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

2. Introduction to Directed Numbers
Numbers have two parts:
Size or Magnitude
Sign or Direction
In the figure:
– 4 F

3. The Four Basic Operations
Addition:
Say “3 plus 7” or “The sum of 3 and 7” or “Add 3 to 7”
Subtraction: 3 – 7
Say “3 minus 7” or “The difference of 3 and 7” or “Subtract 7 from 3”
Multiplication: 3 × 7
Say “3 times 7” or “The product of 3 and 7” or “Multiply 3 and 7”
Division: 3 ÷ 7
Say “3 divided by 7” or “The quotient of 3 and 7” or “Divide 3 by 7”

4. Rules to Remember (p.1.39) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )
正正得正 負負得正
正負得負 負正得負

5. Addition and Subtraction
+3 + (+9) =
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
= 12
–7 + (+12)
= –7 + 12
= 5

6. Addition and Subtraction
+3 + (– 9)
= 3 – 9
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
= – 6
7 – (+12)
= 7 – 12
= – 5

7. Addition and Subtraction
– 6 + (– 7)
= – 6 – 7
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
= – 13
– 3 – (+3)
= – 3 – 3
= – 6

8. Addition and Subtraction
7 – (– 7) =
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
= 14
– 3 – (–3)
= – 3 + 3
= 0

9. Rules to Remember (p.1.39) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )
正正得正 負負得正
正負得負 負正得負

10. Multiplication 3  4 = 12 2  4 = 8 1  4 = 4 0  4 = 0 – 1  4 = ?
3  4 = 12
2  4 = 8
1  4 = 4
0  4 = 0
– 1  4 = ?
– 2  4 = ?
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
– 4
– 8

11. Multiplication 3  (– 5) = – 15 2  (– 5) = – 10 1  (– 5) = – 5
3  (– 5) = – 15
2  (– 5) = – 10
1  (– 5) = – 5
0  (– 5) = 0
– 1  (– 5) = ?
– 2  (– 5) = ?
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – ) 5 10

12. 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)

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

14. Rules to Remember (p.1.39) ( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )
正正得正 負負得正
正負得負 負正得負

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

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

17. Time for Practice Page 1.36 of Textbook 1A Page 1.37 of Textbook 1A
Class Practice
Page 1.37 of Textbook 1A
Questions 4 – 17

18. Reminder Extra Tutorial Standard Homework Quiz (Chapter 1)
26 Sep (Tue)
3 students (Must come)
Standard Homework
1-B1: 26 Sep (Tue)
1-C1: 29 Sep (Fri)
STAR: 29 Sep (Fri)
Quiz (Chapter 1)
4 Oct (Wed)

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