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Fractions and Percentages

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Year 7 Unit on Fractions

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Fractions and Percentages

  1. 1. Fractions and PercentagesTopics we will cover:• Naming Fractions.• Highest Common Factor (HCF) and Lowest Common Multiple(LCM).• Equivalent Fractions.• Simplifying Fractions.• Ordering Fractions.• Adding and Subtracting Fractions.• Adding and Subtracting Mixed Numerals.• Finding a Fraction of a Quantity.• Multiplying Fractions.• Dividing Fractions.• Percentages and Fractions.• Percentages and Decimals.• Converting Percentages.• Finding a Percentage of a Quantity.
  2. 2. Naming Fractions aDefinition: A fraction is a number usually expressed in the form b HOME
  3. 3. Naming Fractions a Definition: A fraction is a number usually expressed in the form b The top number is called the numerator The line in 3 between is 4 called the vinculum.The bottom number is called the denominator. HOME
  4. 4. Naming Fractions a Definition: A fraction is a number usually expressed in the form b The top number is called the numerator The line in 3 between is 4 called the vinculum. The bottom number is called the denominator.Always remember a fraction is the same thing as a division the above fractioncould be written as 3 ÷ 4 . HOME
  5. 5. Naming Fractions a Definition: A fraction is a number usually expressed in the form b The top number is called the numerator The line in 3 between is 4 called the vinculum. The bottom number is called the denominator.Always remember a fraction is the same thing as a division the above fractioncould be written as 3 ÷ 4 . 11Proper Fractions have a numerator less than the denominator e.g. 200 HOME
  6. 6. Naming Fractions a Definition: A fraction is a number usually expressed in the form b The top number is called the numerator The line in 3 between is 4 called the vinculum. The bottom number is called the denominator.Always remember a fraction is the same thing as a division the above fractioncould be written as 3 ÷ 4 . 11Proper Fractions have a numerator less than the denominator e.g. 200 31Improper Fractions have a numerator greater than the denominator e.g. 4 HOME
  7. 7. Naming Fractions a Definition: A fraction is a number usually expressed in the form b The top number is called the numerator The line in 3 between is 4 called the vinculum. The bottom number is called the denominator.Always remember a fraction is the same thing as a division the above fractioncould be written as 3 ÷ 4 . 11Proper Fractions have a numerator less than the denominator e.g. 200 31Improper Fractions have a numerator greater than the denominator e.g. 4 5Mixed Numerals have a whole part and a fraction part e.g. 3 8 HOME
  8. 8. Naming FractionsIt is possible to convert between mixed numerals and improper fractions.Examples: HOME
  9. 9. Naming FractionsIt is possible to convert between mixed numerals and improper fractions.Examples: 3 3Write 1 as an improper fraction (how many quarters are in 1 ?) 4 4 HOME
  10. 10. Naming FractionsIt is possible to convert between mixed numerals and improper fractions.Examples: 3 3Write 1 as an improper fraction (how many quarters are in 1 ?) 4 4 HOME
  11. 11. Naming FractionsIt is possible to convert between mixed numerals and improper fractions.Examples: 3 3Write 1 as an improper fraction (how many quarters are in 1 ?) 4 4 3 7 1 = 4 4 HOME
  12. 12. Naming FractionsIt is possible to convert between mixed numerals and improper fractions.Examples: 3 3Write 1 as an improper fraction (how many quarters are in 1 ?) 4 4 3 7 1 = 4 4 + 3 4 × 1+ 3 7Quick Solution: 1 = = 4 4 4 × HOME
  13. 13. Naming FractionsExamples: 14Write as a mixed numeral (we need to do a division). 3 HOME
  14. 14. Naming FractionsExamples: 14Write as a mixed numeral (we need to do a division). 3Solution: 14 = 14 ÷ 3 3 HOME
  15. 15. Naming FractionsExamples: 14Write as a mixed numeral (we need to do a division). 3Solution: 14 = 14 ÷ 3 3 = 4 remainder 2 HOME
