Solution Manual for Prealgebra, 6th Edition

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SOLUTIONSMANUALBEVERLYFUSFIELDPREALGEBRASIXTHEDITIONMargaret L. LialAmerican River CollegeDiana L. HestwoodMinneapolis Community and Technical College

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Table of ContentsPretest: Whole Numbers Computation..............................................................................................11Introduction to Algebra: Integers............................................................................................... 31.1Place Value • ..................................................................................................31.2Introduction to Integers • ................................................................................51.3Adding Integers • ............................................................................................71.4Subtracting Integers • .....................................................................................131.5Problem Solving: Rounding and Estimating • ................................................181.6Multiplying Integers • .....................................................................................241.7Dividing Integers • ..........................................................................................28Summary Exercises• .............................................33Operations with Integers1.8Exponents and Order of Operations • .............................................................35Chapter 1 Review Exercises • .........................................................................42Chapter 1 Mixed Review Exercises • .............................................................46Chapter 1 Test • ..............................................................................................462Understanding Variables and Solving Equations.................................................................... 492.1Introduction to Variables • ..............................................................................492.2Simplifying Expressions • ..............................................................................53Summary Exercises• ..........................................61Variables and Expressions2.3Solving Equations Using Addition • ...............................................................632.4Solving Equations Using Division • ...............................................................712.5Solving Equations with Several Steps • ..........................................................76Chapter 2 Review Exercises • .........................................................................87Chapter 2 Mixed Review Exercises • .............................................................88Chapter 2 Test • ..............................................................................................90Cumulative Review Exercises (Chapters 1–2) • .............................................923Solving Application Problems....................................................................................................963.1Problem Solving: Perimeter • .........................................................................963.2Problem Solving: Area • ................................................................................. 103Summary Exercises• ..................................................... 111Perimeter and Area3.3Solving Application Problems with One Unknown Quantity • ...................... 1133.4Solving Application Problems with Two Unknown Quantities • ................... 120Chapter 3 Review Exercises • ......................................................................... 127Chapter 3 Mixed Review Exercises • ............................................................. 131Chapter 3 Test • .............................................................................................. 133Cumulative Review Exercises (Chapters 1–3) • ............................................. 1354Rational Numbers: Positive and Negative Fractions............................................................. 1394.1Introduction to Signed Fractions • .................................................................. 1394.2Writing Fractions in Lowest Terms • ............................................................. 1434.3Multiplying and Dividing Signed Fractions • ................................................. 1494.4Adding and Subtracting Signed Fractions • .................................................... 1544.5Problem Solving: Mixed Numbers and Estimating • ...................................... 161Summary Exercises• ........................................ 168Computation with Fractions4.6Exponents, Order of Operations, and Complex Fractions • ........................... 1704.7Problem Solving: Equations Containing Fractions • ...................................... 1774.8Geometry Applications: Area and Volume • .................................................. 186Chapter 4 Review Exercises • ......................................................................... 190Chapter 4 Mixed Review Exercises • ............................................................. 193Chapter 4 Test • .............................................................................................. 196Cumulative Review Exercises (Chapters 1–4) • ............................................. 198

