Successfully reported this slideshow.
Upcoming SlideShare
×

# Fractions and Percentages

2,245 views

Published on

Year 7 Unit on Fractions

Published in: Education
• Full Name
Comment goes here.

Are you sure you want to Yes No
• AWESOME, IT HELPS SO MUCH FOR STUDYING!!!!!!!

Are you sure you want to  Yes  No

### 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