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Solution Manual for Mathematics: Its Power and Utility, 10th Edition

Solution Manual for Mathematics: Its Power and Utility, 10th Edition helps you reinforce learning with in-depth, accurate solutions.

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    Student's Survival and Solutions Manual for MATHEMATICS Its Power and Utility TENTH EDITION Karl J. Smith

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    CONTENTS Page iii CONTENTS PART I: FOUNDATIONS: THE POWER OF MATHEMATICS 1 Arithmetic, Calculators, and Problem Solving ......................... 1 2 Sets of Numbers ......................................................................... 35 3 Introduction to Algebra .............................................................. 63 4 Percents and Problem Solving ................................................... 91 5 Introduction to Geometry ......................................................... 113 6 Measurement and Problem Solving ......................................... 131 PART II: APPLICATIONS: THE UTILITY OF MATHEMATICS 7 Applications of Percent ............................................................. 157 8 Sets and Logic ........................................................................... 195 9 Probability ................................................................................. 229 10 Statistics..................................................................................... 251 11 Graphs ....................................................................................... 279

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    PREFACE Page v PREFACE This manual was designed to help you bridge the gap between the textbook and a working knowledge of mathematics. It has been said that “Mathematics is not a Spectator Sport" and this means you cannot learn mathematics by simply attending class, but instead you must build a body of information that will enable you to do problem solving in the real world. I decided to entitle this supplement, Student's Survival and Solutions Manual because I want it to be more than a Student Solutions Manual. Thirty years of teaching experience have given me the ability to anticipate the types of errors and difficulties you may have while taking this course. Here I will show you some of the steps that are left out of the text, and most all of these steps in the included problems. There are several things you must do if you wish to be successful with mathematics:  Attend every class.  Read the book. Regardless of how clear and lucid your professor's lecture on a particular topic may be, do not attempt to do the problems without first reading the text and studying the examples. It will serve to reinforce and clarify the concepts and procedures.  Problems, problems... Problems, Problems, You must work problems every day; work the assigned problems; work problems. Look over the entire ESSENTIAL IDEA problem set (even those problems which are not assigned).   Ask questions when you are stuck (and you will get stuck that is part of the process).  Keep asking questions until receiving answers that are understandable to you.  Today's calculators are good at obtaining answers, and if all that is desired is an answer, then you have relegated yourself to the level of a machine. Do not work problems to obtain answers. It is the that are important. Even though a solutions concepts manual is basically a “how to" document, always ask a why particular approach was used, and understand the concept the problem is illustrating.

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    PREFACE STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page vi For the most part, this manual includes complete solutions to the odd-numbered problems. Notice that the complete solutions for the self-tests are given at the end of the review sections in the textbook.

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.1 Mathematics Its Power and Utility, Ninth Edition Page 1 CHAPTER 1 Arithmetic, Calculators, and Problem Solving SURVIVAL HINT: If your instructor does not begin with Chapter 1, you might wish to take some time looking over this chapter anyway. Please read page 1 of the textbook because it tells you what this part of the book is all about. As you look through this first chapter you will notice that we cover fractions, decimals, and numeration systems. We also introduce you to using a calculator. If you have a manual for your calculator, do not attempt to read it; part of what this book will do is to teach you how to use a calculator to do the type of problems you are considering at the time. You may remember some things about fractions, decimals, and numeration systems, or you may have forgotten more than you remember. That is ok; --- it is our job.... the book and your instructor have been assigned the relax task of making sure you understand the topic. Find out from your instructor what is expected of you. You will probably need a copy of this textbook, pencils and paper, a straight-edge, and a calculator. (By the way, the cover for your calculator makes a good straight-edge.) Put your name and phone number inside the cover of your calculator, so if you lose it, it is, at least, possible that it be returned. As you begin on your mathematics journey, Bon Voyage! 1.1 Math Anxiety, page 4 SURVIVAL HINT: There are, of course, no right or wrong answers to Problems 1-25. In the book from which these myths were obtained there is a whole chapter justifying that these are ( ) Mind Over Math myths, and the authors cite specific studies to support their conclusions. As you do these problems, remember that a is a popular belief or tradition that has grown up around something which is an myth unfounded or false notion. Don't be afraid to express your own ideas when answering these questions. Problem Set page 9 1.1 , 1. Write a couple of paragraphs about your math history. You are writing this for yourself, not for your teacher. 2 . Read the “Math Anxiety Bill of Rights” on page 6 and then make up your own list. 3 . When you see this stop signal, stop and study the material because it will be used later. 4. When you see this caution sign, make a special note of the material next to the caution sign, because it will be used throughout the rest of the book. 5. The yield sign means that you will need to remember the result, but it is not necessary for you to understand the derivation. 6. The bump sign means that some unexpected or difficult material follows, and you will need to slow down to understand the discussion. 7-36. We will generally not give answers to those questions marked IN YOUR OWN WORDS . This problems do not have “right” or “wrong” answers, but rather are included to help you advance your success in this course. Do you best to answer the question.