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5Rational Numbers: Positive and Negative Decimals..............................................................2025.1Reading and Writing Decimal Numbers • ...................................................... 2025.2Rounding Decimal Numbers • ........................................................................ 2055.3Adding and Subtracting Signed Decimal Numbers • ..................................... 2105.4Multiplying Signed Decimal Numbers • ......................................................... 2185.5Dividing Signed Decimal Numbers • ............................................................. 224Summary Exercises• .......................... 234Computation with Decimal Numbers5.6Fractions and Decimals • ................................................................................ 2375.7Problem Solving with Statistics: Mean, Median, and Mode • ........................ 2435.8Geometry Applications: Pythagorean Theorem and Square Roots • .............. 2465.9Problem Solving: Equations Containing Decimals • ...................................... 2515.10Geometry Applications: Circles, Cylinders, and Surface Area • .................... 256Chapter 5 Review Exercises • ......................................................................... 262Chapter 5 Mixed Review Exercises • ............................................................. 269Chapter 5 Test • .............................................................................................. 271Cumulative Review Exercises (Chapters 1–5) • ............................................. 2736Ratio, Proportion, and Line/Angle/Triangle Relationships.................................................. 2776.1Ratios • ........................................................................................................... 2776.2Rates • ............................................................................................................. 2806.3Proportions • ................................................................................................... 284Summary Exercises• .................................... 292Ratios, Rates, and Proportions6.4Problem Solving with Proportions • ............................................................... 2946.5Geometry: Lines and Angles • ........................................................................ 3016.6Geometry Applications: Congruent and Similar Triangles • .......................... 304Chapter 6 Review Exercises • ......................................................................... 309Chapter 6 Mixed Review Exercises • ............................................................. 313Chapter 6 Test • .............................................................................................. 315Cumulative Review Exercises (Chapters 1–6) • ............................................. 3177Percent....................................................................................................................................... 3217.1The Basics of Percent • ................................................................................... 3217.2The Percent Proportion • ................................................................................ 3277.3The Percent Equation • ................................................................................... 332Summary Exercises• ................................................... 337Percent Computation7.4Problem Solving with Percent • ...................................................................... 3407.5Consumer Applications: Sales Tax, Tips, Discounts, and Simple Interest • .. 347Chapter 7 Review Exercises • ......................................................................... 355Chapter 7 Mixed Review Exercises • ............................................................. 359Chapter 7 Test • .............................................................................................. 359Cumulative Review Exercises (Chapters 1–7) • ............................................. 3618Measurement.............................................................................................................................3658.1Problem Solving with U.S. Measurement Units • .......................................... 3658.2The Metric System—Length • ........................................................................ 3728.3The Metric System—Capacity and Weight (Mass) • ...................................... 375Summary Exercises• ........................... 380U.S. and Metric Measurement Units8.4Problem Solving with Metric Measurement • ................................................ 3818.5Metric–U.S. Measurement Conversions and Temperature • .......................... 384Chapter 8 Review Exercises • ......................................................................... 388Chapter 8 Mixed Review Exercises • ............................................................. 390Chapter 8 Test • .............................................................................................. 392Cumulative Review Exercises (Chapters 1–8) • ............................................. 394

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9Graphs and Graphing.............................................................................................................. 3989.1Problem Solving with Tables and Pictographs • ............................................ 3989.2Reading and Constructing Circle Graphs • ..................................................... 4019.3Bar Graphs and Line Graphs • ........................................................................ 4059.4The Rectangular Coordinate System • ............................................................ 4099.5Introduction to Graphing Linear Equations • ................................................. 411Chapter 9 Review Exercises • ......................................................................... 417Chapter 9 Mixed Review Exercises • ............................................................. 420Chapter 9 Test • .............................................................................................. 420Cumulative Review Exercises (Chapters 1–9) • ............................................. 42210Exponents and Polynomials..................................................................................................... 42610.1The Product Rule and Power Rules for Exponents • ...................................... 42610.2Integer Exponents and the Quotient Rule • .................................................... 428Summary Exercises• .................................................. 431Using Exponent Rules10.3An Application of Exponents: Scientific Notation • ...................................... 43210.4Adding and Subtracting Polynomials • ........................................................... 43610.5Multiplying Polynomials: An Introduction • .................................................. 441Chapter 10 Review Exercises • ....................................................................... 444Chapter 10 Mixed Review Exercises • ........................................................... 446Chapter 10 Test • ............................................................................................ 447Cumulative Review Exercises (Chapters 1–10) • ........................................... 448RWhole Numbers Review........................................................................................................... 450R.1Adding Whole Numbers • .............................................................................. 450R.2Subtracting Whole Numbers • ........................................................................ 454R.3Multiplying Whole Numbers • ....................................................................... 459R.4Dividing Whole Numbers • ............................................................................ 464R.5Long Division • .............................................................................................. 468Appendix: Inductive and Deductive Reasoning............................................................................ 475

