Page 1 of 4
Subtracting Integers
BEFORE
Now
WHY?
You added integers.
You’ll subtract integers.
So you can compare elevations in
South America, as in Ex. 20.
Number line models of the subtraction expression 5 2 and the
addition expression 5 (2) are shown below.
Word Watch
Review Words
opposite, p. 251
Subtraction Model: 5 2
Addition Model: 5 (2)
Add 2.
Subtract 2.
5
1
0
1
2
5
3
4
5
6
7
1
0
1
2
3
4
5
6
7
Notice that the model for 5 2 3 is identical to the model for
5 (2) 3. This suggests the following rule for subtracting integers.
Subtracting Integers
Words To subtract an integer, add its opposite.
Numbers 5 7 5 (7)
EXAMPLE
with
1
Subtracting Integers
a. 2 7 2 (7)
Review
5
Need help with finding
opposites? See p. 251.
14
21
5
Chapter 6
Integers
To subtract 9, add its opposite, 9.
Use rule for adding integers.
d. 10 (5) 10 5
266
To subtract 8, add its opposite, 8.
Use rule for adding integers.
c. 12 (9) 12 9
1. 4 6
To subtract 7, add its opposite, 7.
Use rule for adding integers.
b. 6 8 6 (8)
Your turn now
Algebra a b a (b)
To subtract 5, add its opposite, 5.
Use rule for adding integers.
Find the difference.
2. 7 (8)
3. 2 1
4. 15 (3)
Page 2 of 4
EXAMPLE
Geography
2
Using Integer Subtraction
Geography The highest point in Asia is Mount Everest at 8850 meters.
The shore of the Dead Sea, the lowest point in Asia, is about 410 meters
below sea level. What is the difference between these elevations?
Solution
1 Use integers to represent the two elevations.
Mount Everest: 8850 m
Dead Sea: 410 m
2 Find the difference of 8850 and 410 meters.
8850 (410) 8850 410
■
9260
The Dead Sea
The water in the Dead Sea
is so dense with salt and
minerals that people float
easily. The water in oceans
7
200
and seas is usually salt. The Dead Sea has about
10 times this amount. About
what fraction of the water in
the Dead Sea is salt?
Rule for subtracting integers
Add.
ANSWER The difference between the elevations is 9260 meters.
Change Subtraction can be used to find a change in a variable such as
temperature or elevation. To find the change, subtract the old or start
value of the variable from the new or end value of the variable.
EXAMPLE
3
Finding a Change in Temperature
Weather In Fairfield, Montana, on December 24, 1924, the air
temperature dropped a record amount. At noon, the temperature was
63F. Twelve hours later, the temperature was 21F. What was the
change in temperature?
Solution
Change in temperature end temperature start temperature
21 63
Substitute values.
21 (63)
Rule for subtracting integers
84
Add.
ANSWER The change in temperature was 84F, so the temperature
dropped 84F.
Your turn now
Solve the following problems.
5. Find the difference between an elevation of 535 feet above sea level
and an elevation of 8 feet below sea level.
6. The temperature at 6 A.M. was 12F. At 3 P.M. the temperature was
32F. What was the change in temperature?
Lesson 6.3
Subtracting Integers
267
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 710
Getting Ready to Practice
1. Vocabulary Copy and complete: To simplify the expression 8 (9),
you can add the _?_ of 9 to 8.
Match the subtraction expression with the equivalent addition
expression.
2. 7 3
3. 7 (3)
4. 7 (3)
5. 7 3
A. 7 3
B. 7 (3)
C. 7 (3)
D. 7 3
8. 10 12
9. 16 (2)
Find the difference.
6. 13 (4)
7. 9 3
10. Guided Problem Solving A professional cliff diver dives from a ledge
65 feet above the surface of the water. The diver reaches an underwater
depth of 15 feet before returning to the surface. What was the diver’s
change in elevation from the highest point of the dive to the lowest?
1 What operation do you use to find a change in elevation?
2 What integer represents the highest elevation of the dive?
the lowest elevation of the dive?
Cliff divers in
Acapulco, Mexico
3 Write and evaluate an expression to find the change in elevation.
Practice and Problem Solving
with
Example
1
2
3
Homework
Exercises
11–19
20, 27
21, 28
Find the difference.
11. 17 9
12. 15 (18)
13. 13 24
14. 25 5
15. 7 (7)
16. 5 (25)
17. 54 (7)
18. 56 28
19. 33 (27)
20. Geography The highest point in South America is Mount Aconcagua
Online Resources
at 22,834 feet above sea level. The lowest point in South America is the
Valdes Peninsula at 131 feet below sea level. Find the difference
between these elevations.
CLASSZONE.COM
• More Examples
• eTutorial Plus
21. Death Valley If you were to travel from the lowest point to the
highest point in Death Valley, California, you would begin at 282 feet
below sea level in Badwater and end up at 11,049 feet above sea level
on Telescope Peak. What would your change in elevation be?
22. Compare How is integer subtraction related to integer addition?
268
Chapter 6
Integers
Page 4 of 4
Algebra Evaluate the expression for the given value(s) of the
variable(s).
Science
23. m 5 when m 4
24. 22 x 4 when x 16
25. 10 t (63) when t 17
26. x y when x 9 and y 11
27. Planet Temperatures A temperature
expressed using the Kelvin (K) unit
can be converted to degrees Celsius
(C) by subtracting 273. For example,
300 K (300 273)C 27°C.
Convert the mean surface
temperatures of the planets given
in the table to degrees Celsius.
Planet
Temperature
Mercury
452 K
Earth
281 K
Jupiter
120 K
Saturn
88 K
Pluto
37 K
28. Hiking A group of hikers on a mountain began at an elevation of
■
Planet Temperatures
The Mars Pathfinder landed
on Mars on July 4, 1997,
and recorded information
about the climate of the
planet. The temperatures
it recorded varied from 8F
to 107F. What was the
range of the temperatures?
3350 feet above sea level and stopped for a break at an elevation of
2160 feet above sea level. What was their change in elevation between
these two points? How can you tell from the change in elevation
whether the hikers were going up or down the mountain?
29. Critical Thinking Describe the following pattern: 2, 1, 4, 7, . . . .
Then write the next three integers.
30. Challenge Find two integers whose sum is 2 and whose difference is 8.
Mixed Review
Find the product. (Lesson 2.3)
31. 5.4 2.8
32. 7.3 1.9
33. 0.15 0.28
34. 0.08 0.7
Copy and complete the statement using <, >, or . (Lesson 6.2)
35. 7 _?_ 6
36. 7 _?_ 6
37. 3 _?_ 3
38. 0 _?_ 8
Basic Skills Find a low and high estimate for the product.
39. 12 48
40. 24 47
41. 63 49
42. 116 64
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
43. Multiple Choice Find the difference 14 (7).
A. 21
B. 7
C. 2
D. 7
44. Short Response Write and evaluate the addition expression that is
equivalent to the subtraction expression 1 (4). Then give a
real-world situation that the expression could represent.
Lesson 6.3
Subtracting Integers
269