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 2 37. This sign means that a stop sign is ahead. 39 . This sign means that there is a roundabout ahead. 41 . This sign is used to mean a kangaroo crossing. 43 . This sign is used to designate a woman's rest room. 45 . This sign is used to designate a currency exchange service. 47 . This sign is used to designate a restaurant. 49 . Choice B, employment 51 . Choice A, announcements 53. Choice E, recreation 1.2 Formulating the Problem, page 11 SURVIVAL HINT : It is important that you pay attention to the agreement. This order of operations procedure is used almost every day in this course. There are four main algebraic processes; these are simplify evaluate, solve, factor. , and In this section, we state, “To a numerical expression means simplify to carry out all the operations, according to the order of operations, and to write the answer as a single number. ” New Terms Introduced in this Section Addition Counting number Difference Distributive property Elementary operations Estimation Juxtaposition Natural number Product Quotient Simplify a numerical expression Numerical expression Sum Translation Whole number Problem Set page 18 1.2 , 1. a. b.                Display:  3 . (1) Parentheses first (2) Multiplication and division, reading from left to right (3) Addition and subtraction, reading from left to right 4. Distributive Property: ( + ) = + a b c ab ac SURVIVAL HINT : Take a look at the essential ideas of this section. There are two: 1. State the order of operations. 2. Explain the distributive property in your own words. Because these items are essential to your understanding of the material, we give the answer to all of the essential ideas in this . Your instructor may or may not assign these problems, but Survival Manual it would be a good idea to designate a section of your notebook and then put into ESSENTIAL IDEAS this section of the essential ideas. all

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.2 Mathematics Its Power and Utility, Ninth Edition Page 3 5 .          False; the error was to add first. 7 . 2 (3 + 4) 2 3 + 2 4 is an example of the distributive property; what is shown here is     simplification , so the statement is wrong. 9 . False; it is a whole number. 11 . a.          Since the last operation was addition, we call this a . sum b.          Since the last operation was addition, we call this a . sum 13 . a. 12 6 + 3 2 + 3 5        Since the last operation was addition, we call this a . sum b.                   5 Since the last operation was division, we call this a quotient. 15 a. . 15 3 +           Since the last operation was addition, we call this a . sum b.          3      Since the last operation was subtraction, we call this a . difference 17 a. . 32               Since the last operation was addition, we call this a . sum b. 8 2 8 6 4 56              Since the last operation was addition, we call this a . sum 19 a. . 5 5 5                   Since the last operation was addition, we call this a . sum

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 4 b.                    13 Since the last operation was addition, we call this a . sum 21 a.                               Since the last operation was addition, we call this a . sum b. 19                                      Since the last operation was addition, we call this a . sum 23 a. . 2 18 + 9 3 5 2 36 + 3 10                       Since the last operation was subtraction, we call this a . difference b. 2 (18 + 9) 3 5 2 2 27 3 5 2 54 3                                     Since the last operation was subtraction, we call this a . difference 25 a. b. . 3 (4 + 8) 3 4 + 3 8 7 (9 + 4) 7 9 + 7 4         27 a. . 4 (300 + 20 + 7) = 4 300 + 4 20 + 4 7     b. 6 (500 + 30 + 3) = 6 500 + 6 30 + 6 3     29  “The sum” means “ ” and “the product” means “ ”: 3 + 2 4. Parentheses are not   necessary because the order of operations requires that the product be done before the addition. 31 . “Times” means “ ” and “sum” means “ ”: 10(5 + 6)  The parentheses are used to indicate the order of operations and they are also used to indicate multiplication. 33 . 8 5 + 10; if we wanted 8 (5 + 10) we would need to say “Eight times the quantity   five plus ten.” 35 . 8(11 9); the difference requires parentheses for the correct order of operations.  37 . Press: : 716     Display 261 Since the last operation was subtraction, we call this a . difference 39 . Press: :     Display 800