  16. 16. Naming FractionsExamples: 14Write as a mixed numeral (we need to do a division). 3Solution: 14 = 14 ÷ 3 3 = 4 remainder 2 2 =4 3 HOME
  17. 17. Highest Common Factors and Lowest Common Multiples HOME
  18. 18. Highest Common Factors and Lowest Common MultiplesFinding the HCF and LCM of two numbers are useful skills when calculating withfractions. HOME
  19. 19. Highest Common Factors and Lowest Common MultiplesFinding the HCF and LCM of two numbers are useful skills when calculating withfractions.The HCF of two or more numbers is the largest factor that divides evenly intoall of those numbers. HOME
  20. 20. Highest Common Factors and Lowest Common MultiplesFinding the HCF and LCM of two numbers are useful skills when calculating withfractions.The HCF of two or more numbers is the largest factor that divides evenly intoall of those numbers.ExampleFind the HCF of 24 and 32, (list the factors and find the largest number in bothlists). HOME
  21. 21. Highest Common Factors and Lowest Common MultiplesFinding the HCF and LCM of two numbers are useful skills when calculating withfractions.The HCF of two or more numbers is the largest factor that divides evenly intoall of those numbers.ExampleFind the HCF of 24 and 32, (list the factors and find the largest number in bothlists).24: 1, 2, 3, 4, 6, 8, 12, 24. HOME
  22. 22. Highest Common Factors and Lowest Common MultiplesFinding the HCF and LCM of two numbers are useful skills when calculating withfractions.The HCF of two or more numbers is the largest factor that divides evenly intoall of those numbers.ExampleFind the HCF of 24 and 32, (list the factors and find the largest number in bothlists).24: 1, 2, 3, 4, 6, 8, 12, 24.32: 1, 2, 4, 8, 16, 32. HOME
  23. 23. Highest Common Factors and Lowest Common MultiplesFinding the HCF and LCM of two numbers are useful skills when calculating withfractions.The HCF of two or more numbers is the largest factor that divides evenly intoall of those numbers.ExampleFind the HCF of 24 and 32, (list the factors and find the largest number in bothlists).24: 1, 2, 3, 4, 6, 8, 12, 24.32: 1, 2, 4, 8, 16, 32. HOME
  24. 24. Highest Common Factors and Lowest Common MultiplesFinding the HCF and LCM of two numbers are useful skills when calculating withfractions.The HCF of two or more numbers is the largest factor that divides evenly intoall of those numbers.ExampleFind the HCF of 24 and 32, (list the factors and find the largest number in bothlists).24: 1, 2, 3, 4, 6, 8, 12, 24.32: 1, 2, 4, 8, 16, 32. The HCF of 24 and 32 is 8. HOME
  25. 25. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers. HOME
  26. 26. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). HOME
  27. 27. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........ HOME
  28. 28. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........6: 6, 12, 18...... HOME
  29. 29. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........6: 6, 12, 18...... HOME
  30. 30. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........ The LCM of 4 and 6 is 126: 6, 12, 18...... HOME
  31. 31. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........ The LCM of 4 and 6 is 126: 6, 12, 18......Find the LCM of:b) 3 and 9 HOME
  32. 32. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........ The LCM of 4 and 6 is 126: 6, 12, 18......Find the LCM of:b) 3 and 93: 3, 6, 9, 12........ HOME
  33. 33. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........ The LCM of 4 and 6 is 126: 6, 12, 18......Find the LCM of:b) 3 and 93: 3, 6, 9, 12........9: 9, 18, 27..... HOME
  34. 34. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........ The LCM of 4 and 6 is 126: 6, 12, 18......Find the LCM of:b) 3 and 93: 3, 6, 9, 12........9: 9, 18, 27..... HOME
