Solution Manual for Developmental Mathematics, 1st Edition
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INSTRUCTOR’S
SOLUTIONS MANUAL
DANIEL S. MILLER
Niagara County Community College
DEVELOPMENTAL MATH
FOR COLLEGE STUDENTS
Robert Blitzer
Miami Dade College
SOLUTIONS MANUAL
DANIEL S. MILLER
Niagara County Community College
DEVELOPMENTAL MATH
FOR COLLEGE STUDENTS
Robert Blitzer
Miami Dade College
iii
TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS
DEVELOPMENTAL MATH FOR COLLEGE STUDENTS
Chapter 1: Whole Numbers and Introduction to Algebra ..................................1
Chapter 2: Integers and Introduction to Solving Equations............................. 61
Chapter 3: Fractions .......................................................................................107
Chapter 4: Decimals.......................................................................................219
Chapter 5: Percents ........................................................................................309
Chapter 6: Geometry ......................................................................................357
Chapter 7: Statistics and Probability ..............................................................407
Chapter 8: Linear Equations and Inequalities in One Variable .....................443
Chapter 9: Linear Equations in Two Variables .............................................521
Chapter 10: Systems of Linear Equations .......................................................587
Chapter 11: Exponents and Polynomials .........................................................691
Chapter 12: Factoring Polynomials .................................................................775
Chapter 13: Rational Expressions ....................................................................837
Chapter 14: Basics of Functions ......................................................................971
Chapter 15: Inequalities and Problem Solving ..............................................1011
Chapter 16: Radicals, Radical Functions, and Rational Exponents ..............1077
Chapter 17: Quadratic Equations and Functions ...........................................1165
Chapter 18: Exponential and Logarithmic Functions ....................................1325
Chapter 19: Conic Sections and Systems of Nonlinear Equations ................1407
Chapter 20: Sequences, Series, and the Binomial Theorem ..........................1515
Appendices: ....................................................................................................1591
TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS
DEVELOPMENTAL MATH FOR COLLEGE STUDENTS
Chapter 1: Whole Numbers and Introduction to Algebra ..................................1
Chapter 2: Integers and Introduction to Solving Equations............................. 61
Chapter 3: Fractions .......................................................................................107
Chapter 4: Decimals.......................................................................................219
Chapter 5: Percents ........................................................................................309
Chapter 6: Geometry ......................................................................................357
Chapter 7: Statistics and Probability ..............................................................407
Chapter 8: Linear Equations and Inequalities in One Variable .....................443
Chapter 9: Linear Equations in Two Variables .............................................521
Chapter 10: Systems of Linear Equations .......................................................587
Chapter 11: Exponents and Polynomials .........................................................691
Chapter 12: Factoring Polynomials .................................................................775
Chapter 13: Rational Expressions ....................................................................837
Chapter 14: Basics of Functions ......................................................................971
Chapter 15: Inequalities and Problem Solving ..............................................1011
Chapter 16: Radicals, Radical Functions, and Rational Exponents ..............1077
Chapter 17: Quadratic Equations and Functions ...........................................1165
Chapter 18: Exponential and Logarithmic Functions ....................................1325
Chapter 19: Conic Sections and Systems of Nonlinear Equations ................1407
Chapter 20: Sequences, Series, and the Binomial Theorem ..........................1515
Appendices: ....................................................................................................1591
iii
TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS
DEVELOPMENTAL MATH FOR COLLEGE STUDENTS
Chapter 1: Whole Numbers and Introduction to Algebra ..................................1
Chapter 2: Integers and Introduction to Solving Equations............................. 61
Chapter 3: Fractions .......................................................................................107
Chapter 4: Decimals.......................................................................................219
Chapter 5: Percents ........................................................................................309
Chapter 6: Geometry ......................................................................................357
Chapter 7: Statistics and Probability ..............................................................407
Chapter 8: Linear Equations and Inequalities in One Variable .....................443
Chapter 9: Linear Equations in Two Variables .............................................521
Chapter 10: Systems of Linear Equations .......................................................587
Chapter 11: Exponents and Polynomials .........................................................691
Chapter 12: Factoring Polynomials .................................................................775
Chapter 13: Rational Expressions ....................................................................837
Chapter 14: Basics of Functions ......................................................................971
Chapter 15: Inequalities and Problem Solving ..............................................1011
Chapter 16: Radicals, Radical Functions, and Rational Exponents ..............1077
Chapter 17: Quadratic Equations and Functions ...........................................1165
Chapter 18: Exponential and Logarithmic Functions ....................................1325
Chapter 19: Conic Sections and Systems of Nonlinear Equations ................1407
Chapter 20: Sequences, Series, and the Binomial Theorem ..........................1515
Appendices: ....................................................................................................1591
TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS
DEVELOPMENTAL MATH FOR COLLEGE STUDENTS
Chapter 1: Whole Numbers and Introduction to Algebra ..................................1
Chapter 2: Integers and Introduction to Solving Equations............................. 61
Chapter 3: Fractions .......................................................................................107
Chapter 4: Decimals.......................................................................................219
Chapter 5: Percents ........................................................................................309
Chapter 6: Geometry ......................................................................................357
Chapter 7: Statistics and Probability ..............................................................407
Chapter 8: Linear Equations and Inequalities in One Variable .....................443
Chapter 9: Linear Equations in Two Variables .............................................521
Chapter 10: Systems of Linear Equations .......................................................587
Chapter 11: Exponents and Polynomials .........................................................691
Chapter 12: Factoring Polynomials .................................................................775
Chapter 13: Rational Expressions ....................................................................837
Chapter 14: Basics of Functions ......................................................................971
Chapter 15: Inequalities and Problem Solving ..............................................1011
Chapter 16: Radicals, Radical Functions, and Rational Exponents ..............1077
Chapter 17: Quadratic Equations and Functions ...........................................1165
Chapter 18: Exponential and Logarithmic Functions ....................................1325
Chapter 19: Conic Sections and Systems of Nonlinear Equations ................1407
Chapter 20: Sequences, Series, and the Binomial Theorem ..........................1515
Appendices: ....................................................................................................1591
Chapter 1
Whole Numbers and Introduction to Algebra
1
1.1 Check Points
1. a. millions place
b. ones place
c. hundreds place
d. millions place
2. Work from left to right. Write the name of the three-
digit number in each period, followed by the name
of the period and a comma. Do not write the name
of the last period, “ones.”
a. twenty-seven thousand, one hundred forty-three
b. five hundred twenty-one million, six hundred
thirty thousand, fifty-seven
3. a. Begin by noting how to write the number within
each period.53 406
fifty-three thousand, four hundred six
Write the digits for the number in each period,
followed by a comma.
The standard form for the number is 53,406.
Whole Numbers and Introduction to Algebra
1
1.1 Check Points
1. a. millions place
b. ones place
c. hundreds place
d. millions place
2. Work from left to right. Write the name of the three-
digit number in each period, followed by the name
of the period and a comma. Do not write the name
of the last period, “ones.”
a. twenty-seven thousand, one hundred forty-three
b. five hundred twenty-one million, six hundred
thirty thousand, fifty-seven
3. a. Begin by noting how to write the number within
each period.53 406
fifty-three thousand, four hundred six
Write the digits for the number in each period,
followed by a comma.
The standard form for the number is 53,406.
Chapter 1 Whole Numbers and Introduction to Algebra
2
b. Begin by noting how to write the number within each period.204 932 016
two hundred four million, nine hundred thirty-two thousand, sixteen
Write the digits for the number in each period, followed by a comma.
The standard form for the number is 204,932,016.
4. a. The place value chart shows that 704,663 contains 7 hundred-thousands, 0 ten-thousands, 4 thousands, 6 hundreds, 6
tens, and 3 ones. Thus 704,663 is written in expanded form as follows:704,663 700,000 4000 600 60 3.= + + + +
b. The place value chart shows that 49,063,400 contains 4 ten-millions, 9 millions, 0 hundred-thousands, 6 ten-
thousands, 3 thousands, 4 hundreds, 0 tens, and 0 ones. Thus 49,063,400 is written in expanded form as follows:49, 063, 400 40, 000,000 9, 000, 000 60, 000 3000 400.= + + + +
5. a.14 5 because 14 is to the right of 5 on the number line.
b.0 16 because 0 is to the left of 16 on the number line.
6. a. The digit to the right of the thousands digit is 4, which is less than 5. This indicates to leave the thousands digit the
same. Replace all digits to the right with zeros.57, 498 57,000
b. The digit to the right of the hundred-thousands digit is 5. This indicates to add one to the hundred-thousands digit.
Replace all digits to the right with zeros.4,856,902 4,900, 000
c. The digit to the right of the thousands digit is 6, which is greater than 5. This implies to add one to the thousands
digit. Replace all digits to the right with zeros.9602 10, 000
d. The digit to the right of the millions digit is 2, which is less than 5. This implies to leave the millions digit the same.
Replace all digits to the right with zeros.684, 236, 042 684,000,000
7. a. The digit to the right of the billions digit is 0, which is less than 5. This implies to leave the billions digit the same.
Replace all digits to the right with zeros.7, 058, 746,857 7, 000, 000, 000
b. The digit to the right of the ten-thousands digit is 6, which is greater than 5. This implies to add one to the ten-
thousands digit. Replace all digits to the right with zeros.7, 058,746,857 7,058, 750,000
8. a. The cost of a coronary bypass in the United States is $67,583
b. The country with the least amount in the CT scan column is India.
The average cost for this procedure in India is $43.
c. The charge for an appendectomy in Chile is $5509. The countries in which an appendectomy costs more than in
Chile are Canada, Switzerland, and United States.
9. a. We begin with the number of marriages between an African-American husband and a white wife in 2010. Look at
the bars labeled with the year 2010. The yellow bar to the right represents the number of marriages between an
African-American husband and a white wife. The number above this bar is 390, representing 390 thousand. Thus, in
2010, there were 390,000 marriages between an African-American husband and a white wife.
b. Look for the red bar labeled 61 (for 61 thousand, or 61,000). This is the bar to the left for the year labeled 1990.
Thus, in 1990, there were 61,000 marriages between a white husband and an African-American wife.
2
b. Begin by noting how to write the number within each period.204 932 016
two hundred four million, nine hundred thirty-two thousand, sixteen
Write the digits for the number in each period, followed by a comma.
The standard form for the number is 204,932,016.
4. a. The place value chart shows that 704,663 contains 7 hundred-thousands, 0 ten-thousands, 4 thousands, 6 hundreds, 6
tens, and 3 ones. Thus 704,663 is written in expanded form as follows:704,663 700,000 4000 600 60 3.= + + + +
b. The place value chart shows that 49,063,400 contains 4 ten-millions, 9 millions, 0 hundred-thousands, 6 ten-
thousands, 3 thousands, 4 hundreds, 0 tens, and 0 ones. Thus 49,063,400 is written in expanded form as follows:49, 063, 400 40, 000,000 9, 000, 000 60, 000 3000 400.= + + + +
5. a.14 5 because 14 is to the right of 5 on the number line.
b.0 16 because 0 is to the left of 16 on the number line.
6. a. The digit to the right of the thousands digit is 4, which is less than 5. This indicates to leave the thousands digit the
same. Replace all digits to the right with zeros.57, 498 57,000
b. The digit to the right of the hundred-thousands digit is 5. This indicates to add one to the hundred-thousands digit.
