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Solution Manual for Developmental Mathematics, 1st Edition

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    I NSTRUCTOR ’ S S OLUTIONS M ANUAL D ANIEL S. M ILLER Niagara County Community College D EVELOPMENTAL M ATH FOR C OLLEGE S TUDENTS Robert Blitzer Miami Dade College

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    iii TABLE OF CONTENTS for INSTRUCTOR SOLUTIONS D EVELOPMEN T AL M ATH FOR C OLLEGE S TUDENTS Chapter 1 : Whole Numbers and Introduction to Algebra ................................ .. 1 Chapter 2 : Integers and Introduction to Solving Equations ............................. 61 Chapter 3 : Fractions ................................ ................................ ....................... 1 07 Chapter 4 : Decimals ................................ ................................ ....................... 219 Chapter 5 : Percents ................................ ................................ ........................ 3 09 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 Exp onents .............. 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

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    Chapter 1 Whole Numbers and Intro duction 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.

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    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 co untry 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.

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    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; 5 000 ; 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, t wo hundred eight 23 . The standard form is 3468. 24 . The standard form is 5 283. 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 is 600 40 3. + + 36 . The expanded form is 500 70 2. + + 37 . The expanded form is 5000 40 6. + + 38 . The expanded form is 3000 50 7. + + 39 . The expanded form is 80,000 1000 300 60 4. + + + +

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    Chapter 1 Whole Numbers and Introduction to Algebra 4 40 . The expanded form is 70, 000 2000 500 40 6. + + + + 41 . The expanded form is 50, 000 5000 30 8. + + + 42 . The expanded form is 40, 000 4000 20 9. + + + 43 . The expanded form is 20,000,000 8,000,000 600,000 40,000. + + + 44 . The expanded form is 50,000,000 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, 5 03 rounded to the nearest thousand is 7 3 ,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 9 2 ,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.

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    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 1 07 . – 1 17 . 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.

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    Chapter 1 Whole Numbers and Introduction to Algebra 6 1 29 . 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 as 20 10 15 5 3 7 8 + + + + which is 20 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 +

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    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

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    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 seem s reasonable . 32 . a. 28,612 287,611 7862 30,000 290,000 8000 328,000 + +  + + = b. Yes , the estimate seem s 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 . 50 40 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 + + + + = + + + + = + + =

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    Section 1. 2 Adding Whole Numbers 9 47 . 200 100 96 5 4 195 17 96 4 5 195 17 100 200 17 317 + + + + = + + + + = + + = 48 . 200 100 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 .

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    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.

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    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 .

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    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 9 0 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 side s 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 side s 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 3 6 inches . 107 . Answers will vary. 1 0 8 . 8 2 6 − = because 6 2 8. + = 1 0 9 . Yes, the sum is 92. 78 14 92 + 1 1 0 . 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 + =

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    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 . 15 4 17 5 6 7 4 Check: 4781 8 9 3 893 4 7 8 1 5674 − + 5 . 10 6 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 or Balance before May 10 May 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 − +

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    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 − +

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    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 − =

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    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.

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    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 c heck 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 subtrah end. 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   

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    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  = Attach 2 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

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    Section 1. 4 Multiplying W hole 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 

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    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  +

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    Section 1. 4 Multiplying W hole 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  = Attach 1 2, + or 3 zeros to 63. 70 900 63, 000  =

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    Chapter 1 Whole Numbers and Introduction to Algebra 22 76 . 9 4 36  = Attach 1 2, + or 3 zeros to 36. 90 400 36, 000  = 77 . 2 16 32  = Attach 3 3, + or 6 zeros to 32. 2000 16, 000 32, 000, 000  = 78 . 3 12 36  = Attach 3 3, + or 6 zeros to 36. 3000 12, 000 36,000, 000  = 79 . 83 29 80 30 2400    = Yes, an exact product of 2407 seem s reasonable . 80 . 48 33 50 30 1500    = Yes, an exact product of 1584 seem s reasonable . 81 . 312 58 300 60 18, 000    = Yes, an exact product of 18,906 seem s reasonable . 82 . 519 38 500 40 20, 000    = Yes, an exact product of 19,722 seem s 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 seem s reasonable . 86 . (3906)(517) (4000)(500) 2,000,000  = Yes, an exact product of 2,019,402 seem s 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  + The area is 450 square yards. 102 . 14 3 42  The area is 42 square yards. 103 . 528 603 1584 316800 318,384  + three hundred eighteen thousand, three hundred eighty - four 104 . 528 603 2562 341600 344,162  + three hundred forty - four thousand, one hundred sixty - two

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    Section 1. 4 Multiplying W hole Numbers 23 105 . 227 212 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 20 12 . 110 . 7 140 34 980 34 946  − = − = There were 94 6 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/lodging airfare Total cost 16 378 16 260 6048 4160 10, 208 =  +  = + = The total cost is $10,208. 116 . biographies novels 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 − P aying 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.

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    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 attach 2 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  = because 7 3 21.  = 149 . Yes, the product is 1206. 67 18 536 670 1206  + 150 . (502 47) 15 23,594 15 23,609  + = + =

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    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  = Attach 2 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 

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    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 − P eople 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 expectancy 1950: 48 life expectancy Middle 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  = because 8 7 56.  = b. 27 3 9 = because 3 9 27.  = c . 9 3 27 because 9 3 27.  = 2 . a. 13 1 13  = because 13 1 13.  = b. 13 13 1  = because 1 13 13.  = c . 1 17 17 because 1 17 17.  = d . 17 1 17 because 17 1 17.  = e . 2306 2306 1 = because 2306 1 2306.  = f . 1 2306 2306 because 1 2306 2306.  = 3 . a. 0 9 0 because 0 9 0.  = b. 0 253 0  = because 0 253 0.  = c . 0 0 8 = because 0 8 0.  =

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    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 3 2 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 4 2000 42,520 6 7086 R 4  = Check: 7086 6 42516 4 42520  + 7 . 83 29 2407 232 8 20 20 2 7 00 87 0 Check: 83 29 747 1660 2407  + 8 . 20 22 2 415 32 13292 128 49 32 1 0 2 0 20 60 0 72 1 12 13, 292 32 415 R 12  = Check: 415 32 830 12450 1 00 3280 12 13292  + + 9 . 12 1386 16649 1386 27 2 2 201 89 2772 17 16, 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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