Solution Manual for Prealgebra, 6th Edition

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SOLUTIONSMANUALPREALGEBRASIXTHEDITIONJamie BlairOrange Coast CollegeCosta Mesa, CaliforniaJohn TobeyNorth Shore Community CollegeDanvers, MassachusettsJeffrey SlaterNorth Shore Community CollegeDanvers, MassachusettsJennifer CrawfordNormandale Community CollegeBloomington, Minnesota

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ContentsChapter 11Chapter 234Chapter 359Chapter 484Chapter 5108Chapter 6142Chapter 7160Chapter 8202Chapter 9239Chapter 10259Practice Final Examination281

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1Chapter 11.1 Exercises2.a.6 > 3Six is greater than three.b.3 < 6Three is less than six.c.We can use the inequality symbols to showthe relationship between 6 and 3 in twodifferent ways.4.a.46,362ten thousandsb.46,362hundreds6.a.839,400hundred thousandsb.839,400ten thousands8.a.3,098,269hundred thousandsb.3,098,269thousands10.7632 = 7000 + 600 + 30 + 212.3562 = 3000 + 500 + 60 + 214.913,045 = 900,000 + 10,000 + 3000 + 40 + 516.$274274 = 200 + 70 + 42 hundred-dollar bills, 7 ten-dollar bills, and4 one-dollar bills18.$96a.96 = 90 + 69 ten-dollar bills and 6 one-dollar bills;answers may vary.b.96 = 90 + 5 + 19 ten-dollar bills, 1 five-dollar bill, and1 one-dollar bill; answers may vary.20.4032The number begins with 4 in the thousandsplace. The word name is four thousand, thirty-two.22.33,224The number begins with 3 in the ten thousandsplace. The word name is thirty-three thousand,two hundred twenty-four.24.$379Write 379.00 in the box following $. Write“Three hundred seventy-nine and 00/100” on theline preceding DOLLARS.26.3 ? 13 is greater than 1.3 > 128.9 ? 69 is greater than 6.9 > 630.9 ? 119 is less than 11.9 < 1132.0 ? 90 is less than 9.0 < 934.3010 ? 32103010 is less than 3210.3010 < 321036.101,351 ? 101,251101,351 is greater than 101,251.101,351 > 101,25138.Sevenis less thanten.7<1040.Tenis greater thanseven.10>7

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Chapter 1:Whole Numbers and Introduction to AlgebraISM: Prealgebra242.85Identify the round-off place digit: 85.The digit to the right is 5 or more. Increase theround-off place digit by 1. Replace the digit tothe right with a zero.9044.123Identify the round-off place digit: 123.The digit to the right is less than 5. Do notchange the round-off place digit. Replace thedigit to the right with a zero.12046.12,790Identify the round-off place digit: 12,790.The digit to the right is 5 or more. Increase theround-off place digit by 1. Replace all digits tothe right with zeros.12,80048.701,529Identify the round-off place digit: 701,529.The digit to the right is less than 5. Do notchange the round-off place digit. Replace alldigits to the right with zeros.701,50050.56,212Identify the round-off place digit: 56,212.The digit to the right is less than 5. Do notchange the round-off place digit. Replace alldigits to the right with zeros.56,00052.312,540Identify the round-off place digit: 312,540.The digit to the right is 5 or more. Increase theround-off place digit by 1. Replace all digits tothe right with zeros.313,00054.1,395,999Identify the round-off place digit: 1,395,999.The digit to the right is 5 or more. Increase theround-off place digit by 1. Replace all digits tothe right with zeros.1,400,00056.3,116,201Identify the round-off place digit: 3,116,201.The digit to the right is less than 5. Do notchange the round-off place digit. Replace alldigits to the right with zeros.3,100,00058.$212,875Identify the round-off place digit: 212, 875.The digit to the right is less than 5. Do notchange the round-off place digit. Replace alldigits to the right with zeros.$210,00060.Caravan ? Charger$32,732 ? $32,10632,732 is greater than 32,106.$32, 732$32,106CaravanCharger>>62.$34,775Identify the round-off place digit: 34,775.The digit to the right is 5 or more. Increase theround-off place digit by 1. Replace all digits tothe right with zeros.$35,00064.44,972Identify the round-off place digit: 44,972.The digit to the right is 5 or more. Increase theround-off place digit by 1. Since the round-offplace digit is 9, place a zero in the round-offplace and increase the digit in the next place tothe left by 1. Replace all digits to the right withzeros.45,00066.5,311,192,809,000Identify the round-off place digit:5,311,192,809,000.The digit to the right is 5 or more. Increase theround-off place digit by 1. Replace all digits tothe right with zeros.5,311,193,000,00068.5 hours and 40 minutesSince 40 minutes is more than one-half hour, weround up.6 hours70.15 yards, 4 inchesSince 4 inches is less than one-half yard, weround down.15 yardsClassroom Quiz 1.11.5301 = 5000 + 300 + 12.a.8 ? 08 is greater than 0.8 > 0

