12 fractions
- 1. Fractions Back to Algebra–Ready Review Content.
- 2. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. p q Fractions
- 3. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. p q Fractions 3 6
- 4. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. Fractions are numbers that measure parts of whole items. p q Fractions 3 6
- 5. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. Fractions are numbers that measure parts of whole items. Suppose a pizza is cut into 6 equal slices and we have 3 of them, the fraction that represents this quantity is . p q 3 6 Fractions 3 6
- 6. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. Fractions are numbers that measure parts of whole items. Suppose a pizza is cut into 6 equal slices and we have 3 of them, the fraction that represents this quantity is . p q 3 6 3 6 Fractions
- 7. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. Fractions are numbers that measure parts of whole items. Suppose a pizza is cut into 6 equal slices and we have 3 of them, the fraction that represents this quantity is . p q 3 6 The bottom number is the number of equal parts in the division and it is called the denominator. 3 6 Fractions
- 8. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. Fractions are numbers that measure parts of whole items. Suppose a pizza is cut into 6 equal slices and we have 3 of them, the fraction that represents this quantity is . p q 3 6 The bottom number is the number of equal parts in the division and it is called the denominator. 3 6 Fractions
- 9. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. Fractions are numbers that measure parts of whole items. Suppose a pizza is cut into 6 equal slices and we have 3 of them, the fraction that represents this quantity is . p q 3 6 The bottom number is the number of equal parts in the division and it is called the denominator. The top number “3” is the number of parts that we have and it is called the numerator. 3 6 Fractions
- 10. Fractions are numbers of the form (or p/q) where p, q 0 are whole numbers. Fractions are numbers that measure parts of whole items. Suppose a pizza is cut into 6 equal slices and we have 3 of them, the fraction that represents this quantity is . p q 3 6 The bottom number is the number of equal parts in the division and it is called the denominator. The top number “3” is the number of parts that we have and it is called the numerator. 3 6 Fractions 3/6 of a pizza
- 11. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions
- 12. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions How many slices should we cut the pizza into and how do we do this?
- 13. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions Cut the pizza into 8 pieces,
- 14. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions Cut the pizza into 8 pieces, take 5 of them.
- 15. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 5/8 of a pizza Cut the pizza into 8 pieces, take 5 of them.
- 16. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 7 12 5/8 of a pizza
- 17. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 7 12 5/8 of a pizza Cut the pizza into 12 pieces,
- 18. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 7 12 5/8 of a pizza Cut the pizza into 12 pieces,
- 19. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 7 12 5/8 of a pizza Cut the pizza into 12 pieces, take 7 of them.
- 20. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 7 12 5/8 of a pizza Cut the pizza into 12 pieces, take 7 of them. or
- 21. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 7 12 5/8 of a pizza 7/12 of a pizza or Cut the pizza into 12 pieces, take 7 of them.
- 22. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 7 12 5/8 of a pizza Note that or is the same as 1.8 8 12 12 7/12 of a pizza or
- 23. For larger denominators we can use a pan–pizza for pictures. For example, 5 8 Fractions 7 12 5/8 of a pizza Fact: a a Note that or is the same as 1.8 8 12 12 = 1 (provided that a = 0.) 7/12 of a pizza or
- 24. Fractions We may talk about the fractional amount of a group of items.
- 25. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that?
- 26. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. To calculate such amounts, we always divide the group into parts indicated by the denominator, then retrieve the number of parts indicated by the numerator. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that?
- 27. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. To calculate such amounts, we always divide the group into parts indicated by the denominator, then retrieve the number of parts indicated by the numerator. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that? 3 4 Divide $100 into 4 equal parts.
- 28. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. To calculate such amounts, we always divide the group into parts indicated by the denominator, then retrieve the number of parts indicated by the numerator. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that? 3 4 Divide $100 into 4 equal parts. 100 ÷ 4 = 25 so each part is $25,
- 29. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. To calculate such amounts, we always divide the group into parts indicated by the denominator, then retrieve the number of parts indicated by the numerator. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that? 3 4 Divide $100 into 4 equal parts. Take 3 parts. 100 ÷ 4 = 25 so each part is $25,
- 30. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. To calculate such amounts, we always divide the group into parts indicated by the denominator, then retrieve the number of parts indicated by the numerator. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that? 3 4 Divide $100 into 4 equal parts. Take 3 parts. 100 ÷ 4 = 25 so each part is $25, 3 parts make $75. So ¾ of $100 is $75.
- 31. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. To calculate such amounts, we always divide the group into parts indicated by the denominator, then retrieve the number of parts indicated by the numerator. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that? 3 4 Divide $100 into 4 equal parts. Take 3 parts. 100 ÷ 4 = 25 so each part is $25, 3 parts make $75. So ¾ of $100 is $75. 7 12 Divide 72 people into 12 equal parts.
