1. Exercise 1
Oral Examples

2. Read these numbers
1. 100
9. 900

3. Read the value of each 3 in these numbers.

4. Read the value of each 7 in these numbers.

5. Exercise 2
Oral examples

6.
x 5 x x 5 ÷ 2
÷ 5 x ÷ 5 ÷ 2
x (5 + 2) x 5 + 2
11. (10 + 5) x x 2
x (5 - 2) x 5 - 2
15. (10 - 5) x x 2

7. Exercise 2
Written Examples

8. Are the following correct?
6 + 3 – 2
6 x 3 x 2
6 x 3 ÷ 2
6 ÷ 3 x 2
6 ÷ 3 ÷ 2
6 x (3 + 2) 11 7 5 1 36 9 4 30

9. Find the answers to the following
6 x 3 + 2
(6 + 3) x 2
6 + 3 x 2
6 x (3 - 2)
6 x 3 - 2
(6 - 3) x 2
6 - 3 x 2 20 18 12 6 16

10. Find the answers to the following
8 - (4 + 2)
8 - (4 - 2)
8 x 4 x 2
8 x 4 ÷ 2
8 ÷ 4 x 2 14 10 6 2 64 16 4

11. Find the answers to the following
8 ÷ (4 x 2)
8 ÷ 4 ÷ 2
8 ÷ (4 ÷ 2)
8 x (4 + 2)
8 x 4 + 2
(8 + 4) x 2
8 + 4 x 2 1 4 48 34 24 16

12. Find the answers to the following
8 x (4 - 2)
8 x 4 - 2
(8 - 4) x 2
8 - 4 x 2
8 ÷ (4 - 2)
8 ÷ 4 - 2
(8 - 4) ÷ 2
8 - 4 ÷ 2 16 30 8 4 2 6

13. Find the answers to the following
12 - (6 + 2)
12 - (6 - 2)
12 x 6 x 2
12 x 6 ÷ 2 20 16 8 4
144 36

14. Are the following correct?
12 ÷ 6 x 2
12 ÷ (6 x 2)
12 ÷ 6 ÷ 2
12 ÷ (6 ÷ 2)
12 x (6 + 2)
12 x 6 + 2
(12 + 6) x 2
x 2 4 1 96 74 36 24

15. Find the answers 12 x (6 - 2) 12 x 6 - 2 (12 - 6) x 2 12 - 6 x 2
12 ÷ (6 - 2 )
12 ÷ 6 - 2
(12 - 6) ÷ 2
÷ 2 48 70 12 3 9

16. Use 2 different operations (choosing from + - × ÷ ) to show how three 4's (i.e. the numbers 4, 4 and 4) can be combined to give the following answers. Brackets may be used.
4 x 4 + 4
(4 + 4) x 4
4 x 4 - 4
(4 + 4) 4
4 - (4 4) 20 32 12 5 2 3

17. State these in shorthand.
1. 5 x 5 x 5 x 5 x 5 x 5
2. 6 x 6 x 6 x 6 x 6
3. 8 x 8 x 8
4. 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 56 65 83 38

18. State these in long hand.29 92 74 47
2x2x2x2x2x2x2x2x2
9x9
7x7x7x7
4x4x4x4x4x4x4

19. Evaluate (i.e. find the value of )22 23 24 25 26 27 28 29 4 8 16 32 64
128
256
512

20. Evaluate (i.e. find the value of )62 72 82 92 36 49 64 81

21. Evaluate (i.e. find the value of )32 33 34 35 42 43 52 53 9 27 81
243 16 64 25
125

22. Evaluate (i.e. find the value of )
102
103
104
105
106
1002
1003
10002
100
1000
10 000

23. Evaluate (i.e. find the value of )
202
203
502
503
302
402
3002
4002
400
8000
2500
900
1600
90 000

24. Evaluate (i.e. find the value of )12 13 14 15 21 31 41 51 1 2 3 4 5

25. Evaluate (i.e. find the value of )
22 x 52
23 x 53
23 x 32
22 x 33
5 x 22
2 x 52
4 x 32
3 x 42
100
1000 72
108 20 50 36 48

26. Evaluate (i.e. find the value of )√9
√81
√ 36
√64 √4
√16
√25
√49 3 9 6 8 2 4 5 7

27. Evaluate (i.e. find the value of )√1
√100 √ √
√400
√900
√1600
√2500 1 10
100
1000 20 30 40 50

28. Evaluate (i.e. find the value of )
( 7 + 3)2
(6 - 4)2
√(16 + 9)
√16 + √9
√( )
√100 - √64
100 58 4 20 5 7 6 2

29. Evaluate (i.e. find the value of )
√ 52
√ 72
(√4)2
(√6)2 5 7 4 6

30. Evaluate (i.e. find the value of )7 5 10 11 32

31. Exercise 4: Oral examples
34 x 32
24 x 24
310 x 32 26 23 36 34 28 24
312

32. Exercise 4: Oral examples
59 x 53 58 24 56 59

33. Exercise 4: Written examples
36 x 36
58 x 52
25 x 25
212 28
312 36
510 58
210 34

34. Exercise 4: Written examples
56 x 5 39 36 57 56 22

35. 14.
= 38

36. 15.
= 28

37. 15.
= 59

38. Exercise 5 - Oral examples
{ factors of 15 }
{ factors of 32 }
{ factors of 27 }
{ factors of 28 }
(1, 3, 5, 15)
(1, 2, 4, 8, 16, 32)
(1, 3, 9, 27)
(1, 2, 4, 7, 14, 28)

