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Solution Manual for Prealgebra, 6th Edition

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    S OLUTIONS M ANUAL B EVERLY F USFIELD P REALGEBRA S IXTH E DITION Margaret L. Lial American River College Diana L. Hestwood Minneapolis Community and Technical College

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    Table of Contents Pretest: Whole Numbers Computation..............................................................................................1 1 Introduction to Algebra: Integers............................................................................................... 3 1.1 Place Value • .................................................................................................. 3 1.2 Introduction to Integers • ................................................................................ 5 1.3 Adding Integers • ............................................................................................ 7 1.4 Subtracting Integers • ..................................................................................... 13 1.5 Problem Solving: Rounding and Estimating • ................................................ 18 1.6 Multiplying Integers • ..................................................................................... 24 1.7 Dividing Integers • .......................................................................................... 28 Summary Exercises • ............................................. 33 Operations with Integers 1.8 Exponents and Order of Operations • ............................................................. 35 Chapter 1 Review Exercises • ......................................................................... 42 Chapter 1 Mixed Review Exercises • ............................................................. 46 Chapter 1 Test • .............................................................................................. 46 2 Understanding Variables and Solving Equations.................................................................... 49 2.1 Introduction to Variables • .............................................................................. 49 2.2 Simplifying Expressions • .............................................................................. 53 Summary Exercises • .......................................... 61 Variables and Expressions 2.3 Solving Equations Using Addition • ............................................................... 63 2.4 Solving Equations Using Division • ............................................................... 71 2.5 Solving Equations with Several Steps • .......................................................... 76 Chapter 2 Review Exercises • ......................................................................... 87 Chapter 2 Mixed Review Exercises • ............................................................. 88 Chapter 2 Test • .............................................................................................. 90 Cumulative Review Exercises (Chapters 1–2) • ............................................. 92 3 Solving Application Problems....................................................................................................96 3.1 Problem Solving: Perimeter • ......................................................................... 96 3.2 Problem Solving: Area • ................................................................................. 103 Summary Exercises • ..................................................... 111 Perimeter and Area 3.3 Solving Application Problems with One Unknown Quantity • ...................... 113 3.4 Solving Application Problems with Two Unknown Quantities • ................... 120 Chapter 3 Review Exercises • ......................................................................... 127 Chapter 3 Mixed Review Exercises • ............................................................. 131 Chapter 3 Test • .............................................................................................. 133 Cumulative Review Exercises (Chapters 1–3) • ............................................. 135 4 Rational Numbers: Positive and Negative Fractions............................................................. 139 4.1 Introduction to Signed Fractions • .................................................................. 139 4.2 Writing Fractions in Lowest Terms • ............................................................. 143 4.3 Multiplying and Dividing Signed Fractions • ................................................. 149 4.4 Adding and Subtracting Signed Fractions • .................................................... 154 4.5 Problem Solving: Mixed Numbers and Estimating • ...................................... 161 Summary Exercises • ........................................ 168 Computation with Fractions 4.6 Exponents, Order of Operations, and Complex Fractions • ........................... 170 4.7 Problem Solving: Equations Containing Fractions • ...................................... 177 4.8 Geometry Applications: Area and Volume • .................................................. 186 Chapter 4 Review Exercises • ......................................................................... 190 Chapter 4 Mixed Review Exercises • ............................................................. 193 Chapter 4 Test • .............................................................................................. 196 Cumulative Review Exercises (Chapters 1–4) • ............................................. 198