- 32. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. To calculate such amounts, we always divide the group into parts indicated by the denominator, then retrieve the number of parts indicated by the numerator. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that? 3 4 Divide $100 into 4 equal parts. Take 3 parts. 100 ÷ 4 = 25 so each part is $25, 3 parts make $75. So ¾ of $100 is $75. 7 12 Divide 72 people into 12 equal parts. 72 ÷ 12 = 6 so each part consists of 6 people,
- 33. Fractions Example A. a. What is ¾ of $100? We may talk about the fractional amount of a group of items. To calculate such amounts, we always divide the group into parts indicated by the denominator, then retrieve the number of parts indicated by the numerator. b. Out of an audience of 72 people at a movie, 7/12 of them like the show very much. How many people is that? 3 4 Divide $100 into 4 equal parts. Take 3 parts. 100 ÷ 4 = 25 so each part is $25, 3 parts make $75. So ¾ of $100 is $75. 7 12 Divide 72 people into 12 equal parts. Take 7 parts. 72 ÷ 12 = 6 so each part consists of 6 people, 7 parts make 42 people. So 7/12 of 92 people is 42 people.
- 34. Whole numbers can be viewed as fractions with denominator 1. Fractions
- 35. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = .5 1 x 1 Fractions
- 36. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0.5 1 x 1 0 x Fractions
- 37. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions
- 38. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics:
- 39. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics: The denominator (bottom) of a fraction can't be 0.
- 40. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics: The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.)
- 41. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics: The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.) Fractions that represents the same quantity are called equivalent fractions.
- 42. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics: The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.) Fractions that represents the same quantity are called equivalent fractions. 1 2 = 2 4
- 43. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics: The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.) Fractions that represents the same quantity are called equivalent fractions. 1 2 = 2 4 = 3 6
- 44. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics: The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.) Fractions that represents the same quantity are called equivalent fractions. … are equivalent fractions.1 2 = 2 4 = 3 6 = 4 8
- 45. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics: The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.) Fractions that represents the same quantity are called equivalent fractions. … are equivalent fractions. The fraction with the smallest denominator of all the equivalent fractions is called the reduced fraction. 1 2 = 2 4 = 3 6 = 4 8
- 46. Whole numbers can be viewed as fractions with denominator 1. Thus 5 = and x = . The fraction = 0, where x 0. However, does not have any meaning, it is undefined. 5 1 x 1 0 x x 0 Fractions The Ultimate No-No of Mathematics: The denominator (bottom) of a fraction can't be 0. (It's undefined if the denominator is 0.) Fractions that represents the same quantity are called equivalent fractions. … are equivalent fractions. The fraction with the smallest denominator of all the equivalent fractions is called the reduced fraction. 1 2 = 2 4 = 3 6 = 4 8 is the reduced one in the above list. 1 2
- 47. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. a b a b = a / c Fractions b / c
- 48. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, a b a b = a / c Fractions b / c
- 49. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c = a*c b*c a*c b*c 1 Fractions b / c
- 50. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c
- 51. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c (Often we omit writing the 1’s after the cancellation.)
- 52. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c To reduce a fraction, we keep divide the top and bottom by common numbers until no more division is possible. What's left is the reduced version. (Often we omit writing the 1’s after the cancellation.)
- 53. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c Example B. Reduce the fraction .78 54 To reduce a fraction, we keep divide the top and bottom by common numbers until no more division is possible. What's left is the reduced version. (Often we omit writing the 1’s after the cancellation.)
- 54. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c Example B. Reduce the fraction .78 54 78 54 = To reduce a fraction, we keep divide the top and bottom by common numbers until no more division is possible. What's left is the reduced version. (Often we omit writing the 1’s after the cancellation.)
- 55. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c Example B. Reduce the fraction .78 54 78 54 = 78/2 54/2 To reduce a fraction, we keep divide the top and bottom by common numbers until no more division is possible. What's left is the reduced version. (Often we omit writing the 1’s after the cancellation.)
- 56. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c Example B. Reduce the fraction .78 54 78 54 = 78/2 54/2 To reduce a fraction, we keep divide the top and bottom by common numbers until no more division is possible. What's left is the reduced version. = 39 27 (Often we omit writing the 1’s after the cancellation.)
- 57. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c Example B. Reduce the fraction .78 54 78 54 = 78/2 54/2 To reduce a fraction, we keep divide the top and bottom by common numbers until no more division is possible. What's left is the reduced version. = 39/3 27/3 39 27 (Often we omit writing the 1’s after the cancellation.)
- 58. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c Example B. Reduce the fraction .78 54 78 54 = 78/2 54/2 = 13 9 . To reduce a fraction, we keep divide the top and bottom by common numbers until no more division is possible. What's left is the reduced version. = 39/3 27/3 39 27 (Often we omit writing the 1’s after the cancellation.)
- 59. Factor Cancellation Rule Given a fraction , then that is, if the numerator and denominator are divided by the same quantity c, the result will be an equivalent fraction. In other words, a common factor of the numerator and the denominator may be canceled as 1, i.e. a b a b = a / c a b .= a*c b*c = a*c b*c 1 Fractions b / c Example B. Reduce the fraction .78 54 78 54 = 78/2 54/2 = 13 9 . To reduce a fraction, we keep divide the top and bottom by common numbers until no more division is possible. What's left is the reduced version. = 39/3 27/3 or divide both by 6 in one step. 39 27 (Often we omit writing the 1’s after the cancellation.)
