mth 3-05a 12-jan-16created by mr. lafferty types of numbers multiples and lcm factors and hcf prime...
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MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
Multiples and LCM
Factors and HCF
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Prime numbers
Prime Decomposition
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Starter Starter QuestionsQuestions
Q2. Find the missing angle.
Q.3 Calculate
(a) - 9 - (72 8) (b) (-4) x (-13) (c) (-15) 3+4
1. Find all missing angles.
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45o
100o 92
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MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To be able to write out To be able to write out multiplesmultiples
1. We are learning what multiples are .
2. We are learning how to find the Lowest Common Number.
2.2. Use sets of multiples to Use sets of multiples to identify Lowest identify Lowest Common MultiplesCommon Multiples
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Types of NumbersTypes of NumbersMultiples
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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Multiples
Example : Find the first seven multiples of 3.
M3 = 3, 6 , 9, 12, 15, 18,21
M4 = 4, 8 , 12, 16, 20, ………
Example : Find the first five multiples of 4.
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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Multiples
Example : Describe these sets of numbers.
10, 15, 20, 25, 30
54, 60 , 66, 72, 78
Example : Find the first five multiples of 4.
“ The multiples of 5 from 10 to 30 “
“ The multiples of 6 from 54 to 78 “
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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Lowest Common Multiple
We need to write out multiples in order to findthe Lowest Common Multiple.
LowestCommonMultiple
SmallestSameNumber
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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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
22 Apr 2023 Mr. [email protected]
CM for 2: 2, 4, 6, 8, 10, 12
Find the LCM for these numbers
CM for 5: 5, 10, 15 LCM = 10
CM for 4: 4, 8, 12, 16, 20,24,28,32, 36
CM for 9: 9, 18, 27, 36 LCM =36
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 1Ch3 (page 26)
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Lowest Common Lowest Common MultipleMultiple
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Starter Starter QuestionsQuestions
Q2. Find the missing angle.
Q.3 Calculate
(a) - 6 + (7 - 8) (b) (-7) x (-19) (c) (-3) x (-8) 4
1. Calculate all the missing angles.
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MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To identify factors using To identify factors using factor pairsfactor pairs
1. We are learning what a factor is.
2. We are learning to find the Highest Common Factors for a set of numbers.
2.2. Find HCF for two numbers Find HCF for two numbers by comparing factors.by comparing factors.
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Types of NumbersTypes of NumbersUsing Factors
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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Factors
Example : Find the factors of 56.
F56 = 1 and 56
Always divide by 1 and find its pair
2 and 28
4 and 14
7 and 8
From 2 find other factors and their pairs
22 Apr 2023 Mr. [email protected]
F 24
Find the Factors for these numbers
1 24
2 12
3 8
4 6
F 49 1 49
7 7
1 , 2, 3, 4, 6, 8, 12, 24
1 , 7, 49
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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Highest Common Factor
We need to write out all factor pairs in order to findthe Highest Common Factor.
HighestCommonFactor
LargestSameNumber
MTH 3-05a
F12 = 1 and 12
2 and 6
3 and 4
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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HCF = 4
F8 = 1 and 8
2 and 4
Highest Common Factor
22 Apr 2023 Mr. [email protected]
F 31
Find the HCF for these numbers
1 31
F 8 1 82 4
F 41 1 41 HCF = 1
F 10 1 10 2 5
HCF = 2
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 2Ch3 (page 28)
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Highest Common Highest Common FactorFactor
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Starter Starter QuestionsQuestions
1. Calculate the area of the following shape.
Q2. Find the missing angle in the triangle.
Q.3 Calculate
(a) - 6 +12- 6 (b) (-7) x (8) (c) (-2) x (-18) 9
5 cm
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4 cm
95o
25o
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To know the meaning of To know the meaning of the term Prime Number.the term Prime Number.
1. We are learning what a prime number is and to find all the prime numbers from 1 and 200. 2.2. Find all prime numbers Find all prime numbers
between 1 and 200.between 1 and 200.
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Types of NumbersTypes of NumbersPrime Numbers
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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Prime Numbers
Definition : A prime number is a number with exactlyexactly 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
MTH 3-05a
1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100
Strike the two’s, strike the three’s the Sieve of Eratosthenes
when the multiples sublime, the numbers that remain are prime!
25 primes
Below 100
MTH 3-05a
46 primes below 200
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 47 48 49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 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
Use the method of Eratosthenes to find all primes below 200
What is the largest prime <200?
MTH 3-05a
10311 000 – 12 000
10610 000 – 11 000
1129000 – 10 000
1108000 - 9000
1077000 – 8000
1176000 - 7000
1145000 - 6000
1194000 - 5000
1203000 – 4000
1272000 – 3000
1351000 – 2000
1680 – 1000
Number of Primes
Range
?
MTH 3-05a
1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 7071 72 73 74 75 76 77 78 79 8081 82 83 84 85 86 87 88 89 9091 92 93 94 95 96 97 98 99 100
Strike the two’s, strike the three’s the Sieve of Eratosthenes
when the multiples sublime, the numbers that remain are prime!
Work
sheet
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MTH 3-05a
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 47 48 49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 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
Strike the two’s, strike the three’s the Sieve of Eratosthenes
when the multiples sublime, the numbers that remain are prime!
Work
sheet
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srevis
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om
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 3Ch3 (page 30)
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Highest Common Highest Common FactorFactor
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Starter Starter QuestionsQuestions
Q2. Find the missing angle.
Q.3 Calculate
(a) -16 -12- 6 (b) (-9) x (5) (c) (-22) x (-11) 2
1. Calculate the area of the following shape.
8 cm
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5 cm
119o
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1.1. To know the meaning of To know the meaning of the term prime the term prime decomposition.decomposition.
1. We are learning the technique of prime decomposition .
2.2. Decompose numbers to a Decompose numbers to a product of prime only.product of prime only.
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Types of NumbersTypes of NumbersPrime Decomposition
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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A number is either Prime or Composite. (except for 0)If it is composite, like 12, it can always be expressed asa “product of primes”
Example : Express 12 as a “product of primes”
Prime Decomposition
12
3
3 4
22
12
= 3 x 4
= 3 x 2 x 2All Prime !
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. LaffertyCreated by Mr. Lafferty
Types of Types of NumbersNumbers
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Prime Decomposition
18
3
3 6
23
18
= 3 x 6
= 3 x 3 x 2All Prime !
MTH 3-05a
22 Apr 202322 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.
Now try TJ3b
Ex 4Ch3 (page 32)
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Highest Common Highest Common FactorFactor
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