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.3 Mathematics Its Power and Utility, Ninth Edition Page 5 Since the last operation was subtraction, we call this a . sum 41 . Press: :        Display 1,080 Since the last operation was subtraction, we call this a . sum 43 . Press:            Don't forget the times sign for the indicated multiplication. : Display 1,600 Since the last operation was multiplication, we call this a . product 45 . Press: :       Display 59 Since the last operation was subtraction, we call this a . difference 47 . Press: :         Display 2,700 Since the last operation was subtraction, we call this a . difference 49 . Press: :          Display 285,197 Since the last operation was subtraction, we call this a . sum 51 . Press:              : since the last operation was subtraction, we call this a . Display sum 2,323; Estimates for Problems 53-60 may vary. 53 . Each day has 24 hours so we estimate 8,000          We estimate this time to be 8,000 hours. The exact answer is 8,640 hours. 55 . We estimate , ,                 We estimate the deduction to be $ . The exact answer is $ .      57 . We estimate by assuming a 40 hour work week for 50 weeks a year: ,000 36,000           We estimate the annual salary to be $36,000. The exact answer is $37,440. 59 . We estimate 00          We estimate we can drive 300 miles. The exact answer is 345 miles. 1.3 Fractions and Decimals, page 19 SURVIVAL HINT : A fraction is an indicated division. For example, is one unit (the proverbial pie) 1 2 divided into two parts, so it is This section is devoted to developing your number sense regarding    . fractions. You may or may not have developed this number sense in previous arithmetic classes, but now is a good time for a refresher.

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 6 New Terms Introduced in this Section Approximately equal to symbol Column names Common fraction Decimal Decimal fraction Decimal point Denominator Division by zero Fraction Hundred Improper fraction Mixed number Numerator Place-value names Proper fraction Remainder Repeating decimal Ten Rational number Terminating decimal Trailing zeros Problem Set page 26 1.3 , 3. A fraction is a quotient of a whole number divided by a counting number. 4 a. b. c. d. e. . 1 10 100 1000 10000 The answers are getting larger. Answers vary; it looks like the closer the divisor is to 0 the larger the answer. 5. The place value names (in decreasing order) are: trillions, hundred billions, ten billions, billions, hundred millions, ten millions, millions, hundred thousands, ten thousands, thousands, hundreds, tens, units, decimal point, tenths, hundredths, thousandths, ten- thousandths, hundred-thousandths, and millionths. SURVIVAL HINT: Did you remember to look at the Even if they were not assigned, ESSENTIAL IDEAS? you should add these terms to your notebook: 1. Fraction 2. Common fraction/decimal fraction 3. Division by 0 is not permitted. 4. Place value names 7 . False; can't divide by 0. 9 . True; we can affix any number of trailing zeros. 11 . False; 0.    13 . False; by calculator, the answer is appoximately 27.96709753. 15 . a b . proper; . proper; 8 13 17 21     17 a b . . . 4 2         19 a. . = 5 16 1 3 3 Divide into to obtain , with a remainder of .    b. = 6 25 1 4 4 Divide into to obtain , with a remainder of .   c . = 14 141 1 10 10 Divide into to obtain , with a remainder of .      d. =       3 Divide into to obtain , with a remainder of .    

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.3 Mathematics Its Power and Utility, Ninth Edition Page 7 21 a. . = 1    1 Divide into to obtain , with a remainder of .     b. =   10 10  Divide into to obtain , with a remainder of .     c. 33 1   =  Divide into to obtain , with a remainder of .     d . =     Divide into to obtain , with a remainder of .    23 a. . =    Divide into to obtain , with a remainder of .    b. =    Divide into to obtain     c. = 18  Divide into to obtain    d. =    Divide into to obtain , with a remainder of .    25 a. .          b.          27 a. .             b. 5 1 2      29 a . . =            = b.     2 5 5  31 a. . =            b.     = 33 a. . 1 =           b. 2 =     1       35 a. . =           b . =           7 SURVIVAL HINT : 36-47 In Problems , do not round the decimal representations. For example, 1 3 = 0.3 _ Note the bar over the three; this shows that the three repeats. It is NOT correct to write 1 1 3 3 = 0.33333 or = 0.33 or any other such representation. The three repeats and does not terminate. That is, in doing the long division, there is never a remainder of zero. 37 a. . =     Long division; by calculator: 5   Continue with the division until you see the digits repeat. There is one repeating digit. b. =     Long division; by calculator:     Continue with the division until you see the digits repeat. There is one repeating digit.