- 60. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator.
- 61. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. A participant in a sum or a difference is called a term.
- 62. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression).
- 63. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor.
- 64. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 65. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. 2 + 1 2 + 3 3 5 = A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 66. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. 2 + 1 2 + 3 3 5 = This is addition. Can’t cancel! A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 67. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. 2 + 1 2 + 3 = 2 + 1 2 + 3 3 5 = This is addition. Can’t cancel! A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 68. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. 2 + 1 2 + 3 = 2 + 1 2 + 3 = 1 3 3 5 = This is addition. Can’t cancel! !? A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 69. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. 2 + 1 2 + 3 = 2 + 1 2 + 3 = 1 3 3 5 = This is addition. Can’t cancel! !? 2 * 1 2 * 3 = 1 3 Yes A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 70. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. 2 + 1 2 + 3 = 2 + 1 2 + 3 = 1 3 3 5 = This is addition. Can’t cancel! !? Improper Fractions and Mixed Numbers 2 * 1 2 * 3 = 1 3 Yes A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 71. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. 2 + 1 2 + 3 = 2 + 1 2 + 3 = 1 3 3 5 = This is addition. Can’t cancel! !? A fraction whose numerator is the same or more than its denominator (e.g. ) is said to be improper . Improper Fractions and Mixed Numbers 3 2 2 * 1 2 * 3 = 1 3 Yes A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 72. Fractions One common mistake in cancellation is to cancel a common number that is part of an addition (or subtraction) in the numerator or denominator. 2 + 1 2 + 3 = 2 + 1 2 + 3 = 1 3 3 5 = This is addition. Can’t cancel! !? A fraction whose numerator is the same or more than its denominator (e.g. ) is said to be improper . We may put an improper fraction into mixed form by division. Improper Fractions and Mixed Numbers 3 2 2 * 1 2 * 3 = 1 3 Yes A participant in a sum or a difference is called a term. The “2” in the expression “2 + 3” is a term (of the expression). The “2” is in the expression “2 * 3” is called a factor. Terms may not be cancelled. Only factors may be canceled.
- 73. 23 4 Improper Fractions and Mixed Numbers Example C. Put into mixed form.
- 74. 23 4 23 4 = 5 with remainder 3.· · Improper Fractions and Mixed Numbers Example C. Put into mixed form.
- 75. 23 4 23 4 = 5 with remainder 3. Hence,· · 23 4 = 5 + Improper Fractions and Mixed Numbers Example C. Put into mixed form. 3 4
- 76. 23 4 23 4 = 5 with remainder 3. Hence,· · 23 4 = 5 + 5 3 4 . Improper Fractions and Mixed Numbers Example C. Put into mixed form. 3 4 =
- 77. 23 4 23 4 = 5 with remainder 3. Hence,· · 23 4 = 5 + 5 3 4 . Improper Fractions and Mixed Numbers Example C. Put into mixed form. 3 4 = We may put a mixed number into improper fraction by doing the reverse via multiplication.
- 78. 23 4 23 4 = 5 with remainder 3. Hence,· · 23 4 = 5 + 5 3 4 . Improper Fractions and Mixed Numbers Example C. Put into mixed form. 3 4 = We may put a mixed number into improper fraction by doing the reverse via multiplication. Example C: Put into improper form.5 3 4
- 79. 23 4 23 4 = 5 with remainder 3. Hence,· · 23 4 = 5 + 5 3 4 . 5 3 4 = 4*5 + 3 4 Improper Fractions and Mixed Numbers Example C. Put into mixed form. 3 4 = We may put a mixed number into improper fraction by doing the reverse via multiplication. Example C: Put into improper form.5 3 4
- 80. 23 4 23 4 = 5 with remainder 3. Hence,· · 23 4 = 5 + 5 3 4 . 5 3 4 = 4*5 + 3 4 23 4 = Improper Fractions and Mixed Numbers Example C. Put into mixed form. 3 4 = We may put a mixed number into improper fraction by doing the reverse via multiplication. Example C: Put into improper form.5 3 4
- 81. 23 4 23 4 = 5 with remainder 3. Hence,· · 23 4 = 5 + 5 3 4 . 5 3 4 = 4*5 + 3 4 23 4 = Improper Fractions and Mixed Numbers Example C. Put into mixed form. 3 4 = We may put a mixed number into improper fraction by doing the reverse via multiplication. Example C: Put into improper form.5 3 4
- 82. Improper Fractions and Mixed Numbers B. Convert the following improper fractions into mixed numbers then convert the mixed numbers back to the improper form. 9 2 11 3 9 4 13 5 37 12 86 11 121 17 1. 2. 3. 4. 5. 6. 7. Exercise. A. Reduce the following fractions. 4 6 , 8 12 , 15 9 , 24 18 , 30 42 , 54 36 , 60 48 , 72 108