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Comparing and
Ordering Integers
BEFORE
Now
WHY?
You compared and ordered
whole numbers and fractions.
You’ll compare and order
integers.
So you can order historic dates,
as in Ex. 41.
In the Real World
Word Watch
integer, p. 251
negative integer, p. 251
positive integer, p. 251
opposite, p. 251
Football In three plays of a football game,
there is a gain of 7 yards, a loss of 10 yards,
and a gain of 9 yards. What numbers can
you use to represent each gain or loss?
The following numbers are integers :
. . . , 4, 3, 2, 1, 0, 1, 2, 3, 4, . . .
Negative integers are integers that are less
than zero. Positive integers are integers
that are greater than 0. Zero is neither
positive nor negative.
Integers and Their Opposites
Zero
Negative integers
Positive integers
with
Reading
The integer 4 is read
“negative four.” A number
other than 0 that has no
sign is considered to be
positive, so the integer
4 is read “positive four”
or “four.”
4
3
2
1
0
1
2
3
4
Two numbers are opposites if they are the same distance
from 0 on a number line but are on opposite sides of 0. For
example, 3 is the opposite of 3. The opposite of 0 is 0.
EXAMPLE
1
Writing Integers
You can use integers to represent the gains and losses described above.
7 yard gain: 7
Your turn now
1. 15
10 yard loss: 10
9 yard gain: 9
Write the opposite of the integer.
2. 8
Lesson 6.1
3. 35
4. 100
Comparing and Ordering Integers
251
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Comparing Integers You can use a number line to compare and order
integers. Remember that numbers decrease as you move to the left on
a number line and increase as you move to the right.
EXAMPLE
tch Out!
Wa
2
Comparing Integers Using a Number Line
a. Compare 2 and 5.
5
Don’t confuse
a negative sign with a
subtraction sign. A negative
sign indicates a direction
on a number line, not an
operation.
2
2 is to the right of 5.
6 5 4 3 2 1
1
0
2
ANSWER 2 > 5 or 5 < 2.
b. Compare 6 and 1.
6
1
6 5 4 3 2 1
0
1
6 is to the left of 1.
2
ANSWER 6 < 1 or 1 > 6.
Your turn now
Copy and complete the statement using < or >.
5. 0 _?_ 7
EXAMPLE
3
6. 9 _?_ 4
7. 5 _?_ 4
8. 3 _?_ 13
Ordering Integers Using a Number Line
Weather The table shows the average temperatures, in degrees Celsius,
for six months in the Gobi Desert of Mongolia. Which of these months
has the least average temperature?
Month
Average Temperature
Nov.
Dec.
Jan.
Feb.
Mar.
Apr.
6C
14C
15C
12C
3C
6C
Solution
You can graph each integer on a number line to order the temperatures.
Jan. Dec. Feb.
16 14 12 10 8
Nov.
6
Mar.
4
2
Apr.
0
2
4
6
8
The temperatures from least to greatest are: 15, 14, 12, 6, 3, 6.
ANSWER At 15C, January has the least average temperature.
252
Chapter 6
Integers
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 710
Getting Ready to Practice
1. Vocabulary Which of the following numbers are integers?
3
4
2675, 0, 56, , 75, 0.65
Write the integer that represents the situation. Then write the
opposite of that integer.
2. 1333 feet above sea level
3. Sixteen degrees below zero
4. A nine million dollar loss
5. A $15 account withdrawal
Copy and complete the statement using < or >.
6. 2 _?_ 5
7. 8 _?_ 12
8. 36 _?_ 25
9. 1 _?_ 5
Order the temperatures from least to greatest.
10. 7C, 2C, 4C, 8C
with Homework
Example Exercises
1
12–17, 41
2
18–23, 33–40
3
24, 29–32, 41
Online Resources
CLASSZONE.COM
• More Examples
• eTutorial Plus
11. 5F, 9F, 2F, 3F, 1F
Practice and Problem Solving
Draw a number line and graph the integer. Then give a real-world
situation that the integer could represent.
12. 5
13. 0
14. The opposite of 7
15. 9
16. 4
17. The opposite of 3
Copy and complete the statement using < or >.
18. 34 _?_ 43
19. 17 _?_ 13
20. 42 _?_ 37
21. 18 _?_ 3
22. 7 _?_ 4
23. 26 _?_ 26
24. Miniature Golf In miniature golf, par is the
expected number of strokes to finish a hole.
Your score for the game is the sum of your
number of strokes above or below par for each
hole. The player with the least score wins. Order
the scores given in the table from least to
greatest to determine the order of finish.
Player
Andrew
Mandy
Mitchell
Pedro
Score
5
3
0
4
Algebra Name two integer values of the variable that make the
statement true.
25. 0 < d
26. c < 23
27. 10 > k
Lesson 6.1
Comparing and Ordering Integers
253
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5
28. Writing Is the fraction an integer? Explain your reasoning.
6
History
Order the integers from least to greatest.
29. 28, 18, 7, 17, 0, 12
30. 99, 42, 13, 2, 11, 49
31. 150, 235, 435, 345, 75
32. 66, 21, 9, 10, 22, 44
Tell whether the statement is true or false. Explain your reasoning.
33. 3 < 2
34. 6 > 8
35. 6 > 1
36. 0 > 10
37. 7 > 5
38. 50 < 55
39. 100 > 0
40. 67 < 68
41. Roman Battles The location and date of
five Roman battles are listed in the table.
Use a number line to order the battles from
earliest in time to most recent. Let positive
integers represent the years A.D. and
negative integers represent the years B.C.
(for example, 89 B.C. 89).
■
Roman Battles
Around 160 B.C., the armor
worn by a soldier in the
Roman army often included
a body shield called a
scutum. A scutum weighed
about 10 kg. About how
many pounds did a scutum
weigh? Use the fact that
1 kg ≈ 2.2 lb.
Location
Alexandria
Byzantium
Carthage
Jerusalem
Syracuse
Date
47 B.C.
196 A.D.
147 B.C.
70 A.D.
211 B.C.
42. Challenge If the missing integer in the list of numbers below is
the median of the numbers, what could the missing integer be?
44, 23, 11, 12, 27, _?_, 4, 0, 1
Mixed Review
Find the sum or difference. (Lesson 2.2)
43. 12.7 87.35
44. 98.6 5.01
45. 300 11.3
46. 254.65 9.202
Find the sum or difference. (Lesson 5.6)
47.
4 gal 3 qt
5 gal 1 qt
48.
8 yd 10 in. 49.
5 ft 9 in.
1 yd 11 in.
4 ft 10 in.
50.
13 ft 5 in.
2 ft 7 in.
Basic Skills Find the sum or difference.
51. 63 49
52. 109 57
53. 46 27
54. 513 24
Test-Taking Practice
55. Multiple Choice Which statement is true?
INTERNET
State Test Practice
A. 56 < 58
CLASSZONE.COM
B. 1 < 112
C. 7 > 5
D. 9 > 11
56. Short Response The integers 17, 10, 32, 29, and 0 are temperature
readings in degrees Fahrenheit. Graph the integers on a number line
and find the median temperature.
254
Chapter 6
Integers