1A_Ch1(1)

1
1A_Ch1(1)
2
1A_Ch1(2)
1.1 The Concept and Applications of Directed
Numbers
Index
3
1A_Ch1(3)
1.2 Addition and Subtraction of Directed Numbers
Index
4
1A_Ch1(4)
1.3 Multiplication and Division of Directed
Numbers
Index
5
1A_Ch1(5)
1.1 The Concept and Applications of Directed
Numbers

• Example

The Applications of Directed Numbers
A)

1. A number which carries a positive () sign or a
   negative () sign is called a directed number.
2. The sign attached to a positive number can be
   omitted but a negative number must carry the
   sign.

Index

• Index 1.1

6
1A_Ch1(6)
1.1 The Concept and Applications of Directed
Numbers
Answer the following questions. Use positive
numbers to represent increases in temperature and
negative numbers to represent decreases in
temperature.
(a) An increase of 5C in temperature (b) A
decrease of 2C in temperature (c) An increase of
8C in temperature

1. 5C
2. 2C
3. 8C

• Key Concept 1.1.1

Index
7
1A_Ch1(7)
1.1 The Concept and Applications of Directed
Numbers

• Example

Ordering of Directed Numbers on the Number Line
B)

1. A number line is a straight line with directed
   numbers marked on it in a certain order.

2. On a vertical number line, the values of the
directed numbers increase from bottom to top.
3. On a horizontal number line, the values of the
directed numbers increase from left to right.
Index

• Index 1.1

8
1A_Ch1(8)
1.1 The Concept and Applications of Directed
Numbers
Arrange the following numbers in descending order
and mark them on the number line below.
3, 2, 5, 10, 3, 0
10, 5, 3, 0, 2, 3
3
0
3
5
10
2
Index
9
1A_Ch1(9)
1.1 The Concept and Applications of Directed
Numbers
On the horizontal number line given below, find
the directed numbers represented by the letters
A, B, C, D and E.
8 7 A B 4 3 2 C D 1 2 3
E 5
6
5
A
B
C
D
0
E
4
1

• Key Concept 1.1.2

Index
10
1A_Ch1(10)
1.2 Addition and Subtraction of Directed Numbers

• Example

Addition of Directed Numbers on a Vertical Number
Line
A)
On a vertical number line, 1. if we add a
positive number a to a given number, we move
up a units from the given number to obtain the
sum 2. if we add a negative number b to a
given number, we move down b units from the
given number to obtain the sum.
Index

• Index 1.2

11
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(11)
Find the sum of each of the following.
(a) (2) 5 (b) (3) 5 (c) (4) 5
(5)
(5)
(5)
(2) 5
(3) 5
(4) 5
3
2
1
Index
12
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(12)
Find the sum of each of the following.
(a) 0 (4) (b) 1 (4) (c) 1 (4)
(4)
(4)
(4)
0 (4)
4
1 (4)
3
5
1 (4)
Index
13
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(13)
Use a vertical number line to find the sum of
each of the following.

• (4) 5 (b) (7) 2
• (c) 7 (3) (d) 4 (5)

(4) 5
(7) 2
1
5
(5)
(2)
Index
14
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(14)
(3)
(5)
7 (3)
4 (5)
4
1
Index
15
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(15)
With the help of a vertical number line, find the
sum of (1) (4) (5).
With the help of the vertical number line,
(1) (4)
3
? (1) (4) (5)
(3) (5)
(4)
2
Index
16
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(16)
Yesterday John borrowed 5 from his classmate and
7 from his brother. This morning his mother gave
him 13. Use directed numbers to find out how
much John has after he pays back the borrowed
money.
The amount that John had after borrowing money
(5) (7)
(7)
12
Index
17
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(17)

• Back to Question

The amount that he has now (12) 13
1
(13)

• Key Concept 1.2.1

Index
18
1A_Ch1(18)
1.2 Addition and Subtraction of Directed Numbers
Subtraction of Directed Numbers on a Number Line
B)
On a vertical number line, 1. if we subtract a
positive number a to a given number, we move
down a units from the given number to obtain
the difference 2. if we subtract a negative
number b to a given number, we move up b
units from the given number to obtain the
difference.
Index
19
1A_Ch1(19)
1.2 Addition and Subtraction of Directed Numbers

• Example

Subtraction of Directed Numbers on a Number Line
B)
Note In general,
Index

• Index 1.2

20
1A_Ch1(20)
1.2 Addition and Subtraction of Directed Numbers
Find the difference of each of the following.
(a) 1 (3) (b) 1 (3) (c) (1) (3)
(3)
(3)
(3)
1 (3)
2
1 (3)
4
(1) (3)
2
Index
21
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(21)
Use a vertical number line to find the difference
of each of the following.

