The document provides steps to order fractions and mixed numbers from least to greatest. It reviews finding the LCM of denominators to determine the LCD. It shows setting up new denominators using the LCD and finding equivalent fractions using "the rule". The example problem walks through ordering the fractions 1/2, 5/8, 3/4 by finding the LCM of the denominators, setting up new denominators, finding equivalent fractions, and determining the order is 1/2, 3/4, 5/8 from least to greatest.

2. Comparing and Ordering
Fractions and Mixed
Number
Lesson 7-12

3. Review

4. Review
Order the numbers from least to greatest.

5. Review
Order the numbers from least to greatest.
1. 0.5, 0.53, 0.05

6. Review
Order the numbers from least to greatest.
1. 0.5, 0.53, 0.05
2.1.7, 1.07, 1.77

7. Review
Order the numbers from least to greatest.
1. 0.5, 0.53, 0.05
2.1.7, 1.07, 1.77
3.2.96, 3, 2.99

8. Review
Order the numbers from least to greatest.
1. 0.5, 0.53, 0.05
2.1.7, 1.07, 1.77
3.2.96, 3, 2.99
Hint: Line up the decimals

9. Review
Find the LCM of 4 and 8.

10. Review
Find the LCM of 4 and 8.
4:

11. Review
Find the LCM of 4 and 8.
4:
8:

12. Review
Find the LCM of 4 and 8.
4: 4, 8, 12, 16, 20
8:

13. Review
Find the LCM of 4 and 8.
4: 4, 8, 12, 16, 20
8: 8, 16, 24, 32, 40

14. Review
Find the LCM of 4 and 8.
4: 4, 8, 12, 16, 20
8: 8, 16, 24, 32, 40

15. Review
Find the LCM of 4 and 8.
4: 4, 8, 12, 16, 20
8: 8, 16, 24, 32, 40

16. Review
Find the LCM of 4 and 8.
4: 4, 8, 12, 16, 20
8: 8, 16, 24, 32, 40
Which is the least of 8 and 16?

17. Review
Find the LCM of 4 and 8.
4: 4, 8, 12, 16, 20
8: 8, 16, 24, 32, 40
Which is the least of 8 and 16?
LCM is 8

18. When working with
fractions...

19. When working with
fractions...
The LCM becomes the LCD

20. When working with
fractions...
The LCM becomes the LCD
LCD means Least Common
Denominator

21. Which is greater?

22. Which is greater?
1 3
8

23. Which is greater?
13
82 1
5

24. Which is greater?
1 2 3
8
1
5
Check the whole number first.
The mixed number with the larger whole
number is GREATER.

25. Which is greater?
1 2 3
8
1
5
Check the whole number first.
The mixed number with the larger whole
number is GREATER.

26. Which is greater?

27. Which is greater?
25
8

28. Which is greater?
2 2
5
8
3
4

29. Which is greater?
2 2 5
8
3
4
If the whole numbers are the SAME,
you must compare the fractions.

30. Which is greater?
2 2 5
8
3
4
If the whole numbers are the SAME,
you must compare the fractions.
BUT the denominator are different.

31. Which is greater?
2 2 5
8
3
4
If the whole numbers are the SAME,
you must compare the fractions.
BUT the denominator are different.
You must use LCM to find the LCD.

32. Which is greater?
2 2
5
8
3
4

33. Which is greater?
5 3
8 4

34. Which is greater?
5 3
8 4
STEP ONE: Find the LCM of the
denominators 8 and 4

35. Which is greater?
5 3
8 4
STEP ONE: Find the LCM of the
denominators 8 and 4
8:

36. Which is greater?
5 3
8 4
STEP ONE: Find the LCM of the
denominators 8 and 4
8:
4:

37. Which is greater?
5 3
8 4
STEP ONE: Find the LCM of the
denominators 8 and 4
8: 8, 16, 24, 32, 40
4:

38. Which is greater?
5 3
8 4
STEP ONE: Find the LCM of the
denominators 8 and 4
8: 8, 16, 24, 32, 40
4: 4, 8, 12, 16, 20

39. Which is greater?
5 3
8 4
STEP ONE: Find the LCM of the
denominators 8 and 4
8: 8, 16, 24, 32, 40
4: 4, 8, 12, 16, 20

40. Which is greater?
5 3
8 4
STEP ONE: Find the LCM of the
denominators 8 and 4
8: 8, 16, 24, 32, 40
4: 4, 8, 12, 16, 20

41. Which is greater?
5 3
8 4
STEP ONE: Find the LCM of the
denominators 8 and 4
8: 8, 16, 24, 32, 40
LCM = 8
4: 4, 8, 12, 16, 20

42. Which is greater?
2 2
5
8
3
4

43. Which is greater?
5 3
8 4

44. Which is greater?
5
8
3
4

45. Which is greater?
5 STEP TWO: Set up
NEW DENOMINATORS
8
using the LCD (The LCM
from Step One).
3
4

46. Which is greater?
5 STEP TWO: Set up
= NEW DENOMINATORS
8
using the LCD (The LCM
from Step One).
3=
4

47. Which is greater?
5 STEP TWO: Set up
= NEW DENOMINATORS
8 8
using the LCD (The LCM
from Step One).
3=
4 8

48. Which is greater?
5 STEP TWO: Set up
= NEW DENOMINATORS
8 8
using the LCD (The LCM
from Step One).
3= STEP THREE: Find
the equivalent fractions
4 8 using “The Rule”