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Pretest: Whole Numbers Computation1PRETEST: WHOLE NUMBERS COMPUTATIONAdding Whole Numbers1.$') ##$*!"2.,( !*$ ' !($"$ "''"3.*!"")& #*')$!&$14.,,,&( #!)*"& &* $)(""( &"!""#"5.,("%  $(#)  *  ')$ ((&,,(# "#("%$ (#)* ')$ ((&')) ##'Subtracting Whole Numbers1.% # 'y y ( '$ & !$"#2.$ $ & )y y y y # ( # *' # *#%"$")3.,,$ ! ' ! #y y y yÎÎyy & ( ! )# % ) * %#"!"!**&"&"#4.%!!'  *(% ! ! 'y y y yÎ Î * ($ * ! *$"!"!* *"'5.,,'(* %#!  )) !$$,,,' ( * % # !yyyyy yy ) ) ! $ $& * " $ ) (&$ ""("""!Multiplying Whole Numbers1.$ ‚ $ ‚ ! ‚ ' œ !because!!times any number is.2.,$)%"‚(#' ))(&#3.Ð&#!ÑÐ$!!!Ñ,,&#!‚ $ !!!" &'! !!!4.("‚ #'%#'Ã' ‚ (""%#Ã# ‚ ("")%'5.Multiplyand.$&*%),$&*‚ %)# )(#Ã) ‚ $&*"% $'Ã% ‚ $&*"( #$#%(# $6.)&$ ‚ '!*,!(%#&$")&$‚ '!*( '((Ã* ‚ )&$&"" )!Ã'! ‚ )&$&"* %((Dividing Whole Numbers1.# $$ ' *'**!

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2Pretest: Whole Numbers Computation2.is undefined; you can't divide by."# ƒ !!3.,#& !$'%,'# & *% # &! $ '# %"!)# $# !$ '$ '!4.) ! (( & ' & && '&!& &% *'Answer:)!('R5.$ %&# " ( ' )" & '# ! )# ! )!6.,%& !!! ƒ *!!,& !*!! % &! ! !% &! !! !7.' !$) # $ ! !# # )# !!# !Answer:'!#!R8.,& $ *)$ % %( * *% "&$# *#% *) ! *( % (' #Answer:&$*'#R

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1.1Place Value3CHAPTER 1 INTRODUCTION TO ALGEBRA: INTEGERS1.1 Place Value1.1Margin Exercises1.The whole numbers are:;;;;,&!# $ "% ! '! !!&2.(a)Thein,,is in the thousands)%& '#) ''&place.Thein,,is in the hundred-(b)))!! &!$ '##millions place.Thein,,,is in the billions(c))%#) !!! !!! !!!place.Thein,,is in the hundred-(d))# )$& !("thousands place.3.(a),in words: twenty-three, six#$ '!&thousandhundred.five,,in words: four hundred,(b)%!! !$$ !!(millionthirty-threeseven.thousand,,,,,in words: one hundred(c)"*$ !)! "!# !!! !!!ninety-threeeightyone hundredtrillion,billion,twomillion.4.(a)Eighteen million, two thousand, threehundred fiveThe first group name isso you need tomillion,fillof three digits.three groups,,,,! " ) ! ! # $ ! & œ ") !!# $!&Two hundred billion, fifty million, six(b)hundred sixteenThe first group name isso you need to fillbillion,four groupsof three digits.,,,,,,# ! ! ! & ! ! ! ! ' " ' œ #!! !&! !!! '"'(c)Five trillion, forty-two billion, nine millionThe first group name isso you need totrillion,fillof three digits.five groups! ! & ! % # ! ! * ! ! ! ! ! !,,,,œ & !%# !!* !!! !!!,,,,(d)Three hundred six million, seven hundredthousand, nine hundred fifty-nineThe first group name isso you need tomillion,fillof three digits.three groups$ ! ' ( ! ! * & * œ $!' (!! *&*,,,,1.1Section Exercises1.False; we can also use the digit.!2.True;,,,, andare whole numbers."' &'& # !%!!3.True; none of the numbers are whole numbers.4.False; the left-mosthas a value often-((thousands; the right-mosthas a value oftens.((5.The whole numbers are:;;,"& ! )$ !!"6.The whole numbers are:;;%&( ! '7.The whole numbers are:;,( $'# !%*8.The whole numbers are:,;(& !$* %9.Thein,is in the hundreds place.#'" #)%10.Thein,is in the thousands place.#)# ""!11.Thein,is in the hundred-thousands##)% "!!place.12.Thein,is in the ten-thousands place.#)#$ %"&13.Thein,,is in the ten-place.#(#& )$( "''millions14.Thein,,is in theplace.#%%# '&$ "**millions15.Thein,,,is in the hundred-##&$ !%& (!" !!!billions place.16.Thein,,,is in the ten-#)#$ !!! %"* &'(billionsplace.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)%#"thousandhundredtwenty-.one20.in words: one, nine"*$'thousandhundredthirty-.six21.,in words: forty-six thousand, two%' #!&hundred five.22.,in words: seventy-five thousand, eighty-(& !)*nine.23.To write,,in words, start at the left:$ !'% )!"threethousand, eight hundredmillion, sixty-fourone. Dowrite "eight hundrednotandone" at theend. Use "and" only when there is a decimalpoint in the number.

