Numbers.

Numbers.

LEARNING OUTCOMES:• Recognise squares and cubes numbers.• Calculate square roots and cube roots.• Find reciprocals.• Find multiples, factors and primes.• Find prime factors of numbers.• Find HCF and LCM.

Squares and Cubes Numbers.

Numbers.

1. List the square numbers.


Numbers.

1. List the square numbers.

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169


Numbers.

2. List the cube numbers.


Numbers.

2. List the cube numbers.

1, 8, 27, 64, 125, 216, 343, 512


Numbers.

3. Write down a number from the list which is:

1, 4, 8, 10, 23, 27, 36, 64, 71, 100, 109, 125, 164, 1000

a) The square numbers: ______________________________________________

b) The cube numbers: ________________________________________________


Numbers.

3. Write down a number from the list which is:

1, 4, 8, 10, 23, 27, 36, 64, 71, 100, 109, 125, 164, 1000

a) Square numbers: 1, 4, 36, 64, 100

b) Cube numbers: 1, 8, 27, 64, 125, 1000

Square Roots and Cube Roots.

Numbers.

1. Find the square root.

___

√16

__√ 9

___√ 25

___

√81

___

√100

___

√144


Numbers.

1. Find the square root.

___

√16 = 4

__√ 9 = 3

___√ 25 = 5

___

√81 = 9

___

√100 = 10

___

√144 = 12


Numbers.

2. Find the cube root.

3 ___√ 8

3 ___√216

3 ___√125

3 ___√ 27

3 ___√ 64

3 ______

√1000


Numbers.

2. Find the cube root.

3 ___√ 8 = 2

3 ___√216 = 6

3 ___√125 = 5

3 ___√ 27 = 3

3 ___√ 64 = 4

3 ______

√1000 = 10

Reciprocals.

Numbers.

1. Find the reciprocals of the following numbers.

5 2 7

9 6 3

Reciprocals.

Numbers.


15 ~ 5

12 ~ 2

17 ~ 7

19 ~ 9

16 ~ 6

13 ~ 3

Reciprocals.

Numbers.


15

27

12

59

16

23

Reciprocals.

Numbers.


1 55 ~ 1 = 5

2 77 ~ 2

1 22 ~ 1 = 2

5 99 ~ 5

1 66 ~ 1 = 6

2 33 ~ 2

Reciprocals.

Numbers.


0.5 0.2 0.7

0.1 0.6 0.3

Reciprocals.

Numbers.


5 10 0.5 = 10 ~ 5 = 2

2 10 0.2 = 10 ~ 2 = 5

7 100.7 = 10 ~ 7

1 100.1 = 10 ~ 1 = 10

6 10 50.6 = 10 ~ 6 = 3

3 100.3 = 10 ~ 3

Multiples, Factors and Primes.

Numbers.

1. Write the first five multiples of these numbers.

2: ________________________________________

3: ________________________________________

5: ________________________________________

9: ________________________________________

10: _______________________________________


Numbers.

1. Write the first five multiples of these numbers.

2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39

5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60

9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108

10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110


Numbers.2. From the numbers below, write down those that are:

111, 254, 255, 108, 73, 68, 162, 60, 711, 615, 98, 37, 812, 102, 75, 270

a) Multiples of 2:

_____________________________________________

b) Multiples of 3: _____________________________________________

c) Multiples of 5: _____________________________________________

d) Multiples of 9: _____________________________________________

e) Multiples of 10: _____________________________________________


Numbers.

2. From the numbers below, write down those that are:

111, 254, 255, 108, 73, 68, 162, 60, 711, 615, 98, 37, 812, 102, 75, 270

a) Multiples of 2: 254, 108, 68, 162, 60, 98, 812, 102, 270

b) Multiples of 3: 111, 255, 108, 162, 60, 711, 615, 102, 75, 270

c) Multiples of 5: 255, 60, 615, 75, 270

d) Multiples of 9: 108, 162, 711, 270

e) Multiples of 10: 60, 270


Numbers.

3. List the factors of 12.


Numbers.


1, 2, 3, 4, 6, 12


Numbers.



Numbers.


1, 2, 3, 5, 6, 10, 15, 30


Numbers.



Numbers.


1, 3, 5, 9, 15, 45


Numbers.



Numbers.


1, 2, 3, 4, 6, 8, 12, 16, 24, 48


Numbers.

7. List the prime numbers.


Numbers.

7. List the prime numbers.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47,

53, 59, 61, 67, 71, 73, 79, 83, 89, 97


Numbers.

8. From this list of numbers, write down:

1, 2, 3, 5, 6, 7, 9, 12, 18, 24, 30, 36

a) Any multiples of 6: __________________________________

b) All the factors of 18: _________________________________

c) The prime numbers: ________________________________


Numbers.