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 8 39 a. . =       Long division; by calculator:      Continue with the division until the remainder is zero. b. =      Long division; by calculator:      Continue with the division until you see the digits repeat. There is one repeating digit. 41 a. . =       Long division; by calculator:      Continue with the division until you see the digits repeat. There is one repeating digit. b. =      Long division; by calculator:      Continue with the division until you see the digits repeat. There is one repeating digit. 43 a. . =      Long division; by calculator: 5   Continue with the division until you see the digits repeat. There is one repeating digit. b. =       Long division; by calculator:      Continue with the division until you see the digits repeat. There is one repeating digit. 45 a. . =       Long division; by calculator:      Continue with the division until you see the digits repeat. There is one repeating digit. b. =     Long division; by calculator:     Continue with the division until you see the digits repeat. There is one repeating digit. 47 a. . =     Long division; by calculator:     Continue with the division until the remainder is zero. b. 3 = 3 1 9  9    Long division; by calculator:     9 Continue with the division until you see the digits repeat. There is one repeating digit. 49 a . . The square is divided into one hundred small parts, and we see 82 of them are shaded, so or of the square is shaded.     . The circle is divided into 8 parts and 5 parts are shaded; . b 5 8 SURVIVAL HINT : Your answers to Problems 50-51 may vary. Estimating is not an easy skill to learn,so relax and do the best you can. 51 a . . The square is divided into one hundred small parts, and we see 63 of them are shaded, so 0.63 of the square is shaded. b . The square is divide into one hundred small parts and there are four small triangles, each pair of which can form a square so there is a total of of those squares      are not shared. Thus, the shaded portion is or 0.82 of the large square.      SURVIVAL HINT : Do not round the answers to Problem 53, but use the overbar to indicate the repeating decimals. If your calculator does not show a pattern, you must approximate the answer.

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.4 Mathematics Its Power and Utility, Ninth Edition Page 9 53 a . . Press: : Answer: 0. 7 15   Display .466666666666 . Press: : Answer: 0.318 b 7 22   Display .3181818181818 55 . First, note that = 0.5: $52 $52.5 $5,250 1 2         To multiply by 100, move the decimal point two places to the right. 57 . First, note that = 0.25: $ 2 $ 2. 5 $42.25 $ 4 $8,450 1 4                   To multiply by 100, move the decimal point two places to the right. 59 . First, note that = 0.125: $63 $63.125 8 $6,312.50 1 8        To multiply by 100, move the decimal point two places to the right. 1.4 Rounding and Estimation, page 28 SURVIVAL HINT : Take a look at the essential ideas. Add these ideas to your journal. New Terms Introduced in this Section Rounding money Rounding numbers Problem Set page 31 1.4 , 3. The rounding place digit is the name of the positional column to which the number is being rounded. 4 . Estimation is making a reasonably accurate guess. It is important in everyday life in many situations in which an exact answers is not needed. For example, when making a purchase, deciding on which route to take, how long a task may take to complete, or tipping at a restaurant. 5 . 30. 0 5 rounded to the nearest tenth is 30.1, so the statement is false. The error is that the number was rounded to the nearest unit, rather than the nearest tenth. 7 . 3,6 8 4,999 rounded to the nearest ten thousand is 3,680,000, so the statement is false. The error is that one was added to the rounding place digit and it should not have been.