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    5 Rational Numbers: Positive and Negative Decimals..............................................................202 5.1 Reading and Writing Decimal Numbers • ...................................................... 202 5.2 Rounding Decimal Numbers • ........................................................................ 205 5.3 Adding and Subtracting Signed Decimal Numbers • ..................................... 210 5.4 Multiplying Signed Decimal Numbers • ......................................................... 218 5.5 Dividing Signed Decimal Numbers • ............................................................. 224 Summary Exercises • .......................... 234 Computation with Decimal Numbers 5.6 Fractions and Decimals • ................................................................................ 237 5.7 Problem Solving with Statistics: Mean, Median, and Mode • ........................ 243 5.8 Geometry Applications: Pythagorean Theorem and Square Roots • .............. 246 5.9 Problem Solving: Equations Containing Decimals • ...................................... 251 5.10 Geometry Applications: Circles, Cylinders, and Surface Area • .................... 256 Chapter 5 Review Exercises • ......................................................................... 262 Chapter 5 Mixed Review Exercises • ............................................................. 269 Chapter 5 Test • .............................................................................................. 271 Cumulative Review Exercises (Chapters 1–5) • ............................................. 273 6 Ratio, Proportion, and Line/Angle/Triangle Relationships.................................................. 277 6.1 Ratios • ........................................................................................................... 277 6.2 Rates • ............................................................................................................. 280 6.3 Proportions • ................................................................................................... 284 Summary Exercises • .................................... 292 Ratios, Rates, and Proportions 6.4 Problem Solving with Proportions • ............................................................... 294 6.5 Geometry: Lines and Angles • ........................................................................ 301 6.6 Geometry Applications: Congruent and Similar Triangles • .......................... 304 Chapter 6 Review Exercises • ......................................................................... 309 Chapter 6 Mixed Review Exercises • ............................................................. 313 Chapter 6 Test • .............................................................................................. 315 Cumulative Review Exercises (Chapters 1–6) • ............................................. 317 7 Percent....................................................................................................................................... 321 7.1 The Basics of Percent • ................................................................................... 321 7.2 The Percent Proportion • ................................................................................ 327 7.3 The Percent Equation • ................................................................................... 332 Summary Exercises • ................................................... 337 Percent Computation 7.4 Problem Solving with Percent • ...................................................................... 340 7.5 Consumer Applications: Sales Tax, Tips, Discounts, and Simple Interest • .. 347 Chapter 7 Review Exercises • ......................................................................... 355 Chapter 7 Mixed Review Exercises • ............................................................. 359 Chapter 7 Test • .............................................................................................. 359 Cumulative Review Exercises (Chapters 1–7) • ............................................. 361 8 Measurement.............................................................................................................................365 8.1 Problem Solving with U.S. Measurement Units • .......................................... 365 8.2 The Metric System—Length • ........................................................................ 372 8.3 The Metric System—Capacity and Weight (Mass) • ...................................... 375 Summary Exercises • ........................... 380 U.S. and Metric Measurement Units 8.4 Problem Solving with Metric Measurement • ................................................ 381 8.5 Metric–U.S. Measurement Conversions and Temperature • .......................... 384 Chapter 8 Review Exercises • ......................................................................... 388 Chapter 8 Mixed Review Exercises • ............................................................. 390 Chapter 8 Test • .............................................................................................. 392 Cumulative Review Exercises (Chapters 1–8) • ............................................. 394

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    9 Graphs and Graphing.............................................................................................................. 398 9.1 Problem Solving with Tables and Pictographs • ............................................ 398 9.2 Reading and Constructing Circle Graphs • ..................................................... 401 9.3 Bar Graphs and Line Graphs • ........................................................................ 405 9.4 The Rectangular Coordinate System • ............................................................ 409 9.5 Introduction to Graphing Linear Equations • ................................................. 411 Chapter 9 Review Exercises • ......................................................................... 417 Chapter 9 Mixed Review Exercises • ............................................................. 420 Chapter 9 Test • .............................................................................................. 420 Cumulative Review Exercises (Chapters 1–9) • ............................................. 422 10 Exponents and Polynomials..................................................................................................... 426 10.1 The Product Rule and Power Rules for Exponents • ...................................... 426 10.2 Integer Exponents and the Quotient Rule • .................................................... 428 Summary Exercises • .................................................. 431 Using Exponent Rules 10.3 An Application of Exponents: Scientific Notation • ...................................... 432 10.4 Adding and Subtracting Polynomials • ........................................................... 436 10.5 Multiplying Polynomials: An Introduction • .................................................. 441 Chapter 10 Review Exercises • ....................................................................... 444 Chapter 10 Mixed Review Exercises • ........................................................... 446 Chapter 10 Test • ............................................................................................ 447 Cumulative Review Exercises (Chapters 1–10) • ........................................... 448 R Whole Numbers Review........................................................................................................... 450 R.1 Adding Whole Numbers • .............................................................................. 450 R.2 Subtracting Whole Numbers • ........................................................................ 454 R.3 Multiplying Whole Numbers • ....................................................................... 459 R.4 Dividing Whole Numbers • ............................................................................ 464 R.5 Long Division • .............................................................................................. 468 Appendix: Inductive and Deductive Reasoning............................................................................ 475