Replace all digits to the right with zeros.4,856,902 4,900, 000
c. The digit to the right of the thousands digit is 6, which is greater than 5. This implies to add one to the thousands
digit. Replace all digits to the right with zeros.9602 10, 000
d. The digit to the right of the millions digit is 2, which is less than 5. This implies to leave the millions digit the same.
Replace all digits to the right with zeros.684, 236, 042 684,000,000
7. a. The digit to the right of the billions digit is 0, which is less than 5. This implies to leave the billions digit the same.
Replace all digits to the right with zeros.7, 058, 746,857 7, 000, 000, 000
b. The digit to the right of the ten-thousands digit is 6, which is greater than 5. This implies to add one to the ten-
thousands digit. Replace all digits to the right with zeros.7, 058,746,857 7,058, 750,000
8. a. The cost of a coronary bypass in the United States is $67,583
b. The country with the least amount in the CT scan column is India.
The average cost for this procedure in India is $43.
c. The charge for an appendectomy in Chile is $5509. The countries in which an appendectomy costs more than in
Chile are Canada, Switzerland, and United States.
9. a. We begin with the number of marriages between an African-American husband and a white wife in 2010. Look at
the bars labeled with the year 2010. The yellow bar to the right represents the number of marriages between an
African-American husband and a white wife. The number above this bar is 390, representing 390 thousand. Thus, in
2010, there were 390,000 marriages between an African-American husband and a white wife.
b. Look for the red bar labeled 61 (for 61 thousand, or 61,000). This is the bar to the left for the year labeled 1990.
Thus, in 1990, there were 61,000 marriages between a white husband and an African-American wife.
Loading page 6...
Section 1.1 Basics of Whole Numbers
3
1.1 Concept and Vocabulary Check
1. whole; 0
2. standard
3. periods
4. millions; hundred-thousands; thousands; tens
5. millions; forty-two; nine
6. expanded; 5000; 60; 8
7. number line
8. <
9. >
10. 8; 5; add 1; 9,000,000
11. 2; 3; do not change; 8,542,000
1.1 Exercise Set
Note that exercises #1 - 22 use the following table:
1. hundreds
2. hundreds
3. ones
4. ones
5. hundred-thousands
6. hundred-thousands
7. millions
8. millions
9. ten-millions
10. ten-millions
11. hundred-millions
12. hundred-millions
13. two hundred fifty-eight
14. three hundred twenty-four
15. eight thousand, three hundred seventy-six
16. six thousand, two hundred twenty-six
17. thirty-six thousand, eight hundred eighty
18. fifty-two thousand, seven
19. seven million, five hundred sixty-six thousand
20. four million, three hundred two thousand
21. thirty-five million, two hundred sixty thousand,
three hundred seventy-five
22. fifty-seven million, forty-four thousand, two
hundred eight
23. The standard form is 3468.
24. The standard form is 5283.
25. The standard form is 86,500.
26. The standard form is 58,004.
27. The standard form is 16,402,012.
28. The standard form is 14,204,015.
29. The standard form is 9,000,009.
30. The standard form is 5,000,005.
31. The standard form is 26,034,203.
32. The standard form is 52,028,706.
33. The standard form is 620,595.
34. The standard form is 430,696.
35. The expanded form is600 40 3.+ +
36. The expanded form is500 70 2.+ +
37. The expanded form is5000 40 6.+ +
38. The expanded form is3000 50 7.+ +
39. The expanded form is80,000 1000 300 60 4.+ + + +
3
1.1 Concept and Vocabulary Check
1. whole; 0
2. standard
3. periods
4. millions; hundred-thousands; thousands; tens
5. millions; forty-two; nine
6. expanded; 5000; 60; 8
7. number line
8. <
9. >
10. 8; 5; add 1; 9,000,000
11. 2; 3; do not change; 8,542,000
1.1 Exercise Set
Note that exercises #1 - 22 use the following table:
1. hundreds
2. hundreds
3. ones
4. ones
5. hundred-thousands
6. hundred-thousands
7. millions
8. millions
9. ten-millions
10. ten-millions
11. hundred-millions
12. hundred-millions
13. two hundred fifty-eight
14. three hundred twenty-four
15. eight thousand, three hundred seventy-six
16. six thousand, two hundred twenty-six
17. thirty-six thousand, eight hundred eighty
18. fifty-two thousand, seven
19. seven million, five hundred sixty-six thousand
20. four million, three hundred two thousand
21. thirty-five million, two hundred sixty thousand,
three hundred seventy-five
22. fifty-seven million, forty-four thousand, two
hundred eight
23. The standard form is 3468.
24. The standard form is 5283.
25. The standard form is 86,500.
26. The standard form is 58,004.
27. The standard form is 16,402,012.
28. The standard form is 14,204,015.
29. The standard form is 9,000,009.
30. The standard form is 5,000,005.
31. The standard form is 26,034,203.
32. The standard form is 52,028,706.
33. The standard form is 620,595.
34. The standard form is 430,696.
35. The expanded form is600 40 3.+ +
36. The expanded form is500 70 2.+ +
37. The expanded form is5000 40 6.+ +
38. The expanded form is3000 50 7.+ +
39. The expanded form is80,000 1000 300 60 4.+ + + +
Loading page 7...
Chapter 1 Whole Numbers and Introduction to Algebra
4
40. The expanded form is70, 000 2000 500 40 6.+ + + +
41. The expanded form is50, 000 5000 30 8.+ + +
42. The expanded form is40, 000 4000 20 9.+ + +
43. The expanded form is20,000,000 8,000,000 600,000 40,000.+ + +
44. The expanded form is50,000,000 6,000,000 300,000 7000 30 2.+ + + + +
45.9 3 because 9 is to the right of 3 on the number
line.
46.7 2 because 7 is to the right of 2 on the number
line.
47.0 14 because 0 is to the left of 14 on the number
line.
48.0 16 because 0 is to the left of 16 on the number
line.
49.3600 4500 because 36000 is to the left of 4500 on
the number line.
50.2300 3200 because 2300 is to the left of 3200 on
the number line.
51.200,000 20, 000 because 200,000 is to the right of
20,000 on the number line.
52.300, 000 30, 000 because 300,000 is to the right of
30,000 on the number line.
53. 624 rounded to the nearest ten is 620.
54. 372 rounded to the nearest ten is 370.
55. 627 rounded to the nearest ten is 630.
56. 378 rounded to the nearest ten is 380.
57. 4891 rounded to the nearest hundred is 4900.
58. 5482 rounded to the nearest hundred is 5500.
59. 4831 rounded to the nearest hundred is 4800.
60. 5432 rounded to the nearest hundred is 5400.
61. 61,529 rounded to the nearest thousand is 62,000.
62. 72,503 rounded to the nearest thousand is 73,000.
63. 61,129 rounded to the nearest thousand is 61,000.
64. 72,103 rounded to the nearest thousand is 72,000.
65. 24,628 rounded to the nearest ten-thousand is
20,000.
66. 34,628 rounded to the nearest ten-thousand is
30,000.
67. 345,207 rounded to the nearest ten-thousand is
350,000.
68. 645,308 rounded to the nearest ten-thousand is
650,000.
69. 86,609,100 rounded to the nearest million is
87,000,000.
70. 75,809,100 rounded to the nearest million is
76,000,000.
71. 86,409,100 rounded to the nearest million is
86,000,000.
72. 75,309,100 rounded to the nearest million is
75,000,000.
73. 86,609,100 rounded to the nearest ten-million is
90,000,000.
74. 75,809,100 rounded to the nearest million is
80,000,000.
75. ninety-two quadrillion, two hundred thirty-three
trillion, seven hundred twenty billion, three hundred
sixty-eight million, five hundred forty-seven
thousand, eight hundred.
76. ten-quadrillions
77.700,000, 000, 000 20,000, 000,000+
78.90,000,000,000,000, 000 2,000,000, 000,000,000+
79. 92,233,720,368,547,800 rounded to the nearest ten-
quadrillion is 90,000,000,000,000,000.
The word name is ninety quadrillion.
80. 92,233,720,368,547,800 rounded to the nearest
quadrillion is 92,000,000,000,000,000.
The word name is ninety-two quadrillion
81. Steven Spielberg generates the greatest revenue per
year which is $27,400,000. In word form this is
twenty-seven million, four hundred thousand
dollars.
4
40. The expanded form is70, 000 2000 500 40 6.+ + + +
41. The expanded form is50, 000 5000 30 8.+ + +
42. The expanded form is40, 000 4000 20 9.+ + +
43. The expanded form is20,000,000 8,000,000 600,000 40,000.+ + +
44. The expanded form is50,000,000 6,000,000 300,000 7000 30 2.+ + + + +
45.9 3 because 9 is to the right of 3 on the number
line.
46.7 2 because 7 is to the right of 2 on the number
line.
47.0 14 because 0 is to the left of 14 on the number
line.
48.0 16 because 0 is to the left of 16 on the number
line.
49.3600 4500 because 36000 is to the left of 4500 on
the number line.
50.2300 3200 because 2300 is to the left of 3200 on
the number line.
51.200,000 20, 000 because 200,000 is to the right of
20,000 on the number line.
52.300, 000 30, 000 because 300,000 is to the right of
30,000 on the number line.
53. 624 rounded to the nearest ten is 620.
54. 372 rounded to the nearest ten is 370.
55. 627 rounded to the nearest ten is 630.
56. 378 rounded to the nearest ten is 380.
57. 4891 rounded to the nearest hundred is 4900.
58. 5482 rounded to the nearest hundred is 5500.
59. 4831 rounded to the nearest hundred is 4800.
60. 5432 rounded to the nearest hundred is 5400.
61. 61,529 rounded to the nearest thousand is 62,000.
62. 72,503 rounded to the nearest thousand is 73,000.
63. 61,129 rounded to the nearest thousand is 61,000.
64. 72,103 rounded to the nearest thousand is 72,000.
65. 24,628 rounded to the nearest ten-thousand is
20,000.
66. 34,628 rounded to the nearest ten-thousand is
30,000.
67. 345,207 rounded to the nearest ten-thousand is
350,000.
68. 645,308 rounded to the nearest ten-thousand is
650,000.
69. 86,609,100 rounded to the nearest million is
87,000,000.
70. 75,809,100 rounded to the nearest million is
76,000,000.
71. 86,409,100 rounded to the nearest million is
86,000,000.
72. 75,309,100 rounded to the nearest million is
75,000,000.
73. 86,609,100 rounded to the nearest ten-million is
90,000,000.
74. 75,809,100 rounded to the nearest million is
80,000,000.
75. ninety-two quadrillion, two hundred thirty-three
trillion, seven hundred twenty billion, three hundred
sixty-eight million, five hundred forty-seven
thousand, eight hundred.
76. ten-quadrillions
77.700,000, 000, 000 20,000, 000,000+
78.90,000,000,000,000, 000 2,000,000, 000,000,000+
79. 92,233,720,368,547,800 rounded to the nearest ten-
quadrillion is 90,000,000,000,000,000.
The word name is ninety quadrillion.
80. 92,233,720,368,547,800 rounded to the nearest
quadrillion is 92,000,000,000,000,000.
