1. 1A_Ch0(1)

2. 0.3Multiples and Factors A Multiples B Factors C Prime Numbers and Prime Factors Index 1A_Ch0(2) D Index Notation

3. 0.4Fractions A Introduction B Proper and Improper Fractions C Equal Fractions Index 1A_Ch0(3) D Comparing Fractions E Arithmetic Operations with Fractions

4. 0.5Choosing Appropriate Measuring Tools and Units A Choosing Appropriate Measuring Tool B Choosing Appropriate Unit for Measurement Index 1A_Ch0(4)

5. Numbers 0.1Numbers Index + ExampleExample 1A_Ch0(5) 1.Natural numbers are the numbers we used in counting and they are 1, 2, 3, 4, 5, 6,.... 2.The first five whole numbers are 0, 1, 2, 3 and 4. 3.The whole numbers 0, 2, 4, 6 and 8 are examples of even numbers. They are divisible by the number 2. 4.The whole numbers 1, 3, 5, 7, 9 are examples of odd numbers. When these numbers are divided by 2, there is always a remainder 1.

6. From numbers 0 to 8, list all the (a)natural numbers,(b)whole numbers, (c)even numbers,(d)odd numbers. + Key Concept 0.1.1Key Concept 0.1.1 Index 1A_Ch0(6) 0.1Numbers (a)Natural numbers :1, 2, 3, 4, 5, 6, 7, 8 (b)Whole numbers :0, 1, 2, 3, 4, 5, 6, 7, 8 (c)Even numbers :2, 4, 6, 8 (d)Odd numbers :1, 3, 5, 7

7. The Four Fundamental Arithmetic Operations (+, –, ×, ÷) 0.2The Four Fundamental Arithmetic Operations (+, –, x, ÷) Index + ExampleExample 1A_Ch0(7) 1.In 4 + 7 = 11, the number 11 is called the sum of 4 and 7. 2.In 11 – 7 = 4, the number 4 is called the difference between 11 and 7. 3.In 4 × 7 = 28, the number 28 is called the product of 4 and 7. 4.In 28 ÷ 7 = 4, the number 4 is called the quotient and 7 is called the divisor.

8. Find(a)13 + 8(b)92 – 9 (c)36 × 4(d)56 ÷ 8 Index 1A_Ch0(8) (a)13 + 8 = 21 (b)92 – 9 = 83 (c)36 × 4 = 144 (d)56 ÷ 8 = 7 0.2The Four Fundamental Arithmetic Operations (+, –, x, ÷)

9. Find 5 + 4 × 2. 5 + 4 × 2 Index 1A_Ch0(9) = 5 + 8 = 13 Fulfill Exercise Objective  +, –, × and ÷ 0.2The Four Fundamental Arithmetic Operations (+, –, ×, ÷)

10. Find 250 × 5 ÷ 25. 250 × 5 ÷ 25 Index 1A_Ch0(10) = 1 250 ÷ 25 = 50 Fulfill Exercise Objective  +, –, × and ÷ 0.2The Four Fundamental Arithmetic Operations (+, –, ×, ÷) + Key Concept 0.2.1Key Concept 0.2.1

11. Brackets 0.2The Four Fundamental Arithmetic Operations (+, –, ×, ÷) Index + ExampleExample 1A_Ch0(11) 1.Brackets are used to indicate the priority of operations. 2.We should always do the operations within the brackets first. 3. If more than one pair of brackets are used, the general rule is to use ( ) for the first arithmetic operation, then [ ] and then { }.

