1A_Ch1(1)

1.1The Concept and Applications of Directed Numbers A The Applications of Directed Numbers B Ordering of Directed Numbers on the Number Line Index 1A_Ch1(2)

1.2Addition and Subtraction of Directed Numbers Index 1A_Ch1(3) A Addition of Directed Numbers on a Vertical Number Line Subtraction of Directed Numbers on a Number Line B Addition and Subtraction of Directed Numbers Using a Calculator C Addition and Subtraction of Directed Numbers by Removing Brackets D

1.3Multiplication and Division of Directed Numbers Index 1A_Ch1(4) A Multiplication of Directed Numbers Division of Directed Numbers B Multiplication and Division of Directed Numbers Using a Calculator C Mixed Operations of Directed Numbers Using a Calculator D

The Applications of Directed Numbers 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 A) 1A_Ch1(5) 1.1The Concept and Applications of Directed Numbers + Index 1.1Index ExampleExample

Answer the following questions. Use positive numbers to represent increases in temperature and negative numbers to represent decreases in temperature. Index 1A_Ch1(6) 1.1The Concept and Applications of Directed Numbers (a)An increase of 5°C in temperature (b)A decrease of 2°C in temperature (c)An increase of 8°C in temperature (a)+5°C (b)–2°C (c)+8°C + Key Concept 1.1.1Key Concept 1.1.1

Ordering of Directed Numbers on the Number Line 1.A number line is a straight line with directed numbers marked on it in a certain order. Index B) 1A_Ch1(7) 1.1The Concept and Applications of Directed Numbers 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 1.1Index ExampleExample increasing

Arrange the following numbers in descending order and mark them on the number line below. Index 1A_Ch1(8) 1.1The Concept and Applications of Directed Numbers +3, –2, +5, +10, –3, 0 –4 – – –2 +10, +5, +3, 0, –2, –3

On the horizontal number line given below, find the directed numbers represented by the letters A, B, C, D and E. Index 1A_Ch1(9) 1.1The Concept and Applications of Directed Numbers –8 –7 A B –4 –3 –2 C D E +5 A =B = C =D = –6 0E =+4 –1 –5 + Key Concept 1.1.2Key Concept 1.1.2

Addition of Directed Numbers on a Vertical Number Line 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 A) 1A_Ch1(10) 1.2Addition and Subtraction of Directed Numbers + Index 1.2Index ExampleExample

Find the sum of each of the following. Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(11) (a)(–2) + 5(b)(–3) + 5 (c)(–4) + 5 (a) –1 –2 –3 –4 –5 +(+5) (–2) + 5 = +3 (b) –1 –2 –3 –4 –5 +(+5) (c) –1 –2 –3 –4 –5 +(+5) (–3) + 5 = +2 (–4) + 5 = +1

Find the sum of each of the following. Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(12) (a)0 + (–4)(b)1 + (–4) (c) –1 + (–4) (a) +1 0 –1 –2 –3 –4 –5 +(–4) 0 + (–4) =–4 (b) +1 0 –1 –2 –3 –4 –5 1 + (–4) =–3 (c) +1 0 –1 –2 –3 –4 –5 –1 + (–4) = –5 +(–4)

Index Use a vertical number line to find the sum of each of the following. 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(13) (a)(–4) + 5(b)(–7) + 2 (c)7 + (–3)(d)4 + (–5) (a) –1 –2 –3 –4 +(+5) (–4) + 5 = +1 (b) 0 –1 –2 –3 –4 –5 –6 –7 +(+2) (–7) + 2 = –5

Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(14) +(–3) 7 + (–3) = +4 (c) –1 –2 +(–5) 4 + (–5) = –1 (d) –1 –2 Fulfill Exercise Objective  Addition and subtraction using a number line.

Index With the help of a vertical number line, find the sum of (+1) + (–4) + (+5). 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(15) –1 –2 –3 +(–4) With the help of the vertical number line, (+1) + (–4) =–3 ∴ (+1) + (–4) + (+5) = (–3) + (+5) = +2 Fulfill Exercise Objective  Addition and subtraction using a number line.