  35. 35. Highest Common Factors and Lowest Common MultiplesThe LCM of two or more numbers is the smallest number that is a multiple ofall those numbers.ExampleFind the LCM of:a) 4 and 6 (list the multiples of each number and choose the smallest number inboth lists). 4: 4, 8, 12, 16........ The LCM of 4 and 6 is 126: 6, 12, 18......Find the LCM of:b) 3 and 93: 3, 6, 9, 12........ The LCM of 3 and 9 is 99: 9, 18, 27..... HOME
  36. 36. Equivalent FractionsEquivalent fractions have the same value even though they may look different. HOME
  37. 37. Equivalent FractionsEquivalent fractions have the same value even though they may look different. 1 2 6 are equivalent fractions. = = 2 4 12 HOME
  38. 38. Equivalent FractionsEquivalent fractions have the same value even though they may look different. 1 2 6 are equivalent fractions. = = 2 4 12 HOME
  39. 39. Equivalent FractionsEquivalent fractions have the same value even though they may look different. 1 2 6 are equivalent fractions. = = 2 4 12 HOME
  40. 40. Equivalent FractionsEquivalent fractions have the same value even though they may look different. 1 2 6 are equivalent fractions. = = 2 4 12 HOME
  41. 41. Equivalent FractionsEquivalent fractions are found by multiplying the numerator and denominator bythe same number. HOME
  42. 42. Equivalent FractionsEquivalent fractions are found by multiplying the numerator and denominator bythe same number.Examplesa) Write equivalent fractions for HOME
  43. 43. Equivalent FractionsEquivalent fractions are found by multiplying the numerator and denominator bythe same number.Examplesa) Write equivalent fractions for 4 = 5 HOME
  44. 44. Equivalent FractionsEquivalent fractions are found by multiplying the numerator and denominator bythe same number.Examplesa) Write equivalent fractions for 4 = 5b) Find the missing term in each of these pairs of equivalent fractions HOME
  45. 45. Equivalent FractionsEquivalent fractions are found by multiplying the numerator and denominator bythe same number.Examplesa) Write equivalent fractions for 4 = 5b) Find the missing term in each of these pairs of equivalent fractions 3 i) = 4 20 HOME
  46. 46. Equivalent FractionsEquivalent fractions are found by multiplying the numerator and denominator bythe same number.Examplesa) Write equivalent fractions for 4 = 5b) Find the missing term in each of these pairs of equivalent fractions 3 5 35 i) = ii) = 4 20 9 HOME
  47. 47. Equivalent FractionsEquivalent fractions are found by multiplying the numerator and denominator bythe same number.Examplesa) Write equivalent fractions for 4 = 5b) Find the missing term in each of these pairs of equivalent fractions 3 5 35 16 i) = ii) = iii) = 4 20 9 24 6 HOME
  48. 48. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction. HOME
  49. 49. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both. HOME
  50. 50. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) 5 = 10 HOME
  51. 51. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) 5 5 ×1 = 10 5 × 2 HOME
  52. 52. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) 5 5 ×1 = 10 5 × 2 HOME
  53. 53. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) 5 5 ×1 = 10 5 × 2 HOME
  54. 54. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) 5 5 ×1 = 10 5 × 2 1 = 2 HOME
  55. 55. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) 5 5 ×1 = 10 5 × 2 1 = 2HCF of 5and 10 is 5 HOME
  56. 56. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) 5 5 ×1 4 = = 10 5 × 2 6 1 = 2HCF of 5and 10 is 5 HOME
  57. 57. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) 5 5 ×1 4 2×2 = = 10 5 × 2 6 2×3 1 = 2HCF of 5and 10 is 5 HOME
  58. 58. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) 5 5 ×1 4 2×2 = = 10 5 × 2 6 2×3 1 = 2HCF of 5and 10 is 5 HOME
  59. 59. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) 5 5 ×1 4 2×2 = = 10 5 × 2 6 2×3 1 = 2HCF of 5and 10 is 5 HOME
  60. 60. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) 5 5 ×1 4 2×2 = = 10 5 × 2 6 2×3 1 2 = = 2 3HCF of 5and 10 is 5 HOME
  61. 61. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) 5 5 ×1 4 2×2 = = 10 5 × 2 6 2×3 1 2 = = 2 3HCF of 5 HCF of 4and 10 is 5 and 6 is 2 HOME
