Download Multiplying Integers

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Multiplying Integers
BEFORE
Now
WHY?
You multiplied whole numbers,
decimals, and fractions.
You’ll multiply integers.
So you can find how deep a seal
dives, as in Ex. 33.
You can use patterns to find rules for multiplying integers.
Word Watch
1 Copy and complete Table 1.
Review Words
product, p. 689
2 What pattern do you see as you read down
the Product column in Table 1? Extend Table 1
using this pattern to find the next two
products, 3 p (1) and 3 p (2).
Table 1
Expression
3p3
3p2
3p1
3p0
Product
9
?
?
?
3 What do you notice about the product of a
positive integer and a negative integer?
4 Copy Table 2. Then use your answer from
Step 3 to complete the table.
with
Review
Need help describing and
extending patterns?
See p. 5.
5 What pattern do you see as you read down
the Product column in Table 2? Extend Table 2
using this pattern to find the next two
products, 3 p (1) and 3 p (2).
Table 2
Expression
3 p 3
3 p 2
3 p 1
3 p 0
Product
?
?
?
?
6 What do you notice about the product of two negative integers?
In the activity, you may have found three rules for multiplying integers.
Multiplying Integers
Words
Same Sign The product of
two integers with the same
sign is positive.
Different Signs The product
of two integers with different
signs is negative.
Zero The product of an
integer and 0 is 0.
272
Chapter 6
Integers
Numbers
4p28
4 p (2) 8
4 p (2) 8
4 p 2 8
4p00
4 p 0 0
Page 2 of 4
EXAMPLE
1
Multiplying Integers
a. 5(7) 35
The product of two integers with the
same sign is positive.
b. 8(2) 16
The product of two integers with
different signs is negative.
c. 12(0) 0
The product of an integer and 0 is 0.
Your turn now
Find the product.
2. 3(4)
1. 9(2)
EXAMPLE
2
3. 5(5)
4. 7(7)
5. 0(14)
Evaluating Variable Expressions
a. Evaluate a2 when a 3.
b. Evaluate xyz when x 2, y 4, and z 6.
Solution
a. a 2 (3)2
Geography
Substitute 3 for a.
3(3)
Write 3 as a factor 2 times.
9
Multiply 3 and 3.
b. xyz 2(4)(6)
Substitute 2 for x, 4 for y, and 6 for z.
8(6)
Multiply 2 and 4.
48
Multiply 8 and 6.
EXAMPLE
3
Using Integer Multiplication
Greenland Most of Greenland is covered with ice that in some places is
almost two miles thick. Scientists estimate that 3 feet of this ice melts
each year. Find the change in the thickness of the ice after 10 years.
■
Greenland
One hotel in Greenland
is made entirely of ice.
The temperature inside
a guest room is usually
10°C. If the outside
temperature is 35°C,
what is the difference
between the inside and
outside temperatures?
Solution
You can find the total change in the ice thickness by multiplying the
yearly change by the number of years. Use 3 for the yearly change
because the thickness of the ice decreases by 3 feet each year.
Change in ice thickness 3(10) 30
ANSWER The thickness of the ice will decrease 30 feet after 10 years.
Lesson 6.4
Multiplying Integers
273
Page 3 of 4
INTERNET
Exercises
eWorkbook Plus
CLASSZONE.COM
More Practice, p. 710
Getting Ready to Practice
Vocabulary Copy and complete using positive or negative.
1. The product of two negative integers is _?_.
2. The product of a positive integer and a negative integer is _?_.
Find the product.
3. 4(8)
4. 3(11)
5. 5(6)
6. 2(12)
Algebra Evaluate the expression when k 9.
7. 6k
with
Example
1
2
3
Homework
Exercises
12–23
25–32
33–34
8. k 2
9. 2k
10. 5k
11. Guided Problem Solving The lowest temperature recorded in May at
McMurdo Station, Antarctica, is 3 times the average low temperature
for May. In degrees Fahrenheit, the average low temperature for May is
16 below zero. What is the lowest temperature recorded in May?
1 What operation is needed to solve this problem?
Online Resources
2 What integer represents the average low temperature for May?
CLASSZONE.COM
• More Examples
• eTutorial Plus
3 Write and evaluate an expression to find the lowest temperature
recorded in May at McMurdo Station.
Practice and Problem Solving
Find the product.
12. 11(10)
13. 0(15)
14. 9(7)
15. 8(5)
16. 6(6)
17. 15(2)
18. 5(7)
19. 4(7)
20. 13(0)
21. 4(4)(2)
22. 10(0)(7)
23. 5(1)(9)
24. Writing Explain how to use addition to find the product of 6 and 8.
Algebra Evaluate the expression when a 5, b 2,
and c 7.
25. 7c
26. b4
27. a 2
28. ab
29. 12b
30. 0c 2
31. ab
32. 2bc
33. Diving Seals Antarctic Weddell seals can dive to extraordinary
depths by collapsing their lungs. If a seal is diving at a speed of
2 meters every second, what integer represents the seal’s change in
position after 30 seconds?
274
Chapter 6
Integers
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34. Airplane Landing Suppose an airplane descends 4 feet every second
prior to landing. Write and simplify an expression to represent the
change in the altitude of the airplane after 10 seconds.
Mental Math Solve the equation using mental math.
35. 25s 100
36. 2n 10
37. 6m 60
38. 9p 36
39. 4a 32
40. 5x 65
41. Panama Canal In the Panama Canal, a system of locks releases
water from upper chambers into lower chambers so that ships can
move through the canal. The water level in an upper chamber begins
at 72 feet and falls about 3 feet every minute for 9 minutes. Write and
evaluate an expression that represents the change in the water depth
after 9 minutes. Then find the depth of the water after 9 minutes.
42. Challenge Would you expect the product of the numbers listed
below to be positive or negative? Explain your reasoning.
4300, 5000, 2100, 1500
Panama Canal
Mixed Review
43. Find the median and the lower and upper quartiles of the following set
of data. Then make a box-and-whisker plot of the data. (Lesson 3.4)
28, 23, 25, 29, 16, 21, 26, 21, 13
Find the difference. (Lesson 6.3)
44. 8 3
45. 21 27
46. 39 (9)
47. 18 (31)
Basic Skills Solve the following problem.
48. You distribute a 500 sheet package of printer paper evenly among
4 printers. How many sheets of paper do you load into each printer?
Test-Taking Practice
INTERNET
State Test Practice
CLASSZONE.COM
49. Multiple Choice What is the product of 9 and 11?
A. 99
B. 20
C. 2
D. 99
50. Short Response Your bank account had a balance of $36. You made
a $3 withdrawal from the account each day for 5 days. Write and
evaluate an expression to find the account balance after the 5 days.
If you continue to make the same daily withdrawal, when will the
balance reach $0?
Lesson 6.4
Multiplying Integers
275