39. Exercise 5 - Written examples
{ factors of 4 }
{ factors of 9 }
{ factors of 16 }
{ factors of 25 }
{ factors of 36 }
{ factors of 1 }
{ factors of 6 }
{ factors of 12}
(1, 2, 4)
(1, 3, 9)
(1, 2, 4, 8, 16)
(1, 5, 25)
(1, 2, 3, 4, 6, 9, 12, 18, 36)
(1)
(1, 2, 3, 6)
(1, 2, 3, 4, 6, 12)

40. Exercise 5 - Written examples
{ factors of 18 }
{ factors of 24 }
{ factors of 10 }
{ factors of 20 }
{ factors of 30 }
{ factors of 40 }
{ factors of 2 }
{ factors of 3}
(1, 2, 3, 6, 9, 18)
(1, 2, 3, 4, 6, 8, 12, 24)
(1, 2, 5, 10)
(1, 2, 4, 5, 10, 20)
(1, 2, 3, 5, 6, 10, 15, 30)
(1, 2, 4, 5, 8, 10, 20, 40)
(1, 2,)
(1, 3)

41. Exercise 5 - Written examples
{ factors of 5 }
{ factors of 7}
{ factors of 11 }
{ factors of 13 }
(1, 5)
(1, 7)
(1, 11)
(1, 13)

42. Prime Numbers 1. Prime numbers have exactly 2 factors
( namely 1 and itself).
2. If a factor is a prime number then it is called a prime factor.
{ factors of 100 } = {1, 2, 4, 5, 10, 20, 25, 50, 100 }
{ prime factors of 100 } = { 2, 5 }

43. Prime Numbers
The number 1 is not a prime number and so it is not a prime factor of any number.

44. Exercise 5 - Written examples
{ prime numbers between 0 and 10 }
{ prime numbers between 10 and 20 }
{ prime numbers between 20 and 30 }
{ prime numbers between 30 and 40 }
(2, 3, 5, 7)
(11, 13, 17, 19)
(23, 29)
(31, 37)

45. 25. { prime factors of 6 } Factors of ‘6’ are 1, 2, 3, 6
Prime factors of ‘6’ are 2, 3

46. 26. { prime factors of 10 } Factors of ‘10’ are 1, 2, 5, 10
Prime factors of ‘10’ are 2, 5

47. 27. { prime factors of 14 } Factors of ‘14’ are 1, 2, 7, 14
Prime factors of ‘14’ are 2, 7

48. 28. { prime factors of 15 } Factors of ‘15’ are 1, 3, 5, 15
Prime factors of ‘15’ are 3, 5

49. 29. { prime factors of 21 } Factors of ‘21’ are 1, 3, 7, 21
Prime factors of ‘21’ are 3, 7

50. 30. { prime factors of 35 } Factors of ‘35’ are 1, 5, 7, 35
Prime factors of ‘35’ are 5, 7

51. 31. { prime factors of 30 } Factors of ‘30’ are 1, 3, 5, 6, 10, 30
Prime factors of ‘30’ are 3, 5

52. 32. { prime factors of 42 }
Factors of ‘42’ are 1, 2, 3, 6, 7, 14, 21, 42
Prime factors of ‘42’ are 2, 3, 7

53. Multiples { multiples of 3 } { multiples of 6 } { multiples of 2 }
3, 6, 9, 12, …
6, 12, 18, 24,,…
2, 4, 6, 8, …
4, 8, 12, 16, …

54. { factors of 60 }
{ factors of 360 }
{ prime numbers between 40 and 50 }
{ prime numbers between 50 and 60 }
(1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60)
(1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360)
(41, 43, 47)
(53, 59)