  62. 62. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) c) 5 5 ×1 4 2×2 18 = = = 10 5 × 2 6 2×3 42 1 2 = = 2 3HCF of 5 HCF of 4and 10 is 5 and 6 is 2 HOME
  63. 63. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) c) 5 5 ×1 4 2×2 18 6×3 = = = 10 5 × 2 6 2×3 42 6×7 1 2 = = 2 3HCF of 5 HCF of 4and 10 is 5 and 6 is 2 HOME
  64. 64. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) c) 5 5 ×1 4 2×2 18 6×3 = = = 10 5 × 2 6 2×3 42 6×7 1 2 = = 2 3HCF of 5 HCF of 4and 10 is 5 and 6 is 2 HOME
  65. 65. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) c) 5 5 ×1 4 2×2 18 6×3 = = = 10 5 × 2 6 2×3 42 6×7 1 2 = = 2 3HCF of 5 HCF of 4and 10 is 5 and 6 is 2 HOME
  66. 66. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) c) 5 5 ×1 4 2×2 18 6×3 = = = 10 5 × 2 6 2×3 42 6×7 1 2 3 = = = 2 3 7HCF of 5 HCF of 4and 10 is 5 and 6 is 2 HOME
  67. 67. Simplifying FractionsIn a list of equivalent fractions the one with the smallest possible numeratorand denominator is called the most simple fraction.To find the most simple fraction or to simplify fractions one needs to find theHCF of the numerator and denominator and cancel it out of both.ExamplesSimplify:a) b) c) 5 5 ×1 4 2×2 18 6×3 = = = 10 5 × 2 6 2×3 42 6×7 1 2 3 = = = 2 3 7HCF of 5 HCF of 4 HCF of 18and 10 is 5 and 6 is 2 and 42 is 6 HOME
  68. 68. Simplifying FractionsImproper fractions are simplified in the same manner as proper fractions. Theythen should be written as mixed numerals. HOME
  69. 69. Simplifying FractionsImproper fractions are simplified in the same manner as proper fractions. Theythen should be written as mixed numerals.ExampleSimplify: 36 = 27 HOME
  70. 70. Simplifying FractionsImproper fractions are simplified in the same manner as proper fractions. Theythen should be written as mixed numerals.ExampleSimplify: 36 9 × 4 = 27 9 × 3 HOME
  71. 71. Simplifying FractionsImproper fractions are simplified in the same manner as proper fractions. Theythen should be written as mixed numerals.ExampleSimplify: 36 9 × 4 = 27 9 × 3 HOME
  72. 72. Simplifying FractionsImproper fractions are simplified in the same manner as proper fractions. Theythen should be written as mixed numerals.ExampleSimplify: 36 9 × 4 = 27 9 × 3 HOME
  73. 73. Simplifying FractionsImproper fractions are simplified in the same manner as proper fractions. Theythen should be written as mixed numerals.ExampleSimplify: 36 9 × 4 = 27 9 × 3 4 = 3 HOME
  74. 74. Simplifying FractionsImproper fractions are simplified in the same manner as proper fractions. Theythen should be written as mixed numerals.ExampleSimplify: 36 9 × 4 = 27 9 × 3 4 = 3 1 =1 3 HOME
  75. 75. Simplifying FractionsMixed numerals can have their fraction part simplified. HOME
  76. 76. Simplifying FractionsMixed numerals can have their fraction part simplified.ExamplesSimplify: 11 6 = 33 HOME
  77. 77. Simplifying FractionsMixed numerals can have their fraction part simplified.ExamplesSimplify: 11 11× 1 6 =6 33 11× 3 HOME
  78. 78. Simplifying FractionsMixed numerals can have their fraction part simplified.ExamplesSimplify: 11 11× 1 6 =6 33 11× 3 HOME
  79. 79. Simplifying FractionsMixed numerals can have their fraction part simplified.ExamplesSimplify: 11 11× 1 6 =6 33 11× 3 HOME
  80. 80. Simplifying FractionsMixed numerals can have their fraction part simplified.ExamplesSimplify: 11 11× 1 6 =6 33 11× 3 1 =6 3 HOME
  81. 81. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa. HOME
  82. 82. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? 7 7 HOME
  83. 83. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 HOME
  84. 84. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 6 6 2 is larger, or we may write > 7 7 7 HOME
  85. 85. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 6 6 2 is larger, or we may write > 7 7 7 3 4b) Which is smaller or ? 8 9 HOME
  86. 86. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 6 6 2 is larger, or we may write > 7 7 7 3 4 (Denominators are different, we need equivalent fractionsb) Which is smaller or ? with a common denominator. Multiply both fractions by the 8 9 denominator of the other) HOME
