Transcript Types of Numbers - Mathsrevision.com

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Types of Numbers
Multiples and LCM
Factors and HCF
Prime numbers
Prime Decomposition
Squares, cubes and square roots
Thursday, 06 April 2017
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1
Starter Questions
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1.
Find all missing angles.
45
o
Q2. Find the missing angle.
100 92
o
o
Q.3 Calculate
(a)
- 9 - (72  8)
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(b) (-4) x (-13)
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(c) (-15)  3 + 4
2
Types of Numbers
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Multiples
Learning Intention
Success Criteria
1. To explain that Multiples
are the times tables
2. To explain how to find the
Lowest Common Number.
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1. To be able to write out
multiples
2. Use sets of multiples to
identify Lowest Common
Multiples
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Types of Numbers
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Multiples
Example 1 : Find the first seven multiples of 3.
M3 = 3, 6 , 9, 12, 15, 18,21
Example 2 : Find the first five multiples of 4.
M4 = 4, 8 , 12, 16, 20, ………
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Types of Numbers
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Lowest Common Multiple
Lowest
Common
Multiple
Smallest
Same
Number
We need to write out multiples in order to find
the Lowest Common Multiple.
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Types of Numbers
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Lowest Common Multiple
Example :
Find the LCM of 3 and 4.
M3 = 3, 6 , 9, 12, 15, ………
M4 = 4, 8 , 12, 16, 20, ………
LCM = 12
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Types of Numbers
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Revision of Level E
Now try Exercise 1
Ch5 (page 28)
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Starter Questions
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1.
Calculate all the missing angles.
65
o
Q2. Find the missing angle.
150 52
o
o
Q.3 Calculate
(a)
- 6 + (7 - 8)
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(b) (-7) x (-19)
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(c) (-3) x (-8)  4
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Types of Numbers
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Using Factors
Learning Intention
Success Criteria
1. To explain that a factor
divides into a number with
no remainder
1. To identify factors using
factor pairs
2. To explain how to find
Highest Common Factors
2. Find HCF for two numbers
by comparing factors.
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Types of Numbers
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Factors
Example :
Find the factors of 56.
Always divide by 1 and find its pair
F56 = 1 and 56
From 2 find other factors and their pairs
2 and 28
4 and 14
7 and
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Types of Numbers
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Highest Common Factor
Highest
Common
Factor
Largest
Same
Number
We need to write out all factor pairs in order to find
the Highest Common Factor.
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Types of Numbers
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Highest Common Factor
Example :
Find the HCF of 8 and 12.
F8 = 1 and 8
F12 = 1 and 12
2 and 4
2 and 6
3 and 4
HCF = 4
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Types of Numbers
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Revision of Level E
Now try Exercise 2
Ch5 (page 30)
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Starter Questions
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1.
Calculate the area of the following shape.
4 cm
5 cm
Q2. Find the missing angle.
Q.3 Calculate
(a)
- 6 +12 - 6
Thursday, 06 April 2017
(b) (-7) x (8)
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(c) (-2) x (-18)  9
14
Types of Numbers
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Prime Numbers
Learning Intention
Success Criteria
1. To explain what a prime
number is and to find all
the prime numbers from 1
and 200.
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1. To know the meaning of
the term Prime Number.
2. Find all prime between 1 and
200.
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Types of Numbers
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Prime Numbers
Definition : A prime number is a number with
exactly 2 factors.
Example :
Is 7 a prime number. Explain?
Yes, only two factors 1,7
Example :
Is 10 a prime number. Explain?
No, more than two factors 1,2,5,10
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Strike the two’s, strike the three’s the Sieve of Eratosthenes
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
Thursday, 06 April 2017
3
13
23
33
43
53
63
73
83
93
when the multiples
4
14
24
34
44
54
64
74
84
94
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
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sublime,
the numbers that
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9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
remain are prime!
25 primes
Below 100
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Use the method of Eratosthenes to find all primes below 200
1
2
3
4
5
6
7
8
9
10
11
12
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49
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56
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58
59
60
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95
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99 100
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
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What is the largest prime
<200?
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46 primes below 200
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Range
0 – 1000
1000 – 2000
2000 – 3000
3000 – 4000
4000 - 5000
5000 - 6000
6000 - 7000
7000 – 8000
8000 - 9000
9000 – 10 000
10 000 – 11 000
11 000 – 12 000
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Number of Primes
168
135
127
120
119
114
117
107
110
112
106
103
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?