• 4 (5) (b) (4) (6)
• (c) 2 (3) (d) (6) (4)

4 (5)
(4) (6)
1
10
(5)
(6)
Index
22
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(22)

• Back to Question

(3)
(4)
2 (3)
(6) (4)
5
2
Index
23
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(23)
Jane has 3 more than Winnie while Winnie has 7
less than May. Does Jane have more or less money
than May? By how much?
The amount by which Jane has more than May
(3) (7)
4
(7)
i.e. Jane has 4 less than May.
Index
24
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(24)
On a certain day in Beijing, the temperature in
the morning was 5C. It was expected to drop to
3C at midnight.
(a) By how many degrees was the temperature
expected to drop? (b) If the temperature at
midnight was 2C higher than expected, what was
the actual drop in temperature?
Index
25
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(25)

• Back to Question

• The expected drop in temperature
• 5 (3) C

(3)
8C
(b) The actual drop in temperature 8 (2)
C
(2)
6C

• Key Concept 1.2.2

Index
26
1A_Ch1(26)
1.2 Addition and Subtraction of Directed Numbers
Addition and Subtraction of Directed Numbers
Using a Calculator
C)

1. To input a positive number, we just press the key
   corresponding to the numerical value of the
   number.

Index
27
1A_Ch1(27)
1.2 Addition and Subtraction of Directed Numbers

• Example

Use a calculator to express the following
directed numbers.
C)
Directed number
Keying Sequence
256
1 820
Index

• Index 1.2

28
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(28)
Use a calculator to evaluate each of the
following.
(a) 21 (60)
? 21 (60)
39
Index
29
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(29)

• Back to Question

(b) 34 (16)
34
16
? 34 (16)
18
(c) 5.2 9.3
9.3
5.2
? 5.2 9.3
4.1
Index
30
1.2 Addition and Subtraction of Directed Numbers
1A_Ch1(30)

• Back to Question

1
3
5
2

• Key Concept 1.2.3

Index
31
1A_Ch1(31)
1.2 Addition and Subtraction of Directed Numbers

• Example

Addition and Subtraction of Directed Numbers by
Removing Brackets
D)
? Rules for removing brackets attached to
directed numbers
Index

• Index 1.2

32
1A_Ch1(32)
1.2 Addition and Subtraction of Directed Numbers
Find the values of the following.

• 14 (25) (b) 14 (25)
• (c) 14 (25) (d) 14 (25)

(a) 14 (25)
14 25
(b) 14 (25)
14 25
39
39
(c) 14 (25)
14 25
(d) 14 (25)
14 25
11
11

• Key Concept 1.2.4

Index
33
1A_Ch1(33)
1.3 Multiplication and Division of Directed
Numbers

• Example

Multiplication of Directed Numbers
A)
? For positive numbers a, b and negative
numbers a, b,
Index

• Index 1.3

34
1A_Ch1(34)
1.3 Multiplication and Division of Directed
Numbers
Find the value of each of the following.

1. 4 3 (b) (4) 3 (c) 4 (3)

12
(a) 4 x 3
12
(b) (4) 3
(c) 4 (3)
12
Index
35
1A_Ch1(35)
1.3 Multiplication and Division of Directed
Numbers
Find the value of each of the following.

1. (1) (5) (b) (2) (5)

5
(a) (1) (5)
10
(b) (2) (5)
Index
36
1A_Ch1(36)
1.3 Multiplication and Division of Directed
Numbers
Find the value of each of the following.