  87. 87. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 6 6 2 is larger, or we may write > 7 7 7 3 4 (Denominators are different, we need equivalent fractionsb) Which is smaller or ? with a common denominator. Multiply both fractions by the 8 9 denominator of the other)3 3 × 9 27 = =8 8 × 9 72 HOME
  88. 88. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 6 6 2 is larger, or we may write > 7 7 7 3 4 (Denominators are different, we need equivalent fractionsb) Which is smaller or ? with a common denominator. Multiply both fractions by the 8 9 denominator of the other)3 3 × 9 27 = =8 8 × 9 72 4 4 × 8 32 = = 9 9 × 8 72 HOME
  89. 89. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 6 6 2 is larger, or we may write > 7 7 7 3 4 (Denominators are different, we need equivalent fractionsb) Which is smaller or ? with a common denominator. Multiply both fractions by the 8 9 denominator of the other)3 3 × 9 27 27 32 = = <8 8 × 9 72 72 72 4 4 × 8 32 = = 9 9 × 8 72 HOME
  90. 90. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 6 6 2 is larger, or we may write > 7 7 7 3 4 (Denominators are different, we need equivalent fractionsb) Which is smaller or ? with a common denominator. Multiply both fractions by the 8 9 denominator of the other)3 3 × 9 27 27 32 = = <8 8 × 9 72 72 72 4 4 × 8 32 3 4 = = ∴ < 9 9 × 8 72 8 9 HOME
  91. 91. Ordering FractionsOrdering fractions is simply placing them in order from smallest to largest or viceversa.Examples:a) Which is larger 6 or 2 ? (When the denominators are the same this is an easy task) 7 7 6 6 2 is larger, or we may write > 7 7 7 3 4 (Denominators are different, we need equivalent fractionsb) Which is smaller or ? with a common denominator. Multiply both fractions by the 8 9 denominator of the other)3 3 × 9 27 27 32 = = <8 8 × 9 72 72 72 4 4 × 8 32 3 4 = = ∴ < (Always refer back to original fractions) 9 9 × 8 72 8 9 HOME
  92. 92. Adding and Subtracting FractionsFractions with the same denominator, simply add or subtract the numerators. HOME
  93. 93. Adding and Subtracting FractionsFractions with the same denominator, simply add or subtract the numerators.Examples:a) 1 2 3 + = 5 5 5 HOME
  94. 94. Adding and Subtracting FractionsFractions with the same denominator, simply add or subtract the numerators.Examples:a) 1 2 3 + = 5 5 5 + HOME
  95. 95. Adding and Subtracting FractionsFractions with the same denominator, simply add or subtract the numerators.Examples:a) 1 2 3 + = 5 5 5 + = HOME
  96. 96. Adding and Subtracting FractionsFractions with the same denominator, simply add or subtract the numerators.Examples:a) 1 2 3 + = 5 5 5 + =b) 5 2 3 − = 7 7 7 HOME
  97. 97. Adding and Subtracting FractionsFractions with the same denominator, simply add or subtract the numerators.Examples:a) 1 2 3 + = 5 5 5 + =b) 5 2 3 − = 7 7 7 − HOME
  98. 98. Adding and Subtracting FractionsFractions with the same denominator, simply add or subtract the numerators.Examples:a) 1 2 3 + = 5 5 5 + =b) 5 2 3 − = 7 7 7 − = HOME
  99. 99. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators. HOME
  100. 100. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 + = + 4 6 12 12 HOME
  101. 101. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 HOME
  102. 102. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 HOME
  103. 103. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 HOME
  104. 104. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 13 1 = =1 12 12 HOME
  105. 105. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 13 1 = =1 12 12Examples:b) 2 3 8 3 − = − 5 20 20 20 HOME
  106. 106. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 13 1 = =1 12 12Examples:b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new − = − denominator) 5 20 20 20 HOME
  107. 107. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 13 1 = =1 12 12Examples:b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new − = − denominator) 5 20 20 20 HOME