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ISM: PrealgebraChapter 1:Whole Numbers and Introduction to Algebra3b.2 ? 112 is less than 11.2 < 113.3571a.Identify the round-off place digit: 3571.The digit to the right is 5 or more. Increasethe round-off place digit by 1. Replace alldigits to the right with zeros.4000b.Identify the round-off place digit: 3571.The digit to the right is less than 5. Do notchange the round-off place digit. Replace alldigits to the right with zeros.35701.2Understanding the ConceptAddition Facts Made Simple1.8 + 5 = (3 + 5) + 5 = 3 + (5 + 5) = 3 + 10 = 132.6 + 8 = 6 + (6 + 2) = (6 + 6) + 2 = 12 + 2 = 141.2Understanding the ConceptUsing Inductive Reasoning to Reach aConclusion1.8, 14, 20, 26, 32, 38, ...We observe a pattern that each number is 6 morethan the preceding number: 14 = 8 + 6,20 = 14 + 6, and so on. Therefore, if we add 6 to38, we conclude that the next number in thesequence is 44.2.17, 28, 39, 50, 61, ...We observe a pattern that each number is 11more than the preceding number: 28 = 17 + 11,39 = 28 + 11, and so on. Therefore, if we add 11to 61, we conclude that the next number in thesequence is 72.1.2 Exercises2.7+xSeven plus a numberAnswers may vary.4.Because the commutative property allows us tochange the order of additionwithoutchangingthe value of the sum.6.(x+ 6) + 3 = (6 +x) + 3The order of the addition is changed. This is thecommutative property of addition.8.Two added to a number:m+ 210.the sum of eight andx: 8 +xorx+ 812.Twelve more than a number:y+ 1214.A number plus four:y+ 416.y+ 6 = 6 +y18.5 +x=x+ 520.By the commutative property of addition,8790 + 157 = 157 + 8790, so157 + 8790 = 8947.22.By the commutative property of addition,8 +x=x+ 8, sox+ 8 = 31.24.a+ 6 + 2 =a+ (6 + 2) =a+ 826.4 + 4 +y= (4 + 4) +y= 8 +y=y+ 828.x+ 3 + 0 =x+ (3 + 0) =x+ 330.(x+ 5) + 1 =x+ (5 + 1) =x+ 632.3 + (4 +x) = (3 + 4) +x= 7 +x34.(a+ 3) + 7 =a+ (3 + 7) =a+ 1036.(y+ 1) + 4 =y+ (1 + 4) =y+ 538.(4)5(4)5(45)9xxxx++=++=++=+40.5(3)(53)88aaaa++=++=+=+42.3(2)1(3)(21)(3)3(33)6+++=+++=++=++=+nnnnn44.(64)4(64)4(10)4(104)14xxxxx+++=+++=++=++=+46.(28)5(28)5(10)5(105)15nnnnn+++=+++=++=++=+48.a.Replacenwith 4.n+ 8 = 4 + 8 = 12Whennis equal to 4,n+ 8 is equal to 12.

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Chapter 1:Whole Numbers and Introduction to AlgebraISM: Prealgebra4b.Replacenwith 7.n+ 8 = 7 + 8 = 15Whennis equal to 7,n+ 8 is equal to 15.50.Replaceawith 5 andbwith 10.a+b= 5 + 10 = 15Whenais 5 andbis 10,a+bis 15.52.Replacexwith 11,ywith 18, andzwith 15.x+y+z= 11 + 18 + 15 = 44Whenais 11,bis 18, andcis 15,x+y+zis 44.54.Replacexwith 33 andywith 43.x+y+ 21 = 33 + 43 + 21 = 97Whenxis 33 andyis 43,x+y+ 21 is 97.56.a.Bonus25015015250$415xy=++=++=b.Bonus25012518250$393xy=++=++=58.711283+60.33157388+62.33116454+64.308724575635+66.53121718766+68.56265133760+70.33661524854003+72.836,147992, 4134, 000842, 659+74.2, 9029, 05012986,100998, 064+76.a.347746148091+Total deposits were $8091.b.120350013885008+Total debits were $5008.78.5622761424951475+Shawnee spent $1475 on her car.80.7 in. + 1 in. + 7 in. + 1 in. = 16 in.The perimeter is 16 inches.82.8 ft + 8 ft + 8 ft + 8 ft = 32 ftThe perimeter is 32 feet.84.3 ft + 8 ft + 8 ft = 19 ftThe perimeter is 19 feet.86.The length of the unlabeled side is 3 ft + 21 ft or24 ft.23 ft + 3 ft + 5 ft + 21 ft + 18 ft + 24 ft = 94 ftThe perimeter is 94 feet.88.The length of the unlabeled side on the left is145 in., and the length of the right side of thefigure is 145 in. + 15 in. or 160 in.145 in. + 40 in. + 15 in. + 155 in. + 160 in.+ 195 in. = 710 in.The perimeter is 710 inches.