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 10 9 . 23 12 25 10 = 250; estimate is correct.    11 . 2. 3 12 Rounding place digit is marked. 2.3 Digit to the right is a 1, so delete the “12”. 13 . 6,287.4 5 13 Rounding place digit is marked. 6,287.45 Digit to the right is a 1, so delete the “13”. 15 . 5. 2 91 Digit to the right is a 9, so add one 5.3 to the rounding place digit and delete the “91”. 17 . 6, 2 87.4513 Digit to the right is an 8, so add 6,300 one to the rounding place digit and change the digits to the right to zeros. Drop the zeros to the right of the decimal point. 19 . 12.8 1 97 Digit to the right is a 9, so 12.82 add one to the rounding place digit and delete the “97”. 21 . 4.81 7 92 Digit to the right is a 9, so 4.818 add one to the rounding place digit and delete the “92”. 23 . 4 .8199 Digit to the right is a 8, so 5 add one to the rounding place digit and delete the “.8199”. 25 . $12.9 9 3 Digit to the right is a 3, so $12.99 delete the “3”. 27 . $14.9 9 8 Digit to the right is a 8, so $15.00 add one to the rounding place digit and delete the “8”. Note that adding 1 to 9 causes a carry into the next column. That is, $14.99 + $0.01 = $15.00. 29 . 6 9 4.3814 Digit to the right is an 4, so 690 change the numerals to the right of the rounding place digit to zeros; then delete those to the right of the decimal point. 31 . $8 6 ,125 Digit to the right is an 1, so $86,000 change the digits to the right of the rounding place digit to zeros. 33 . From the calculator display, we see 2/3 is represented as 0.66 6 6666667. The digit to the right is a 6, so add 1 to the rounding place digit and drop the digits to the right to obtain: 0.667. 35 . From the calculator display, we see 2/17 is represented as 0.11 7 6470588. The digit to the right is a 6, so add 1 to the rounding place digit and drop the digits to the right to obtain: 0.118. 37 . From the calculator display, we see 7/51 is represented as 0.13 7 254902. The digit to the right is a 2, so do not change the rounding place digit but drop the digits to the right to obtain: 0.137. 39 . 2 6 0.3333333333; rounded answer: 0.333; by calculator:  2 6  

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.5 Mathematics Its Power and Utility, Ninth Edition Page 11 41 . 0.41666666666; rounded answer: 0.417; by calculator: 5 12  5 12   43 . 0.3179916318; rounded answer: 0.318; by calculator: 152 478  152 478   45 . B : 4.82 5 mi, so it is about 10 miles round trip; 5 10 = 50. Think   47 . C : $35,000 $36,000 and $36,000 12 = $3,000. Think   49 . B : $1,000 $1,200 and $1,200 12 = $100. Think   51 . $15,000 12 = $1,250 ; by calculator: 15000 12   53 . = $12.125 ; rounded answer: $12.13; by calculator: $1,818.75 150 1818.75 150   55 . $70.8333333 ; rounded answer: $70.83 by calculator: $850 12   850 12   57 . $112.333333 ; rounded answer $112.33; by calculator: $674 6  674 6   1.5 Exponents and Prime Factorization, page 33 SURVIVAL HINT: There are many ideas in this section which you will use daily in your future math work. Be sure you understand the concept of an exponent, and that of a prime factorization. New Terms Introduced in this Section Base Composite Cubed Exponent Exponential notation Factor Factoring Factorization Factor tree Googol Power Powers of ten Prime factorization Prime number Scientific notation Squared Problem Set page 39 1.5 , 3. An exponent is a number used to indicate repeated multiplication. In other words, it is the number of repeated factors. In it is the number . b n n 4. A number is in scientific notation when that number is written as a power of 10 or as a decimal number between 1 and 10 times a power of 10. 5. An excellent way to find the prime factorization is to use factor trees. 6. The is an exponent key and EE is used for scientific notation. y x SURVIVAL HINT : Take a look at the four preceding essential ideas. Add these ideas to your journal. 7. a b. c. d. . one million 10 6 10 10 10 10 10 10      8 . a b. c. d. . one thousand 10 3 10 10 10   9 . a. b. c. d. one-tenth 10 1 0.1  10 . a b. c. d. . one-hundredth 10  

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 12 11 . False; means .   13 . False; there are two multiplications (not three).      15 . a . In scientific notation, the decimal point goes after the first nonzero digit: 3.2 10 = 3,200   Decide on the exponent by counting the number of decimal places necessary to write this number, 3.2, as the given number. We see it is three places. Move the decimal point 3 places to the right. b . 2.5 10 = 25,000  Move the decimal point 4 places to the right. c . 1.8 10 = 18,000,000   Move the decimal point 7 places to the right. d . 6.4 10 = 640   Move the decimal point 2 places to the right. 17 . a . 4.21 10 = 0.0000     Move the decimal point 6 places to the left. b . 9.2 10 = 92,000,000   Move the decimal point 7 places to the right. c . 1 10 =    Don't move the decimal point. d . 1.5 10 =    Don't move the decimal point. 19 a . . “E9” means “ 10 ”, so 6.34E9 = 6.34 10     b . 5.2019E11 = 5.2019 10   c . “08” means “ 10 ”, so 4.093745 08 = 4.093745 10   d . 8.291029292 12 8.291029292 10    21 a . . 7.2 10 = 72,000,000,000   Move the decimal point places to the right. 10 b . 4.5 10 = 4,500   Move the decimal point places to the right. 3 23 a . . 2.1 10 = 0.    Move the decimal point places to the left. 3 b . 4.6 10 = 0.     Move the decimal point places to the left. 7 25 a . . . 10 =      Move the decimal point places.  b . . 10 =       Move the decimal point places to the left. 4