  108. 108. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 13 1 = =1 12 12Examples:b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new − = − denominator) 5 20 20 20 8−3 = 20 HOME
  109. 109. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 13 1 = =1 12 12Examples:b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new − = − denominator) 5 20 20 20 8−3 = 20 5 1 = = HOME 20 4
  110. 110. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 13 1 = =1 12 12Examples:b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new − = − denominator) 5 20 20 20 8−3 = 20 5 1 = = HOME 20 4
  111. 111. Adding and Subtracting FractionsFractions with different denominators need to be converted to equivalentfractions with the same denominator. This common denominator should bethe LCM of the original denominators.Examples:a) 1 5 3 10 (The LCM of 4 and 6 is 12 so that is our new + = + denominator) 4 6 12 12 3 + 10 = 12 13 1 = =1 12 12Examples:b) 2 3 8 3 (The LCM of 5 and 20 is 20 so that is our new − = − denominator) 5 20 20 20 8−3 = 20 (Always simplify fractions if you can) 5 1 = = HOME 20 4
  112. 112. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions. HOME
  113. 113. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1− = 8 HOME
  114. 114. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 1− = − 8 1 8 HOME
  115. 115. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 1− = − 8 1 8 8 1 = − 8 8 HOME
  116. 116. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 1− = − 8 1 8 8 1 = − 8 8 7 = 8 HOME
  117. 117. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 b) 3 1− = − 7− = 8 1 8 5 8 1 = − 8 8 7 = 8 HOME
  118. 118. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 b) 3 7 3 1− = − 7− = − 8 1 8 5 1 5 8 1 = − 8 8 7 = 8 HOME
  119. 119. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 b) 3 7 3 1− = − 7− = − 8 1 8 5 1 5 8 1 35 3 = − = − 8 8 5 5 7 = 8 HOME
  120. 120. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 b) 3 7 3 1− = − 7− = − 8 1 8 5 1 5 8 1 35 3 = − = − 8 8 5 5 7 32 = = 8 5 HOME
  121. 121. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 b) 3 7 3 1− = − 7− = − 8 1 8 5 1 5 8 1 35 3 = − = − 8 8 5 5 7 32 = = 8 5 2 =6 5 HOME
  122. 122. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 b) 3 7 3 c) 1 1 1− = − 7− = − 6 −4 = 8 1 8 5 1 5 3 2 8 1 35 3 = − = − 8 8 5 5 7 32 = = 8 5 2 =6 5 HOME
  123. 123. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions.ExamplesEvaluate the following:a) 1 1 1 b) 3 7 3 c) 1 1 19 9 1− = − 7− = − 6 −4 = − 8 1 8 5 1 5 3 2 3 2 8 1 35 3 = − = − 8 8 5 5 7 32 = = 8 5 2 =6 5 HOME
  124. 124. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions. LCM of 2Examples and 3 is 6Evaluate the following:a) 1 1 1 b) 3 7 3 c) 1 1 19 9 1− = − 7− = − 6 −4 = − 8 1 8 5 1 5 3 2 3 2 8 1 35 3 19 × 2 9 × 3 = − = − = − 8 8 5 5 3× 2 2 × 3 7 32 = = 8 5 2 =6 5 HOME
  125. 125. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions. LCM of 2Examples and 3 is 6Evaluate the following:a) 1 1 1 b) 3 7 3 c) 1 1 19 9 1− = − 7− = − 6 −4 = − 8 1 8 5 1 5 3 2 3 2 8 1 35 3 19 × 2 9 × 3 = − = − = − 8 8 5 5 3× 2 2 × 3 7 32 38 27 = = = − 8 5 6 6 2 =6 5 HOME
  126. 126. Adding and Subtracting Mixed NumeralsTo add or subtract mixed numerals convert them to improper fractions and followthe rules adding and subtracting proper fractions. LCM of 2Examples and 3 is 6Evaluate the following:a) 1 1 1 b) 3 7 3 c) 1 1 19 9 1− = − 7− = − 6 −4 = − 8 1 8 5 1 5 3 2 3 2 8 1 35 3 19 × 2 9 × 3 = − = − = − 8 8 5 5 3× 2 2 × 3 7 32 38 27 = = = − 8 5 6 6 2 11 =6 = 5 6 5 =1 6 HOME
  127. 127. Adding and Subtracting Mixed Numerals HOME
  128. 128. Adding and Subtracting Mixed NumeralsExamplesEvaluate the following:a) HOME
  129. 129. Adding and Subtracting Mixed NumeralsExamplesEvaluate the following:a) 5 1 6 +4 6 9 HOME
  130. 130. Adding and Subtracting Mixed NumeralsExamplesEvaluate the following:a) 5 1 41 37 6 +4 = + 6 9 6 9 HOME
  131. 131. Adding and Subtracting Mixed NumeralsExamplesEvaluate the following:a) 5 1 41 37 6 +4 = + 6 9 6 9 41× 3 37 × 2 = + 6×3 9×2 LCM of 6 and 9 is 18 HOME
