Exercise 1 Oral Examples

Read these numbers 1. 100 2. 1000 3. 10 000 4. 100 000 5. 1 000 000 6. 10 000 000 7. 100 000 000 8. 1 000 000 000 9. 900 10. 4000 11. 70 000 12. 200 000 13. 8 000 000 14. 50 000 000 15. 300 000 000 16. 6 000 000 000

Read the value of each 3 in these numbers. 13. 19 37 14. 57 193 15. 532 76 16. 798 231 17. 9 213 867 18. 7 306 842 19. 3 074 586 20. 5 947 283 21. 693 750 22. 759 631 23. 5 436 827 24. 7 021 398 25. 19 384 572 26. 302 875 469 27. 573 264 891 28. 7 139 528 640

Read the value of each 7 in these numbers. 13. 19 37 14. 57 193 15. 532 76 16. 798 231 17. 9 213 867 18. 7 306 842 19. 3 074 586 20. 5 947 283 21. 693 750 22. 759 631 23. 5 436 827 24. 7 021 398 25. 19 384 572 26. 302 875 469 27. 573 264 891 28. 7 139 528 640

Exercise 2 Oral examples

1. 10 + 5 + 2 2. 10 + 5 - 2 3. 10 - 5 + 2 4. 10 - 5 - 2 5. 10 x 5 x 2 6. 10 x 5 ÷ 2 7. 10 ÷ 5 x 2 8. 10 ÷ 5 ÷ 2 9. 10 x (5 + 2) 10. 10 x 5 + 2 11. (10 + 5) x 2 12. 10 + 5 x 2 13. 10 x (5 - 2) 14. 10 x 5 - 2 15. (10 - 5) x 2 16. 10 - 5 x 2

Exercise 2 Written Examples

Are the following correct? 6 + 3 + 2 6 + 3 – 2 6 - 3 + 2 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

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

Find the answers to the following 8 + 4 + 2 8 + 4 - 2 8 - 4 + 2 8 - (4 + 2) 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

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

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

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

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 12 + 6 x 2 4 1 96 74 36 24

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 12 - 6 ÷ 2 48 70 12 3 9

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 4 - (4 4) 20 32 12 5 2 3

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

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

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

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

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

Evaluate (i.e. find the value of ) 102 103 104 105 106 1002 1003 10002 100 1000 10 000 100 000 1 000 000

Evaluate (i.e. find the value of ) 202 203 502 503 302 402 3002 4002 400 8000 2500 125 000 900 1600 90 000 160 000

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

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

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

Evaluate (i.e. find the value of ) √1 √100 √ 10 000 √1 000 000 √400 √900 √1600 √2500 1 10 100 1000 20 30 40 50

Evaluate (i.e. find the value of ) ( 7 + 3)2 72 + 32 (6 - 4)2 62 - 42 √(16 + 9) √16 + √9 √(100 - 64) √100 - √64 100 58 4 20 5 7 6 2

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

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

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

Exercise 4: Oral examples 28 24 59 x 53 512 53 58 24 56 59

Exercise 4: Written examples 212 24 36 x 36 312 36 58 x 52 510 52 25 x 25 36 32 212 28 312 36 510 58 210 34

Exercise 4: Written examples 39 33 56 x 5 57 5 39 36 57 56 22

14. = 38

15. = 28

15. = 59

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)

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)

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)

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

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 }

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

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)

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

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

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

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

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

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

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

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

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, …

{ 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)

Exercise 6 - Prime factors 42 6 7

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

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

Product of prime factors 42 6 7 2 3

Exercise 6 - Prime factors 28 4 7

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

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

Product of prime factors 28 4 7 2 2

Exercise 6 - Prime factors 64 8 8

Prime factors 64 8 8 4 2 2 4

Prime factors 64 8 8 4 2 2 4 2 2 2 2

Product of Prime factors 64 8 8 4 2 2 4 2 2 2 2

Exercise 6 - Prime factors 72 8 9

Prime factors 72 8 9 3 2 3 4

Prime factors 72 8 9 3 2 3 4 2 2

Product of Prime factors 72 8 9 3 2 3 4 2 2

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

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

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

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

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

Exercise 6 - 34 Find the next smallest number which is the product of 4 different prime factors. 2 x 3 x 5 x 11 = 330

Exercise 6 - 35 Find the smallest number which is the product of 4 prime factors (not necessarily different). 2 x 2 x 2 x 2 = 16

Exercise 6 - 36 Find the next smallest number which is the product of 4 prime factors (not necessarily different). 2 x 2 x 2 x 3 = 24

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 }

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

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

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