49. Which is greater?
5 x1 STEP TWO: Set up
= NEW DENOMINATORS
8 x1 8
using the LCD (The LCM
from Step One).
3= STEP THREE: Find
the equivalent fractions
4 8 using “The Rule”

50. Which is greater?
5 x1 5 STEP TWO: Set up
= NEW DENOMINATORS
8 x1 8
using the LCD (The LCM
from Step One).
3= STEP THREE: Find
the equivalent fractions
4 8 using “The Rule”

51. Which is greater?
5 x1 5 STEP TWO: Set up
= NEW DENOMINATORS
8 x1 8
using the LCD (The LCM
from Step One).
3 x2
=
STEP THREE: Find
the equivalent fractions
4 x2 8 using “The Rule”

52. Which is greater?
5 x1 5 STEP TWO: Set up
= NEW DENOMINATORS
8 x1 8
using the LCD (The LCM
from Step One).
3 x2 6
=
STEP THREE: Find
the equivalent fractions
4 x2 8 using “The Rule”

53. Which is greater?
5
8
6
8

54. Which is greater?
5 Don’t forget
about the whole
8 numbers.
6
8

55. Which is greater?
2 5
8
Don’t forget
about the whole
numbers.
2 6
8

56. Which is greater?
2 5
8
Don’t forget
about the whole
numbers.
2
With the new
6 equivalent
fractions, which
8
is larger?

57. Which is greater?
2 5
8
Don’t forget
about the whole
numbers.
2
With the new
6 equivalent
fractions, which
8
is larger?

58. Order the distances from least to greatest
2 2 2 5
8
1
2
3
4

59. Order the distances from least to greatest
5 1 3
8 2 4

60. Order the distances from least to greatest
5
8
1
2
3
4

61. Order the distances from least to greatest
5 The LCM of 8,2,4
is 8. So the LCD is 8
8
1
2
3
4

62. Order the distances from least to greatest
5 = The LCM of 8,2,4
is 8. So the LCD is 8
8
1
=
2
3 =
4

63. Order the distances from least to greatest
5 = The LCM of 8,2,4
is 8. So the LCD is 8
8 8
1
=
2 8
3 =
4 8

64. Order the distances from least to greatest
5 = The LCM of 8,2,4
is 8. So the LCD is 8
8 8
1
= Find equivalent fractions
2 8 using “The Rule”
3 =
4 8

65. Order the distances from least to greatest
5 = 5 The LCM of 8,2,4
is 8. So the LCD is 8
8 8
1 4
= Find equivalent fractions
2 8 using “The Rule”
3 = 6
4 8

66. Order the distances from least to greatest
5 = 5 The LCM of 8,2,4
is 8. So the LCD is 8
8 8
1 4
= Find equivalent fractions
2 8 using “The Rule”
3 = 6 Determine which is
4 8 least to greatest

67. Order the distances from least to greatest
5
8
4
8
6 Determine which is
8 least to greatest

68. Order the distances from least to greatest
5
8
4
8
6 Determine which is
8 least to greatest

69. Order the distances from least to greatest
4 5
8 8
6 Determine which is
8 least to greatest

70. Order the distances from least to greatest
4 5 6
8 8 8
Determine which is
least to greatest

71. Order the distances from least to greatest
Don’t forget the
whole numbers
4 5 6
8 8 8
Determine which is
least to greatest

72. Order the distances from least to greatest
Don’t forget the
whole numbers
2 2 2 4
8
5
8
6
8
Determine which is
least to greatest

73. Compare. Write > < =.

74. Compare. Write > < =.
2 3
3 7

75. Compare. Write > < =.
2 3 Denominators
are different
3 7

76. Compare. Write > < =.
2 3 Denominators
are different
3 7 Find the LCM
Find equivalent
fractions
using LCD
(LCM).

77. Compare. Write > < =.
2 3 Denominators
are different
3 7 Find the LCM
Find equivalent
3: 3, 6, 9, 12, 15, 18, 21 fractions
using LCD
(LCM).

78. Compare. Write > < =.
2 3 Denominators
are different
3 7 Find the LCM
Find equivalent
3: 3, 6, 9, 12, 15, 18, 21 fractions
using LCD
7: 7, 14, 21, 28, 35 (LCM).

79. Compare. Write > < =.
2 3 Denominators
are different
3 7 Find the LCM
Find equivalent
3: 3, 6, 9, 12, 15, 18, 21 fractions
using LCD
7: 7, 14, 21, 28, 35 (LCM).

80. Compare. Write > < =.
2 3 Denominators
are different
3 7 Find the LCM
Find equivalent
3: 3, 6, 9, 12, 15, 18, 21 fractions
using LCD
7: 7, 14, 21, 28, 35 (LCM).
LCM = 21

82. 2
3

83. 2
3
3
7

84. 2 LCM = 21
3
3
7

85. 2 LCM = 21
3 Set up for
equivalent
3 fractions
7

86. 2 LCM = 21
=
3 Set up for
equivalent
3 fractions
=
7

87. 2 LCM = 21
=
3 21 Set up for
equivalent
3 fractions
=
7 21

88. 2 LCM = 21
=
3 21 Set up for
equivalent
3 fractions
=
7 21 Apply the
rule

89. 2 14 LCM = 21
=
3 21 Set up for
equivalent
3 fractions
=
7 21 Apply the
rule

90. 2 14 LCM = 21
=
3 21 Set up for
equivalent
3 9 fractions
=
7 21 Apply the
rule

92. 2 3
3 7

93. 2 3
3 7
14 9
21 21

94. 2 3
3 7
14
21 > 9
21