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.5 Mathematics Its Power and Utility, Ninth Edition Page 13 27 a. b . .              29 a . . 2.18928271 10 21,892,827,100                      b . 0.0000329 07 0.0000329 10 329                  31 .             33 .                 35 . 7               37 a b . . . (2 2) 5 2 5                         39 a b . . . 2 2 64 2 2 2 32 2 2 2 2 16 2 2 2 2 2 8 2 2 2 2 2 2 4 2 2 2 2 2 2 2 2 2                                                        41 a b . . . , 2 2 2 5 2 5 2 5 2 5 2 5 2 5 2 5 10 10 2 5                                          43 a . . See which prime divides evenly into the given number. If it does not divide evenly, move to the next prime. If it does divide evenly, try that same number again.

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 14 , 7 637 7 7 91 7 7 7 13 7 13              b . , 13 17,641 13 13 1,357 13 13 23 59 13 23 59                45 a . . Use your calculator and the list of primes to see which prime divides evenly into the given number. If it does not divide evenly, move to the next prime. If it does divide evenly, try that same number again. , 19 2,407 19 29 83       b . , 31 961 31 31 31 31          47 . First estimate the number of seconds in a year:                 60 60 365 24 6 10 6 10 3.65 10 24 6 6 3.65 10  Now multiply this number by your age (in years) to see that the most reasonable exponent is the one shown in choice A. 49 . Choice A is a penny, choice B is a dime, and choice C is a dollar; the best choice is C. 51 . Choice B is a very small number (and not even a possibility), and choice C is too large, so the best choice must be A. 53 . 41,840,000 = 4.184 10   55 . 3.33 10 = 333,000  57 a . . , , , , , , ,             By calculator, b.                    59 . NOTE: no calculator; this is an estimation problem. $ $ $ $ $ $ $ $ $ $                $ $ $ $ + $ + $ + $ + $1 + $ $ $ $ $ $1              $ $2 $20 (Actual, with calculator is $    

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.6 Mathematics Its Power and Utility, Ninth Edition Page 15 1.6 Common Fractions, page 42 SURVIVAL HINT : You may have had problems with fractions in the past, but the emphasis here is on understanding fractions and learning how to use a calculator to help you with calculation involving fractions. If you are feeling anxious about this topic, it may be time to take a break with some of the anxiety reducing techniques introduced in the first section of this book. Relax.... ask questions, and you will succeed! New Terms Introduced in this Section Canceling Completely reduce fraction Complex decimal Divide fractions Fundamental property of fractions Invert Multiply fractions Reciprocal Reduced fraction Reducing fractions Simplify a fractional expression Problem Set page 48 1.6 , 3. Use the fundamental property of fractions (see the answer to Problem 1) to eliminate all common factors (other than 1 or 1).  4. A fraction is reduced when there is no number (except 1) that divides into both the numerator and denominator. 5. To multiply fractions, multiply numerators and multiply denominators. 6. To divide fractions, invert and multiply. 7 . A terminating decimal is a fraction whose decimal representation ends. 8. (1) Multiply the given number without its decimal point by the decimal name of the last digit. (2) By the decimal name of the last digit, we mean: one place is tenth, or ; two places is 1 10 hundredth, or ; three places is thousandth, or ; . 1 1 100 1,000  9 . A reduced fraction is one in which there is no common factor (other than and )   between the numerator and denominator; this is true. 11 . F;         13 . but These results are different, so the statement is                 false. 15 . a b c d . . . .                                        