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4Chapter 1Introduction to Algebra: Integers24.,,in words: sevenhundred( *!! %!)million, ninethousand, 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, sixmillion, eight hundred eighty-eight thousand,three hundred twenty-one.28.,,,in words: ninety-nine** !%' ($$ #"%billion,forty-six million, seven hundred thirty-threethousand, two hundred fourteen.29.,,,,in words: three trillion, seven$ !!! ("# !!! !!!hundred twelve million.30.,,,,in words: fifty trillion, nine&! *") !!! !!! '!!hundred eighteenhundred.billion, six31.Forty-six thousand, eight hundred fiveThe first group name isthousand, so you need tofillof three digits.two groups,! % ' ) ! & œ,%' )!&32.Seventy-nine thousand, forty-sixThe first group name isthousand,so you need tofillof three digits.two groups,! ( * ! % ' œ,(* !%'33.Five million, six hundred thousand, eighty-twoThe first group name ismillion,so you need tofillof three digits.three groups,,! ! & ' ! ! ! ) # œ,,& '!! !)#34.One million, thirty thousand, fiveThe first group name ismillion,so you need tofillof three digits.three groups,,! ! " ! $ ! ! ! & œ,," !$! !!&35.Two hundred seventy-one million, nine hundredthousandThe first group name ismillion,so you need tofillof three digits.three groups,,# ( " * ! ! ! ! ! œ,,#(" *!! !!!36.Three hundred eleven million, four hundredThe first group name ismillion,so you need tofillof three digits.three groups,,$ " " ! ! ! % ! ! œ,,$"" !!! %!!37.Twelve billion, four hundred seventeen million,six hundred twenty-five thousand, three hundredtenThe first group name isbillion,so you need to fillfour groupsof three digits.,,,! " # % " ( ' # & $ " ! œ,,,"# %"( '#& $"!38.Seventy-five billion, eight hundred sixty-ninemillion, four hundred eighty-eight thousand, fivehundred sixThe first group name isbillion,so you need to fillfour groupsof three digits.,,,,,,! ( & ) ' * % ) ) & ! ' œ (& )'* %)) &!'39.Six hundred trillion, seventy-one million, fourhundredThe first group name istrillion,so you need tofillof three digits:five groupstrillions, billions, millions, thousands, and ones.' ! ! ! ! ! ! ( " ! ! ! % ! !,,,,There are no billions or thousands, so fill thosegroups with zeros.The number is'!! !!! !(" !!! %!!,,,,.40.Four hundred forty trillion, thirty-six thousand,one hundred twoThe first group name istrillion, so you need tofillof three digits.five groups% % ! ! ! ! ! ! ! ! $ ' " ! # œ,,,,%%! !!! !!! !$' "!#,,,,41.in words: nine thousand, six hundred*'%"forty-one42.in words: two thousand, three hundred#$'(sixty-seven43.$,,in words: one hundred thirty"$! "!! !!!million, one hundred thousand44.,,in words: six hundred sixty-nine''* $'! !!!million, three hundred sixty thousand45.$,,,in words: seventy-nine billion,(* #!! !!! !!!two hundred million46.$,,,in words: thirty-three billion,$$ %!! !!! !!!four hundred million47.Seventy-four million, fifty-nine thousand: Thefirst group ismillions,threeso you need to fillgroupsof three digits.! ( % ! & * ! ! !,,There are no ones, so fill the ones group withzeros.The number is,,.(% !&* !!!48.Four million, one hundred sixty-seven thousand,thirty-four is,,.% "'( !$%