12. Find(a)(20 – 8) ÷ (5 – 3) (b)3 × (8 + 3) – (4 – 2) Index 1A_Ch0(12) (b)3 × (8 + 3) – (4 – 2) = 3 × 11 – 2 = 33 – 2 = 31 (a) (20 – 8) ÷ (5 – 3) = 12 ÷ 2 = 6 0.2The Four Fundamental Arithmetic Operations (+, –, ×, ÷)

13. Find 6 × {100 ÷ [(6 – 2) × 5] – 5}. 6 × {100 ÷ [(6 – 2) × 5] – 5} Index 1A_Ch0(13) = 6 × {100 ÷ [4 × 5] – 5} = 6 × {100 ÷ 20 – 5} = 6 × {5 – 5} = 6 × 0 = 0 0.2The Four Fundamental Arithmetic Operations (+, –, ×, ÷) Fulfill Exercise Objective  Expressions involving brackets. + Key Concept 0.2.2Key Concept 0.2.2

14. Several verbs used to describe the arithmetic operations 0.2The Four Fundamental Arithmetic Operations (+, –, ×, ÷) Index + ExampleExample 1A_Ch0(14) Divide 20 by 4, or20 is divided by 4 Multiply 7 by 3, or7 times 3 Subtract 6 from 10, or10 minus 6 Add 5 to 2, or2 plus 5 Arithmetic operationsTerms and descriptions 2 + 5 10 – 6 7 × 3 20 ÷ 4

15. Index 1A_Ch0(15) 0.2The Four Fundamental Arithmetic Operations (+, –, ×, ÷) Write down the result of each of the following. (a)Find the difference when 7 is subtracted from 18. (b)Find the product of 6 and 12. (c)When 100 is divided by 5, find the quotient. (a)18 – 7= 11 (b)6 × 12= 72 (c)100 ÷ 5= 20 + Key Concept 0.2.3Key Concept 0.2.3

16. Multiples 0.3Multiples and Factors Index + ExampleExample 1A_Ch0(16) ‧ When we multiply a number by the natural numbers 1, 2, 3, 4 and so on, we get multiples of that number. E.g. The first 4 multiples of 6 are : 6, 12, 18 and 24. A) + Index 0.3Index 0.3

17. List the first four multiples of 5. Index 0.3Multiples and Factors 1A_Ch0(17) 5 × 1 = 5, 5 × 2 = 10, 5 × 3 = 15, 5 × 4 = 20 ∴ ∴ The first four multiples of 5 are 5, 10, 15 and 20. 51015 20 5 × 15 × 25 × 35 × 4

18. Index 1A_Ch0(18) Write down the first 5 multiples of each of the following numbers. 0.3Multiples and Factors 15 12 9 6 Multiples 6 × 1, 6 × 2, 6 × 3, 6 × 4, 6 × 5 9 × 1, 9 × 2, 9 × 3, 9 × 4, 9 × 5 12 × 1, 12 × 2, 12 × 3, 12 × 4, 12 × 5 15 × 1, 15 × 2, 15 × 3, 15 × 4, 15 × 5 6, 12, 18, 24, 30 9, 18, 27, 36, 45 12, 24, 36, 48, 60 15, 30, 45, 60, 75 + Key Concept 0.3.1Key Concept 0.3.1

19. Factors 0.3Multiples and Factors Index 1A_Ch0(19) 1.When a given number is expressed as a product of two or more natural numbers, then each of these natural numbers is a factor of the given number. 2.In general, the method of division can be used to test whether a number is a factor of another number. E.g. Since 48 is divisible by 4, 4 is a factor of 48. B)

20. Note : 0.3Multiples and Factors Index + ExampleExample 1A_Ch0(20) B) i.All numbers are divisible by 1, therefore 1 is a factor of any number. ii.All even numbers are divisible by 2, therefore 2 is a factor of any even number. iii.Any number (except 0) is divisible by itself, therefore any number is a factor of itself. + Index 0.3Index 0.3

21. Determine whether 5 is a factor of 30. Since 30 ÷ 5 = 6, we say 30 is divisible by 5. Therefore 5 is a factor of 30. Index 0.3Multiples and Factors 1A_Ch0(21)

