Page 1 of 4
Comparing and
Ordering Fractions
BEFORE
Now
WHY?
You compared and
ordered decimals.
You’ll compare and
order fractions.
So you can determine the greater
fraction of games won, as in Ex. 36.
In the Real World
Word Watch
least common denominator
(LCD), p. 181
Kayaking Julie and Seth are kayaking
down a river. Julie kayaks a distance
7
10
3
4
of mile, and Seth kayaks mile.
Who kayaked the greater distance?
You can compare fractions by using
the least common denominator. The
least common denominator (LCD)
of two or more fractions is the least
common multiple of the denominators.
Comparing Two or More Fractions
1. Find the LCD of the fractions.
2. Use the LCD to write equivalent fractions.
3. Compare the numerators.
EXAMPLE
1
Comparing Fractions Using the LCD
To find who kayaked the greater distance, as described above,
7
10
3
4
you need to compare and .
1 Find the LCD of the fractions.
Because the LCM of 10 and 4 is 20, the LCD is 20.
2 Use the LCD to write equivalent fractions.
7
10
72
10 2
14
20
35
45
3
4
Julie: 15
20
Seth: 14
15
7
3
3 Compare the numerators: 20 < 20, so 10 < 4.
ANSWER Seth kayaked the greater distance.
Lesson 4.5
Comparing and Ordering Fractions
181
Page 2 of 4
EXAMPLE
2
Ordering Fractions Using the LCD
2 3 1
3 8 6
3
4
Order the fractions , , , and from least to greatest.
1 Find the LCD of the fractions.
Because the LCM of 3, 8, 6, and 4 is 24, the LCD is 24.
2 Use the LCD to write equivalent fractions.
2
28
16
3
38
24
9
3
33
24
8
83
4
1
14
24
6
64
3
36
18
4
46
24
4
9
16
18
1
3
2
3
3 Compare the numerators: 24 < 24 < 24 < 24, so 6 < 8 < 3 < 4.
1 3 2
6 8 3
3
4
ANSWER From least to greatest, the fractions are , , , and .
Copy and complete the statement using <, >, or .
Your turn now
7
5
1. _?_ 12
8
9
5
2. _?_ 10
6
3
1
3. _?_ 14
4
Order the fractions from least to greatest.
9 5 3 5
5. , , , 14 7 4 28
2 5 1 1
4. , , , 3 6 2 6
EXAMPLE
3
5 1 1 7
6. , , , 48 2 6 12
Comparing Fractions Using Approximation
13
24
15
34
Use approximation to tell which fraction is greater, or .
13
24
15
34
1
2
Notice that and are both approximately equal to because
the numerator of each fraction is about half the denominator.
1
2
12
24
13
24
1
2
1
2
17
34
15
34
1
2
Because , you know that > .
Because , you know that < .
13
24
15
34
ANSWER So, > .
182
Chapter 4
Number Patterns and Fractions
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 708
Getting Ready to Practice
1. Vocabulary Copy and complete: The _?_ of two or more fractions is the
least common multiple of the denominators of the fractions.
Copy and complete the statement using <, >, or .
9
3
2. _?_ 16
4
9
17
3. _?_ 18
34
6
2
4. _?_ 13
5
Order the fractions from least to greatest.
1 2 3 11
5. , , , 3 5 10 30
3 2 5 7
6. , , , 4 5 8 10
5 7 1 3
7. , , , 18 9 2 4
Use approximation to tell which fraction is greater.
9 8
8. , 17 16
10 15
9. , 21 28
15 27
10. , 31 50
3
1
11. Pies After Thanksgiving dinner, of an apple pie and of a
10
4
pumpkin pie are left uneaten. Which pie has the greater portion left?
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
12–20, 36
21–27
28–35
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
Copy and complete the statement using <, >, or .
5
7
12. _?_ 6
8
11
2
13. _?_ 15
3
11
7
14. _?_ 12
9
7
5
15. _?_ 10
12
13
26
16. _?_ 14
28
15
2
17. _?_ 56
7
5
1
18. _?_ 24
6
7
28
19. _?_ 24
81
20. Carousels Carousel horses that move up
and down are called jumpers. The Broadway
Flying Horses carousel in San Diego has
28 jumpers out of 40 horses. The carousel
at the San Francisco Zoo has 24 jumpers
out of 36 horses. Which carousel has the
greater fraction of jumpers?
Order the fractions from least to greatest.
3 9 1 5
21. , , , 8 32 4 16
3 1 1 9
22. , , , 7 3 2 14
17 5 13 2
23. , , , 81 9 27 3
13 11 5 7
24. , , , 20 15 8 12
5 3 19 7
25. , , , 12 4 36 8
7 32 20 2
26. , , , 9 45 27 3
Lesson 4.5
Comparing and Ordering Fractions
183
Page 4 of 4
27. Wrenches The sizes, in inches, of several wrenches are as follows:
7
11 3 3 1 5
, , , , , and . Order the wrenches from smallest to largest.
16
16 8 4 2 8
Sports
Use approximation to tell which fraction is greater.
15 8
28. , 56 35
40 23
29. , 79 48
13 10
30. , 30 19
19 16
31. , 30 33
55 35
32. , 108 72
47 38
33. , 100 75
37 57
34. , 70 120
223 28
35. , 500 54
36. Tennis At a summer tennis camp, Veronica won 13 games and lost
15 games. Audrey won 17 games and lost 20 games. Write a fraction
for the number of games won to the total number of games played by
each girl. Did Veronica or Audrey win the greater fraction of games?
■
3
3
37. Challenge Write a fraction that is exactly halfway between and .
7
5
Tennis
A tennis racket from
1886 weighed about
14.5 ounces. A modern
tennis racket weighs about
9.3 ounces. What is the
difference in the weights
of the two tennis rackets?
Explain how you found the fraction.
Mixed Review
Order the numbers from least to greatest. (Lesson 2.1)
38. 1.02, 1.2, 1.202, 1.12 39. 9.07, 9.17, 9.71, 9.7 40. 0.54, 0.5, 0.546, 0.55
Find the least common multiple of the numbers. (Lesson 4.4)
41. 15, 27
42. 36, 48
43. 21, 84, 126
Basic Skills Estimate the difference.
44.
4766
2581
45.
43,027
17,985
46.
124,017
78,143
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
47. Multiple Choice Which fractions are in order from least to greatest?
8 5 3
15 9 5
A. , , 7 2 5
18 9 12
B. , , 5 13 16
6 18 27
C. , , 3 5 15
8 16 32
D. , , 48. Short Response Jon and Anne raised money for a school fundraiser.
Jon’s fundraising goal was $225. Anne’s fundraising goal was $175. Jon
raised $150, and Anne raised $90. Write a fraction for how much money
each student raised compared with each student’s fundraising goal.
Who raised the greater fraction of his or her goal?
184
Chapter 4
Number Patterns and Fractions