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    Pretest: Whole Numbers Computation 1 PRETEST: WHOLE NUMBERS COMPUTATION Adding Whole Numbers 1. $')  ## $*! " 2. , ( !*$  ' !($ "$ "'' " 3. *! "" )&  #*') $!&$ 1 4. , , , &( #!) *"&  &* $)( ""( &"! " "# " 5. , ("%  $(#)  *  ')$ ((& , , ( # "# ("% $ (#) *  ')$ ((& ')) ##' Subtracting Whole Numbers 1. % # ' y y  ( ' $ & ! $ "# 2. $ $ & ) y y y y  # ( # * ' # * # % "$ ") 3. , , $ ! ' ! # y y y y Î Î y y  & ( ! ) # % ) * % # "! "! * * & "& "# 4. %!!'  *( % ! ! ' y y y y Î Î  * ( $ * ! * $ "!"! * * "' 5. , , '(* %#!  )) !$$ , , , ' ( * % # ! y y y y y y y  ) ) ! $ $ & * " $ ) ( & $ " "( "" "! Multiplying Whole Numbers 1. $ ‚ $ ‚ ! ‚ ' œ ! because ! ! times any number is . 2. , $)%" ‚ ( #' ))( &# 3. Ð&#!ÑÐ$!!!Ñ , , &#! ‚ $ !!! " &'! !!! 4. (" ‚ #' %#' à ' ‚ (" "%# à # ‚ (" ")%' 5. Multiply and . $&* %) , $&* ‚ %) # )(# à ) ‚ $&* "% $' à % ‚ $&* "( #$# %( # $ 6. )&$ ‚ '!* , ! (%# &$" )&$ ‚ '!* ( '(( à * ‚ )&$ &"" )! à '! ‚ )&$ &"* %(( Dividing Whole Numbers 1. # $ $ ' * ' * * !

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    2 Pretest: Whole Numbers Computation 2. is undefined; you can't divide by . "# ƒ ! ! 3. , #& !$' % , ' # & * % # & ! $ ' # % " ! ) # $ # ! $ ' $ ' ! 4. ) ! ( ( & ' & & & ' & ! & & % * ' Answer: )!( ' R 5. $ % &# " ( ' ) " & ' # ! ) # ! ) ! 6. , %& !!! ƒ *!! , & ! *!! % & ! ! ! % & ! ! ! ! 7. ' ! $) # $ ! ! # # ) # ! ! # ! Answer: '! #! R 8. , & $ * )$ % % ( * * % " & $ # * # % * ) ! * ( % ( ' # Answer: &$* '# R

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    1.1 Place Value 3 CHAPTER 1 INTRODUCTION TO ALGEBRA: INTEGERS 1.1 Place Value 1.1 Margin Exercises 1. The whole numbers are: ; ; ; ; , &!# $ "% ! '! !!& 2. (a) The in , , is in the thousands ) %& '#) ''& place. The in , , is in the hundred- (b) ) )!! &!$ '## millions place. The in , , , is in the billions (c) ) %#) !!! !!! !!! place. The in , , is in the hundred- (d) ) # )$& !(" thousands place. 3. (a) , in words: twenty-three , six #$ '!& thousand hundred . five , , in words: four hundred , (b) %!! !$$ !!( million thirty-three seven. thousand, , , , , in words: one hundred (c) "*$ !)! "!# !!! !!! ninety-three eighty one hundred trillion, billion, two million. 4. (a) Eighteen million, two thousand, three hundred five The first group name is so you need to million, fill of three digits. three groups , , , , ! " ) ! ! # $ ! & œ ") !!# $!& Two hundred billion, fifty million, six (b) hundred sixteen The first group name is so you need to fill billion, four groups of three digits. , , , , , , # ! ! ! & ! ! ! ! ' " ' œ #!! !&! !!! '"' (c) Five trillion, forty-two billion, nine million The first group name is so you need to trillion, fill of three digits. five groups ! ! & ! % # ! ! * ! ! ! ! ! ! , , , , œ & !%# !!* !!! !!! , , , , (d) Three hundred six million, seven hundred thousand, nine hundred fifty-nine The first group name is so you need to million, fill of three digits. three groups $ ! ' ( ! ! * & * œ $!' (!! *&* , , , , 1.1 Section Exercises 1. False; we can also use the digit . ! 2. True; , , , , and are whole numbers. "' &'& # ! %!! 3. True; none of the numbers are whole numbers. 4. False; the left-most has a value of ten- ( ( thousands; the right-most has a value of tens. ( ( 5. The whole numbers are: ; ; , "& ! )$ !!" 6. The whole numbers are: ; ; %&( ! ' 7. The whole numbers are: ; , ( $'# !%* 8. The whole numbers are: , ; (& !$* % 9. The in , is in the hundreds place. # '" #)% 10. The in , is in the thousands place. # )# ""! 11. The in , is in the hundred-thousands # #)% "!! place. 12. The in , is in the ten-thousands place. # )#$ %"& 13. The in , , is in the ten- place. # (#& )$( "'' millions 14. The in , , is in the place. # %%# '&$ "** millions 15. The in , , , is in the hundred- # #&$ !%& (!" !!! billions place. 16. The in , , , is in the ten- # )#$ !!! %"* &'( billions place. 17. Name the place value for each zero in $!# !"' %&! !*) &(! , , , , . From left to right: ten-trillions, hundred-billions, millions, hundred-thousands, and ones. 18. Name the place value for each zero in )"! (!% !'* )!* !$& , , , , . From left to right: trillions, ten-billions, hundred- millions, ten-thousands, and hundreds. 19. in words: eight , four )%#" thousand hundred twenty- . one 20. in words: one , nine "*$' thousand hundred thirty- . six 21. , in words: forty-six thousand, two %' #!& hundred five. 22. , in words: seventy-five thousand, eighty- (& !)* nine. 23. To write , , in words, start at the left: $ !'% )!" three thousand, eight hundred million, sixty-four one. Do write "eight hundred not and one" at the end. Use "and" only when there is a decimal point in the number.

