Form 1 Mathematics Chapter 1 Directed Numbers Form 1 Mathematics Chapter 1

Result of Summer Homework Quiz Highest: 30 (WU SHAN Hao Yi) Lowest: 10 Average: 21.4 Number of students below 24: 24 Major Problems Not serious enough No units No answer (also in MC!)

Revision on Directed Numbers What does the negative mean? Money in bank: +$1,100 – $950 Students in class (36 students in class) Mon: – 2; Tue: – 1; Wed: 0; Thu: – 3; Fri:0 World time: Sydney: +2; Rome: – 6; London: – 8; New York: – 13 Stairs in the building (up is “+”): Go up 3 steps: +3; Go down 4 steps: – 4

Directed numbers on a number line How do we write & say this? + – -6 -2 4 7 7 0 -2 -6 > > > This called “Descending Order” -2 0 4 7 < < < This called “Ascending Order”

Rules to Remember (p.50) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) 正正得正 負負得正 正負得負 負正得負

Addition +3 + (+9) = 3 + 9 = 12 –7 + (+12) = –7 + 12 = 5 = 3 + 9 ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) = 12 –7 + (+12) = –7 + 12 = 5

Addition +3 + (– 9) = 3 – 9 = – 6 – 6 + (– 7) = – 6 – 7 = – 13 = 3 – 9 ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) = – 6 – 6 + (– 7) = – 6 – 7 = – 13

Subtraction 7 – (+12) = 7 – 12 = – 5 – 3 – (+3) = – 3 – 3 = – 6 = 7 – 12 ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) = – 5 – 3 – (+3) = – 3 – 3 = – 6

Subtraction 7 – (– 7) = 7 + 7 = 14 – 3 – (–3) = – 3 + 3 = 0 = 7 + 7 ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) = 14 – 3 – (–3) = – 3 + 3 = 0

Addition and Subtraction (+ A) + (+ B) = A + B (+ A) + (– B) = A – B (– A) + (+ B) = – A + B (– A) + (– B) = – A – B ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) (+ A) – (+ B) = A – B (+ A) – (– B) = A + B (– A) – (+ B) = – A – B (– A) – (– B) = – A + B

Time for Practice Page 53 of Textbook 1A Page 22 of Workbook 1A Questions 18 – 22 Page 22 of Workbook 1A Questions 8 – 10

Rules to Remember (p.50) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) 正正得正 負負得正 正負得負 負正得負

Multiplication (+ 7)  (+ 7) = 7  7 = 49 (– 8)  3 = – 8  3 = – 24 = 7  7 ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) = 49 (– 8)  3 = – 8  3 = – 24 Same as (– 8) + (– 8) + (– 8) = (– 24)

Multiplication 4  (– 2) = – (4  2) = – 8 (– 8)  (– 7) = + (8  7) = – (4  2) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) = – 8 (– 8)  (– 7) = + (8  7) = 56 Note: (– 8)  (– 7) = (– 8) (– 7)

Division (+ 7)  (+ 7) = 7  7 = 1 (– 9)  3 = – 9  3 = – 3 = 7  7 ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) = 1 (– 9)  3 = – 9  3 = – 3 Note: (– 9) = (– 3) + (– 3) + (– 3)

Division 4  (– 2) = – (4  2) = – 2 (– 12)  (– 6) = + (12  6) = 2 = – (4  2) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) = – 2 (– 12)  (– 6) = + (12  6) = 2

Multiplication and Division (+ A)  (+ B) = A  B (+ A)  (– B) = – (A  B) (– A)  (+ B) = – (A  B) (– A)  (– B) = A  B ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + ) ( + ) ( – ) = ( – ) ( – ) ( + ) = ( – ) (+ A)  (+ B) = A  B (+ A)  (– B) = – (A  B) (– A)  (+ B) = – (A  B) (– A)  (– B) = A  B

Time for Practice Page 62 of Textbook 1A Page 24 of Workbook 1A Questions 10 – 16 Page 24 of Workbook 1A Questions 5 – 7

Operations of Directed Numbers Same sign “+” Different sign “–” http://zh.wikipedia.org/wiki/%E8%B4%9F%E6%95%B0#.E8.B4.9F.E6.95.B0.E7.9A.84.E5.9B.9B.E5.89.87.E9.81.8B.E7.AE.97

Reminder Standard Homework (II) Open Book Quiz (Chapter 1) Today! Open Book Quiz (Chapter 1) Close Book Quiz (Chapter 1) 17 Oct (Wed)

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