1, 2, 3, 5, 6, 7, 9, 12, 18, 24, 30, 36

a) Any multiples of 6: 6, 12, 18, 24, 30, 36

b) All the factors of 18: 1, 2, 3, 6, 9, 18

c) The prime numbers: 2, 3, 5, 7

Prime Factors.

Numbers.

1. Write number 180:

a) As a product of its prime factors: ____________________________ b) As a product of its prime factors in index notation (using powers): ____________

Prime Factors.

Numbers.


a) As a product of its prime factors: 180 = 2 x 2 x 3 x 3 x 5

2 2

b) As a product of its prime factors in index notation (using powers): 180 = 2 x 3 x 5

Prime Factors.

Numbers.

2. Write number 60:

a) As a product of its prime factors: ___________________________________

b) As a product of its prime factors in index notation (using powers): ____________

Prime Factors.

Numbers.

2. Write number 60:

a) As a product of its prime factors: 60 = 2 x 2 x 3 x 5

2

b) As a product of its prime factors in index notation (using powers):60 = 2 x 3 x 5

Prime Factors.

Numbers.




Prime Factors.

Numbers.



2


Prime Factors.

Numbers.




Prime Factors.

Numbers.


a) As a product of its prime factors: 720 = 2 x 2 x 2 x 2 x 3 x 3 x 5 4 2


Prime Factors.

Numbers.




Prime Factors.

Numbers.



2


Prime Factors.

Numbers.

m

6. The number 56 can be written as 2 x n, where m and n are prime numbers. Find the value of m and n.

Prime Factors.

Numbers.

m

6. The number 56 can be written as 2 x n, where m and n are prime numbers. Find the value of m and n.

3

56 = 2 x 2 x 2 x 7 = 2 x 7

m = 3, n = 7

HCF and LCM.

Numbers.

1. Find HCF and LCM of 60 and 96.

HCF and LCM.

Numbers.


HCF = 2 x 2 x 3 = 12

LCM = 12 x 5 x 2 x 2 x 2 = 480

HCF and LCM.

Numbers.


HCF and LCM.

Numbers.


HCF = 2 x 7 = 14

LCM = 14 x 2 x 3 = 84

HCF and LCM.

Numbers.


HCF and LCM.

Numbers.


HCF = 2 x 2 x 2 = 8

LCM = 8 x 3 x 7 = 168

HCF and LCM.

Numbers.


HCF and LCM.

Numbers.


HCF = 7

LCM = 7 x 3 x 5 = 105

HCF and LCM.

Numbers.


HCF and LCM.

Numbers.


HCF = 2 x 2 = 4

LCM = 4 x 3 x 2 x 2 x 2 = 96

HCF and LCM.

Numbers.


HCF and LCM.

Numbers.


HCF = 3 x 3 = 9

LCM = 9 x 2 x 3 = 54

HCF and LCM.

Numbers.


HCF and LCM.

Numbers.


HCF = 5

LCM = 5 x 3 x 5 = 75

HCF and LCM.

Numbers.


HCF and LCM.

Numbers.


HCF = 2 x 2 x 2 x 2 = 16

LCM = 16 x 3 x 2 x 2 = 192

Review “Numbers”.1. From the numbers below find:

5, 19, 20, 49, 64, 121, 125, 200, 800, 1000

a) The square numbers: ___________________

b) The cube numbers: ______________________

c) The square root of 400: ________________

d) The cube root of 125: ___________________

Review “Numbers”.

1. From the numbers below find:

5, 19, 20, 49, 64, 121, 125, 200, 800, 1000

a) The square numbers: 49, 64, 121

b) The cube numbers: 64, 125, 1000

c) The square root of 400: 20

d) The cube root of 125: 5



4 857

16 0.4 0.9



14 ~ 4

18 ~ 8

5 77 ~ 5

1 66 ~ 1 = 6

4 10 50.4 = 10 ~ 4 = 2

9 100.9 = 10 ~ 9

Review “Numbers”.3. From this list of numbers, write down:

1, 3, 8, 12, 16, 7, 20, 13, 15, 2, 17, 24, 6, 5

a) The prime numbers: ________________________________

b) All the factors of 6: _________________________________

c) Any multiples of 4: __________________________________



1, 3, 8, 12, 16, 7, 20, 13, 15, 2, 17, 24, 6, 5

a) The prime numbers: 3, 7, 13, 2, 17, 5

b) All the factors of 6: 1, 3, 2, 6

c) Any multiples of 4: 8, 12, 16, 20, 24




b) As a product of its prime factors in index notation (using powers): ___________



a) As a product of its prime factors: 360 = 2 x 2 x 2 x 3 x 3 x 5 3 2




HCF = 2 x 3 x 3 = 18

LCM = 18 x 2 x 3 = 108

Numbers.

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