  132. 132. Adding and Subtracting Mixed NumeralsExamplesEvaluate the following:a) 5 1 41 37 6 +4 = + 6 9 6 9 41× 3 37 × 2 = + 6×3 9×2 LCM of 6 = 123 74 + and 9 is 18 18 18 HOME
  133. 133. Adding and Subtracting Mixed NumeralsExamplesEvaluate the following:a) 5 1 41 37 6 +4 = + 6 9 6 9 41× 3 37 × 2 = + 6×3 9×2 LCM of 6 = 123 74 + and 9 is 18 18 18 197 = 18 17 = 10 18 HOME
  134. 134. Adding and Subtracting Mixed NumeralsExamplesEvaluate the following:a) Your Turn! b) 5 1 41 37 2 3 6 +4 = + 5 +3 = 6 9 6 9 3 4 41× 3 37 × 2 = + 6×3 9×2 LCM of 6 = 123 74 + and 9 is 18 18 18 197 = 18 17 = 10 18 HOME
  135. 135. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: HOME
  136. 136. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4 HOME
  137. 137. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4So the problem of finding becomes, what is ? HOME
  138. 138. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4So the problem of finding becomes, what is ? 3 12 = × 4 1 HOME
  139. 139. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4So the problem of finding becomes, what is ? 3 12 = × 4 1 3 12 = × 1 4 HOME
  140. 140. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4So the problem of finding becomes, what is ? 3 12 = × 4 1 3 12 = × 1 4 36 = 4 =9 HOME
  141. 141. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4So the problem of finding becomes, what is ? 3 12 = × or 4 1 3 12 = × 1 4 36 = 4 =9 HOME
  142. 142. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4So the problem of finding becomes, what is ? 3 12 1 = × or Find of 12 and multiply by 3. 4 1 4 3 12 = × 1 4 36 = 4 =9 HOME
  143. 143. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4So the problem of finding becomes, what is ? 3 12 1 = × or Find of 12 and multiply by 3. 4 1 4 3 12 = × ⎛ 1 ⎞ 1 4 ⎜ × 12 ⎟ × 3 = 3 × 3 ⎝ 4 ⎠ 36 = 4 =9 HOME
  144. 144. Finding a Fraction of a QuantityIn mathematics the word “of” can be replaced by a multiplication symbol.For example: 3 3 of 12 = × 12 4 4So the problem of finding becomes, what is ? 3 12 1 = × or Find of 12 and multiply by 3. 4 1 4 3 12 = × ⎛ 1 ⎞ 1 4 ⎜ × 12 ⎟ × 3 = 3 × 3 ⎝ 4 ⎠ 36 = =9 4 =9 HOME
  145. 145. Finding a Fraction of a QuantityFind:a) 1 of 1 kilometre in metres 10 HOME
  146. 146. Finding a Fraction of a QuantityFind:a) 1 of 1 kilometre in metres 10 1 = × 1000m 10 HOME
  147. 147. Finding a Fraction of a QuantityFind:a) 1 of 1 kilometre in metres 10 1 = × 1000m 10 1 1000 = × 10 1 HOME
  148. 148. Finding a Fraction of a QuantityFind:a) 1 of 1 kilometre in metres 10 1 = × 1000m 10 1 1000 = × 10 1 1 1000 = × 1 10 HOME
  149. 149. Finding a Fraction of a QuantityFind:a) 1 of 1 kilometre in metres 10 1 = × 1000m 10 1 1000 = × 10 1 1 1000 = × 1 10 = 100m HOME
  150. 150. Finding a Fraction of a QuantityFind:a) 1 b) of 1 kilometre in metres 5 10 of 7.2cm 8 1 = × 1000m 10 1 1000 = × 10 1 1 1000 = × 1 10 = 100m HOME
  151. 151. Finding a Fraction of a QuantityFind:a) 1 b) of 1 kilometre in metres 5 10 of 7.2cm 8 1 = × 1000m 5 72 10 = × mm 8 1 1 1000 = × 10 1 1 1000 = × 1 10 = 100m HOME
  152. 152. Finding a Fraction of a QuantityFind:a) 1 b) of 1 kilometre in metres 5 10 of 7.2cm 8 1 = × 1000m 5 72 10 = × mm 8 1 1 1000 5 72 = × = × mm 10 1 1 8 1 1000 = × 1 10 = 100m HOME
  153. 153. Finding a Fraction of a QuantityFind:a) 1 b) of 1 kilometre in metres 5 10 of 7.2cm 8 1 = × 1000m 5 72 10 = × mm 8 1 1 1000 5 72 = × = × mm 10 1 1 8 1 1000 = 45mm = × 1 10 = 100m HOME
  154. 154. Finding a Fraction of a QuantityFind:a) 1 b) of 1 kilometre in metres 5 10 of 7.2cm 8 1 = × 1000m 5 72 10 = × mm 8 1 1 1000 5 72 = × = × mm 10 1 1 8 1 1000 = 45mm or = 4.5cm = × 1 10 = 100m HOME
  155. 155. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.ExamplesFind: 3 7a) × 5 8 HOME
  156. 156. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.ExamplesFind: 3 7 3× 7a) × = 5 8 5×8 HOME
  157. 157. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.ExamplesFind: 3 7 3× 7a) × = 5 8 5×8 21 = 40 HOME