22. Index 1A_Ch0(22) Write down all the factors of each of the following numbers. 32 22 12 4 Factors 1 × 4, 2 × 2, 4 × 1 1 × 12, 2 × 6, 3 × 4, 4 × 3, 12 × 1 1 × 22, 2 × 11, 11 × 2, 22 × 1 1 × 32, 2 × 16, 4 × 8, 8 × 4, 16 × 2, 32 × 1 1, 2, 4 1, 2, 3, 4, 6, 12 1, 2, 11, 22 1, 2, 4, 8, 16, 32 0.3Multiples and Factors + Key Concept 0.3.2Key Concept 0.3.2

23. Prime Numbers and Prime Factors 0.3Multiples and Factors Index 1A_Ch0(23) 1.A prime number is a natural number (other than 1) which is not divisible by any natural number except 1 and itself. 2.Consider the factors of 24, 2 and 3 are prime numbers and they are therefore called prime factors of 24. C) + ExampleExample + Index 0.3Index 0.3

24. Index 1A_Ch0(24) List all the prime numbers (a)from 80 to 150,(b)from 200 to 250. (a)The prime numbers from 80 to 150 : 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149 (b)The prime numbers from 200 to 250 : 211, 223, 227, 229, 233, 239, 241 0.3Multiples and Factors

25. Express 120 as a product of prime factors. 120 Index 1A_Ch0(25) Fulfill Exercise Objective  Prime factors. 2120 260 230 315 5 0.3Multiples and Factors = 2 × 60 = 2 × 2 × 30 = 2 × 2 × 2 × 15 = 2 × 2 × 2 × 3 × 5 + Key Concept 0.3.3Key Concept 0.3.3

26. Index Notation 0.3Multiples and Factors Index 1A_Ch0(26) 1.When a number is multiplied by itself several times, we can express the product using the index notation. 2.Consider the index notation 7 2, 7 3, 7 4 and 7 5. The number 7 is called the base and the numbers 2, 3, 4 and 5 are each called the index. D) + ExampleExample + Index 0.3Index 0.3

27. Index 1A_Ch0(27) Using index notation, express each of the following numbers as a product of prime factors. 0.3Multiples and Factors (a)50(b)132 (c)180(d)225 (a)50(b)132= 2 × 5 2 = 2 2 × 3 × 11 (c)180(d)225= 2 2 × 3 2 × 5= 3 2 × 5 2 + Key Concept 0.3.4Key Concept 0.3.4

28. Introduction 0.4Fractions Index + ExampleExample 1A_Ch0(28) A) ‧ The number or is called a fraction in which 4 is called the denominator and 1 or 3 is called the numerator of the fraction. + Index 0.4Index 0.4

29. Index 1A_Ch0(29) 8 triangles are shaded. 0.4Fractions Shade of the triangles below. How many triangles have you shaded? + Key Concept 0.4.1Key Concept 0.4.1

30. Proper and Improper Fractions Index 1A_Ch0(30) B) 0.4Fractions 1.Examples of proper fractions are :, and, where the numerator of the fraction is smaller than the denominator. 2.Examples of improper fractions are :, and, where the numerator of the fraction is greater than or equal to the denominator. 3.Examples of mixed numbers are :, and, where the fraction is written as a sum of a whole number and a proper fraction. + ExampleExample + Index 0.4Index 0.4

31. Index 1A_Ch0(31) (a)Improper fractions : 0.4Fractions (a)Which of the following are improper fractions? (b)Express the improper fractions in (a) as mixed numbers. (b) can be written as, can be written as. + Key Concept 0.4.2Key Concept 0.4.2

32. Equal Fractions Index 1A_Ch0(32) C) 0.4Fractions 1.When we multiply the numerator and the denominator of a fraction by the same non-zero number, the value of the faction remains the same. E.g. 2222 2222 2222 2.When the numerator and the denominator of a fraction have no common factor except 1, the fraction is said to be in its simplest form. + ExampleExample + Index 0.4Index 0.4

33. Index 1A_Ch0(33) 0.4Fractions Match the equal fractions.

34. Index 1A_Ch0(34) Fulfill Exercise Objective  Reduce fractions. 0.4Fractions Reduce to its simplest form. 6 15 2 5 + Key Concept 0.4.3Key Concept 0.4.3