The word name is ninety-two quadrillion
81. Steven Spielberg generates the greatest revenue per
year which is $27,400,000. In word form this is
twenty-seven million, four hundred thousand
dollars.
Loading page 8...
Section 1.1 Basics of Whole Numbers
5
82. Tom Cruise generates the greatest revenue per
movie which is $17,100,000. In word form this is
seventeen million, one hundred thousand dollars.
83. Samuel L. Jackson generates the least revenue per
movie. His yearly revenue is $24,400,000. In word
form this is twenty-four million, four hundred
thousand dollars.
84. Johnny Depp generates between ten million dollars
and eleven million dollars per movie. His yearly
revenue is $24,300,000. In word form this is twenty-
four million, three hundred thousand dollars.
85. Tom Cruise and Tom Hanks generate the same
revenue per year.
Tom Cruise generates the greatest revenue per
movie which is $17,100,000. In word form this is
seventeen million, one hundred thousand dollars.
86. Tom Cruise and Tom Hanks generate the same
revenue per year.
Tom Hanks generates the lesser revenue per movie
which is$12,000,000. In word form this is 12
million dollars.
87. $53,664
88. $53,285
89. 2011
90. 2010
91. The maximum is shown by the highest bar in the
graph. This occurs in 2007 at $55,627.
92. The minimum is shown by the lowest bar in the
graph. This occurs in 2012 at $51,017.
93. 2,376,206; two million, three hundred seventy-six
thousand, two hundred six
94. 1,857,160; one million; eight hundred fifty-seven
thousand, one hundred sixty
95. Williams
96. Brown and Jones
97. 1,857,160 rounded to the nearest hundred-thousand
is 1,900,000.
98. 2,376,206 rounded to the nearest hundred-thousand
is 2,400,000.
99. The 3 is in the ten-thousands place.
100. The 8 is in the ten-thousands place.
101. 1,380,145 < 1,534,042
102. 1,857,160 > 1,380,145
103. two thousand, four hundred fifty-three
104. two hundred two thousand, twenty-two
105. 102,063
106. 12,042
107. – 117. Answers will vary.
118. does not make sense; Explanations will vary.
Sample explanation: Adding one to this number
would create a bigger number.
119. makes sense
120. makes sense
121. makes sense
122. true
123. false; Changes to make the statement true will vary.
A sample change is: The number 32,864 is written
in standard form.
124. false; Changes to make the statement true will vary.
A sample change is: When rounding whole
numbers, the digit to be rounded either stays the
same or increases by 1.
125. false; Changes to make the statement true will vary.
A sample change is: When comparing numbers of
various items, tables are just as effective as bar
graphs.
126. The whole numbers from 10 to 40 would be
rounded to 10 or 20 or 30 or 40. So there are four
different rounded numbers.
127. a. 46 rounded to the nearest ten is 50.
b. 23 rounded to the nearest ten is 20.
c.46 23 50 20 70+ + =
128. a. 10; 10
b. 8; 8
c. No the order does not make a difference.
5
82. Tom Cruise generates the greatest revenue per
movie which is $17,100,000. In word form this is
seventeen million, one hundred thousand dollars.
83. Samuel L. Jackson generates the least revenue per
movie. His yearly revenue is $24,400,000. In word
form this is twenty-four million, four hundred
thousand dollars.
84. Johnny Depp generates between ten million dollars
and eleven million dollars per movie. His yearly
revenue is $24,300,000. In word form this is twenty-
four million, three hundred thousand dollars.
85. Tom Cruise and Tom Hanks generate the same
revenue per year.
Tom Cruise generates the greatest revenue per
movie which is $17,100,000. In word form this is
seventeen million, one hundred thousand dollars.
86. Tom Cruise and Tom Hanks generate the same
revenue per year.
Tom Hanks generates the lesser revenue per movie
which is$12,000,000. In word form this is 12
million dollars.
87. $53,664
88. $53,285
89. 2011
90. 2010
91. The maximum is shown by the highest bar in the
graph. This occurs in 2007 at $55,627.
92. The minimum is shown by the lowest bar in the
graph. This occurs in 2012 at $51,017.
93. 2,376,206; two million, three hundred seventy-six
thousand, two hundred six
94. 1,857,160; one million; eight hundred fifty-seven
thousand, one hundred sixty
95. Williams
96. Brown and Jones
97. 1,857,160 rounded to the nearest hundred-thousand
is 1,900,000.
98. 2,376,206 rounded to the nearest hundred-thousand
is 2,400,000.
99. The 3 is in the ten-thousands place.
100. The 8 is in the ten-thousands place.
101. 1,380,145 < 1,534,042
102. 1,857,160 > 1,380,145
103. two thousand, four hundred fifty-three
104. two hundred two thousand, twenty-two
105. 102,063
106. 12,042
107. – 117. Answers will vary.
118. does not make sense; Explanations will vary.
Sample explanation: Adding one to this number
would create a bigger number.
119. makes sense
120. makes sense
121. makes sense
122. true
123. false; Changes to make the statement true will vary.
A sample change is: The number 32,864 is written
in standard form.
124. false; Changes to make the statement true will vary.
A sample change is: When rounding whole
numbers, the digit to be rounded either stays the
same or increases by 1.
125. false; Changes to make the statement true will vary.
A sample change is: When comparing numbers of
various items, tables are just as effective as bar
graphs.
126. The whole numbers from 10 to 40 would be
rounded to 10 or 20 or 30 or 40. So there are four
different rounded numbers.
127. a. 46 rounded to the nearest ten is 50.
b. 23 rounded to the nearest ten is 20.
c.46 23 50 20 70+ + =
128. a. 10; 10
b. 8; 8
c. No the order does not make a difference.
Loading page 9...
Chapter 1 Whole Numbers and Introduction to Algebra
6
129. a. 9
b. 9
c. No the group changes does not change the
answer.
1.2 Check Points
1.7243
632
7875
+
2.1 1
2, 09 7
8,5 4 4
10, 6 4 1
+
3.2 2 2
25,572
329,874
4,882
360,328
+
4.Exact Estimate
25,572 26,000
329,874 330,000
4,882 5,000
361,000
+ +
The exact sum from Check Point 3 seems
reasonable.
5. a. associative property of addition
b. identity property of addition
c. commutative property of addition
d. commutative property of addition
6.15 3 5 7 8+ + + + could be rearranged as20 10
15 5 3 7 8+ + + +
which is20 10 8 38.+ + =
7. a.Billy Crystal's number
Johnny Carson's number 4
5 4
9
= +
= +
=
Billy Crystal hosted the Oscars 9 times.
b.Bob Hope's number
Johnny Carson's number 13
5 13
18
= +
= +
=
Bob Hope hosted the Oscars 18 times.
c.5 9 18 32+ + =
Johnny Carson, Billy Crystal, and Bob Hope
hosted the Oscars a total of 32 times.
8.11 feet 11 feet 9 feet 9 feet 13 feet 53 feet+ + + + =
9.38 yd
19 yd
38 yd
19 yd
114 yd
+
The yard requires 114 yd of fencing.
1.2 Concept and Vocabulary Check
1. sum; addends
2. carrying
3. identity
4. commutative
5. associative
6. rectangle; length
7. perimeter
1.2 Exercise Set
1.23
42
65
+
2.26
33
59
+
3.53
340
393
+
6
129. a. 9
b. 9
c. No the group changes does not change the
answer.
1.2 Check Points
1.7243
632
7875
+
2.1 1
2, 09 7
8,5 4 4
10, 6 4 1
+
3.2 2 2
25,572
329,874
4,882
360,328
+
4.Exact Estimate
25,572 26,000
329,874 330,000
4,882 5,000
361,000
+ +
The exact sum from Check Point 3 seems
reasonable.
5. a. associative property of addition
b. identity property of addition
c. commutative property of addition
d. commutative property of addition
6.15 3 5 7 8+ + + + could be rearranged as20 10
15 5 3 7 8+ + + +
which is20 10 8 38.+ + =
7. a.Billy Crystal's number
Johnny Carson's number 4
5 4
9
= +
= +
=
Billy Crystal hosted the Oscars 9 times.
b.Bob Hope's number
Johnny Carson's number 13
5 13
18
= +
= +
=
Bob Hope hosted the Oscars 18 times.
c.5 9 18 32+ + =
Johnny Carson, Billy Crystal, and Bob Hope
hosted the Oscars a total of 32 times.
8.11 feet 11 feet 9 feet 9 feet 13 feet 53 feet+ + + + =
9.38 yd
19 yd
38 yd
19 yd
114 yd
+
The yard requires 114 yd of fencing.
1.2 Concept and Vocabulary Check
1. sum; addends
2. carrying
3. identity
4. commutative
5. associative
6. rectangle; length
7. perimeter
1.2 Exercise Set
1.23
42
65
+
2.26
33
59
+
3.53
340
393
+
Loading page 10...
Section 1.2 Adding Whole Numbers
7
4.67
230
297
+
5.4762
124
4886
+
6.5643
325
5968
+
7.2542
126
2668
+
8.3427
261
3688
+
9.89
32
121
+
10.97
54
151
+
11.4308
2956
7264
+
12.5706
3645
9351
+
13.5274
6298
11,572
+
14.3748
8397
12,145
+
15.741
325
986
2052
+
16.876
521
994
2391
+
17.62,833
8,763
98
71,694
+
18.57,926
5,843
79
63,848
+
19.804,127
39,705
2,008
845,840
+
20.906,238
29,507
4,007
939,752
+
21.3,788
9,546
2,030
+ 83,947
99,311
22.5,877
8,493
5,060
+ 94,726
114,156
7
4.67
230
297
+
5.4762
124
4886
+
6.5643
325
5968
+
7.2542
126
2668
+
8.3427
261
3688
+
9.89
32
121
+
10.97
54
151
+
11.4308
2956
7264
+
12.5706
3645
9351
+
13.5274
6298
11,572
+
14.3748
8397
12,145
+
15.741
325
986
2052
+
16.876
521
994
2391
+
17.62,833
8,763
98
71,694
+
18.57,926
5,843
79
63,848
+
19.804,127
39,705
2,008
845,840
+
20.906,238
29,507
4,007
939,752
+
21.3,788
9,546
2,030
+ 83,947
99,311
22.5,877
8,493
5,060
+ 94,726
114,156
Loading page 11...
Chapter 1 Whole Numbers and Introduction to Algebra
8
23.Exact Estimate
49 50
37 40
22 20
110
+ +
24.Exact Estimate
62 60
43 40
19 20
120
+ +
25.Exact Estimate
2513 2500
864 900
1937 1900
5300
+ +
26.Exact Estimate
3416 3400
778 800
1926 1900
6100
+ +
27.Exact Estimate
62,534 63,000
4107 4 000
8612 9 000
76,000
+ +
28.Exact Estimate
84,517 85,000
6103 6 000
7814 8000
99,000
+ +
29. a.6234 7983 6000 8000
14, 000
+ +
=
b. No, the estimate does not seem reasonable.
30. a.6807 4150 7000 4000
11, 000
+ +
=
b. No, the estimate does not seem reasonable.
31. a.18,972 378,641 6874
20,000 380,000 7000
407,000
+ +
+ +
=
b. Yes, the estimate seems reasonable.
32. a.28,612 287,611 7862
30,000 290,000 8000
328,000
+ +
+ +
=
b. Yes, the estimate seems reasonable.