  158. 158. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.ExamplesFind: 3 7 3× 7 2 5a) × = b) × 5 8 5×8 5 7 21 = 40 HOME
  159. 159. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.ExamplesFind: 3 7 3× 7 2 5 2×5a) × = b) × = 5 8 5×8 5 7 5×7 21 = 40 HOME
  160. 160. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.ExamplesFind: 3 7 3× 7 2 5 2×5a) × = b) × = 5 8 5×8 5 7 5×7 21 10 = = 40 35 HOME
  161. 161. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.ExamplesFind: 3 7 3× 7 2 5 2×5a) × = b) × = 5 8 5×8 5 7 5×7 21 10 = = 40 35 2 = 7 HOME
  162. 162. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples orFind: 3 7 3× 7 2 5 2×5a) × = b) × = 5 8 5×8 5 7 5×7 21 10 = = 40 35 2 = 7 HOME
  163. 163. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 or ×Find: 5 7 3 7 3× 7 2 5 2×5a) × = b) × = 5 8 5×8 5 7 5×7 21 10 = = 40 35 2 = 7 HOME
  164. 164. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5a) × = b) × = 5 8 5×8 5 7 5×7 21 10 = = 40 35 2 = 7 HOME
  165. 165. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5a) × = b) × = 5 8 5×8 5 7 5×7 21 10 = = 40 35 2 = 7 HOME
  166. 166. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5a) × = b) × = 5 8 5×8 5 7 5×7 21 10 = = 40 35 2 = 7 HOME
  167. 167. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5 2a) × = b) × = = 5 8 5×8 5 7 5×7 7 21 10 = = 40 35 2 = 7 HOME
  168. 168. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5 2a) × = b) × = = 5 8 5×8 5 7 5×7 7 21 10 Why? = = 40 35 2 = 7 HOME
  169. 169. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5 2a) × = b) × = = 5 8 5×8 5 7 5×7 7 21 10 Why? = = 40 35 2 5 = × 2 5 7 = 7 HOME
  170. 170. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5 2a) × = b) × = = 5 8 5×8 5 7 5×7 7 21 10 Why? = = 40 35 2 5 = × 2 5 7 = 7 2×5 = 5×7 HOME
  171. 171. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5 2a) × = b) × = = 5 8 5×8 5 7 5×7 7 21 10 Why? = = 40 35 2 5 = × 2 5 7 = 7 2×5 = 5×7 5×2 = 5×7 HOME
  172. 172. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5 2a) × = b) × = = 5 8 5×8 5 7 5×7 7 21 10 Why? = = 40 35 2 5 = × 2 5 7 = 7 2×5 = 5×7 5×2 = 5×7 2 = 1× 7 HOME
  173. 173. Multiplying FractionsTo multiply Fractions, multiply the numbers in the numerator and then multiply thenumbers in the denominator.Examples 2 5 2 5 or × = ×Find: 5 7 5 7 3 7 3× 7 2 5 2×5 2a) × = b) × = = 5 8 5×8 5 7 5×7 7 21 10 Why? = = 40 35 2 5 = × 2 5 7 = 7 2×5 = 5×7 5×2 = 5×7 2 = 1× 7 2 = 7 HOME
  174. 174. Dividing FractionsConsider the following examples:Examples: HOME
  175. 175. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = HOME
  176. 176. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = b) 4 ÷ 2 = HOME
  177. 177. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = b) 4 ÷ 2 = c) 6 ÷ 2 = HOME
  178. 178. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = b) 4 ÷ 2 = c) 6 ÷ 2 = d) 8 ÷ 2 = HOME
  179. 179. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = b) 4 ÷ 2 = c) 6 ÷ 2 = d) 8 ÷ 2 = e)10 ÷ 2 = HOME
  180. 180. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5 HOME
  181. 181. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5 1f) 2 ÷ = 2 HOME
  182. 182. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5 1 1f) 2 ÷ = g) 4 ÷ = 2 2 HOME
  183. 183. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5 1 1 1f) 2 ÷ = g) 4 ÷ = h) 6 ÷ = 2 2 2 HOME
  184. 184. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5 1 1 1 1f) 2 ÷ = g) 4 ÷ = h) 6 ÷ = i) 8 ÷ = 2 2 2 2 HOME
  185. 185. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5 1 1 1 1 1f) 2 ÷ = g) 4 ÷ = h) 6 ÷ = i) 8 ÷ = j) 10 ÷ = 2 2 2 2 2 HOME
  186. 186. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5 1 1 1 1 1f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20 2 2 2 2 2 HOME
  187. 187. Dividing FractionsConsider the following examples:Examples:a) 2 ÷ 2 = 1 b) 4 ÷ 2 = 2 c) 6 ÷ 2 = 3 d) 8 ÷ 2 = 4 e)10 ÷ 2 = 5 1 1 1 1 1f) 2 ÷ = 4 g) 4 ÷ = 8 h) 6 ÷ = 12 i) 8 ÷ = 16 j) 10 ÷ = 20 2 2 2 2 2Conclusion: HOME

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