.E5.88.86.E9.A1.9E http://zh.wikipedia.org/zh- hk/%E5%88%86%E5%BC%8F#.E5.88.86.E9.A1.9E

12. Ronald HUI Comparing Fractions The following fractions are equal The following fractions are equal We can then compare different fractions We can then compare different fractions

13. Ronald HUI Addition, Subtraction Use improper fractions Use improper fractions Change to same denominators Change to same denominators Do operations on numerators Do operations on numerators LCM of 3, 2, 4 is 12

14. Ronald HUI Multiplication, Division Use improper fractions Use improper fractions Use reciprocal for division Use reciprocal for division Multiply numerators and denominators separately Multiply numerators and denominators separatelySimplestForm!

15. Ronald HUI Time for Practice Pages 21 of Textbook 1A Pages 21 of Textbook 1A Questions 16 – 20 Questions 16 – 20 Ascending ( 遞升 )  increasing Ascending ( 遞升 )  increasing Descending ( 遞降 )  decreasing Descending ( 遞降 )  decreasing Pages 10 – 12 of Workbook 1A Pages 10 – 12 of Workbook 1A Questions 7 – 10 Questions 7 – 10

16. Ronald HUI Reminder BCA Online Exercise BCA Online Exercise Deadline: 10 Sep (Mon) Deadline: 10 Sep (Mon) Standard Homework (III) Standard Homework (III) Deadline: 18 Sep (Tue) Deadline: 18 Sep (Tue) PowerPoint files PowerPoint files http://personal.tsss.edu.hk/roh http://personal.tsss.edu.hk/roh http://personal.tsss.edu.hk/roh

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