33. commutative property of addition
34. commutative property of addition
35. associative property of addition
36. associative property of addition
37. identity property of addition
38. identity property of addition
39. identity property of addition
40. identity property of addition
41. commutative property of addition
42. commutative property of addition
43.20 10
12 7 8 3 12 8 7 3
20 10
30
+ + + = + + +
= +
=
44.20 10
18 9 2 1 18 2 9 1
20 10
30
+ + + = + + +
= +
=
45.5040
32 7 11 8 39 32 8 11 39 7
40 50 7
97
+ + + + = + + + +
= + +
=
46.30 60
22 4 1 8 59 22 8 1 59 4
30 60 4
94
+ + + + = + + + +
= + +
=
8
23.Exact Estimate
49 50
37 40
22 20
110
+ +
24.Exact Estimate
62 60
43 40
19 20
120
+ +
25.Exact Estimate
2513 2500
864 900
1937 1900
5300
+ +
26.Exact Estimate
3416 3400
778 800
1926 1900
6100
+ +
27.Exact Estimate
62,534 63,000
4107 4 000
8612 9 000
76,000
+ +
28.Exact Estimate
84,517 85,000
6103 6 000
7814 8000
99,000
+ +
29. a.6234 7983 6000 8000
14, 000
+ +
=
b. No, the estimate does not seem reasonable.
30. a.6807 4150 7000 4000
11, 000
+ +
=
b. No, the estimate does not seem reasonable.
31. a.18,972 378,641 6874
20,000 380,000 7000
407,000
+ +
+ +
=
b. Yes, the estimate seems reasonable.
32. a.28,612 287,611 7862
30,000 290,000 8000
328,000
+ +
+ +
=
b. Yes, the estimate seems reasonable.
33. commutative property of addition
34. commutative property of addition
35. associative property of addition
36. associative property of addition
37. identity property of addition
38. identity property of addition
39. identity property of addition
40. identity property of addition
41. commutative property of addition
42. commutative property of addition
43.20 10
12 7 8 3 12 8 7 3
20 10
30
+ + + = + + +
= +
=
44.20 10
18 9 2 1 18 2 9 1
20 10
30
+ + + = + + +
= +
=
45.5040
32 7 11 8 39 32 8 11 39 7
40 50 7
97
+ + + + = + + + +
= + +
=
46.30 60
22 4 1 8 59 22 8 1 59 4
30 60 4
94
+ + + + = + + + +
= + +
=
Loading page 12...
Section 1.2 Adding Whole Numbers
9
47.200100
96 5 4 195 17 96 4 5 195 17
100 200 17
317
+ + + + = + + + +
= + +
=
48.200100
93 4 7 196 12 93 7 4 196 12
100 200 12
312
+ + + + = + + + +
= + +
=
49.412 123 535+ =
50.514 226 740+ =
51.89 45 134+ =
52.93 28 121+ =
53.5492 12,326 17,818+ =
54.8943 13,517 22, 460+ =
55.127,813 2799 130,612+ =
56.138,514 3786 142,300+ =
57.87 93 8 2015 2203+ + + =
58.94 72 5 3017 3188+ + + =
59.2917 306 14,999 18, 222+ + =
60.3716 504 15,998 20, 218+ + =
61.8 inches
10 inches
8 inches
10 inches
36 inches
+
The perimeter is 36 inches.
62.14 inches
9 inches
14 inches
9 inches
46 inches
+
The perimeter is 46 inches.
63.9 feet
7 feet
11 feet
27 feet
+
The perimeter is 27 feet.
64.10 feet
16 feet
9 feet
35 feet
+
The perimeter is 35 feet.
65.6 yards
8 yards
6 yards
8 yards
28 yards
+
The perimeter is 28 yards.
66.7 yards
18 yards
7 yards
18 yards
50 yards
+
The perimeter is 50 yards.
67.250 inches
250 inches
250 inches
250 inches
1000 inches
+
The perimeter is 1000 inches.
68.50 inches
50 inches
50 inches
50 inches
200 inches
+
The perimeter is 200 inches.
9
47.200100
96 5 4 195 17 96 4 5 195 17
100 200 17
317
+ + + + = + + + +
= + +
=
48.200100
93 4 7 196 12 93 7 4 196 12
100 200 12
312
+ + + + = + + + +
= + +
=
49.412 123 535+ =
50.514 226 740+ =
51.89 45 134+ =
52.93 28 121+ =
53.5492 12,326 17,818+ =
54.8943 13,517 22, 460+ =
55.127,813 2799 130,612+ =
56.138,514 3786 142,300+ =
57.87 93 8 2015 2203+ + + =
58.94 72 5 3017 3188+ + + =
59.2917 306 14,999 18, 222+ + =
60.3716 504 15,998 20, 218+ + =
61.8 inches
10 inches
8 inches
10 inches
36 inches
+
The perimeter is 36 inches.
62.14 inches
9 inches
14 inches
9 inches
46 inches
+
The perimeter is 46 inches.
63.9 feet
7 feet
11 feet
27 feet
+
The perimeter is 27 feet.
64.10 feet
16 feet
9 feet
35 feet
+
The perimeter is 35 feet.
65.6 yards
8 yards
6 yards
8 yards
28 yards
+
The perimeter is 28 yards.
66.7 yards
18 yards
7 yards
18 yards
50 yards
+
The perimeter is 50 yards.
67.250 inches
250 inches
250 inches
250 inches
1000 inches
+
The perimeter is 1000 inches.
68.50 inches
50 inches
50 inches
50 inches
200 inches
+
The perimeter is 200 inches.
Loading page 13...
Chapter 1 Whole Numbers and Introduction to Algebra
10
69.9 yards
9 yards
12 yards
12 yards
21 yards
21 yards
84 yards
+
The perimeter is 84 yards.
70.5 inches
13 inches
9 inches
4 inches
14 inches
17 inches
62 inches
+
The perimeter is 62 inches.
71.517 517
517 0 514 3+ = +
72.825 825
825 0 821 4+ = +
73.117 115
53 64 41 74+ +
74.94 90
62 14 18 23 49 18+ + + +
75.71 85
61 10 50 35+ +
76.87 88
57 30 66 22+ +
77.3097 1917
239 1268 1590 598 1248 71+ + + +
78.9297 4928
2105 2892 4300 1400 3429 99+ + + +
79.Number of dogs named Bella Number of dogs named Lucy 2089
3571 2089
5660
= +
= +
=
5660 dogs are named Bella.
10
69.9 yards
9 yards
12 yards
12 yards
21 yards
21 yards
84 yards
+
The perimeter is 84 yards.
70.5 inches
13 inches
9 inches
4 inches
14 inches
17 inches
62 inches
+
The perimeter is 62 inches.
71.517 517
517 0 514 3+ = +
72.825 825
825 0 821 4+ = +
73.117 115
53 64 41 74+ +
74.94 90
62 14 18 23 49 18+ + + +
75.71 85
61 10 50 35+ +
76.87 88
57 30 66 22+ +
77.3097 1917
239 1268 1590 598 1248 71+ + + +
78.9297 4928
2105 2892 4300 1400 3429 99+ + + +
79.Number of dogs named Bella Number of dogs named Lucy 2089
3571 2089
5660
= +
= +
=
5660 dogs are named Bella.
Loading page 14...
Section 1.2 Adding Whole Numbers
11
80.Number of dogs named Bailey Number of dogs named Lucy 417
3571 417
3988
= +
= +
=
3988 dogs are named Bailey.
81.Number of dogs named Bailey Number of dogs named Molly 707
3281 707
3988
= +
= +
=
3988 dogs are named Bailey.
82.Number of dogs named Bella Number of dogs named Molly 2379
3281 2379
5660
= +
= +
=
5660 dogs are named Bella.
83.5660 Named Bella (from a previous exercise)
3958 Named Max (from bar graph)
3571 Named Max (from bar graph)
13,189
+
84.3988 Named Bailey (from a previous exercise)
3958 Named Max (from bar graph)
3571 Named Max (from bar graph)
11,517
+
85. a.Exact Estimate
59 feet 60 feet
23 feet 20 feet
25 feet 30 feet
46 feet 50 feet
43 feet 40 feet
200 feet
+ +
The estimate is 200 feet.
b.59 feet
23 feet
25 feet
46 feet
43 feet
196 feet
+
The perimeter is 196 feet.
11
80.Number of dogs named Bailey Number of dogs named Lucy 417
3571 417
3988
= +
= +
=
3988 dogs are named Bailey.
81.Number of dogs named Bailey Number of dogs named Molly 707
3281 707
3988
= +
= +
=
3988 dogs are named Bailey.
82.Number of dogs named Bella Number of dogs named Molly 2379
3281 2379
5660
= +
= +
=
5660 dogs are named Bella.
83.5660 Named Bella (from a previous exercise)
3958 Named Max (from bar graph)
3571 Named Max (from bar graph)
13,189
+
84.3988 Named Bailey (from a previous exercise)
3958 Named Max (from bar graph)
3571 Named Max (from bar graph)
11,517
+
85. a.Exact Estimate
59 feet 60 feet
23 feet 20 feet
25 feet 30 feet
46 feet 50 feet
43 feet 40 feet
200 feet
+ +
The estimate is 200 feet.
b.59 feet
23 feet
25 feet
46 feet
43 feet
196 feet
+
The perimeter is 196 feet.
Loading page 15...
Chapter 1 Whole Numbers and Introduction to Algebra
12
86. a.Exact Estimate
3 feet 0 feet
15 feet 20 feet
21 feet 20 feet
15 feet 20 feet
9 feet 10 feet
24 feet 20 feet
90 feet
+ +
The estimate is 90 feet.
b.3 feet
15 feet
21 feet
15 feet
9 feet
24 feet
87 feet
+
The perimeter is 87 feet.
87. – 96. Answers will vary.
97. does not make sense; Explanations will vary.
Sample explanation: No column's sum exceeded 9.
98. makes sense
99. makes sense
100. makes sense
101. false; Changes to make the statement true will vary.
A sample change is: The expressions are equal
because of the commutative property of addition.
102. true
103. true
104. true
105. The two smaller vertical sides total 7 inches, so the
unlabeled vertical side must also be 7 inches. The
two smaller horizontal sides total 9 inches, so the
unlabeled horizontal side must also be 9 inches.3 inches
4 inches
7 inches
3 inches
6 inches
9 inches
32 inches
+
The perimeter is 32 inches.
106. The labeled vertical side is 8 inches, so the 2 smaller
vertical sides must total 8 inches. Since one of these
vertical sides is labeled 3 inches, the unlabeled
vertical side must be 5 inches
The horizontal vertical side is 10 inches, so the 2
smaller horizontal sides must total 10 inches. Since
one of these horizontal sides is labeled 5 inches, the
unlabeled horizontal side must also be 5 inches.8 inches
5 inches
3 inches
10 inches
5 inches
5 inches
36 inches
+
The perimeter is 36 inches.