Index 1.2Addition 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 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10 –11 –12 –13 The amount that John had after borrowing money = $[(–5) + (–7)] +(–7) = – $12

Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(17) –1 –2 –3 –4 –5 –6 –7 –8 –9 –10 –11 –12 –13 The amount that he has now = $[(–12) + 13] = +$1 Fulfill Exercise Objective  Real-life applications. +(+13) + Key Concept 1.2.1Key Concept Back to QuestionBack to Question

Subtraction of Directed Numbers on a Number Line 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 B) 1A_Ch1(18) 1.2Addition and Subtraction of Directed Numbers

Subtraction of Directed Numbers on a Number Line Note : In general, Index B) 1A_Ch1(19) 1.2Addition and Subtraction of Directed Numbers + ExampleExample + Index 1.2Index 1.2 Subtract (+)Add (–) = Subtract (–)Add (+) =

Index 1A_Ch1(20) 1.2Addition and Subtraction of Directed Numbers Find the difference of each of the following. (a)1 – (+3)(b)1 – (–3) (c) (–1) – (–3) (a) –1 –2 –3 –(+3) 1 – (+3) =–2 (b) –1 –2 –(–3) 1 – (–3) =+4 (c) –1 –2 –3 –(–3) (–1) – (–3) =+2

Index Use a vertical number line to find the difference of each of the following. 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(21) (a)4 – (+5)(b)(–4) – (+6) (c)2 – (–3)(d)(–6) – (–4) (a) –1 –2 –3 –(+5) 4 – (+5) = –1 (–4) – (+6) = –10 (b) 0 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10 –(+6)

Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(22) (c) –1 –(–3) 2 – (–3) = +5 (d) +1 0 –1 –2 –3 –4 –5 –6 –(–4) (–6) – (–4) = –2 Fulfill Exercise Objective  Addition and subtraction using a number line. + Back to QuestionBack to Question

Index 1.2Addition 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? –1 –2 –3 –4 –5 The amount by which Jane has more than May = $[(+3) – (+7)] = –$4 i.e. Jane has $4 less than May. –(+7) Fulfill Exercise Objective  Real-life applications.

Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(24) On a certain day in Beijing, the temperature in the morning was 5°C. It was expected to drop to –3°C at midnight. (a)By how many degrees was the temperature expected to drop? (b)If the temperature at midnight was 2°C higher than expected, what was the actual drop in temperature?

Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(25) (a)The expected drop in temperature = [5 – (–3)] °C –(–3) = 8°C (b)The actual drop in temperature = [8 – (+2)] °C = 6°C –(+2) Fulfill Exercise Objective  Real-life applications. + Key Concept 1.2.2Key Concept Back to QuestionBack to Question

Addition and Subtraction of Directed Numbers Using a Calculator 1.To input a positive number, we just press the key corresponding to the numerical value of the number. Index C) 1A_Ch1(26) 1.2Addition and Subtraction of Directed Numbers 2.To input a negative number, first press the key, then press the key(s) corresponding to its numerical value. (–)

Index 1A_Ch1(27) 1.2Addition and Subtraction of Directed Numbers C) Use a calculator to express the following directed numbers. Directed numberKeying Sequence –1 820 (–) – 1 3 a b c + ExampleExample + Index 1.2Index 1.2

Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(28) Use a calculator to evaluate each of the following. (a)–21 – (–60)(b)34 – (+16) (c) – (d) (a)–21 – (–60) Keying Sequence (–) – EXE Answer 39. ∴ –21 – (–60) =

Keying Sequence Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(29) Keying Sequence 34 – Answer 18. ∴ 34 – (+16) =18 (b)34 – (+16) EXE (–)5.2 + ∴ – =4.1 (c)– EXE 9.3 Answer Back to QuestionBack to Question 16

Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(30) (d) Keying Sequence (–) EXE a b c 3 5 a b c Answer ∴ = Fulfill Exercise Objective  Addition and subtraction using a calculator. + Key Concept 1.2.3Key Concept Back to QuestionBack to Question