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    4 Chapter 1 Introduction to Algebra: Integers 24. , , in words: seven hundred ( *!! %!) million, nine thousand, four hundred eight. 25. , , in words: eight hundred forty )%! """ !!$ million, one hundred eleven thousand, three. 26. , , in words: three hundred four $!% !!) %!" million, eight thousand, four hundred one. 27. , , , in words: fifty-one &" !!' ))) $#" billion, six million, eight hundred eighty-eight thousand, three hundred twenty-one. 28. , , , in words: ninety-nine ** !%' ($$ #"% billion, forty-six million, seven hundred thirty-three thousand, two hundred fourteen. 29. , , , , in words: three trillion, seven $ !!! ("# !!! !!! hundred twelve million. 30. , , , , in words: fifty trillion, nine &! *") !!! !!! '!! hundred eighteen hundred. billion, six 31. Forty-six thousand, eight hundred five The first group name is thousand , so you need to fill of three digits. two groups , ! % ' ) ! & œ , %' )!& 32. Seventy-nine thousand, forty-six The first group name is thousand, so you need to fill of three digits. two groups , ! ( * ! % ' œ , (* !%' 33. Five million, six hundred thousand, eighty-two The first group name is million, so you need to fill of three digits. three groups , , ! ! & ' ! ! ! ) # œ , , & '!! !)# 34. One million, thirty thousand, five The first group name is million, so you need to fill of three digits. three groups , , ! ! " ! $ ! ! ! & œ , , " !$! !!& 35. Two hundred seventy-one million, nine hundred thousand The first group name is million, so you need to fill of three digits. three groups , , # ( " * ! ! ! ! ! œ , , #(" *!! !!! 36. Three hundred eleven million, four hundred The first group name is million, so you need to fill of three digits. three groups , , $ " " ! ! ! % ! ! œ , , $"" !!! %!! 37. Twelve billion, four hundred seventeen million, six hundred twenty-five thousand, three hundred ten The first group name is billion, so you need to fill four groups of three digits. , , , ! " # % " ( ' # & $ " ! œ , , , "# %"( '#& $"! 38. Seventy-five billion, eight hundred sixty-nine million, four hundred eighty-eight thousand, five hundred six The first group name is billion, so you need to fill four groups of three digits. , , , , , , ! ( & ) ' * % ) ) & ! ' œ (& )'* %)) &!' 39. Six hundred trillion, seventy-one million, four hundred The first group name is trillion, so you need to fill of three digits: five groups trillions, billions, millions, thousands, and ones. ' ! ! ! ! ! ! ( " ! ! ! % ! ! , , , , There are no billions or thousands, so fill those groups with zeros. The number is '!! !!! !(" !!! %!! , , , , . 40. Four hundred forty trillion, thirty-six thousand, one hundred two The first group name is trillion , so you need to fill of three digits. five groups % % ! ! ! ! ! ! ! ! $ ' " ! # œ , , , , %%! !!! !!! !$' "!# , , , , 41. in words: nine thousand, six hundred *'%" forty-one 42. in words: two thousand, three hundred #$'( sixty-seven 43. $ , , in words: one hundred thirty "$! "!! !!! million, one hundred thousand 44. , , in words: six hundred sixty-nine ''* $'! !!! million, three hundred sixty thousand 45. $ , , , in words: seventy-nine billion, (* #!! !!! !!! two hundred million 46. $ , , , in words: thirty-three billion, $$ %!! !!! !!! four hundred million 47. Seventy-four million, fifty-nine thousand: The first group is millions, three so you need to fill groups of three digits. ! ( % ! & * ! ! ! , , There are no ones, so fill the ones group with zeros. The number is , , . (% !&* !!! 48. Four million, one hundred sixty-seven thousand, thirty-four is , , . % "'( !$%