107. Answers will vary.
108.8 2 6− = because6 2 8.+ =
109. Yes, the sum is 92.78
14
92
+
110.5 3 2− =
1.3 Check Points
1. a.13 10 3− =
Check:3 10 13+ =
b.8 2 6− =
Check:6 2 8+ =
c.12 12 0− =
Check:0 12 12+ =
d.40 0 40− =
Check:40 0 40+ =
12
86. a.Exact Estimate
3 feet 0 feet
15 feet 20 feet
21 feet 20 feet
15 feet 20 feet
9 feet 10 feet
24 feet 20 feet
90 feet
+ +
The estimate is 90 feet.
b.3 feet
15 feet
21 feet
15 feet
9 feet
24 feet
87 feet
+
The perimeter is 87 feet.
87. – 96. Answers will vary.
97. does not make sense; Explanations will vary.
Sample explanation: No column's sum exceeded 9.
98. makes sense
99. makes sense
100. makes sense
101. false; Changes to make the statement true will vary.
A sample change is: The expressions are equal
because of the commutative property of addition.
102. true
103. true
104. true
105. The two smaller vertical sides total 7 inches, so the
unlabeled vertical side must also be 7 inches. The
two smaller horizontal sides total 9 inches, so the
unlabeled horizontal side must also be 9 inches.3 inches
4 inches
7 inches
3 inches
6 inches
9 inches
32 inches
+
The perimeter is 32 inches.
106. The labeled vertical side is 8 inches, so the 2 smaller
vertical sides must total 8 inches. Since one of these
vertical sides is labeled 3 inches, the unlabeled
vertical side must be 5 inches
The horizontal vertical side is 10 inches, so the 2
smaller horizontal sides must total 10 inches. Since
one of these horizontal sides is labeled 5 inches, the
unlabeled horizontal side must also be 5 inches.8 inches
5 inches
3 inches
10 inches
5 inches
5 inches
36 inches
+
The perimeter is 36 inches.
107. Answers will vary.
108.8 2 6− = because6 2 8.+ =
109. Yes, the sum is 92.78
14
92
+
110.5 3 2− =
1.3 Check Points
1. a.13 10 3− =
Check:3 10 13+ =
b.8 2 6− =
Check:6 2 8+ =
c.12 12 0− =
Check:0 12 12+ =
d.40 0 40− =
Check:40 0 40+ =
Loading page 16...
Section 1.3 Subtracting Whole Numbers
13
2.6893 Check: 6172
721 721
6172 6893
− +
3.5 12
5 6 2 Check: 517
4 5 45
5 17 562
− +
4.154 17
5 6 7 4 Check: 4781
8 9 3 893
4 7 8 1 5674
− +
5.106
7 0
10
9
0 Check: 444
2 5 6 256
4 4 4 700
− +
6.Exact Estimate
5674 6000
893 1000
5000
− −
The exact difference of 4781, determined in Check
Point 4, seems reasonable.
7. a.130, 490 (Lawyers)
45,230 (All Occupations)
85, 260
−
The difference is $85,260.
b.130, 490 (Lawyers)
60,360
70,130 (Accountants)
−
The average salary for accountants is $70,130.
8.Withdrawls on orBalance before May 10May 1
Balance after May 10 820 (450 85 5 37)
820 577
243
= − + + +
= −
=
The balance after May 10 is $243.
1.3 Concept and Vocabulary Check
1. minuend; subtrahend; difference
2. 2; 10; 12
3. 0
4. borrowing
1.3 Exercise Set
1.87 Check: 62
25 25
62 87
− +
2.73 Check: 31
42 42
31 73
− +
3.598 Check: 273
325 325
273 598
− +
4.752 Check: 321
431 431
321 752
− +
5.376 Check: 324
52 52
324 376
− +
6.387 Check: 322
65 65
322 387
− +
7.6288 Check: 6110
178 178
6110 6288
− +
8.9366 Check: 9120
246 246
9120 9366
− +
13
2.6893 Check: 6172
721 721
6172 6893
− +
3.5 12
5 6 2 Check: 517
4 5 45
5 17 562
− +
4.154 17
5 6 7 4 Check: 4781
8 9 3 893
4 7 8 1 5674
− +
5.106
7 0
10
9
0 Check: 444
2 5 6 256
4 4 4 700
− +
6.Exact Estimate
5674 6000
893 1000
5000
− −
The exact difference of 4781, determined in Check
Point 4, seems reasonable.
7. a.130, 490 (Lawyers)
45,230 (All Occupations)
85, 260
−
The difference is $85,260.
b.130, 490 (Lawyers)
60,360
70,130 (Accountants)
−
The average salary for accountants is $70,130.
8.Withdrawls on orBalance before May 10May 1
Balance after May 10 820 (450 85 5 37)
820 577
243
= − + + +
= −
=
The balance after May 10 is $243.
1.3 Concept and Vocabulary Check
1. minuend; subtrahend; difference
2. 2; 10; 12
3. 0
4. borrowing
1.3 Exercise Set
1.87 Check: 62
25 25
62 87
− +
2.73 Check: 31
42 42
31 73
− +
3.598 Check: 273
325 325
273 598
− +
4.752 Check: 321
431 431
321 752
− +
5.376 Check: 324
52 52
324 376
− +
6.387 Check: 322
65 65
322 387
− +
7.6288 Check: 6110
178 178
6110 6288
− +
8.9366 Check: 9120
246 246
9120 9366
− +
Loading page 17...
Chapter 1 Whole Numbers and Introduction to Algebra
14
9.6785 Check: 4400
2385 2385
4400 6785
− +
10.8453 Check: 5200
3253 3253
5200 8453
− +
11.78,993 Check: 74,502
4, 491 4, 491
74,502 78,993
− +
12.67,876 Check: 64,605
3, 271 3, 271
64,605 67,876
− +
13.25,176 Check: 0
25,176 25,176
0 25,176
− +
14.32,574 Check: 0
32,574 32,574
0 32,574
− +
15.82 Check: 47
35 35
47 82
− +
16.63 Check: 35
28 28
35 63
− +
17.80 Check: 53
27 27
53 80
− +
18.90 Check: 47
43 43
47 90
− +
19.857 Check: 184
673 673
184 857
− +
20.634 Check: 182
452 452
182 634
− +
21.933 Check: 476
457 457
476 933
− +
22.746 Check: 347
399 399
347 746
− +
23.800 Check: 277
523 523
277 800
− +
24.500 Check: 224
276 276
224 500
− +
25.253 Check: 206
47 47
206 253
− +
26.468 Check: 409
59 59
409 468
− +
27.7382 Check: 6922
460 460
6922 7382
− +
28.8249 Check: 7929
320 320
7929 8249
− +
29.1533 Check: 1484
49 49
1484 1533
− +
30.1746 Check: 1657
89 89
1657 1746
− +
14
9.6785 Check: 4400
2385 2385
4400 6785
− +
10.8453 Check: 5200
3253 3253
5200 8453
− +
11.78,993 Check: 74,502
4, 491 4, 491
74,502 78,993
− +
12.67,876 Check: 64,605
3, 271 3, 271
64,605 67,876
− +
13.25,176 Check: 0
25,176 25,176
0 25,176
− +
14.32,574 Check: 0
32,574 32,574
0 32,574
− +
15.82 Check: 47
35 35
47 82
− +
16.63 Check: 35
28 28
35 63
− +
17.80 Check: 53
27 27
53 80
− +
18.90 Check: 47
43 43
47 90
− +
19.857 Check: 184
673 673
184 857
− +
20.634 Check: 182
452 452
182 634
− +
21.933 Check: 476
457 457
476 933
− +
22.746 Check: 347
399 399
347 746
− +
23.800 Check: 277
523 523
277 800
− +
24.500 Check: 224
276 276
224 500
− +
25.253 Check: 206
47 47
206 253
− +
26.468 Check: 409
59 59
409 468
− +
27.7382 Check: 6922
460 460
6922 7382
− +
28.8249 Check: 7929
320 320
7929 8249
− +
29.1533 Check: 1484
49 49
1484 1533
− +
30.1746 Check: 1657
89 89
1657 1746
− +
Loading page 18...
Section 1.3 Subtracting Whole Numbers
15
31.1967 Check: 39
1928 1928
39 1967
− +
32.2952 Check: 5
2947 2947
5 2952
− +
33.42,566 Check: 28,858
13,708 13,708
28,858 42,566
− +
34.65, 722 Check: 38,915
26,807 26,807
38,915 65,722
− +
35.60, 000 Check: 32,017
27,983 27,983
32,017 60, 000
− +
36.80, 000 Check: 40,018
39,982 39,982
40,018 80, 000
− +
37.86, 497 Check: 60,647
25,850 25,850
60,647 86, 497
− +
38.71,111 Check: 52,113
18,998 18,998
52,113 71,111
− +
39.Exact Estimate
338 340
223 220
120
− −
40.Exact Estimate
586 590
123 120
470
− −
41.Exact Estimate
1875 1900
1387 1400
500
− −
42.Exact Estimate
2813 2800
2271 2300
500
− −
43.Exact Estimate
18,963 19,000
16,218 16,000
3000
− −
44.Exact Estimate
24,817 25,000
13,199 13,000
12,000
− −
45. a.Exact Estimate
3635 3600
462 500
3100
− −
b. No; An exact difference of 2173 does not seem
reasonable.
46. a.Exact Estimate
1852 1900
427 400
1500
− −
b. No; An exact difference of 1025 does not seem
reasonable.
47.53 6 47− =
48.73 7 66− =
49.71 11 60− =
50.57 35 22− =
51.88 62 26− =
52.97 55 42− =
53.49 7 42− =
15
31.1967 Check: 39
1928 1928
39 1967
− +
32.2952 Check: 5
2947 2947
5 2952
− +
33.42,566 Check: 28,858
13,708 13,708
28,858 42,566
− +
34.65, 722 Check: 38,915
26,807 26,807
38,915 65,722
− +
35.60, 000 Check: 32,017
27,983 27,983
32,017 60, 000
− +
36.80, 000 Check: 40,018
39,982 39,982
40,018 80, 000
− +
37.86, 497 Check: 60,647
25,850 25,850
60,647 86, 497
− +
38.71,111 Check: 52,113
18,998 18,998
52,113 71,111
− +
39.Exact Estimate
338 340
223 220
120
− −
40.Exact Estimate
586 590
123 120
470
− −
41.Exact Estimate
1875 1900
1387 1400
500
− −
42.Exact Estimate
2813 2800
2271 2300
500
− −
43.Exact Estimate
18,963 19,000
16,218 16,000
3000
− −
44.Exact Estimate
24,817 25,000
13,199 13,000
12,000
− −
45. a.Exact Estimate
3635 3600
462 500
3100
− −
b. No; An exact difference of 2173 does not seem
reasonable.
46. a.Exact Estimate
1852 1900
427 400
1500
− −
b. No; An exact difference of 1025 does not seem
reasonable.
47.53 6 47− =
48.73 7 66− =
49.71 11 60− =
50.57 35 22− =
51.88 62 26− =
52.97 55 42− =
53.49 7 42− =
Loading page 19...
Chapter 1 Whole Numbers and Introduction to Algebra
16
54.55 4 51− =
55.43 3 40− =
56.68 8 60− =
57.80 36 44− =
58.90 39 51− =
59.548 30 518− =
60.876 60 816− =
61.758 654 104− =
62.497 293 204− =
63.9083 134 8949− =
64.3935 885 3050− =
65.905,008
280,034
624,974
−
66.2,013,000
507,093
1,505,907
−
67.20 20
35 15 80 60− = −
68.5 5
40 35 85 80− = −
69.374 386
458 84 716 330− −
70.68 55
121 53 761 706− −
71.70 (Minuend)
40 (Subtrahend)
30 (Difference)
−
72.100 (Minuend)
90 (Subtrahend)
10 (Difference)
−
73.1550
122
1428
−
The difference is 1428 years.
