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Wednesday 19 April 2023Wednesday 19 April 2023 Created by Mr. Lafferty Created by Mr. Lafferty @[email protected]

Multiples and LCM

Factors and HCF

Types of Types of NumbersNumbers

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Prime numbers

Prime Decomposition

Squares, cubes and square roots

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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

o

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Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. To be able to write out To be able to write out multiplesmultiples

1. To explain that Multiples are the times tables

2. To explain 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

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Multiples

Example 1 :Find the first seven multiples of 3.

M3 = 3, 6 , 9, 12, 15, 18,21

M4 = 4, 8 , 12, 16, 20, ………

Example 2 :Find the first five multiples of 4.

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Lowest Common Multiple

We need to write out multiples in order to findthe Lowest Common Multiple.

LowestCommonMultiple

SmallestSameNumber

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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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Now try Exercise 1Ch5 (page 28)

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Types of NumbersTypes of NumbersRevision of Level E

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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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65o

150o 52

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1.1. To identify factors using To identify factors using factor pairsfactor pairs

1. To explain that a factor divides into a number with no remainder

2. To explain how to find Highest Common Factors

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

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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

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Highest Common Factor

We need to write out all factor pairs in order to findthe Highest Common Factor.

HighestCommonFactor

LargestSameNumber

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HCF = 4

F8 = 1 and 8

2 and 4

F12 = 1 and 12

2 and 6

3 and 4

Highest Common Factor

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1313




Q.3 Calculate

(a) - 6 +12- 6 (b) (-7) x (8) (c) (-2) x (-18) 9

1. Calculate the area of the following shape.

5 cm

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4 cm

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1.1. To know the meaning of To know the meaning of the term Prime Number.the term Prime Number.

1. To explain what a prime number is and to find all the prime numbers from 1 and 200.

2.2. Find all prime between 1 Find all prime between 1 and 200.and 200.

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Types of NumbersTypes of NumbersPrime Numbers

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Prime Numbers

Definition : A prime number is a number withexactly 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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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

Wednesday 19 April 2023

17Created by Mr. Lafferty @www.mathsrevision.com

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?



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

?Wednesday 19 April 2023


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



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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



Work

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2222




Q.3 Calculate

(a) -16 -12- 6 (b) (-9) x (5) (c) (-22) x (-11) 2


8 cm

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5 cm

119o

2323



1.1. To know the meaning of To know the meaning of the term prime the term prime decomposition.decomposition.

1. To explain what prime decomposition is and use it to decompose numbers into a product of prime numbers only. 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

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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

Prime Factors are 2, 2, 3

126

3

1

22

3

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Prime Decomposition

Prime Factors are 2, 2, 3, 5, 11

660330

165

55

22

3

115

11

1

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Types of NumbersTypes of Numbers

Some words to learn

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 Sum is what you get when numbers are added together

The Quotient is what you get when one number is divided by another.

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Examples

The Difference between 45 and 20 is

The Product of 2,5 and 6 is

The Sum of 3, 5 and 9 is

The Quotient when 30 is divided by 5 is

17

25

60

6

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Now try Exercise 9.1

Ch1 (page 15)

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Q.3 Calculate

(a) -16 -12- 6 (b) (-9) x (5) (c) (-22) x (-11) 2


10 cm

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6 cm

114o

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1.1. To understand what a To understand what a square, cube and square square, cube and square root of a number is.root of a number is.

1. To explain what a square, cube and square root of a number is.

2.2. Calculate the square, cube Calculate the square, cube and square root of a and square root of a number.number.

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Types of NumbersTypes of NumbersPrime Decomposition

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Square, Cube and Square, Cube and Square RootSquare Root

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When we multiply a number by itself we say we have squared the number.

2 4

2

3

34

We write above as

22 = 4 32 = 9 42 = 16


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3333

When we multiply a number by itself we say we have squared the number.

Calculate

92 = 102 =

a2 = a x aRead as a to the power 2

202 = 81 100 400


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When we cube a number we mean

Calculate

33 = 43 = 53 =

a3 = a x a x a

23 = 2 x 2 x 2 = 8

27 64 125


Now try Ex 10.1Q1 to Q5

Ch1 (page 17)

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SQUARE ROOT“ A factor of a number that can be multiplied by

itself to produce the original number “

525 2552 because

749 4972 because


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The square root of a number is another number than when you multiply it by itself

the answer is the original number

525 2552 because

81

Calculate

1219 11


Now try Ex 10.1Q6 to Q9

Ch1 (page 18)

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