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Chapter 5

Chapter 5. Working With Number. Recognise even/odd numbers Find multiples of a number Find factors of a number Recognise prime numbers Write numbers in index form Find prime factors of a number Write a number as the product of its prime factors Find least common multiple of numbers

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Chapter 5

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  1. Chapter 5 Working With Number

  2. Recognise even/odd numbers Find multiples of a number Find factors of a number Recognise prime numbers Write numbers in index form Find prime factors of a number Write a number as the product of its prime factors Find least common multiple of numbers Find highest common factor of numbers Find square numbers Find cube numbers Find reciprocals Find powers of numbers Find square roots of numbers Multiply numbers with powers Divide numbers with powers Recognise surds Do calculations with surds Learning Objectives

  3. Even numbers End in 0, 2, 4, 6, 8 Odd numbers End in 1, 3, 5, 7, 9 Even/Odd Numbers Example Are the following even or odd? 2, 32, 65, 64, 345, 1234, 6543, 546, 65, 109, 100

  4. Multiples These are the answers to the multiplication tables Examples Write down the 1st 5 multiples of 12 What is the 7th multiple of 6? The 5th multiple of a number is 40. What is the number? Factors These are numbers that divide in exactly Best to do it in pairs Examples What are the factors of 12? What are the factors of 40? Multiples & Factors

  5. Prime Numbers • Prime numbers have 2 factors – itself & 1 • 2, 3, 5, 7, 11, 13, 17 Example Which of the following are prime numbers? 1, 5, 3, 7, 6, 19, 21, 25, 29, 100, 91

  6. Powers/ Indices • Short-hand way of writing multiplication Examples • 2×2×2×2×2×2×2 • 0.1×0.1×0.1×0.1×0.1×0.1×0.1×0.1×0.1×0.1×0.1×0.1×0.1×0.1 • 2×2×2×3×3×3×3×3×4×4

  7. Prime Factors • Put a list of prime numbers at the top of the page • Keep dividing by the smallest prime number that goes in evenly EXAMPLES Find the prime factors of: • 12 • 40

  8. Product of Prime Factors • Find the prime factors and write as a multiplication (use powers if needed) EXAMPLES Write the following as a product of prime factors: (a) 20 (b) 50 (c) 150 (d) 70

  9. Least Common Multiples • Write as products of prime factors • Include all numbers to the highest power EXAMPLES Find the LCM of • 12 and 8 • 45, 90 and 105

  10. Homework for Friday • Find the LCM of 12 and 66 • Find the LCM of 15, 39 & 45 • Find all the factors of 18 • Is 15 a prime number? • Find the prime factors of 36 • Find the LCM of 8 & 12 • Find the 1st 5 multiples of 5 • Find all the factors of 24 • Find the prime factors of 24 • Find the LCM of 48, 60 & 100

  11. Highest Common Factor • Find the prime factors of each number • Include only the numbers common to both EXAMPLES Find the HCF of • 18 and 45 • 40 and 36 • 45, 90 and 105

  12. Square Numbers • A square number is when you multiply a number by itself EXAMPLES 22= 32 = 42 = 52 = 62 = 72 =

  13. Cube Numbers • A cube number is when you multiply a number by itself and by itself EXAMPLES 23= 33 = 43 = 53 = 63 = 73 =

  14. Any Powers • Use the power button on your calculator xy or yx or ^ EXAMPLES 26= 34 = 40.5 = 52.5 = 6-1 = 7-1 =

  15. Square Roots • These are the opposite of square numbers • They can be written as √ of power of ½ EXAMPLES √16 = 250.5 = 3√125 = 3√64 =

  16. Reciprocals • In an ordinary number reciprocal means 1/ • Eg rec of 4 = , rec of 10 = , rec of 3 = • In a fraction reciprocal means up-side-down • Eg rec of 2/3 = , rec of ¾ = , rec of 4/5 =

  17. Multiplying with Indices • Consider 23×24 Shortcut: • When we multiply numbers that are the same we add the indices

  18. Dividing with Indices • Consider 27÷24 Shortcut: • When we divide numbers that are the same we subtract the indices am÷an = am-n

  19. Examples 1. 29×26 2. 29÷26 3. 23×26×32×35 4. 66÷6 5. 49×46÷42 6. 10-4×10-3 7. 10-4÷10-3

  20. Surds • Surds do not have exact √ Example Which of the following are surds? √4 √25 √2 √100 √10 √36 √5 √9

  21. Adding/Subtracting Surds • Make sure the surds are the same before you add/subtract them Examples • √2 + 3√2 • 4√3 - √3 • 5√2 - 3√2

  22. Simplifying Surds • Find the factors of the numbers and see if you can break down some of the surds Examples 1. √12 2. √75 3. √90 4. √8 5. √40

  23. Dividing Surds • Split into 2 parts and do each surd separately and then cancel at the end Examples • √(9/4) • √(10/4) • √(27/9) • √(15/12)

  24. Multiplying Surds Examples 1. √5×√5 2. √12×√3 3. √7×√14 4. 3√2×√2 5. √2×3√2

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