Solution manual for introductory algebra 5th edition by tussy

Complete the statement: The answer to an addition problem is called a sum.. Complete the statement: The answer to a multiplication problem is called a product.. Complete the statem

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STUDY SET Section 1.1

VOCABULARY

1 Complete the statement:

The answer to an addition problem is called

a sum The answer to a subtraction

problem is called a difference

The answer to a multiplication problem is

called a product The answer to a

division problem is called a quotient

Variables are letters that stand for

numbers

Variables and numbers can be combined

with the operations of addition, subtraction,

multiplication, and division to create

algebraic expressions

An equation is a mathematical sentence

that contains an = symbol

An equation such as t = 2b, which expresses

a known relationship between two or more

variables, is called a formula

The illustration in Exercise 8 shows a

line graph shown

In the illustration below, the horizontal

axis of the graph has been scaled in units of

1 second The vertical axis of the graph

has been scaled in units of 50 feet

9 Classify as expression or equation:

−

c

is an algebraic expression

a The expression 5x – 16 contains the

operations of multiplication and subtraction

b The variable in the expression is x

a The expression

25

12+t

contains the operations of addition and division

b The variable is t

a The equation m + 1 = 20 – m contains

the operations of addition and subtraction

b The variable is m

INSTRUCTOR USE ONLY

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operations of addition and

multiplication

b The variable is y

21 Interpret the graph:

a The dashed lines help us determine that

15–year–old machinery is worth

$35,000

b As the machinery ages, its value

decreases

a The income received from 30 customers

b As the number of customers increases,

the income increases

GUIDED PRACTICE

250 tires are needed to make 125 bicycles

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59 Complete the table:

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67 Translate verbal model into equation:

77 Construct a bar graph:

79 a Complete the table:

b Construct a line graph:

80 a Complete the table:

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WRITING

81–84 Answers may vary

VOCABULARY

A factor is a number being multiplied

Numbers that have only 1 and themselves

as factors, such as 23, 37, and 41, are called

prime numbers

When we write 60 as 2⋅2⋅3⋅5, we say

that we have written 60 in prime–factored

form

The numerator of the fraction

4

3

is 3, and the denominator is 4

Two fractions that represent the same

3 is the reciprocal of 2, because

their product is 1

The least or lowest common denominator for a set of fractions is the smallest number each denominator will divide exactly

The mixed number

3

1

7 represents the sum

of a whole number and a fraction:

c a d

c b

d a d

c b

b d

a To simplify a fraction, we remove

factors equal to 1 in the form of ,

4

4,3

3,22

3,2

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13 Equivalent fractions:

a

30

255

56

1516216

158

16

125

13

375

311

535

24

13713

68

767

55

242

33

313

338

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5469

4916

571

751

861

6618

369

42428

73514

51540

is in lowest terms because 33 and 56

have no common factors

50 Simplify the fraction:

21

26

is in lowest terms because 26 and 21

have no common factors

51 Simplify the fraction:

3

21339

132639

87264

936225

35175490

335

35

3

=

+

=+

56 Perform the operation:

3

19

39

149

19

267

27

6513

613

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2424242424

101725

1025

175

225

4470

54970

570

4914

110

202724

2024

276

58

35645

3545

69

715

1550

1410

325

7

=+

20

3280

42280

63280

10540

956

56120

9120

6540

324

)7(

1418

518

318

1218

56

13

2

=

=+

−

=+

520

720

1420

1220

710

75

2160

2460

2060

255

23

112

5

=

−+

=

−+

9

245

1045

2045

945

219

45

115

981

73

1473

3128

21728

311

728

31

516

4016

51

85

161

85

13

910

4510

31

153

101

153

13

699

743

239

743

279

3110

3810

315

1910

135

4

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1015

93

25

3

=

+

=+

6

296

2186

216

82

73

5524

551

624

72

12

75

12

612

112

312

812

14

13

35353535355

142114

335

5235

4625

27315

7315

2045

163

4

=

=+

66

19198

57198

2198

5599

118

34

124

31

34

73

123

315

32

537

54

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858

132

58

512

321

81121

821

735

121935

1235

14116

12416

1016

58

714

348

16

9716

818

811

48

110

STUDY SET Section 1.3 VOCABULARY

The set of natural numbers is {1, 2, 3, 4, 5, }

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{0, 1, 2, 3, 4, 5, }

The set of integers is

{ , –2, –1, 0, 1, 2, }

Numbers less than zero are negative ,

and numbers greater than zero are

positive

The symbols < and > are inequality

symbols

A rational number can be written as a

quotient (ratio) of two integers

In set–builder notation, the set of rational

numbers is written as

An irrational number is a nonterminating,

nonrepeating decimal

An irrational number cannot be

expressed as a quotient (ratio) of two

integers

All numbers that can be represented by

points on the number line are called real

numbers

Two numbers represented by points on the

number line that are the same distance away

from 0, but on opposite sides of it, are

;10

33.0

;2

72

13

;8

7

;1

99

;1

66

14 Represent as signed number:

a A loss of $15 million –$15 million

b A rainfall total 0.75 inch below average

Numbers that are a distance of 8 from 5 on the number line are 13 and − 3

b Write the statement 16 > –25 using an

inequality symbol that points in the other direction –25 <16

19 Find length of diagonal:

2 in

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d “Irrational numbers are nonterminating,

