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Enriching Your Mathematical Word Power
Multiplication property 0 a a 0 0
of zero
900
(0)(4) 0
Algebraic Concepts
Examples
Algebraic
expressions
Any meaningful combination of numbers,
variables, and operations
x2 y2, 5abc
Term
An expression containing a number or the
product of a number and one or more variables
raised to powers
3x2, 7x2y, 8
Like terms
Terms with identical variable parts
4bc 8bc 4bc
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ENRICHING YOUR MATHEMATICAL WORD POWER
c. the distance from 0 on the number line
d. the opposite of a number
For each mathematical term, choose the correct meaning.
1.
term
a. an expression containing a number or the product of
a number and one or more variables raised to powers
b. the amount of time spent in this course
c. a word that describes a number
d. a variable
2.
like terms
a. terms that are identical
b. the terms of a sum
c. terms that have the same variables with the same
exponents
d. terms with the same variables
3. variable
a. a letter that is used to represent some numbers
b. the letter x
c. an equation with a letter in it
d. not the same
7. natural numbers
a. the counting numbers
b. numbers that are not irrational
c. the nonnegative numbers
d. numbers that we find in nature
8. rational numbers
a. the numbers 1, 2, 3, and so on
b. the integers
c. numbers that make sense
d. numbers of the form a where a and b are integers
b
with b 0
9. irrational numbers
a. cube roots
b. numbers that cannot be expressed as a ratio of
integers
c. numbers that do not make sense
d. integers
4. additive inverse
a. the number 1
b. the number 0
c. the opposite of addition
d. opposite
10. additive identity
a. the number 0
b. the number 1
c. the opposite of a number
d. when two sums are identical
5. order of operations
a. the order in which operations are to be performed in
the absence of grouping symbols
b. the order in which the operations were invented
c. the order in which operations are written
d. a list of operations in alphabetical order
11.
6. absolute value
a. a definite value
b. a positive number
multiplicative identity
a. the number 0
b. the number 1
c. the reciprocal
d. when two products are identical
12. dividend
a
a. a in b
a
c. the result of b
a
b. b in b
d. what a bank pays on deposits
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The Real Numbers
13. divisor
a:
a
a in b
a
c: the result of b
b:
a
b in b
d: two visors
14. quotient
a
a: a in b
a
c: b
a
b: b in b
d: the divisor plus the remainder
REVIEW EXERCISES
Let A 1, 2, 3, B 3, 4, 5, C 1, 2, 3, 4, 5, D 3,
and E 4, 5. Determine whether each statement is true
or false.
1. A B D
2. A B E
3. A B E
1.1
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
ABC
BCC
ACB
AA
A
(A B) E B
(C B) A D
BC
AE
AB
BC
3D
5A
0E
D
E
1A
Write each interval of real numbers in interval notation
and graph it.
27. The set of real numbers greater than 0
29. The set of real numbers between 5 and 6
30. The set of real numbers between 5 and 6 inclusive
31. The set of real numbers greater than or equal to 1 and
less than 2
32. The set of real numbers greater than 3 and less than or
equal to 6
Note how the review exercises are arranged according to the sections in this chapter. If you are having trouble with a certain type of
problem, refer back to the appropriate section for examples and
explanations.
Which elements of the set
2, 1, 0, 1, 1.732, 3, , 272, 31
are members of these sets?
21. Whole numbers
22. Natural numbers
23. Integers
24. Rational numbers
26. Real numbers
28. The set of real numbers less than 4
Study Tip
1.2
25. Irrational numbers
Write each union or intersection as a single interval.
33. (0, 2) (1, 5)
34.
35.
36.
37.
38.
(0, 2) (1, 5)
(2, 4) (3, )
(, 3) (1, 6)
[2, 6) (4, 8)
[2, 1] [0, 5)
1.3
Evaluate.
4 9
3 (5)
25 37
6 10
(4)(6)
(7)(6)
(8) (4)
39.
40.
41.
42.
43.
44.
45.
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Review Exercises
46. 40 (8)
1
1
47. 4 12
1
1
48. 3
12
5 3
83. 4 2
20
49. 2
30
50. 6
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
1.4
0.04 10
0.05 (3)
6 (2)
0.2 (0.04)
0.5 0.5
0.04 0.2
3.2 (0.8)
(0.2)(0.9)
0 (0.3545)
(6)(0.5)
Evaluate each expression.
61. 4 7(5)
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
(1-53) 53
(4 7)5
(4 7)2
4 72
53643
6 (7 8)
(6 8) (5 9)
5 6 8 10
3 5(6 2 5)
42 9 32
52 (6 5)2
34258
32 42
2
52
74. 13
73.
4 5
75. 7 (2)
59
76. 24
6 3
84. 39
Let a 2, b 3, and c 1. Find the value of each
algebraic expression.
b2 4ac
2
4b
86. a
85.
87. (c b)(c b)
88. (a b)(a b)
89. a2 2ab b2
90. a2 2ab b2
91. a3 b3
92. a3 b3
bc
93. ab
bc
94. 2b a
95. a b 96. b a 97. (a b)c
98. ac bc
1.5
99.
100.
101.
102.
103.
104.
105.
106.
107.
108.
109.
110.
111.
112.
113.
114.
Name the property that justifies each equation.
axxa
050
3(x 1) 3x 3
10 (10) 0
5(2x) (5 2)x
wyyw
1yy
1
4 1
4
5(0.2) 1
313
12 0 0
x11x
18 0 18
2w 2m 2(w m)
5 5 0
2 (3 4) (2 3) 4
77. 1 (0.8)(0.3)
78.