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1.2Introduction to Integers549.,,in words: threethousand$ !!& !!!million, five50.,,in words: two# %!" $$$million, four hundredone thousand, three hundred thirty-three51.Fifteen million is,,."& !!! !!!Five billion, four hundred seventy-five million is& %(& !!! !!!,,,.52.Four hundred million is,,.%!! !!! !!!One hundred forty-six billion is,,,."%' !!! !!! !!!Relating Concepts (Exercises 53–56)53.To make the largest possible whole number,arrange the digits from largest to smallest.,,*('&""!! Ä *( '&" "!!In words: ninety-sevenhundredmillion, sixfifty-one thousand, one hundred.To make the smallest possible whole number,arrange the numbers from smallest to largest withone exception: because we must use all thedigits, start with the smallest nonzero digit.,,"!!"&'(* Ä "! !"& '(*In words: tenthousand, sixmillion, fifteenhundred seventy-nine.54.Answers will vary.sixty-foursthirty-twossixteenseightsfourstwosones55."""""""(a)binary& œ %  " œ"!"binary(b)"! œ )  # œ"!"!binary(c)"& œ )  %  #  " œ""""56.Answers will vary but should mention that(a)the location or place in which a digit is writtengives it a different value.(b)VIII) œ &  $ œ$) œ $!  &  $ œXXXVIII#(& œ #!!  &!  #!  & œCCLXXV$$## œ $!!!  $!!  #!  #MMMCCCXXIIœThe Roman system isa place value(c)notsystem because no matter what place it's in,M, C, etc. One disadvantage isœ "!!!œ "!!that it takes much more space to write many largenumbers; another is that there is no symbol forzero.1.2Introduction to Integers1.2Margin Exercises1.(a)"Below zero" implies a negative number:&"#degrees(b)"Lostpounds" implies a negative number:"#"#pounds(c)"Deposit" implies a positive number:$or$#"!Þ$&#"!Þ$&(d)"Overdrawn" implies a negative number:$'&(e)"Below the surface of the sea" implies anegative number:"!!feet(f)"Wonpoints" implies a positive number:&!&!pointsorpoints&!2.(a)(b)(c)(d)(e)#%#!%(f)(g)(h)(i)$""#"$3.(a)is to theofon the number line, so&%&rightis. Write.greater than%&  %is to theofon the number line, sois(b)!#!leftless than. Write.#!  #(c)$#is to theofon the number line, soleft$#$  #is..less thanWriteis to theofon the number line,(d)"%rightsois.."%"  %greater thanWriteis to theofon the number line, so(e)##right###is..greater thanWrite# is to theofon the number line, so(f)&"left&"&  "is..less thanWrite4.(a)because the distance fromto"$ œ "$!"$on the number line isspaces."$because the distance fromto(b)((œ (!on the number line isspaces.(because the distance fromtoon(c) ! œ !!!the number line isspaces.!because the distance from(d)$&! œ $&!!toon the number line isspaces.$&!$&!because the distance from(e)'!!! œ '!!!!toon the number line isspaces.'!!!'!!!