Addition and Subtraction of Directed Numbers by Removing Brackets ‧ Rules for removing brackets attached to directed numbers Index D) 1A_Ch1(31) 1.2Addition and Subtraction of Directed Numbers + (+) = ++ (–) = –– (–) = +– (+) = – + ExampleExample + Index 1.2Index 1.2

Index 1A_Ch1(32) 1.2Addition and Subtraction of Directed Numbers Find the values of the following. (a)14 + (+25)(b)–14 + (–25) (c)14 – (+25)(d)–14 – (–25) (a)14 + (+25)= = 39 (b) –14 + (–25)= –14 – 25 = –39 (c)14 – (+25)= 14 – 25 = –11 (d) –14 – (–25)= – = 11 + Key Concept 1.2.4Key Concept 1.2.4

Multiplication of Directed Numbers Index A) 1A_Ch1(33) 1.3Multiplication and Division of Directed Numbers ‧ For positive numbers +a, +b and negative numbers –a, –b, (+a) × (+b) = +(a × b) (–a) × (–b) = +(a × b) (–a) × (+b) = –(a × b) (+a) × (–b) = –(a × b) + ExampleExample + Index 1.3Index 1.3

Find the value of each of the following. (a)4 x 3 = Index 1A_Ch1(34) 1.3Multiplication and Division of Directed Numbers (a)4 × 3(b)(–4) × 3(c)4 × (–3) (b) (–4) × 3 = (c)4 × (–3) = 12 –12

Find the value of each of the following. (a) (–1) × (–5) = Index 1A_Ch1(35) 1.3Multiplication and Division of Directed Numbers (a)(–1) × (–5)(b)(–2) × (–5) (b) (–2) × (–5) = (+) = +– (–) = + + (–) = –– (+) = –

(a)(+9) × (–6) Index 1A_Ch1(36) 1.3Multiplication and Division of Directed Numbers (a)(+9) × (–6)(b)(–5) × (–7) × (–2) Find the value of each of the following. = –(9 × 6) = –54 (b) (–5) × (–7) × (–2) = +(5 × 7) × (–2) = (+35) × (–2) = –(35 × 2) = –70 Fulfill Exercise Objective  Multiplication and division without using a calculator. + Key Concept 1.3.1Key Concept 1.3.1

Division of Directed Numbers Index B) 1A_Ch1(37) 1.3Multiplication and Division of Directed Numbers ‧ For positive numbers +a, +b and negative numbers –a, –b, + ExampleExample + Index 1.3Index 1.3 = (+a)(+b)(+a)(+b) = (–a)(+b)(–a)(+b) = (–a)(–b)(–a)(–b) = (+a)(–b)(+a)(–b) abab + ( ) abab – abab + abab –

Find the value of each of the following. Index 1A_Ch1(38) 1.3Multiplication and Division of Directed Numbers (a)(b)(c)(d)(a) = = +6 (b) = = –6 (c) = = +6 (d) = = –6

Index 1A_Ch1(39) 1.3Multiplication and Division of Directed Numbers Find the value of each of the following. (a)(+42) ÷ (–7) (c)(–57) ÷ (–3) (b)(–48) ÷ (+6) (d) (+12) ÷ (+2) ÷ (–3) (a)(+42) ÷ (–7) = –(42 ÷ 7) = –6 (b) (–48) ÷ (+6) = –(48 ÷ 6) = –8

Index 1A_Ch1(40) 1.3Multiplication and Division of Directed Numbers Fulfill Exercise Objective  Multiplication and division without using a calculator. (c)(–57) ÷ (–3) = +(57 ÷ 3) = +19 (d)(+12) ÷ (+2) ÷ (–3) = +(12 ÷ 2) ÷ (–3) = (+6) ÷ (–3) = –(6 ÷ 3) = –2 + Key Concept 1.3.2Key Concept Back to QuestionBack to Question

Multiplication and Division of Directed Numbers Using a Calculator Index C) 1A_Ch1(41) 1.3Multiplication and Division of Directed Numbers ‧ Calculator can be used to multiply and divide directed numbers by pressing the buttons and. × ÷