79.
80.
81.
82.
5 (0.2)(0.1)
(3)2 (4)(1)(2)
32 4(1)(3)
3247
3461
Use the distributive property to rewrite each sum or difference
as a product, and each product as a sum of difference, whichever is appropriate.
115. 3x 3a
116. 5x 5y
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(1-54)
117.
118.
119.
120.
121.
122.
123.
124.
125.
126.
3(w 1)
2(m 14)
7x 7
3w 3
5(x 5)
13(b 3)
3(2x 5)
2(5 4x)
p pt
ab b
1.6
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Chapter 1
Page 54
The Real Numbers
150. 37y 37x
z
151. (47y)
w
152. 3w 3y
1
153. (xw)
y
Simplify each expression.
3a 7 4a 5
2m 6 m 2
5(t 4) 3(2t 6)
2(x 3) 2(3 x)
(a 2) 2 a
(w y) 3(y w)
5 3(x 2) 7(x 4) 6
7 2(x 7) 7 x
0.2(x 0.1) (x 0.5)
0.1(x 0.2) (x 0.1)
0.05(x 3) 0.1(x 20)
0.02(x 100) 0.2(x 50)
1
1
139. (x 4) (x 8)
2
4
127.
128.
129.
130.
131.
132.
133.
134.
135.
136.
137.
138.
1
1
140. (2x 1) (x 1)
2
4
9x2 6x 3
141. 3
4x 2
4x 2
142. 2
2
1
154. (xz)
x
155. 5(x y)(z w)
156. (4x 7y)(w xz)
Solve each problem.
157. Teamwork. Istvan can attach one shingle using a nail gun
in 0.2 minute while Robin takes 0.5 minute to attach one
shingle using a hammer. How many shingles per minute
will they be attaching if they work together?
158. Carpeting costs. Write an algebraic expression for the
cost of carpeting a rectangular room that is x yards by
x 2 yards if carpeting costs $20 per square yard?
159. Inflationary spiral. If car prices increase 5% annually,
then in n years a car that currently costs P dollars will cost
P(1.05)n dollars.
a) Use this algebraic expression to predict the price of a
new 2010 Camaro Z28 Convertible, if the price of the
2002 model was $27,759 (www.edmunds.com).
MISCELLANEOUS
Evaluate these expressions for w 24, x 6, y 6, and
z 4. Name the property or properties used.
143. 32z(x y)
148. (42 x) y
149. 752x 752y
Cost (thousands of $)
1
144. (wz) w
145. 768z 768y
146. 28z 28y
147. (12z x) y
b) Use the accompanying graph to predict the first year
in which the price of this car will be over $50,000.
60
50
40
30
20
10
0
4
8
12
Years after 2002
16
FIGURE FOR EXERCISE 159
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Chapter 1 Test
160. Lots of water. The volume of water in a round swimming
pool with radius r feet and depth h feet is 7.5πr 2h gallons.
Find the volume of water in a pool that has diameter
24 feet and depth 3 feet.
r
h
FIGURE FOR EXERCISE 160
CHAPTER 1 TEST
Let A 2, 4, 6, 8, 10, B 3, 4, 5, 6, 7, and C 6, 7, 8, 9, 10. List the elements in each of these sets.
1. A B
2. B C
3. A (B C)
3 (7)
16. 35
6 2
17. 42
Study Tip
18.
Before you take an in-class exam on this chapter, work the sample
test given here. Set aside one hour to work this test and use the answers in the back of this book to grade yourself.Even though your instructor might not ask exactly the same questions, you will get a
good idea of your test readiness.
1
Which elements of 4, 3
, , 0, 1.65, 5
, , 8 are
2
members of these sets?
4. Whole numbers
5. Integers
6. Rational numbers
2
1
4
1
8
19. 24 7
2
7
20. 3 5(2) 21. 5 2 6 10 22. (452 695)[2(4) 8]
23. 478(8) 478(2)
24. 8 3 4(6 9 23)
Evaluate each expression for a 3, b 4, and c 2.
25. b2 4ac
7. Irrational numbers
Graph each of these sets.
8. The integers between 3 and 5
1
3 1 3 2 a2 b2
26. ba
Identify the property that justifies each equation.
28. 2(5 7) 10 14
29. 57 4 4 57
30. 2 (6 x) (2 6) x
9. The interval (3, 5]
31. 6 6 0
32. 1 (6) (6) 1
Write each union or intersection as a single interval.
10. (, 2) (1, 4)
11. (2, 8) [4, 9)
Evaluate each expression.
12. 6 3(5)
13. (2)2 4(3)(
5)
14. 5 6 12
15. 0.02 2
ab 6c
27. b2 c2
Simplify each expression.
33. 3(m 5) 4(2m 3)
34. x 3 0.05(x 2)
1
1
35. (x 4) (x 3)
2
4
36. 3(x2 2y) 2(3y 4x2)
6x2 4x 2
37. 2
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The Real Numbers
Use the distributive property to rewrite each expression as a
product.
38. 5x 40
39. 7t 7
perimeter and the area of the table. Find the actual perimeter and area using x 9.
Solve each problem.
40. If Celeste and her crew of loggers can cut and load one tree
in 0.0625 hour, then how many trees per hour can they cut
and load?
41. The rectangular table for table tennis is x feet long and
x 4 feet wide. Write algebraic expressions for the
42. If the population of the earth grows at 3% annually, then in
n years the present population P will grow to P(1.03)n.
Assuming an annual growth rate of 3% and a present population of 6 billion people, what will the population be in 25
years?