74.1550
405
1145
−
The difference is 1145 years.
75.405
195
210
−
The extreme lifespan of a whale is 210 years.
76.405
328
77
−
The extreme lifespan of a cockatoo is 77 years.
77.122
28
94
−
The extreme lifespan of a dog is 94 years less than
the extreme lifespan of a human.
78.122
38
84
−
The extreme lifespan of a cat is 84 years less than
the extreme lifespan of a human.
79.Deposits Withdrawls
Balance (1050 435) (525 185 4 100 190)
1485 1004
481
= + − + + + +
= −
=
The balance after June 25 is $481.
80.Deposits Withdrawls
Balance (1120 350) (615 145 225 300 4)
1470 1289
181
= + − + + + +
= −
=
The balance after December 31 is $181.
16
54.55 4 51− =
55.43 3 40− =
56.68 8 60− =
57.80 36 44− =
58.90 39 51− =
59.548 30 518− =
60.876 60 816− =
61.758 654 104− =
62.497 293 204− =
63.9083 134 8949− =
64.3935 885 3050− =
65.905,008
280,034
624,974
−
66.2,013,000
507,093
1,505,907
−
67.20 20
35 15 80 60− = −
68.5 5
40 35 85 80− = −
69.374 386
458 84 716 330− −
70.68 55
121 53 761 706− −
71.70 (Minuend)
40 (Subtrahend)
30 (Difference)
−
72.100 (Minuend)
90 (Subtrahend)
10 (Difference)
−
73.1550
122
1428
−
The difference is 1428 years.
74.1550
405
1145
−
The difference is 1145 years.
75.405
195
210
−
The extreme lifespan of a whale is 210 years.
76.405
328
77
−
The extreme lifespan of a cockatoo is 77 years.
77.122
28
94
−
The extreme lifespan of a dog is 94 years less than
the extreme lifespan of a human.
78.122
38
84
−
The extreme lifespan of a cat is 84 years less than
the extreme lifespan of a human.
79.Deposits Withdrawls
Balance (1050 435) (525 185 4 100 190)
1485 1004
481
= + − + + + +
= −
=
The balance after June 25 is $481.
80.Deposits Withdrawls
Balance (1120 350) (615 145 225 300 4)
1470 1289
181
= + − + + + +
= −
=
The balance after December 31 is $181.
Loading page 20...
Section 1.3 Subtracting Whole Numbers
17
81.Rectangle: Square:
17 feet 14 feet
13 feet 14 feet
17 feet 14 feet
13 feet 14 feet
60 feet 56 feet
+ +Difference:
60 feet (Rectangle)
56 feet (Square)
4 feet
−
The rectangular garden requires 4 more feet of
fencing than the square garden.
82.Rectangle: Square:
23 feet 16 feet
11 feet 16 feet
23 feet 16 feet
11 feet 16 feet
68 feet 64 feet
+ +Difference:
68 feet (Rectangle)
64 feet (Square)
4 feet
−
The rectangular garden requires 4 more feet of
fencing than the square garden.
83. – 88. Answers will vary.
89. does not make sense; Explanations will vary.
Sample explanation: To check a subtraction
problem by add the difference to the subtrahend.
90. does not make sense; Explanations will vary.
Sample explanation: Borrowing is unnecessary
because each digit in the subtrahend exceeds the
corresponding digit in the minuend.
91. makes sense
92. makes sense
93. true
94. true
95. false; Changes to make the statement true will vary.
A sample change is: When 30 is subtracted from 50,
30 is the subtrahend.
96. true
97.479
184
295
−
98.849
355
494
−
99. No; the associative property cannot be applied to
subtraction.10 (6 1) 10 5 5− − = − =(10 6) 1 4 1 3− − = − =
100. Answers will vary.
101. eighty-nine thousand, one hundred sixty-two
102.35, 287
4,956
40, 243
+
103.Exact Estimate
35, 287 35,000
4,956 5,000
40,000
+ +
104. a.5 3 5 5 5 15 = + + =
b.2 4 2 2 2 2 8 = + + + =
c.6 7 6 6 6 6 6 6 6 42 = + + + + + + =
105. a.(2 3) 5 6 5 30 = =
b.2 (3 5) 2 15 30 = =
c. No; the grouping did not change the answer.
106. a.2839 3000
b.621 600
c.2839 621 3000 600
17
81.Rectangle: Square:
17 feet 14 feet
13 feet 14 feet
17 feet 14 feet
13 feet 14 feet
60 feet 56 feet
+ +Difference:
60 feet (Rectangle)
56 feet (Square)
4 feet
−
The rectangular garden requires 4 more feet of
fencing than the square garden.
82.Rectangle: Square:
23 feet 16 feet
11 feet 16 feet
23 feet 16 feet
11 feet 16 feet
68 feet 64 feet
+ +Difference:
68 feet (Rectangle)
64 feet (Square)
4 feet
−
The rectangular garden requires 4 more feet of
fencing than the square garden.
83. – 88. Answers will vary.
89. does not make sense; Explanations will vary.
Sample explanation: To check a subtraction
problem by add the difference to the subtrahend.
90. does not make sense; Explanations will vary.
Sample explanation: Borrowing is unnecessary
because each digit in the subtrahend exceeds the
corresponding digit in the minuend.
91. makes sense
92. makes sense
93. true
94. true
95. false; Changes to make the statement true will vary.
A sample change is: When 30 is subtracted from 50,
30 is the subtrahend.
96. true
97.479
184
295
−
98.849
355
494
−
99. No; the associative property cannot be applied to
subtraction.10 (6 1) 10 5 5− − = − =(10 6) 1 4 1 3− − = − =
100. Answers will vary.
101. eighty-nine thousand, one hundred sixty-two
102.35, 287
4,956
40, 243
+
103.Exact Estimate
35, 287 35,000
4,956 5,000
40,000
+ +
104. a.5 3 5 5 5 15 = + + =
b.2 4 2 2 2 2 8 = + + + =
c.6 7 6 6 6 6 6 6 6 42 = + + + + + + =
105. a.(2 3) 5 6 5 30 = =
b.2 (3 5) 2 15 30 = =
c. No; the grouping did not change the answer.
106. a.2839 3000
b.621 600
c.2839 621 3000 600
Loading page 21...
Chapter 1 Whole Numbers and Introduction to Algebra
18
1.4 Check Points
1. a.73 1 73 =
b.73 0 0 =
c.0(14) 0=
d.1 13 13 =
2. a. associative property of multiplication
b. commutative property of multiplication
c. commutative property of multiplication
3. a.10(4 5) 10 4 10 5+ = +
b.10(4 5) 10(9) 90+ = =10 4 10 5 40 50 90 + = + =
Yes, both methods give the same answer.
4.243
2
486
5.1 2
8 2 3
7
5761
6.258
24
1032
5160
6192
+
7.437
253
1311
21850
87400
110,561
+
8.723
205
3615
144600
148, 215
+
9. a.953 1000 953, 000 =
b.4026 100 402, 600 =
10.10 21
2 7 5 3 2 5 7 3
10 21
210
=
=
=
11. a.28
7
196
Attach 3 zeros to 196.28(7000) 196,000=
b.2 8 16 =
Attach2 3,+ or 5 zeros to 16.200 8000 1,600,000 =
12.4796 817 5000 800
4, 000, 000
=
13.amount spent on housing and utilities (5 126) 35
630 35
665
= +
= +
=
The amount spent on housing and utilities is $665.
14.Adult tickets Child tickets
Total Sales 83 12 57 5
996 285
1281
= +
= +
=
The total amount collected in ticket sales is $1281.
15. a.21
18
168
210
378
+
The area of the floor is 378 square feet.
b.378
7
2646
The cost of the carpeting is $2646.
1.4 Concept and Vocabulary Check
1.6 6 6+ +
2. factors; product
3. 0
4. identity
5. commutative
18
1.4 Check Points
1. a.73 1 73 =
b.73 0 0 =
c.0(14) 0=
d.1 13 13 =
2. a. associative property of multiplication
b. commutative property of multiplication
c. commutative property of multiplication
3. a.10(4 5) 10 4 10 5+ = +
b.10(4 5) 10(9) 90+ = =10 4 10 5 40 50 90 + = + =
Yes, both methods give the same answer.
4.243
2
486
5.1 2
8 2 3
7
5761
6.258
24
1032
5160
6192
+
7.437
253
1311
21850
87400
110,561
+
8.723
205
3615
144600
148, 215
+
9. a.953 1000 953, 000 =
b.4026 100 402, 600 =
10.10 21
2 7 5 3 2 5 7 3
10 21
210
=
=
=
11. a.28
7
196
Attach 3 zeros to 196.28(7000) 196,000=
b.2 8 16 =
Attach2 3,+ or 5 zeros to 16.200 8000 1,600,000 =
12.4796 817 5000 800
4, 000, 000
=
13.amount spent on housing and utilities (5 126) 35
630 35
665
= +
= +
=
The amount spent on housing and utilities is $665.
14.Adult tickets Child tickets
Total Sales 83 12 57 5
996 285
1281
= +
= +
=
The total amount collected in ticket sales is $1281.
15. a.21
18
168
210
378
+
The area of the floor is 378 square feet.
b.378
7
2646
The cost of the carpeting is $2646.
1.4 Concept and Vocabulary Check
1.6 6 6+ +
2. factors; product
3. 0
4. identity
5. commutative
Loading page 22...
Section 1.4 Multiplying Whole Numbers
19
6. associative
7. distributive; distributes
8. five
9. length; width; square
1.4 Exercise Set
1.27 1 27 =
2.39 1 39 =
3.0 27 0 =
4.0 39 0 =
5.(1)(1205) 1205=
6.(1)(1372) 1372=
7.7 0 3 0 =
8.7 0 5 0 =
9. commutative property of multiplication
10. commutative property of multiplication
11. associative property of multiplication
12. associative property of multiplication
13. distributive property
14. distributive property
15. commutative property of addition
16. commutative property of addition
17. commutative property of multiplication
18. commutative property of multiplication
19. a.4(3 5) 4 3 4 5+ = +
b.4(3 5) 4(8) 32+ = =4 3 4 5 12 20 32 + = + =
Yes, both methods give the same answer.
20. a.3(4 5) 3 4 3 5+ = +
b.3(4 5) 3(9) 27+ = =3 4 3 5 12 15 27 + = + =
Yes, both methods give the same answer.
21.23
3
69
22.41
2
82
23.62
4
248
24.73
2
146
25.402
3
1206
26.503
3
1509
27.52
8
416
28.48
3
144
29.56
9
504
30.38
9
342
31.614
6
3684
19
6. associative
7. distributive; distributes
8. five
9. length; width; square
1.4 Exercise Set
1.27 1 27 =
2.39 1 39 =
3.0 27 0 =
4.0 39 0 =
5.(1)(1205) 1205=
6.(1)(1372) 1372=
7.7 0 3 0 =
8.7 0 5 0 =
9. commutative property of multiplication
10. commutative property of multiplication
11. associative property of multiplication
12. associative property of multiplication
13. distributive property
14. distributive property
15. commutative property of addition
16. commutative property of addition
17. commutative property of multiplication
18. commutative property of multiplication
19. a.4(3 5) 4 3 4 5+ = +
b.4(3 5) 4(8) 32+ = =4 3 4 5 12 20 32 + = + =
Yes, both methods give the same answer.