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    1.2 Introduction to Integers 5 49. , , in words: three thousand $ !!& !!! million, five 50. , , in words: two # %!" $$$ million, four hundred one thousand, three hundred thirty-three 51. Fifteen million is , , . "& !!! !!! Five billion, four hundred seventy-five million is & %(& !!! !!! , , , . 52. Four hundred million is , , . %!! !!! !!! One hundred forty-six billion is , , , . "%' !!! !!! !!! Relating Concepts (Exercises 53–56) 53. To make the largest possible whole number, arrange the digits from largest to smallest. , , *('&""!! Ä *( '&" "!! In words: ninety-seven hundred million, six fifty-one thousand, one hundred. To make the smallest possible whole number, arrange the numbers from smallest to largest with one exception: because we must use all the digits, start with the smallest nonzero digit. , , "!!"&'(* Ä "! !"& '(* In words: ten thousand, six million, fifteen hundred seventy-nine. 54. Answers will vary. sixty-fours thirty-twos sixteens eights fours twos ones 55. " " " " " " " (a) binary & œ %  " œ "!" binary (b) "! œ )  # œ "!"! binary (c) "& œ )  %  #  " œ """" 56. Answers will vary but should mention that (a) the location or place in which a digit is written gives it a different value. (b) VIII ) œ &  $ œ $) œ $!  &  $ œ XXXVIII #(& œ #!!  &!  #!  & œ CCLXXV $$## œ $!!!  $!!  #!  # MMMCCCXXII œ The Roman system is a place value (c) not system because no matter what place it's in, M , C , etc. One disadvantage is œ "!!! œ "!! that it takes much more space to write many large numbers; another is that there is no symbol for zero. 1.2 Introduction to Integers 1.2 Margin Exercises 1. (a) "Below zero" implies a negative number: & " # degrees (b) "Lost pounds" implies a negative number: "# "# pounds (c) "Deposit" implies a positive number:  $ or $ #"!Þ$& #"!Þ$& (d) "Overdrawn" implies a negative number:  $ '& (e) "Below the surface of the sea" implies a negative number: "!! feet (f) "Won points" implies a positive number: &! &! points or points &! 2. (a) (b) (c) (d) (e) # % # ! % (f) (g) (h) (i) $ " " # " $ 3. (a) is to the of on the number line, so & % & right is . Write . greater than % &  % is to the of on the number line, so is (b) ! # ! left less than . Write . # !  # (c) $ # is to the of on the number line, so left $ # $  # is . . less than Write is to the of on the number line, (d) " % right so is . . " % "  % greater than Write is to the of on the number line, so (e) # # right # # # is . . greater than Write #  is to the of on the number line, so (f) & " left & " &  " is . . less than Write 4. (a) because the distance from to   "$ œ "$ ! "$ on the number line is spaces. "$ because the distance from to (b)   ( ( œ ( ! on the number line is spaces. ( because the distance from to on (c)   ! œ ! ! ! the number line is spaces. ! because the distance from (d)   $&! œ $&! ! to on the number line is spaces. $&! $&! because the distance from (e)   '!!! œ '!!! ! to on the number line is spaces. '!!! '!!!