35. Comparing Fractions Index 1A_Ch0(35) D) 0.4Fractions ‧ Fractions can be compared when they are expressed with the same denominators. To do this, we need to know the L.C.M. of their original denominators. + ExampleExample + Index 0.4Index 0.4

36. Index 1A_Ch0(36) The L.C.M. of 3 and 5 is 15. 0.4Fractions Compare and. ， ∴ is greater than. ∴

37. Index 1A_Ch0(37) Fulfill Exercise Objective  Compare fractions. 0.4Fractions Arrange the fractions, and in ascending order of value. ，， Arrange these in ascending order of value, we have, i.e.. 12 24 16 24 9 24 The L.C.M. of 2, 3 and 8 is 24. ∴ The fractions, and are in ascending order of value. + Key Concept 0.4.4Key Concept 0.4.4

38. Index 1A_Ch0(38) 0.4Fractions Arrange the fractions, and in descending order of value. ，， Arrange these in descending order of value, we have,i.e.. 10 20 15 20 8 20 The L.C.M. of 2, 4 and 5 is 20. ∴ The fractions, and are in descending order of value. + Key Concept 0.4.4Key Concept 0.4.4

39. Arithmetic Operations with Fractions Index 1A_Ch0(39) E) 0.4Fractions 1.When adding or subtracting fractions, we often start by changing the denominators of these fractions into the same numbers first. + ExampleExample

40. Arithmetic Operations with Fractions Index 1A_Ch0(40) E) 0.4Fractions 2.When we multiply or divide fractions, we often change the mixed numbers into improper fractions first and then look for factors to cancel from the numerators and denominators. + ExampleExample + Index 0.4Index 0.4

41. Index 1A_Ch0(41) 0.4Fractions Calculate.

42. Index 1A_Ch0(42) Fulfill Exercise Objective  Expressions involving fractions. 0.4Fractions Calculate.

43. Index 1A_Ch0(43) Fulfill Exercise Objective  Expressions involving fractions. 0.4Fractions Calculate. + Key Concept 0.4.5Key Concept 0.4.5

44. Index 1A_Ch0(44) 0.4Fractions (a)(b) Calculate : (a)(b) 2 3

45. Index 1A_Ch0(45) Fulfill Exercise Objective  Expressions involving fractions. 0.4Fractions Calculate. 2 1

46. Index 1A_Ch0(46) Fulfill Exercise Objective  Everyday applications. 0.4Fractions Mr Chan earns $15 000 a month. If he spends of his income and saves the rest, how much does he save in a month? The amount he saves = $15 000 = $3 000 + Key Concept 0.4.6Key Concept 0.4.6

47. Choosing Appropriate Measuring Tool Index 1A_Ch0(47) A) 0.5Choosing Appropriate Measuring Tools and Units ‧ When we measure a quantity, we have to choose an appropriate measuring tool to achieve a particular purpose. + ExampleExample + Index 0.5Index 0.5

48. Index 1A_Ch0(48) Which of the following is an appropriate measuring tool for measuring the length of a monitor screen? A.Mechanical scale B.Thermometer C.Ruler D.Syringe C 0.5Choosing Appropriate Measuring Tools and Units + Key Concept 0.5.1Key Concept 0.5.1

49. Choosing Appropriate Unit for Measurement Index 1A_Ch0(49) B) 0.5Choosing Appropriate Measuring Tools and Units ‧ When we measure a quantity, we have to choose an appropriate unit so that other people can understand the result easily. + ExampleExample + Index 0.5Index 0.5

50. What unit and quantity would you use to tell others (a)for how long has Aaron sung this song? (b)how much does the fish weigh? Index + Key Concept 0.5.2Key Concept 0.5.2 1A_Ch0(50) 0.5Choosing Appropriate Measuring Tools and Units (a)Aaron has sung this song for 3 min, rather than 180 s or 0.05 h. (b)The weight of the fish is 1.5 kg, rather than 1 500 g or 0.001 5 tonne.