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6Chapter 1Introduction to Algebra: Integers1.2Section Exercises1."Above sea level" implies a positive number.#* !#*#* !#*,feet or,feet2."Below the surface" implies a negative number.&$&$feet3."Below zero" implies a negative number."$&Þ)degrees4.*)Þ'*)Þ'degrees ordegrees5."Lost a total ofyards" implies a")negativenumber:yards")6."Gainedyards" implies a#&positive number.#&#&yards oryards7."Won $" implies a"!!positive number.$or $"!!"!!8.Overdrawn bank account implies a negativenumber:$ $(9."Lostpounds" implies a'"#negative number.'"#pounds10."Gainedounces" implies a#"#positive number.##""##orouncesounces11.Graph$ $ ! &,,,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 greaterthan negative seventeen16.(a)$  (in words: three is greater thannegative seven, or,three is greater thanpositivenegative sevenin words: twelve is less than(b)"#  ##twenty-two, or, positive twelve is less thanpositive twenty-two17.is to the"!rightofon the number line, sois#"!greater than.#Write."!  #18.is to the'rightofon the number line, sois!'greater than.!Write.'  !19."!"is to theofon the number line, soisleftless than. Write!"  !.20.$"$is to theofon the number line, soleftis. Writeless than"$".21."!#"!is to theofon the number line, soleftis. Writeless than#"!  #.22.*(*is to theofon the number line, soisleftless than. Write(*  (.23.is to the$'rightofon the number line, so$'$'isgreater than.Write.24.is to the!rightofon the number line, sois"!greater than.""Write.! 25."!#is to theofon the number line, soleft"!#"!#is. Writeless than.26.is to the&"rightofon the number line, so&&"isgreater than.Write." 27.is to the!rightofon the number line, sois)!greater than.))Write.! 28.is to the'rightofon the number line, sois%'greater than.%%Write.' 29.is to the"!rightofon the number line, so#"!isgreater than.#Write."! #30.#"#is to theofon the number line, soisleftless than. Write"#  ".31.%%%is to theofon the number line, soisleftless than. Write%%  %.32.is to the*rightofon the number line, sois**greater than.**Write.* 33."& œ "&!"&because the distance fromtoonthe number line isspaces."&34."! œ "!!"!because the distance fromtoonthe number line isspaces."!35.$$œ $!because the distance betweenandon the number line isspaces.$36.)œ )!)because the distance fromtoonthe number line isspaces.)37. ! œ !!!because the distance fromtoon thenumber line isspaces.!38."!! œ "!!!"!!because the distance fromtoon the number line isspaces."!!

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1.3Adding Integers739.#!! œ #!!!because the distance betweenand#!!#!!on the number line isspaces.40.**œ **!**because the distance fromtoon the number line isspaces.**41.(& œ (&!because the distance betweenand(&on the number line isspaces.(&42.'$#! œ '$#!!because the distance fromto'$#!'$#!on the number line isspaces.43.)!%# œ )!%#!because the distance betweenandon the number line isspaces.)!%#)!%#44. ! œ !!!because the distance fromtoon thenumber line isspaces.!Relating Concepts (Exercises 45–48)45.Graph$!#"as A,as B,as C, andas D.46.From Exercise 45, in order from lowest tohighest:$# " !,,,47.A:$#Þ&is in the Belowrange. This patienthas osteoporosis.B:is in the Aboverange. This patient is!"normal.C:#"#Þ&is in thetorange. This patient isat risk for developing osteoporosis.D:is in theto""#Þ&range. This patient isat risk for developing osteoporosis.48.(a)A patient who did not understand theimportance of the negative sign would think theinterpretation of$was "above normal" (rangeAbove) and"wouldn't get treatment.For Patient B's score of, the sign plays no(b)!role. Zero is neither positive nor negative.1.3Adding Integers1.3Margin Exercises1.(a)# #œ %(b)#  # œ %(c)"! "œ ""(d)"!  " œ ""(e)$ (œ "!(f)$  ( œ "!2.(a)' 'Addingsigned integerslikeStep 1''œ 'œ ''  ' œ "#;; AddBoth numbers are negative, so the sum isStep 2negative.' 'œ "#like(b)Addingsigned integers*  (Step 1  * œ *( œ (*  ( œ "';; AddStep 2Both numbers are positive, so the sum ispositive.*  ( œ "'(c)& "!Addingsigned integerslikeStep 1&"!œ &œ "!&  "! œ "&;; AddStep 2Both numbers are negative, so the sum isnegative.& "!œ "&(d)"# %Addingsigned integerslikeStep 1"#%œ "#œ %"#  % œ "';; AddStep 2Both numbers are negative, so the sumis negative."# %œ"'Addingsigned integers(e)"$  #like;; AddStep 1 "$ œ "$# œ #"$  # œ "&Both numbers are positive, so the sum isStep 2positive."$  # œ "&3.(a)$  (Addingsigned integersunlike;; SubtractStep 1 $ œ( œ(  $ œ$(%has the larger absolute value and isStep 2(positive, so the sum is positive.$  ( œ %or%(b)' "#Addingsigned integersunlike;; SubtractStep 1 ' œ 'œ "#"#"#  ' œ 'Step 2"#has the larger absolute value and isnegative, so the sum is negative.' "#œ '(c)"# (Addingsigned integersunlike;; SubtractStep 1"#(œ "#œ ("#  ( œ &Step 2"#has the larger absolute value and ispositive, so the sum is positive."# (œ &&or