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    6 Chapter 1 Introduction to Algebra: Integers 1.2 Section Exercises 1. "Above sea level" implies a positive number. #* !#* #* !#* , feet or , feet 2. "Below the surface" implies a negative number. &$&$ feet 3. "Below zero" implies a negative number. "$&Þ) degrees 4. *)Þ' *)Þ' degrees or degrees 5. "Lost a total of yards" implies a ") negative number: yards ") 6. "Gained yards" implies a #& positive number. #& #& yards or yards 7. "Won $ " implies a "!! positive number.  $ or $ "!! "!! 8. Overdrawn bank account implies a negative number: $  $( 9. "Lost pounds" implies a ' " # negative number. ' " # pounds 10. "Gained ounces" implies a # " # positive number. # # " " # # or ounces ounces 11. Graph $ $ ! & , , , 12. Graph # # ! & , , , 13. Graph " % # & , , , 14. Graph , $ % " & , , 15. (a) in words: zero is less than five, or, !  & zero is less than positive five (b)  "( "!  in words: negative ten is greater than negative seventeen 16. (a) $  ( in words: three is greater than negative seven, or, three is greater than positive negative seven in words: twelve is less than (b) "#  ## twenty-two, or, positive twelve is less than positive twenty-two 17. is to the "! right of on the number line, so is # "! greater than . # Write . "!  # 18. is to the ' right of on the number line, so is ! ' greater than . ! Write . '  ! 19. " ! " is to the of on the number line, so is left less than . Write ! "  ! . 20. $ " $ is to the of on the number line, so left is . Write less than " $ "  . 21. "! # "! is to the of on the number line, so left is . Write less than # "!  # . 22. * ( * is to the of on the number line, so is left less than . Write ( *  ( . 23. is to the $ ' right of on the number line, so $ ' $ ' is greater than . Write .  24. is to the ! right of on the number line, so is " ! greater than . " " Write . !  25. "! # is to the of on the number line, so left "! # "! # is . Write less than  . 26. is to the  & " right of on the number line, so  &  & " is greater than . Write . "  27. is to the ! right of on the number line, so is ) ! greater than . ) ) Write . !  28. is to the ' right of on the number line, so is % ' greater than . % % Write . '  29. is to the "! right of on the number line, so # "! is greater than .   # Write . "!  # 30. # " # is to the of on the number line, so is left less than . Write " #  " . 31. % % % is to the of on the number line, so is left less than . Write % %  % . 32. is to the * right of on the number line, so is * * greater than . * * Write . *  33.   "& œ "& ! "& because the distance from to on the number line is spaces. "& 34.   "! œ "! ! "! because the distance from to on the number line is spaces. "! 35.   $ $ œ $ ! because the distance between and on the number line is spaces. $ 36.   )  œ ) ! ) because the distance from to on the number line is spaces. ) 37.   ! œ ! ! ! because the distance from to on the number line is spaces. ! 38.   "!! œ "!! ! "!! because the distance from to on the number line is spaces. "!!

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    1.3 Adding Integers 7 39.   #!! œ #!! ! because the distance between and #!! #!! on the number line is spaces. 40.   **  œ ** ! ** because the distance from to on the number line is spaces. ** 41.   (& œ (& ! because the distance between and (& on the number line is spaces. (& 42.   '$#! œ '$#! ! because the distance from to '$#! '$#! on the number line is spaces. 43.   )!%# œ )!%# ! because the distance between and on the number line is spaces. )!%# )!%# 44.   ! œ ! ! ! because the distance from to on the number line is spaces. ! Relating Concepts (Exercises 45–48) 45. Graph $ ! # " as A, as B, as C, and as D. 46. From Exercise 45, in order from lowest to highest:   $ # " ! , , , 47. A: $ #Þ& is in the Below range. This patient has osteoporosis. B: is in the Above range. This patient is ! " normal. C: # " #Þ& is in the to range. This patient is at risk for developing osteoporosis. D: is in the to " " #Þ& range. This patient is at risk for developing osteoporosis. 48. (a) A patient who did not understand the importance of the negative sign would think the interpretation of $ was "above normal" (range Above ) and " wouldn't get treatment. For Patient B's score of , the sign plays no (b) ! role. Zero is neither positive nor negative. 1.3 Adding Integers 1.3 Margin Exercises 1. (a) #  # œ %   (b) #  # œ % (c) "!  " œ ""   (d) "!  " œ "" (e) $  ( œ "!   (f) $  ( œ "! 2. (a) '  '   Adding signed integers like Step 1     ' ' œ ' œ ' '  ' œ "# ; ; Add Both numbers are negative, so the sum is Step 2 negative. '  ' œ "#   like (b) Adding signed integers *  ( Step 1     * œ * ( œ ( *  ( œ "' ; ; Add Step 2 Both numbers are positive, so the sum is positive. *  ( œ "' (c) &  "!   Adding signed integers like Step 1     & "! œ & œ "! &  "! œ "& ; ; Add Step 2 Both numbers are negative, so the sum is negative. &  "! œ "&   (d) "#  %   Adding signed integers like Step 1     "# % œ "# œ % "#  % œ "' ; ; Add Step 2 Both numbers are negative, so the sum is negative.    "#  % œ "'   Adding signed integers (e) "$  # like ; ; Add Step 1     "$ œ "$ # œ # "$  # œ "& Both numbers are positive, so the sum is Step 2 positive. "$  # œ "& 3. (a) $  ( Adding signed integers unlike ; ; Subtract Step 1     $ œ ( œ (  $ œ $ ( % has the larger absolute value and is Step 2 ( positive, so the sum is positive. $  ( œ % or % (b) '    "# Adding signed integers unlike ; ; Subtract Step 1     ' œ ' œ "# "# "#  ' œ ' Step 2 "# has the larger absolute value and is negative, so the sum is negative. '    "# œ ' (c) "#    ( Adding signed integers unlike ; ; Subtract Step 1     "# ( œ "# œ ( "#  ( œ & Step 2 "# has the larger absolute value and is positive, so the sum is positive. "#  ( œ & &   or

