1. 1A_Ch1(1)

2. 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)

3. 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

4. 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

5. 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 1.1 + ExampleExample

6. 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

7. 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 1.1 + ExampleExample increasing

8. 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 –1 +1 +4 +6 –30+3+5+10–2 +10, +5, +3, 0, –2, –3

9. 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 +1 +2 +3 E +5 A =B = C =D = –6 0E =+4 –1 –5 + Key Concept 1.1.2Key Concept 1.1.2

10. 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 1.2 + ExampleExample

11. 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) +3 +2 +1 0 –1 –2 –3 –4 –5 +(+5) (–2) + 5 = +3 (b) +3 +2 +1 0 –1 –2 –3 –4 –5 +(+5) (c) +3 +2 +1 0 –1 –2 –3 –4 –5 +(+5) (–3) + 5 = +2 (–4) + 5 = +1

12. 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)

13. 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) +3 +2 +1 0 –1 –2 –3 –4 +(+5) (–4) + 5 = +1 (b) 0 –1 –2 –3 –4 –5 –6 –7 +(+2) (–7) + 2 = –5

14. Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(14) +(–3) 7 + (–3) = +4 (c) +7 +6 +5 +4 +3 +2 +1 0 –1 –2 +(–5) 4 + (–5) = –1 (d) +4 +3 +2 +1 0 –1 –2 Fulfill Exercise Objective  Addition and subtraction using a number line.

15. 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) +2 +1 0 –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.

16. 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. +2 +1 0 –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

17. Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(17) +2 +1 0 –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 1.2.1 + Back to QuestionBack to Question

18. 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

19. 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 (+) =

20. 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) +3 +2 +1 0 –1 –2 –3 –(+3) 1 – (+3) =–2 (b) +4 +3 +2 +1 0 –1 –2 –(–3) 1 – (–3) =+4 (c) +3 +2 +1 0 –1 –2 –3 –(–3) (–1) – (–3) =+2

21. 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) +4 +3 +2 +1 0 –1 –2 –3 –(+5) 4 – (+5) = –1 (–4) – (+6) = –10 (b) 0 –1 –2 –3 –4 –5 –6 –7 –8 –9 –10 –(+6)

22. Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(22) (c) +6 +5 +4 +3 +2 +1 0 –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

23. 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? +4 +3 +2 +1 0 –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.

24. 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?

25. Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(25) (a)The expected drop in temperature = [5 – (–3)] °C +9 +8 +7 +6 +5 +4 +3 +2 +1 0 –(–3) = 8°C (b)The actual drop in temperature = [8 – (+2)] °C = 6°C +9 +8 +7 +6 +5 –(+2) Fulfill Exercise Objective  Real-life applications. + Key Concept 1.2.2Key Concept 1.2.2 + Back to QuestionBack to Question

26. 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. (–)

27. Index 1A_Ch1(27) 1.2Addition and Subtraction of Directed Numbers C) Use a calculator to express the following directed numbers. Directed numberKeying Sequence 256 256 –1 820 (–) 1820 1313 – 1 3 a b c + ExampleExample + Index 1.2Index 1.2

28. 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) –5.2 + 9.3(d) (a)–21 – (–60) Keying Sequence (–) – EXE Answer 39. ∴ –21 – (–60) =39 21 60

29. 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 + ∴ –5.2 + 9.3 =4.1 (c)–5.2 + 9.3 EXE 9.3 Answer 4.1 + Back to QuestionBack to Question 16

30. Index 1.2Addition and Subtraction of Directed Numbers 1A_Ch1(30) (d) Keying Sequence (–) 1 2 + EXE a b c 3 5 a b c Answer -11 15 ∴ = Fulfill Exercise Objective  Addition and subtraction using a calculator. + Key Concept 1.2.3Key Concept 1.2.3 + Back to QuestionBack to Question

31. 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

32. 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)= 14 + 25 = 39 (b) –14 + (–25)= –14 – 25 = –39 (c)14 – (+25)= 14 – 25 = –11 (d) –14 – (–25)= –14 + 25 = 11 + Key Concept 1.2.4Key Concept 1.2.4

33. 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

34. 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

35. 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) = 5 10 + (+) = +– (–) = + + (–) = –– (+) = –

36. (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

37. 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 –

38. 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

39. 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

40. 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 1.3.2 + Back to QuestionBack to Question

41. 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. × ÷

42. 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

43. 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 (–) ÷ 14 12 8 × EXE Answer 21. ∴ (–14) × 12 ÷ (–8) =21 (–)

44. 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

45. 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 1.3.3 + Back to QuestionBack to Question

46. 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

47. 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 ÷ ( 3 + 4 ) ∴ 14 ÷ (3 + 4) =2

48. 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

49. 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 × ÷ ( 10 + 5 )

50. 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

51. 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

52. 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

53. 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 1.3.4 + Back to QuestionBack to Question