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8Chapter 1Introduction to Algebra: Integers(d)"!  #Addingsigned integersunlikeStep 1 "! œ "!# œ #;; Subtract"!  # œ )Step 2"!has the larger absolute value and isnegative, so the sum is negative."!  # œ )(e)& *Addingsigned integersunlikeStep 1 & œ &œ **  & œ %;; Subtract*Step 2*has the larger absolute value and isnegative, so the sum is negative.& *œ %4.(a)Starting temperature in the morning is"&degrees. A rise ofdegrees implies a positive#"number. A drop ofdegrees implies a negative"!number."&  #" "!"!%œ ' œAdd left to right.The new temperature isdegrees below zero or%%degrees.(b)The beginning balance is $. Deposits'!imply positive numbers and payments implynegative numbers..'!œ "%& œ "#&œ &! )&#!(&#!(&(&Add left to rightHis 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 $)  Ð&  #&Ñ$)  $!)œœ1.3Section Exercises1.#  & œ $or$2.or$  % œ ""3.& #œ (4.# #œ %5.$ %œ "6.& %"œ %or7.(a)& &Addingsigned integerslikeAdd the absolute values.Step 1& œ &Addto get.&  &"!Both integers are negative, so the sum isStep 2negative.& &œ "!Addingsigned integers(b)&  & œ "!likeBoth addends are positive, so the sum is positive.

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1.3Adding Integers98.(a)(Both addends are* *œ ")negative, so the sum is negative.)(b)*  * œ ")9.(a)(  & œ "#Addingsigned integerslikeBoth addends are positive, so the sum is positive.Addingsigned(b)( &œ "#likeintegersAdd the absolute values.Step 1;(&œ (œ &Addto get.(  &"#Both integers are negative, so the sum isStep 2negative.( &œ "#10.(a)$  ' œ *(Both addends are(b)$ 'œ *negative, so the sum is negative.)11.(a)#& #&œ &!Addingsigned integerslikeAdd the absolute values.Step 1#& œ #&Addto get.#&  #&&!Both integers are negative, so the sum isStep 2negative.#& #&œ &!Addingsigned integers(b)#&  #& œ &!likeBoth addends are positive, so the sum is positive.12.(a)(Both addends are$! $!œ '!negative, so the sum is negative.)(b)$!  $! œ '!13.(a)%)  ""! œ "&)Addingsigned integers Both addends arelikepositive, so the sum is positive.Addingsigned(b)%) ""!œ "&)likeintegersAdd the absolute values.Step 1;%)""!œ %)œ ""!Addto get.%)  ""!"&)Both numbers are negative, so the sum isStep 2negative.%) ""!œ "&)14.(a)#$&  #" œ #&'(b)(Both addends are#$& #"œ #&'negative, so the sum is negative.)15.The absolute values are the same in each pair ofanswers, so the only difference in the sums is thecommon sign.16.Add the absolute values and use the commonsign as the sign of the sum.17.(a)Addingsigned integers'  )unlike;Step 1 ' œ ') œ )Subtractto get.)  '#has the larger absolute value and isStep 2)positive, so the sum is positive.'  ) œ #or#(b)Addingsigned integers' )unlike;Step 1 'œ ') œ )Subtractto get.)  '#has the larger absolute value and isStep 2)negativenegative, so the sum is.' )œ #18.(a)Addingsigned integers$  (unlike;Step 1 $ œ $( œ (Subtractto get.(  $%has the larger absolute value and isStep 2(positive, so the sum is positive.$  ( œ %%orAddingsigned integers(b)$ (unlike;Step 1 $ œ $œ ((Subtractto get.(  $%has the larger absolute value and isStep 2(negativenegative, so the sum is.$ (œ %19.(a)Addingsigned integers*  #unlike;Step 1 * œ *# œ #Subtractto get.*  #(has the larger absolute value and isStep 2*negativenegative, so the sum is.*  # œ (Addingsigned integers(b)* #unlike;Step 1 * œ *œ ##Subtractto get.*  #(has the larger absolute value and isStep 2*positive, so the sum is positive.* #œ ((or