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    8 Chapter 1 Introduction to Algebra: Integers (d) "!  # Adding signed integers unlike Step 1     "! œ "! # œ # ; ; Subtract "!  # œ ) Step 2 "! has the larger absolute value and is negative, so the sum is negative. "!  # œ ) (e) &    * Adding signed integers unlike Step 1     & œ & œ * *  & œ % ; ; Subtract * Step 2 * has the larger absolute value and is negative, so the sum is negative. &  * œ %   4. (a) Starting temperature in the morning is "& degrees. A rise of degrees implies a positive #" number. A drop of degrees implies a negative "! number. "&  #"  "! "! %   œ '  œ   Add left to right . The new temperature is degrees below zero or % % degrees. (b) The beginning balance is $ . Deposits '! imply positive numbers and payments imply negative numbers. . '!  œ "%&  œ "#& œ &!  )& #!  (& #!  (&  (&           Add left to right His account balance is $ . &! 5. (a) "(&  #& œ #&  "(& Both sums are . #!! (b) (    $( œ  $( ( Both sums are . $! (c) "'  "' œ  "' "'   Both sums are . ! (d) *  %" œ      %" * Both sums are . &! 6. (a) "#  "#  "* œ Ð"#  "#Ñ  "* "* "*     œ !  œ   (b) $"   (& œ $"  ! œ $"   (& œ $"  Ð(&  (&Ñ (c) "  * œ "!  œ  "' œ Ð"  *Ñ  "' "' '       (d) $)  &  #& œ $)  Ð&  #&Ñ $)  $! ) œ œ 1.3 Section Exercises 1. #  & œ $ or $ 2. or $  % œ " " 3. &  # œ    ( 4. #  # œ    % 5. $    % œ " 6. &  %   " œ % or 7. (a) &  &   Adding signed integers like Add the absolute values. Step 1   & œ & Add to get . &  & "! Both integers are negative, so the sum is Step 2 negative. &  & œ "!   Adding signed integers (b) &  & œ "! like Both addends are positive, so the sum is positive.

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    1.3 Adding Integers 9 8. (a) (Both addends are *  * œ    ") negative, so the sum is negative.) (b) *  * œ ") 9. (a) (  & œ "# Adding signed integers like Both addends are positive, so the sum is positive. Adding signed (b) (  & œ    "# like integers Add the absolute values. Step 1 ;     ( & œ ( œ & Add to get . (  & "# Both integers are negative, so the sum is Step 2 negative. (  & œ "#   10. (a) $  ' œ * (Both addends are (b) $  ' œ    * negative, so the sum is negative.) 11. (a) #&  #& œ &!   Adding signed integers like Add the absolute values. Step 1   #& œ #& Add to get . #&  #& &! Both integers are negative, so the sum is Step 2 negative. #&  #& œ &!   Adding signed integers (b) #&  #& œ &! like Both addends are positive, so the sum is positive. 12. (a) (Both addends are $!  $! œ    '! negative, so the sum is negative.) (b) $!  $! œ '! 13. (a) %)  ""! œ "&) Adding signed integers Both addends are like positive, so the sum is positive. Adding signed (b) %)  ""! œ    "&) like integers Add the absolute values. Step 1 ;     %) ""! œ %) œ ""! Add to get . %)  ""! "&) Both numbers are negative, so the sum is Step 2 negative. %)  ""! œ "&)   14. (a) #$&  #" œ #&' (b) (Both addends are #$&  #" œ    #&' negative, so the sum is negative.) 15. The absolute values are the same in each pair of answers, so the only difference in the sums is the common sign. 16. Add the absolute values and use the common sign as the sign of the sum. 17. (a) Adding signed integers '  ) unlike ; Step 1     ' œ ' ) œ ) Subtract to get . )  ' # has the larger absolute value and is Step 2 ) positive, so the sum is positive. '  ) œ # or # (b) Adding signed integers '  )   unlike ; Step 1     '  œ ' ) œ ) Subtract to get . )  ' # has the larger absolute value and is Step 2 ) negative negative , so the sum is . '  ) œ #   18. (a) Adding signed integers $  ( unlike ; Step 1     $ œ $ ( œ ( Subtract to get . (  $ % has the larger absolute value and is Step 2 ( positive, so the sum is positive. $  ( œ % % or Adding signed integers (b) $  (   unlike ; Step 1     $ œ $ œ ( ( Subtract to get . (  $ % has the larger absolute value and is Step 2 ( negative negative , so the sum is . $  ( œ %   19. (a) Adding signed integers *  # unlike ; Step 1     * œ * # œ # Subtract to get . *  # ( has the larger absolute value and is Step 2 * negative negative , so the sum is . *  # œ ( Adding signed integers (b) *  #   unlike ; Step 1     * œ * œ # # Subtract to get . *  # ( has the larger absolute value and is Step 2 * positive, so the sum is positive. *  # œ ( (   or