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 16 17 a b c d . . . . . 3 42 3 14 16 2 8 5 3 14 14 24 3 8 24 5 2 3                            19 a b c d . . . . . 40 5 48 5,670 672 14 48 ,150 5 1                                            21 . Shade two of the five rows and three of the four columns. There are 6 of the 20 squares that are double shaded. This can also be stated as three-tenths of the large square. 23 . Shade four of the five rows and one of the three columns. There are 4 of the 15 squares that are double shaded. 25 . Divide the side into six parts and the top into three parts. Then, shade one of the six rows and two of the three columns. There are 2 of the 18 squares that are double shaded. This can also be stated as one-ninth of the large square. 27 . In this problem, you are verifying for yourself that division gives the same result as “invert and multiply.” a. The divisor is 5, and the answer is 3. Also, 15     b. The divisor is 3, the answer is 2. Also,      29 . In this problem, you are verifying for yourself that division gives the same result as “invert and multiply.” a. The divisor is , and the answer is . Also,      The divisor is , the answer is . Also, b.           31 a. b. .                         c. d.                                    7 100 20 14 SURVIVAL HINT: Note is reduced. You do not need to write this answer as the mixed number    2  e. f.                                   

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.6 Mathematics Its Power and Utility, Ninth Edition Page 17 33 a. b. c. .                                          d. e. f.                                           35 a. b. c. .                            d. e. f.                                SURVIVAL HINT: You may be able to do these mentally, any number divided by itself is .  37 a. b. c. .                               d. e. f.                                39 a. b. .                          c. d.                                    e. f.                     

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 18 41 a. b. . 1 8 2 9                                            c. d.                                        e. f.                                      43 . a b c . 0. . .                   , 45 . a. b c                      . . , 47 . a. b. c.                                                             16 1 7 7 50 1 6 SURVIVAL HINT: You may know these answers from memory. 49 . a. b. c.                                                    1 51 . $ $ 1 1 10 10 $ ,        AGE SALARY       

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.7 Mathematics Its Power and Utility, Ninth Edition Page 19 53 . $ , $ , 1 1 10 10 $ ,         AGE SALARY        SURVIVAL HINT: Translate the word “of to mean multiply. ” 55 . 3 16  $12,512 = $2,346 By calculator: 3       57 . $227.00 $     By calculator:     59 . $ , $44,000 22 1 5 $44,000 5 1 22 $2,000 22 5 22 $10,000            1.7 Adding and Subtracting Fractions, page 50 SURVIVAL HINT : The in the first two problems summarize what you need to ESSENTIAL IDEAS remember from this section. New Terms Introduced in this Section Common denominator Extended order of operations LCD Lowest common denominator Subtraction of fractions Problem Set page 56 1.7 , 1 . Step 1 Find the LCD. Step 2 Change the forms of the fractions to obtain forms with common denominators. Step 3 Add the numerators of the fractions with common denominators. 3 . This job would require at least two cuts, so the total is: 2 + 5 + 7 + 5 + 5 + 7 + 5 1 1 1 3 2 4 8 3 16 4 2 16 16 16 16 16 17 17 16 18 1 16    

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 20 The smallest single length is 18 inches.   5 . (1) First, perform any operations enclosed in parentheses. (2) Next, perform any operations that involve raising to a power. (3) Perform multiplication and division, reading from left to right. (4) Do addition and subtraction, reading from left to right. 6. Step 1 Factor all given denominators into prime factors; write this factorization using exponents. Step 2 List each different prime factor you found in the prime factorization of the denominators. Step 3 On each prime in the list from Step 2, place the largest exponent that appears on that prime factor anywhere in the factorization of the denominators. Step 4 The LCD is the product of the prime factors with the exponents found in Step 3. 7 . False; do not add the denominators; the correct answer is + = . 3 4 7 8 8 8 9 . This problem and solution have no errors. 11 . This problem and solution have no errors. 13 . 19 20 1 40 40 2 = The correct response is A.  15 . 19 3 20 12 40 10 40 40        The correct response is D. 17 . If I multiply a number by a number larger than 1, the result is larger, but if I multiply a number by a number smaller than 1, the result is smaller. The correct response is B. 19 . If I divide a number by a number larger than 1 the result is smaller, but if I divide a number by a number smaller than 1, then the result is larger. The correct response is A. 21 a b c . . + . + . + 2 1 3 3 5 8 5 3 8 5 5 5 7 7 7 11 11 11    SURVIVAL HINT: A number is if there is no number other than 1 that divides into both the reduced numerator and denominator. This means, for example, the result in Problem 21b is reduced. d. e f 3 5 5 1 2 9 9 . . +                  