Index 1A_Ch1(42) 10 C) Use a calculator to evaluate each of the following. Expression 10 × 11 × 11 (–) (–5) × 3 5 × 3 ÷ 4 1.3Multiplication and Division of Directed Numbers Keying Sequence EXE 20 ÷ (–4) (–) 20 EXE + ExampleExample + Index 1.3Index 1.3

Index 1A_Ch1(43) Use a calculator to evaluate each of the following. (a)(–14) × 12 ÷ (–8)(b)(–50) × 9 ÷ 15 × 0 (c) (a) (–14) × 12 ÷ (–8) 1.3Multiplication and Division of Directed Numbers Keying Sequence (–) ÷ × EXE Answer 21. ∴ (–14) × 12 ÷ (–8) =21 (–)

Keying Sequence Index 1A_Ch1(44) (b) (–50) × 9 ÷ 15 × 0 1.3Multiplication and Division of Directed Numbers (–)50 ∴ (–50) × 9 ÷ 15 × 0 =0 EXE 9 Answer 0. ÷ × 15 × 0 + Back to QuestionBack to Question

Index 1A_Ch1(45) 1.3Multiplication and Division of Directed Numbers (c) 392 Answer 392. Keying Sequence (–)37 EXE 4.9 ÷ × 0.25÷(–) 1.85 ∴ = Fulfill Exercise Objective  Multiplication and division using a calculator. + Key Concept 1.3.3Key Concept Back to QuestionBack to Question

Mixed Operations of Directed Numbers Using a Calculator Index D) 1A_Ch1(46) 1.3Multiplication and Division of Directed Numbers ‧ Calculator can be used to evaluate an expression which may involve addition, subtraction, multiplication and division. + ExampleExample + Index 1.3Index 1.3

Index 1A_Ch1(47) Use a calculator to evaluate each of the following. (a)14 ÷ (3 + 4)(b)(–3) × (5 + 2) 1.3Multiplication and Division of Directed Numbers (a)14 ÷ (3 + 4) Answer 2. Keying Sequence 14 EXE ÷ ( ) ∴ 14 ÷ (3 + 4) =2

Index 1A_Ch1(48) (b)(–3) × (5 + 2) 1.3Multiplication and Division of Directed Numbers Answer –21. ∴ (–3) × (5 + 2) =–21 Keying Sequence (–)3 EXE ( ×5 + 2 ) + Back to QuestionBack to Question

Index 1A_Ch1(49) Use a calculator to evaluate each of the following. (a)0 × (–15) ÷ (10 + 5)(b)(–28) × 7 ÷ [13 + (–13)] (a) 0 × (–15) ÷ (10 + 5) 1.3Multiplication and Division of Directed Numbers ∴ 0 × (–15) ÷ (10 + 5) =0 Answer 0. Keying Sequence (–) 0 EXE 15 × ÷ ( )

Keying Sequence Index 1A_Ch1(50) (b)(–28) × 7 ÷ [13 + (–13)] 1.3Multiplication and Division of Directed Numbers ∴ (–28) × 7 ÷ [13 + (–13)] is meaningless. Answer MATH ERROR (–) EXE 28 × ÷ ( +) 7 13 (–) 13 Fulfill Exercise Objective  Mixed operations using a calculator. + Back to QuestionBack to Question

Index 1A_Ch1(51) 1.3Multiplication and Division of Directed Numbers (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? 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. + SolnSoln + SolnSoln

Index 1A_Ch1(52) 1.3Multiplication and Division of Directed Numbers (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 Ming’s final score = [18 + (–8)] marks = 10 marks + Back to QuestionBack to Question

Index 1A_Ch1(53) 1.3Multiplication and Division of Directed Numbers (b)The score obtained for 1 correct answer = 1 × 3 marks = 3 marks Since Tai Kwong’s 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) = = 6 Fulfill Exercise Objective  Real-life applications. + Key Concept 1.3.4Key Concept Back to QuestionBack to Question