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    10 Chapter 1 Introduction to Algebra: Integers 20. (a) Adding signed integers )  ( unlike ; Step 1     ) œ ) ( œ ( Subtract to get . )  ( " has the larger absolute value and is Step 2 ) negative negative , so the sum is . )  ( œ " Adding signed integers (b) )  (   unlike ; Step 1     ) œ ) œ ( ( Subtract to get . )  ( " has the larger absolute value and is Step 2 ) positive, so the sum is positive. )  ( œ " "   or 21. (a) Adding signed integers #!  #&   unlike ; Step 1     #! œ #! #& œ #&  Subtract to get . #&  #! & has the larger absolute value and is Step 2 #& negative negative , so the sum is . #!  #& œ &   Adding signed integers (b) #!  #& unlike ; Step 1     #! #& œ #! œ #& Subtract to get . #&  #! & has the larger absolute value and is Step 2 #& positive, so the sum is positive. #!  #& œ & & or 22. (a) Adding signed integers $!  %!   unlike ; Step 1     $! œ $! œ %! %! Subtract to get . %!  $! "! has the larger absolute value and is Step 2 %! negative negative , so the sum is . $!  %! œ "!   Adding signed integers (b) $!  %! unlike ; Step 1     $! œ $! %! œ %! Subtract to get . %!  $! "! has the larger absolute value and is Step 2 %! positive, so the sum is positive. $!  %! œ "! or "! 23. (a) Adding signed integers #!!  &!   unlike ; Step 1     #!! &! œ #!! œ &! Subtract to get . #!!  &! "&! has the larger absolute value and is Step 2 #!! positive, so the sum is positive. #!!  &! œ "&! "&!   or Adding signed integers (b)   &! #!! unlike ; Step 1     #!! œ #!! &! œ &! Subtract to get . #!!  &! "&! has the larger absolute value and Step 2 #!! is , so the sum is . negative negative   &! œ "&! #!! 24. (a) Adding signed "&!  "!!   unlike integers ; Step 1     "& œ "&! œ "!! ! "!! Subtract to get . "&!  "!! &! has the larger absolute value and is Step 2 "&! positive, so the sum is positive. "&!  "!! œ &! &!   or Adding signed integers (b) "&  "!! ! unlike ; Step 1     "&! œ "&! "!! œ "!! Subtract to get . "&!  "!! &! has the larger absolute value and Step 2 "&! is , so the sum is . negative negative "&  "!! œ &! ! 25. Each pair of answers differs only in the sign of the answer. This occurs because the signs of the addends are reversed. 26. Subtract the lesser absolute value from the greater absolute value. Use the sign of the number with the greater absolute value as the sign of the sum. 27. )  & Adding signed integers unlike ; Step 1     ) œ ) & œ & Subtract to get . )  & $ has the larger absolute value and is Step 2 ) negative negative , so the sum is . )  & œ $ 28. $  # œ " 29. "  ) Adding signed integers unlike ; Step 1     " œ " ) œ ) Subtract to get . )  " ( has the larger absolute value and is Step 2 ) positive, so the sum is positive. "  ) œ ( ( or 30. %  "! œ ' or '

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