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.7 Mathematics Its Power and Utility, Ninth Edition Page 21 23 a. b. c. .                   d. e. f.                                       5 25 . Pick larger exponents for LCD. These are shown in boldface. LCD LCD a. b.                                         c. d. LCD LCD 2 3 5 7 = 630                                            27 . Pick larger exponents for LCD. These are shown in boldface. , LCD , LCD , a. b.                                                   c. d. LCD , LCD 2 3 5 ,                                                              29 a b . . LCD is 6; . LCD is 24; + + 5 1 5 2 5 5 20 15 6 3 6 6 6 8 24 24            

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 22 . LCD is 24; LCD is 12; c d.                         . LCD is 30; . LCD is 12; e f                      31 a b. c. . .                                   33 a. . LCD 2 3                                                 LCD b.                                                    

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.7 Mathematics Its Power and Utility, Ninth Edition Page 23 35 a. . LCD 2 3                                                      b.                           LCD 37 a. .                     b.                           39 a. b. .                           

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 24 41 . Multiplication before addition: + + 4 17 4 78 4 17 78 5 95 5 95 5 95 95 1 4 5          By calculator:                    Display : 0.8 Answer is 0.8 or . 4 5 43 . Parentheses first: + + 2 + + 2 4 2 1 12 10 1 5 3 5 15 15 5 22 5 15 1 + 2 22 6 3 3 + 28 3            By calculator:              Display : 9.333333333 Answer is 9. or .     45 . By calculator:               Display : (This is an approximate answer.) .4487116145 47 . First find the regions labeled “B” and add up their areas: The first one at the left is of ; 1 1 2 4 The second one is at the right and is of : 1 1 3 2 + + 1 1 1 1 1 1 2 4 3 2 8 6 1 3 1 4 8 3 6 4 + 3 4 24 24 + 7 24               49 . For this one, we find the portion that is not C. The C portion at the left is and the C 1 4 portion at the right is of or : + + 1 1 1 3 1 2 4 6 4 3 6 2 3 2 12 12 + 5 12 1 1 1 3 2 6       

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    STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR SECTION 1.7 Mathematics Its Power and Utility, Ninth Edition Page 25 Thus, the portion that is not C is: 1 = 5 7 12 12  51 . This is the portion that is not B. From Problem 47, the portion that is B is . Thus, we 7 24 find 1 = 7 17 24 24  53 . We see the square is divided into three columns of equal size. We are looking for the parts labeled K: in the first column K is of or of that column; in the second column it is 1 1 1 3 2 3  of that column; there is no K in the third column. Thus, 1 1 1 1 1 1 1 6 3 3 3 3 18 9 + + 0 + 1 2 18 18 + 3 18 1 6        55 . We see the square is divided into three columns of equal size. We are looking for the parts labeled Y: in the first column Y is of that column; in the second column it is of that 1 1 2 3 column; there is no Y in the third column. Thus, 1 1 1 1 1 1 1 2 3 3 3 3 6 9 + + 0 + 3 2 18 18 + 5 18       57 . R or G or Y is everything that is not K: 1 = 1 5 6 6  The fact that K is of the square was found in Problem 53. 1 6

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    CHAPTER 1 STUDENT'S SURVIVAL AND SOLUTION MANUAL FOR Mathematics Its Power and Utility, Ninth Edition Page 26 59    1 + 2 + 3 1 + 2 + 3 1 2 1 3 8 6 4 3 2 12 12 12 6 17 12 7 5 12  The total weight is 7 pounds.  1.8 Hindu-Arabic Numeration System, page 58 SURVIVAL HINT : The in the first three problems summarize what you need to ESSENTIAL IDEAS remember from this section. New Terms Introduced in this Section Abacus Expanded notation Hindu-Arabic numerals Number Number Numeral Numeration system Problem Set page 61 1.8 , 1. A decimal numeration system refers to a numeration system with 10 symbols and rules for combining those symbols to represent all numbers. If we refer to the decimal numeration system we use everyday then (1) there are ten symbols, (2) larger numbers are expressed in terms of powers of 10, and (3) it is positional. 3 . A Hindu-Arabic numeral is one of the decimal numerals we use everyday:           and . 5 . A is an expression of quantity whereas a is a symbol used to represent a number numeral number. 6. Expanded notation is writing a number by showing the meaning of each digit in that number. 7 8 a. b. . . a b . 100 . 64  2 9.                                                                                                                           

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