20. a.3(4 5) 3 4 3 5+ = +
b.3(4 5) 3(9) 27+ = =3 4 3 5 12 15 27 + = + =
Yes, both methods give the same answer.
21.23
3
69
22.41
2
82
23.62
4
248
24.73
2
146
25.402
3
1206
26.503
3
1509
27.52
8
416
28.48
3
144
29.56
9
504
30.38
9
342
31.614
6
3684
Loading page 23...
Chapter 1 Whole Numbers and Introduction to Algebra
20
32.613
7
4291
33.277
8
2216
34.488
6
2928
35.3074
5
15,370
36.4038
5
20,190
37.19
18
152
190
342
+
38.23
15
115
230
345
+
39.53
53
159
2650
2809
+
40.64
64
256
3840
4096
+
41.163
23
489
3260
3749
+
42.136
32
272
4080
4352
+
43.706
83
2118
56480
58,598
+
44.807
46
4842
32280
37,122
+
45.2357
79
21213
164990
186, 203
+
46.5732
97
40124
515880
556, 004
+
47.135
112
270
1350
13500
15,120
+
48.351
114
1404
3510
35100
40, 014
+
49.3427
828
27416
68540
2741600
2,837,556
+
20
32.613
7
4291
33.277
8
2216
34.488
6
2928
35.3074
5
15,370
36.4038
5
20,190
37.19
18
152
190
342
+
38.23
15
115
230
345
+
39.53
53
159
2650
2809
+
40.64
64
256
3840
4096
+
41.163
23
489
3260
3749
+
42.136
32
272
4080
4352
+
43.706
83
2118
56480
58,598
+
44.807
46
4842
32280
37,122
+
45.2357
79
21213
164990
186, 203
+
46.5732
97
40124
515880
556, 004
+
47.135
112
270
1350
13500
15,120
+
48.351
114
1404
3510
35100
40, 014
+
49.3427
828
27416
68540
2741600
2,837,556
+
Loading page 24...
Section 1.4 Multiplying Whole Numbers
21
50.4372
288
34976
349760
874400
1, 259,136
+
51.324
609
2916
194400
197,316
+
52.721
807
5047
576800
581,847
+
53.985
230
29550
197000
226,550
+
54.658
320
13160
197400
210,560
+
55.332
2400
13280
664000
796,800
+
56.234
4200
46800
936000
982,800
+
57.(749)(58)(0) 0=
58.(972)(85)(0) 0=
59.157 10 1570 =
60.238 10 2380 =
61.8 100 800 =
62.7 100 700 =
63.22(1000) 22,000=
64.37(1000) 37,000=
65.4207 10, 000 42, 070, 000 =
66.5306 10, 000 53,060, 000 =
67.100
4 6 25 4 25 6
100 6
600
=
=
=
68.100
4 7 25 4 25 7
100 7
700
=
=
=
69.10 27
2 9 5 3 2 5 9 3
10 27
270
=
=
=
70.10 27
5 9 3 2 5 2 9 3
10 27
270
=
=
=
71.7 4000 28, 000 =
72.3 8000 24, 000 =
73.53
7
371
Attach 4 zeros to 371.53(70,000) 3,710,000=
74.47
8
376
Attach 4 zeros to 376.47(80,000) 3,760,000=
75.7 9 63 =
Attach1 2,+ or 3 zeros to 63.70 900 63, 000 =
21
50.4372
288
34976
349760
874400
1, 259,136
+
51.324
609
2916
194400
197,316
+
52.721
807
5047
576800
581,847
+
53.985
230
29550
197000
226,550
+
54.658
320
13160
197400
210,560
+
55.332
2400
13280
664000
796,800
+
56.234
4200
46800
936000
982,800
+
57.(749)(58)(0) 0=
58.(972)(85)(0) 0=
59.157 10 1570 =
60.238 10 2380 =
61.8 100 800 =
62.7 100 700 =
63.22(1000) 22,000=
64.37(1000) 37,000=
65.4207 10, 000 42, 070, 000 =
66.5306 10, 000 53,060, 000 =
67.100
4 6 25 4 25 6
100 6
600
=
=
=
68.100
4 7 25 4 25 7
100 7
700
=
=
=
69.10 27
2 9 5 3 2 5 9 3
10 27
270
=
=
=
70.10 27
5 9 3 2 5 2 9 3
10 27
270
=
=
=
71.7 4000 28, 000 =
72.3 8000 24, 000 =
73.53
7
371
Attach 4 zeros to 371.53(70,000) 3,710,000=
74.47
8
376
Attach 4 zeros to 376.47(80,000) 3,760,000=
75.7 9 63 =
Attach1 2,+ or 3 zeros to 63.70 900 63, 000 =
Loading page 25...
Chapter 1 Whole Numbers and Introduction to Algebra
22
76.9 4 36 =
Attach1 2,+ or 3 zeros to 36.90 400 36, 000 =
77.2 16 32 =
Attach3 3,+ or 6 zeros to 32.2000 16, 000 32, 000, 000 =
78.3 12 36 =
Attach3 3,+ or 6 zeros to 36.3000 12, 000 36,000, 000 =
79.83 29 80 30
2400
=
Yes, an exact product of 2407 seems reasonable.
80.48 33 50 30
1500
=
Yes, an exact product of 1584 seems reasonable.
81.312 58 300 60
18, 000
=
Yes, an exact product of 18,906 seems reasonable.
82.519 38 500 40
20, 000
=
Yes, an exact product of 19,722 seems reasonable.
83.273 114 300 100
30, 000
=
No, an exact product of 311,222 does not seem
reasonable.
84.386 217 400 200
80, 000
=
No, an exact product of 837,622 does not seem
reasonable.
85.(4826)(523) (5000)(500)
2,500,000
=
Yes, an exact product of 2,523,998 seems
reasonable.
86.(3906)(517) (4000)(500)
2,000,000
=
Yes, an exact product of 2,019,402 seems
reasonable.
87.90 4 360 =
88.60 7 420 =
89.18 9 162 =
90.26 5 130 =
91.4 800 3200 =
92.3 900 2700 =
93.2 307 614 =
94.2 408 816 =
95.2 1873 3746 =
96.2 2946 5892 =
97.3 3240 9720 =
98.3 4320 12,960 =
99.6 9 54 =
The area is 54 square feet.
100.20
24
80
400
480
+
The area is 480 square feet.
101.30
15
150
300
450
+
22
76.9 4 36 =
Attach1 2,+ or 3 zeros to 36.90 400 36, 000 =
77.2 16 32 =
Attach3 3,+ or 6 zeros to 32.2000 16, 000 32, 000, 000 =
78.3 12 36 =
Attach3 3,+ or 6 zeros to 36.3000 12, 000 36,000, 000 =
79.83 29 80 30
2400
=
Yes, an exact product of 2407 seems reasonable.
80.48 33 50 30
1500
=
Yes, an exact product of 1584 seems reasonable.
81.312 58 300 60
18, 000
=
Yes, an exact product of 18,906 seems reasonable.
82.519 38 500 40
20, 000
=
Yes, an exact product of 19,722 seems reasonable.
83.273 114 300 100
30, 000
=
No, an exact product of 311,222 does not seem
reasonable.
84.386 217 400 200
80, 000
=
No, an exact product of 837,622 does not seem
reasonable.
85.(4826)(523) (5000)(500)
2,500,000
=
Yes, an exact product of 2,523,998 seems
reasonable.
86.(3906)(517) (4000)(500)
2,000,000
=
Yes, an exact product of 2,019,402 seems
reasonable.
87.90 4 360 =
88.60 7 420 =
89.18 9 162 =
90.26 5 130 =
91.4 800 3200 =
92.3 900 2700 =
93.2 307 614 =
94.2 408 816 =
95.2 1873 3746 =
96.2 2946 5892 =
97.3 3240 9720 =
98.3 4320 12,960 =
99.6 9 54 =
The area is 54 square feet.
100.20
24
80
400
480
+
The area is 480 square feet.
101.30
15
150
300
450
+
Loading page 26...
Section 1.4 Multiplying Whole Numbers
23
105.227212
64 8 300 3 79 10 − −
106.322 331
87 6 200 53 7 40 − −
107.180 104
59 6 3 58 39 8 52 4 − −
108.84 85
12(4 3) 2 41 3+ +
109.3 486 232 1458 232
1226
− = −
=
There were 1226 billionaires in 2012.
110.7 140 34 980 34
946
− = −
=
There were 946 billionaires in 2007.
111.485
12
970
4850
5820
+
It will travel 5820 miles.
112.38
12
76
380
456
+
You can travel 456 miles.
113.12
18
96
120
216
+
It will take 216 minutes.
114.28
31
28
840
868
+
You use 868 gallons.
115.food/lodgingairfare
Total cost 16 378 16 260
6048 4160
10, 208
= +
= +
=
The total cost is $10,208.
116.biographiesnovels
Total 17 14 13 23
238 299
537
= +
= +
=
They took in $537.
117. 9 A.M. to 5 P.M. is 8 hours.7 2 5 14 5
19
+ = +
=
The total cost is $19.
118.Cost if using monthly payments 14 50 100
700 100
800
= +
= +
=
Savings:800
750
50
−
Paying the total amount at the time of the purchase
will save $50.
119. a.18
14
72
180
252
+
The area of the floor is 252 square feet.
b.252
8
2016
The cost of the carpeting is $2016.
120. a.19
15
95
190
285
+
The area of the floor is 285 square feet.
b.285
8
2280
The cost of the carpeting is $2280.
23
105.227212
64 8 300 3 79 10 − −
106.322 331
87 6 200 53 7 40 − −
107.180 104
59 6 3 58 39 8 52 4 − −
108.84 85
12(4 3) 2 41 3+ +
109.3 486 232 1458 232
1226
− = −
=
There were 1226 billionaires in 2012.
110.7 140 34 980 34
946
− = −
=
There were 946 billionaires in 2007.
111.485
12
970
4850
5820
+
It will travel 5820 miles.
112.38
12
76
380
456
+
You can travel 456 miles.
113.12
18
96
120
216
+
It will take 216 minutes.
114.28
31
28
840
868
+
You use 868 gallons.
115.food/lodgingairfare
Total cost 16 378 16 260
6048 4160
10, 208
= +
= +
=
The total cost is $10,208.
116.biographiesnovels
Total 17 14 13 23
238 299
537
= +
= +
=
They took in $537.
117. 9 A.M. to 5 P.M. is 8 hours.7 2 5 14 5
19
+ = +
=
The total cost is $19.
118.Cost if using monthly payments 14 50 100
700 100
800
= +
= +
=
Savings:800
750
50
−
Paying the total amount at the time of the purchase
will save $50.
119. a.18
14
72
180
252
+
The area of the floor is 252 square feet.
b.252
8
2016
The cost of the carpeting is $2016.
120. a.19
15
95
190
285
+
The area of the floor is 285 square feet.
b.285
8
2280
The cost of the carpeting is $2280.