nonrepeating decimals” is a true

statement

22 True or False:

a “Irrational numbers are real numbers” is

a true statement

b “Every whole number is a rational

number” is a true statement

c “Every rational number can be written

as a fraction” is a true statement

d “Every rational number is a whole

number” is a false statement

23 Signed numbers:

If we begin with the number –4 and find its

opposite, and then find the opposite of that

result, what number do we obtain? –4

33 Interpret the symbol:

5 is read “the square root of 5.”

−15 is read “the absolute value of −15.”

The symbol ≈ means is approximately equal to

The symbols { }, called braces , are used when writing a set

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inequalities

The symbol is called an ellipsis and it

indicates that a set follows an established

pattern that continues forever

41 Name the opposite:

The opposite of the absolute value of

.5

63 Classify the numbers:

34,0,99.35,6

5

natural: none; whole: 0; integers: 0, –50; rational:

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natural: 6; whole: 6; integers: 6, –23;

rational: –0.001, 10½, 6, –23, –5.6;

irrational: π, 7; real: all

irrational: 3 ; real: all

67 Graph the numbers:

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85 Compare the numbers:

2 2

1(− < −

−

−0.666 >−1.34

APPLICATIONS

natural, whole, integers: 750, 5,000;

rational: all; irrational: none; real: all

a natural, whole, integers: 9; rational: 9,

8

13,16

a 4 years had a surplus

b 21 years had a deficit less than $300

billion

1 in., 3 in., 2 in

96 Set the cursor on 1 1

101–104 Answers may vary REVIEW

105 Simplify the expression:

9

454

245

84

5123

93

179

233

179

523

430

915

210

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111 Write in decimal form:

37

5

=+

VOCABULARY

Real numbers that are greater than zero are

called positive real numbers Real

numbers that are less than zero are called

negative real numbers

The only real number that is neither positive

nor negative is zero

The commutative property of addition

states that two numbers can be added in

either order to get the same result

The grouping symbols ( ) are called

parentheses

The property that allows us to group

numbers in addition in any way we want is

called the associative property of

addition

Whenever we add opposites , or

additive inverses , the result is 0

To add two real numbers, with the same sign, add their absolute values and attach their common sign to the sum

To add two real numbers with different signs, subtract their absolute values, the smaller from the larger , and attach the sign of the number with the larger absolute value

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67 + (–67 + 127) = (67 + –67) + 127 = 0 + 127 = 127

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15

−

=+

3

=+

24

14

8(16

3)2

1(16

3

−

=

−+

=

−+

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The stock fell $0.38

1,704.29 + 713.87 + 1,245.57 – 813.45 – 937.49 – 1,532.79 – 500 = –120

(Overdrawn $120)

Matt 50 – (2 + 10 + 8 + 1) = 29 Gonzalo –15 + 50 = 35

Hydecki –2 – (10 + 5 + 6) = –23

–161 + (–28) + (–39) + 61 = –$167 million

A net loss of $167 million

10+3+2+1=16 no WRITING

91–92 Answers may vary

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VOCABULARY

Subtraction finds the difference between

two numbers

In a subtraction, the result is called the

difference

To subtract b from a, add the opposite of b

to a

The difference between the maximum and

the minimum values of a collection of

measurements is called the range of the

values

CONCEPTS

–(–a) = a

To subtract two real numbers, change the

subtraction to addition and take the

opposite of the second number:

a−b=a+( b− )

NOTATION

The expression –7 is read as negative 7

The expression –(–5) is read as the opposite

48

38

14

416

9)4

1(16

9

−

=+

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444

)4

−

5544223344)22(

−

569.714,17)47.592,27(039.307,

−

39937716299)37(71

−

155185321751)85(32

−

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25

912

104

36

1435

155

27

215

915

25

1122

82

111

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The answer to multiplication is called a

product The answer to division is

called a quotient

The numbers –4 and –6 are said to have

like signs The numbers –10 and 12 are

said to have unlike signs

The commutative property of

multiplication states that two numbers can

be multiplied in either order to get the same

result

The statement (ab)c = a(bc) expresses the

associative property of multiplication

undefined

If the product of two numbers is 1, the numbers are called reciprocals or multiplicative inverses

CONCEPTS

The expression –5 + (–5) + (–5) + (–5) can

be represented by the multiplication statement

4(–5)

The quotient of two numbers with unlike signs is negative

The product of two negative numbers is positive

The product of zero and any number is 0

The product of 1 and any number is that number

The division fact 5

a If we multiply two different numbers

and the answer is 0, one of the numbers must be 0

b If we multiply two different numbers

and the answer is 1, the numbers must

be reciprocals (multiplicative inverses)

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