1. (9) (6) (b) (5) (7) (2)

1. (9) (6)

(9 6) 54
(b) (5) (7) (2)
(5 7) (2) (35) (2) (35 2)
70

• Key Concept 1.3.1

Index
37
1A_Ch1(37)
1.3 Multiplication and Division of Directed
Numbers

• Example

Division of Directed Numbers
B)
? For positive numbers a, b and negative
numbers a, b,
Index

• Index 1.3

38
1A_Ch1(38)
1.3 Multiplication and Division of Directed
Numbers
Find the value of each of the following.
6
6
6
6
Index
39
1A_Ch1(39)
1.3 Multiplication and Division of Directed
Numbers
Find the value of each of the following.
(42 7) 6

1. (42) (7)

(48 6) 8
(b) (48) (6)
Index
40
1A_Ch1(40)
1.3 Multiplication and Division of Directed
Numbers

• Back to Question

(57 3) 19
(c) (57) (3)
(12 2) (3) (6) (3) (6 3) 2
(d) (12) (2) (3)

• Key Concept 1.3.2

Index
41
1A_Ch1(41)
1.3 Multiplication and Division of Directed
Numbers
Multiplication and Division of Directed Numbers
Using a Calculator
C)
Index
42
1A_Ch1(42)
1.3 Multiplication and Division of Directed
Numbers

• Example

Use a calculator to evaluate each of the
following.
C)
Keying Sequence
Expression
10 11
(5) 3
20 (4)
Index

• Index 1.3

43
1A_Ch1(43)
1.3 Multiplication and Division of Directed
Numbers
Use a calculator to evaluate each of the
following.
(a) (14) 12 (8)
12
14
8
? (14) 12 (8)
21
Index
44
1A_Ch1(44)
1.3 Multiplication and Division of Directed
Numbers

• Back to Question

(b) (50) 9 15 0
9
50
15
0
? (50) 9 15 0
0
Index
45
1A_Ch1(45)
1.3 Multiplication and Division of Directed
Numbers

• Back to Question

4.9
37
1.85
0.25
392

• Key Concept 1.3.3

Index
46
1A_Ch1(46)
1.3 Multiplication and Division of Directed
Numbers

• Example

Mixed Operations of Directed Numbers Using a
Calculator
D)
? Calculator can be used to evaluate an
expression which may involve addition,
subtraction, multiplication and division.
Index

• Index 1.3

47
1A_Ch1(47)
1.3 Multiplication and Division of Directed
Numbers
Use a calculator to evaluate each of the
following.

1. 14 (3 4) (b) (3) (5 2)

(a) 14 (3 4)
14
3
4
? 14 (3 4)
2
Index
48
1A_Ch1(48)
1.3 Multiplication and Division of Directed
Numbers

• Back to Question

(b) (3) (5 2)
3
5
2
? (3) (5 2)
21
Index
49
1A_Ch1(49)
1.3 Multiplication and Division of Directed
Numbers
Use a calculator to evaluate each of the
following.

1. 0 (15) (10 5) (b) (28) 7 13 (13)

(a) 0 (15) (10 5)
15
0
5
10
? 0 (15) (10 5)
0
Index
50
1A_Ch1(50)
1.3 Multiplication and Division of Directed
Numbers

• Back to Question

(b) (28) 7 13 (13)
28
7
13
13
? (28) 7 13 (13) is meaningless.
Index
51
1A_Ch1(51)
1.3 Multiplication and Division of Directed
Numbers
There are 10 multiple choice questions in a test.
3 marks will be given for a correct answer, 2
marks for a wrong answer and no marks if the
question is unanswered.
(a) If Siu Ming answered all the questions in the
test and got 6 correct answers, find his final
score. (b) If the final score of Tai Kwong was
9 marks and he only got 1 correct answer, how
many of his answers were wrong?

• Soln

• Soln

Index
52
1A_Ch1(52)
1.3 Multiplication and Division of Directed
Numbers

• Back to Question

(a) The total score obtained for the 6 correct
answers 6 3 marks 18 marks The total
score obtained for the wrong answers (10 6)
(2) marks 8 marks
? Siu Mings final score
18 (8) marks 10 marks
Index
53
1A_Ch1(53)
1.3 Multiplication and Division of Directed
Numbers

• Back to Question

(b) The score obtained for 1 correct answer 1
3 marks 3 marks Since Tai Kwongs final
score was 9 marks, the total score obtained for
his wrong answers (9) 3 marks 12 marks
? The number of wrong answers
(12) (2)

• Key Concept 1.3.4

6
Index