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10Chapter 1Introduction to Algebra: Integers20.(a)Addingsigned integers)  (unlike;Step 1 ) œ )( œ (Subtractto get.)  ("has the larger absolute value and isStep 2)negativenegative, so the sum is.)  ( œ "Addingsigned integers(b)) (unlike;Step 1 ) œ )œ ((Subtractto get.)  ("has the larger absolute value and isStep 2)positive, so the sum is positive.) (œ ""or21.(a)Addingsigned integers#! #&unlike;Step 1#! œ #!#& œ #&Subtractto get.#&  #!&has the larger absolute value and isStep 2#&negativenegative, so the sum is.#! #&œ &Addingsigned integers(b)#!  #&unlike;Step 1#!#&œ #!œ #&Subtractto get.#&  #!&has the larger absolute value and isStep 2#&positive, so the sum is positive.#!  #& œ &&or22.(a)Addingsigned integers$! %!unlike;Step 1$! œ $!œ %!%!Subtractto get.%!  $!"!has the larger absolute value and isStep 2%!negativenegative, so the sum is.$! %!œ "!Addingsigned integers(b)$!  %!unlike;Step 1$! œ $!%! œ %!Subtractto get.%!  $!"!has the larger absolute value and isStep 2%!positive, so the sum is positive.$!  %! œ "!or"!23.(a)Addingsigned integers#!! &!unlike;Step 1#!!&!œ #!!œ &!Subtractto get.#!!  &!"&!has the larger absolute value and isStep 2#!!positive, so the sum is positive.#!! &!œ "&!"&!orAddingsigned integers(b) &!#!!unlike;Step 1#!! œ #!!&! œ &!Subtractto get.#!!  &!"&!has the larger absolute value andStep 2#!!is, so the sum is.negativenegative &! œ "&!#!!24.(a)Addingsigned"&! "!!unlikeintegers;Step 1"&œ "&!œ "!!!"!!Subtractto get."&!  "!!&!has the larger absolute value and isStep 2"&!positive, so the sum is positive."&! "!!œ &!&!orAddingsigned integers(b)"& "!!!unlike;Step 1"&! œ "&!"!! œ "!!Subtractto get."&!  "!!&!has the larger absolute value andStep 2"&!is, so the sum is.negativenegative"& "!! œ &!!25.Each pair of answers differs only in the sign ofthe answer. This occurs because the signs of theaddends are reversed.26.Subtract the lesser absolute value from thegreater absolute value. Use the sign of thenumber with the greater absolute value as thesign of the sum.27.)  &Addingsigned integersunlike;Step 1 ) œ )& œ &Subtractto get.)  &$has the larger absolute value and isStep 2)negativenegative, so the sum is.)  & œ $28.$  # œ "29."  )Addingsigned integersunlike;Step 1 " œ ") œ )Subtractto get.)  "(has the larger absolute value and isStep 2)positive, so the sum is positive."  ) œ ((or30.%  "! œ 'or'

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