Loading page 27...
Chapter 1 Whole Numbers and Introduction to Algebra
24
121. a.50
94
200
4500
4700
+
The area of the court is 4700 square feet.
b.400
12
800
4000
4800
+
12 gallons will cover 4800 square feet.
c. Yes; 12 gallons are enough to refinish the court.
122. a.50
84
200
4000
4200
+
The area of the court is 4200 square feet.
b.400
9
3600
9 gallons will cover 3600 square feet.
c. No; 9 gallons are not enough to refinish the
court.
123. – 132. Answers will vary.
133. makes sense
134. makes sense
135. does not make sense; Explanations will vary.
Sample explanation: You must attach2 3,+ or 5
zeros.
136. does not make sense; Explanations will vary.
Sample explanation: The area of a regulation tennis
court is 2808 square feet.
137. false; Changes to make the statement true will vary.
A sample change is: Deleting 0 as a factor might
change the product from being 0 to being non-zero.
138. false; Changes to make the statement true will vary.
A sample change is: The distributive property states
that multiplication distributes over addition .
139. true
140. true
141.613
6
3678
142.32
14
128
320
448
+
143. a.5(7 3) 5(4) 20− = =5 7 5 3 35 15 20 − = − =
b.10(8 2) 10(6) 60− = =10 8 10 2 80 20 60 − = − =
c. yes
144. Answers will vary.
145. 305,640
146.863
7697
8560
+
147.9002
897
8105
+
148.21 3 7 = because7 3 21. =
149. Yes, the product is 1206.67
18
536
670
1206
+
150.(502 47) 15 23,594 15
23,609
+ = +
=
24
121. a.50
94
200
4500
4700
+
The area of the court is 4700 square feet.
b.400
12
800
4000
4800
+
12 gallons will cover 4800 square feet.
c. Yes; 12 gallons are enough to refinish the court.
122. a.50
84
200
4000
4200
+
The area of the court is 4200 square feet.
b.400
9
3600
9 gallons will cover 3600 square feet.
c. No; 9 gallons are not enough to refinish the
court.
123. – 132. Answers will vary.
133. makes sense
134. makes sense
135. does not make sense; Explanations will vary.
Sample explanation: You must attach2 3,+ or 5
zeros.
136. does not make sense; Explanations will vary.
Sample explanation: The area of a regulation tennis
court is 2808 square feet.
137. false; Changes to make the statement true will vary.
A sample change is: Deleting 0 as a factor might
change the product from being 0 to being non-zero.
138. false; Changes to make the statement true will vary.
A sample change is: The distributive property states
that multiplication distributes over addition .
139. true
140. true
141.613
6
3678
142.32
14
128
320
448
+
143. a.5(7 3) 5(4) 20− = =5 7 5 3 35 15 20 − = − =
b.10(8 2) 10(6) 60− = =10 8 10 2 80 20 60 − = − =
c. yes
144. Answers will vary.
145. 305,640
146.863
7697
8560
+
147.9002
897
8105
+
148.21 3 7 = because7 3 21. =
149. Yes, the product is 1206.67
18
536
670
1206
+
150.(502 47) 15 23,594 15
23,609
+ = +
=
Loading page 28...
Mid-Chapter Check Point
25
Mid-Chapter Check Point – Chapter 1
1. eight billion, sixty-three million, five hundred sixty-
one thousand, four
2. 54,302,628
3. a. nearest hundred:64,517 64,500
b. nearest thousand:64,517 65,000
4.18 0
5.18 19
6.5809
3762
9571
+
7.652
378
274
−
8.876
4
3504
9.87
36
522
2610
3132
+
10.324
162
648
19440
32400
52, 488
+
11.4 9 36 =
Attach2 3,+ or 5 zeros to 36.400 9000 3,600,000 =
12.57 93 0 0 =
13.17
96
113
+
14.8000
57
7943
−
15.52
38
14
−
16.(8 3) 6 24 6 18 − = − =
17.2 15 7 30 7 23 − = − =
18.Exact Estimate
876 900
337 300
1058 100
2300
+ +
19.Exact Estimate
9846 10,000
2317 2000
8000
− −
20.Exact Estimate
(2893)(648) (3000)(600)
1,800,000
=
21. associative property of multiplication
22. distributive property
23. commutative property of addition
24. Perimeter:4 yards
13 yards
4 yards
13 yards
34 yards
+
Area:13 yards
4 yards
52 square yards
25
Mid-Chapter Check Point – Chapter 1
1. eight billion, sixty-three million, five hundred sixty-
one thousand, four
2. 54,302,628
3. a. nearest hundred:64,517 64,500
b. nearest thousand:64,517 65,000
4.18 0
5.18 19
6.5809
3762
9571
+
7.652
378
274
−
8.876
4
3504
9.87
36
522
2610
3132
+
10.324
162
648
19440
32400
52, 488
+
11.4 9 36 =
Attach2 3,+ or 5 zeros to 36.400 9000 3,600,000 =
12.57 93 0 0 =
13.17
96
113
+
14.8000
57
7943
−
15.52
38
14
−
16.(8 3) 6 24 6 18 − = − =
17.2 15 7 30 7 23 − = − =
18.Exact Estimate
876 900
337 300
1058 100
2300
+ +
19.Exact Estimate
9846 10,000
2317 2000
8000
− −
20.Exact Estimate
(2893)(648) (3000)(600)
1,800,000
=
21. associative property of multiplication
22. distributive property
23. commutative property of addition
24. Perimeter:4 yards
13 yards
4 yards
13 yards
34 yards
+
Area:13 yards
4 yards
52 square yards
Loading page 29...
Chapter 1 Whole Numbers and Introduction to Algebra
26
25. a. The James Bond franchise had the greatest
number of movies.
The total world gross for this franchise was
$5,116,147,171.
b. three billion, two hundred eighty-seven million,
two hundred eighty-five thousand, five dollars
c. Star Wars had 7 movies.$4,279,632,749 $4,000,000,000
d. Shrek and Lord of the Rings each had total
world gross less than $3,500,000,000.
26. a.61 (1980)
28 (Ancient Greece and Rome)
33
−
People born in 1980 are expected to live 33
years more than people born in ancient Greece
and Rome.
b. Average life expectancy was 48 years in 1950.
c. The following life expectancies round to 30.Stone Age: 25 30
Ancient Greece and Rome: 28 30
Middle Ages: 30 30
1900: 31 30
d. life expectancy1950: 48
life expectancyMiddle Ages: 30?
?
?
48 2 30 12
48 60 12
48 48 true
= −
= −
=
27.Deposits Withdrawls
Balance (730 250) (29 156 347)
980 532
448
= + − + +
= −
=
The balance is $448.
28.58,952
51,723
7 229
−
The change in the city’s population was 7229.
29.(8)(1480) (5)(1245) 11,840 6225
996 285
18,065
+ = +
= +
=
The total cost is $18,065.
30.14
12
28
140
168
+
The area of the floor is 378 square feet.168 10 1680 =
The cost of the carpeting is $1680.
1.5 Check Points
1. a.56 7 8 = because8 7 56. =
b.27 3
9 = because3 9 27. =
c.9
3 27 because9 3 27. =
2. a.13 1 13 = because13 1 13. =
b.13 13 1 = because1 13 13. =
c.1
17 17 because1 17 17. =
d.17
1 17 because17 1 17. =
26
25. a. The James Bond franchise had the greatest
number of movies.
The total world gross for this franchise was
$5,116,147,171.
b. three billion, two hundred eighty-seven million,
two hundred eighty-five thousand, five dollars
c. Star Wars had 7 movies.$4,279,632,749 $4,000,000,000
d. Shrek and Lord of the Rings each had total
world gross less than $3,500,000,000.
26. a.61 (1980)
28 (Ancient Greece and Rome)
33
−
People born in 1980 are expected to live 33
years more than people born in ancient Greece
and Rome.
b. Average life expectancy was 48 years in 1950.
c. The following life expectancies round to 30.Stone Age: 25 30
Ancient Greece and Rome: 28 30
Middle Ages: 30 30
1900: 31 30
d. life expectancy1950: 48
life expectancyMiddle Ages: 30?
?
?
48 2 30 12
48 60 12
48 48 true
= −
= −
=
27.Deposits Withdrawls
Balance (730 250) (29 156 347)
980 532
448
= + − + +
= −
=
The balance is $448.
28.58,952
51,723
7 229
−
The change in the city’s population was 7229.
29.(8)(1480) (5)(1245) 11,840 6225
996 285
18,065
+ = +
= +
=
The total cost is $18,065.
30.14
12
28
140
168
+
The area of the floor is 378 square feet.168 10 1680 =
The cost of the carpeting is $1680.
1.5 Check Points
1. a.56 7 8 = because8 7 56. =
b.27 3
9 = because3 9 27. =
c.9
3 27 because9 3 27. =
2. a.13 1 13 = because13 1 13. =
b.13 13 1 = because1 13 13. =
c.1
17 17 because1 17 17. =
d.17
1 17 because17 1 17. =
Loading page 30...
Section 1.5 Dividing Whole Numbers
27
d.8 undefined
0 =
e.0 undefined
0 =
4.171
3 513
3
21
21
0
03
200
2
32
Check:171
3
513
5.2
2
20
748
6 4488
42
28
24
48
8
200
4
0
20
Check:748
6
4488
6.7086
6 42520
42
05
0
52
4
2
22
20
20
200
200
8
40
36
4200042,520 6 7086 R 4 =
Check:7086
6
42516
4
42520
+
7.83
29 2407
232
820
20
2
7
00
87
0
Check:83
29
747
1660
2407
+
8.20
22
2
415
32 13292
128
49
32
10
2 0
20
60
0
72
1
1213, 292 32 415 R 12 =
Check:415
32
830
12450
1
00
3280
12
13292
+
+
9.12
1386 16649
1386
272
2
201
89
2772
1716, 649 1386 12 R 17 =
Check:1386
12
2772
13860
00
16632
17
16649
+
+
10. a.240 60 240 60 24 6 4 = = =
b.53,000 53000 530 530
100 100 1
= = =
c.3000
5000 15,000,000 5000 15000000 5 15000= =
27
d.8 undefined
0 =
e.0 undefined
0 =
4.171
3 513
3
21
21
0
03
200
2
32
Check:171
3
513
5.2
2
20
748
6 4488
42
28
24
48
8
200
4
0
20
Check:748
6
4488
6.7086
6 42520
42
05
0
52
4
2
22
20
20
200
200
8
40
36
4200042,520 6 7086 R 4 =
Check:7086
6
42516
4
42520
+
7.83
29 2407
232
820
20
2
7
00
87
0
Check:83
29
747
1660
2407
+
8.20
22
2
415
32 13292
128
49
32
10
2 0
20
60
0
72
1
1213, 292 32 415 R 12 =
Check:415
32
830
12450
1
00
3280
12
13292
+
+
9.12
1386 16649
1386
272
2
201
89
2772
1716, 649 1386 12 R 17 =
Check:1386
12
2772
13860
00
16632
17
16649
+
+
10. a.240 60 240 60 24 6 4 = = =
b.53,000 53000 530 530
100 100 1
= = =
c.3000
5000 15,000,000 5000 15000000 5 15000= =
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Subject
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