55. Exercise 6 - Prime factors42 6 7

56. Prime factors 42 6 7
‘7’ is a prime number

57. Prime factors 42 6 7 2 3
2, 3, and 7 are all prime numbers

58. Product of prime factors42 6 7 2 3

59. Exercise 6 - Prime factors28 4 7

60. Prime factors 28 4 7
‘7’ is a prime number

61. Prime factors 28 4 7 2 2
2, and 7 are all prime numbers

62. Product of prime factors28 4 7 2 2

63. Exercise 6 - Prime factors64 8 8

64. Prime factors 64 8 8 4 2 2 4

65. Prime factors 64 8 8 4 2 2 4 2 2 2 2

66. Product of Prime factors64 8 8 4 2 2 4 2 2 2 2

67. Exercise 6 - Prime factors72 8 9

68. Prime factors 72 8 9 3 2 3 4

69. Prime factors 72 8 9 3 2 3 4 2 2

70. Product of Prime factors72 8 9 3 2 3 4 2 2

71. Exercise 6 6 10 14 15 21 35 30 70
2 x 3
2 x 5
2 x 7
3 x 5
3 x 7
5 x 7
2 x 3 x 5
2 x 5 x 7

72. Exercise 6 4 8 16 32 9 27 25 49
2 x 2 = 22
2 x 2 x 2 = 23
2 x 2 x 2 x 2 = 24 25
3 x 3 = 32
3 x 3 x 3 = 33
5 x 5 = 52
7 x 7 = 72

73. Exercise 6 12 18 20 50 45 75 36 60
2 x 2 x 3 = 22 x 3
2 x 3 x 3 = 2 x 32
2 x 2 x 5 = 22 x 5
2 x 5 x 5 =2 x 52
5 x 3 x 3 = 5 x 32
3 x 5 x 5 = 3 x 52
2 x 2 x 3 x 3 = 22 x 32
2 x 2 x 3 x 5 = 22 x 3 x 5

74. Exercise 6 24 54 40 56 48 80 90 84
23 x 3
2 x 33
23 x 5
7 x 23
24 x 3
24 x 5
2 x 32 x 5
22 x 3 x 7

75. Exercise 6
Find the smallest number which is the product of 4 different prime factors.
2 x 3 x 5 x 7 = 210

76. Exercise
Find the next smallest number which is the product of 4 different prime factors.
2 x 3 x 5 x 11 = 330

77. Exercise
Find the smallest number which is the product of 4 prime factors (not necessarily different).
2 x 2 x 2 x 2 = 16

78. Exercise
Find the next smallest number which is the product of 4 prime factors (not necessarily different).
2 x 2 x 2 x 3 = 24

79. H.C.F (highest common factor)
{ factors of 8 } = { 1, 2, 4, 8 }
{ factors of 12 } = { 1, 2, 3, 4, 6, 12 }
The H.C.F. is 4

80. L.C.M (lowest common multiple)
{ multiples of 8 } = { 8, 16, 24, 32… }
{ multiples of 12 } = {12, 24, 36… }
The L.C.M. is 24

81. 2 and 6
H.C.F 2
L.C.M 6

82. 2 and 10
H.C.F 2
L.C.M 10

83. 3 and 6
H.C.F 3
L.C.M 6

84. 3 and 12
H.C.F 3
L.C.M 12

85. 4 and 12
H.C.F 4
L.C.M 12

86. 5 and 10
H.C.F 5
L.C.M 10

87. 4 and 6
H.C.F 2
L.C.M 12

88. 6 and 8
H.C.F 2
L.C.M 24

89. 6 and 9
H.C.F 3
L.C.M 18

90. 9 and 12
H.C.F 3
L.C.M 36

91. 4 and 10
H.C.F 2
L.C.M 20

92. 6 and 10
H.C.F 2
L.C.M 30

93. 2, 4 and 8
H.C.F 2
L.C.M 8

94. 4, 6 and 8
H.C.F 2
L.C.M 24

95. 3, 6 and 12
H.C.F 3
L.C.M 12

96. 6, 9 and 12
H.C.F 3
L.C.M 36

97. Exercise 7 - Oral examples
5 is a factor of 10.
5 is a multiple of 10.
10 is a factor of 5.
10 is a multiple of 5.
7 is a factor of 7.
7 is a multiple of 7.
7 is a prime number.
9 is a prime number.
3 is a prime factor of 12.
True
False
true

98. Exercise 7 2 _____ { 1, 2, 3 } { 2 } ____ { 1, 2, 3 }
2 _____ { 1, 2, 3 }
{ 2 } ____ { 1, 2, 3 }
7 ______ { 4, 5, 6 }
{ 7 }____ { 4, 5, 6 }
3 _____ { 2, 3, 4 }
8 ______ { 5, 6, 7 }
{ 3 } ____ { 2, 3, 4 }
{ 8 } ____ { 5, 6, 7 }

99. Exercise 7 5 ______ { factors of 5 } 5 _____ { multiples of 5 }

100. Exercise 7 { 4 } ____ { factors of 8 } { 4 } _____ { multiples of 8 }
17 ______ { prime numbers }
{ 17 } ____ { prime numbers }
27 _____ { prime numbers }
{ 27 } ____ { prime numbers }

101. Exercise 7 1 ____ { prime factors of 3 } 2 ____ { prime factors of 6 }