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Worksheet – www.mathsrevision.com
Strike the two’s, strike the three’s the Sieve of Eratosthenes
1
11
21
31
41
51
61
71
81
91
2
12
22
32
42
52
62
72
82
92
3
13
23
33
43
53
63
73
83
93
4
14
24
34
44
54
64
74
84
94
Thursday,
06 April
2017
when
the
multiples
5
15
25
35
45
55
65
75
85
95
6
16
26
36
46
56
66
76
86
96
7
17
27
37
47
57
67
77
87
97
8
18
28
38
48
58
68
78
88
98
9
19
29
39
49
59
69
79
89
99
10
20
30
40
50
60
70
80
90
100
Createdthe
by Mr.numbers
Lafferty
sublime,
that remain are prime!
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20
Worksheet – www.mathsrevision.com
Strike the two’s, strike the three’s the Sieve of Eratosthenes
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
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49
50
51
52
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55
56
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58
59
60
61
62
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65
66
67
68
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70
71
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77
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79
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82
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86
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99 100
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140
141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160
161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180
181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200
Thursday,
06 April
2017
when
the
multiples
Createdthe
by Mr.numbers
Lafferty
sublime,
that remain are prime!
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Types of Numbers
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Revision of Level E
Now try Exercise 3
Ch5 (page 32)
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Starter Questions
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1.
Calculate the area of the following shape.
5 cm
8 cm
Q2. Find the missing angle.
119
o
Q.3 Calculate
(a)
-16 -12 - 6
Thursday, 06 April 2017
(b) (-9) x (5)
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(c) (-22) x (-11)  2
23
Types of Numbers
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Prime Decomposition
Learning Intention
Success Criteria
1. To explain what prime
decomposition is and use it
to decompose numbers into
a product of prime
numbers only.
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1. To know the meaning of
the term prime
decomposition.
2. Decompose numbers to a
product of prime only.
24
Types of Numbers
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Prime Decomposition
A number is either Prime or Composite. (except for 0)
If it is composite, like 12, it can always be expressed as
a “product of primes”
Example :
Express 12 as a “product of primes”
2 12
2 6
3 3
Prime Factors are 2, 2, 3
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Types of Numbers
Prime Decomposition
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Example :
Express 660 as a “product of primes”
2 660
2 330
3 165
5 55
11 11
1
Prime Factors are 2, 2, 3, 5, 11
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Types of Numbers
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Some words to learn
The Sum is what you get when numbers are added together
The Difference between two numbers is found by subtracting
one number from the other
The Product is what you get when numbers are multiplied together
The Quotient is what you get when one number is divided by another.
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Types of Numbers
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Examples
The Sum of 3, 5 and 9 is
17
The Difference between 45 and 20 is
25
The Product of 2,5 and 6 is
60
The Quotient when 30 is divided by 5 is
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Types of Numbers
Now try Exercise 9.1
Ch1 (page 15)
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Starter Questions
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1.
Calculate the area of the following shape.
6 cm
10 cm
Q2. Find the missing angle.
114
o
Q.3 Calculate
(a)
-16 -12 - 6
Thursday, 06 April 2017
(b) (-9) x (5)
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(c) (-22) x (-11)  2
30
Types of Numbers
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Prime Decomposition
Learning Intention
Success Criteria
1. To explain what a square,
cube and square root of a
number is.
1. To understand what a
square, cube and square
root of a number is.
2. Calculate the square, cube
and square root of a number.
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Square, Cube and
Square Root
When we multiply a number by itself
we say we have squared the number.
4
3
2
2
3
We write above as
22 = 4
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32 = 9
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4
42 = 16
32
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Square, Cube and
Square Root
When we multiply a number by itself
we say we have squared the number.
Read as a to
the power 2
a2 = a x a
Calculate
92 = 81
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102 = 100
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202 = 400
33
Square, Cube and
Square Root
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When we cube a number we mean
a3 = a x a x a
23 = 2 x 2 x 2 = 8
Calculate
33 = 27
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43 = 64
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53 = 125
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Types of Numbers
Now try Ex 10.1
Q1 to Q5
Ch1 (page 17)
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Square, Cube and
Square Root
SQUARE ROOT
“ A factor of a number that can be multiplied by itself
to produce the original number “
25  5
because
5  25
49  7
because
7  49
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Square, Cube and
Square Root
The square root of a number is
another number than when you multiply it by itself
the answer is the original number
25  5
because
5  25
2
Calculate
81  9
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121  11
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Types of Numbers
Now try Ex 10.1
Q6 to Q9
Ch1 (page 18)
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