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ISM: PrealgebraChapter 1:Whole Numbers and Introduction to Algebra590.2, 4, 6, 8, 10, 12, ...Each number is 2 more than the precedingnumber. The next number is 12 + 2 or 14.92.24, 31, 38, 45, 52, 59, 66, ...Each number is 7 more than the precedingnumber. The next number is 66 + 7 or 73.94.12, 25, 38, 51, 64, ...Each number is 13 more than the precedingnumber. The next number is 64 + 13 or 77.Classroom Quiz 1.21.a.(5)6(5)6(56)11xxxx++=++=++=+b.1(56)1(56)1(11)(111)12or12nnnnnn+++=+++=++=++=++2.Replaceawith 13 andbwith 29.a+b+ 12 = 13 + 29 + 12 = 54Whenais 13 andbis 29,a+b+ 12 is equal to54.3.The length of the unlabeled side on the left is14 ft, and the length of the right side of thefigure is 14 ft + 13 ft or 27 ft.14 ft + 14 ft + 13 ft + 115 ft + 27 ft + 129 ft= 312 ftThe perimeter is 312 feet.1.3Understanding the ConceptMoney and Borrowing1.We can borrow only from a place value that hasa nonzero whole number. For example, in $400there are only 100-dollar bills to break down(borrow from).2.When we change the ten-dollar bill to 10 one-dollar bills, we have 0 ten-dollar bills and10 one-dollar bills, which is similar toborrowing:0 102 1 0.1.3 Exercises2.102: Two subtracted from 10Answers may vary.4.The English phrase “five less thanx” writtenusing symbols, is 5x. This statement is false.6.53 = 28.72 = 510.42 = 212.65 = 114.140 = 1416.1212 = 018.900800 = 100900801 = 99900802 = 98900803 = 97900804 = 96900805 = 95900806 = 9420.800700 = 100800701 = 99800702 = 98800703 = 97800704 = 96800705 = 9522.Three decreased by a number: 3a24.The difference of three and a number: 3n26.Seven subtracted from a number:x728.Eight minus two: 8230.Nine less than twelve: 12932.Replacenwith 6.9n= 96 = 3Ifnis equal to 6, 9nis equal to 3.34.Replacenwith 1.9n= 91 = 8Ifnis equal to 1, 9nis equal to 8.36.Replacexwith 5.x2 = 52 = 3Ifxis equal to 5,x2 is equal to 3.38.Replacexwith 10.x2 = 102 = 8Ifxis equal to 10,x2 is equal to 8.40.982573Check:257398+

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Chapter 1:Whole Numbers and Introduction to AlgebraISM: Prealgebra642.764135Check:413576+44.573819Check:381957+46.733538Check:353873+48.764545219Check:545219764+50.70029671Check:67129700+52.87116448067Check:80676448711+54.880145834218Check:458342188801+56.29, 0023, 66725,335Check:3, 66725,33529, 002+58.796, 02068, 431727, 589Check:68, 431727, 589796, 020+60.The length of the unlabeled side on the top is20 in.8 in. or 12 in., and the length of the rightside of the figure is 18 in.7 in. or 11 in.18 in. + 12 in. + 7 in. + 8 in. + 11 in. + 20 in.= 76 in.The perimeter is 76 inches.62.The length of the unlabeled side on the right is20 in.9 in. or 11 in., and the length of theunlabeled top side of the figure is 38 in.17 in.or 21 in.20 in. + 17 in. + 9 in. + 21 in. + 11 in. + 38 in.= 116 in.The perimeter is 116 inches.64.1289038The top speed of Intimidator 305 is 38 miles perhour slower than the top speed of Kingda Ka.66.32830028The maximum drop of Superman: Escape fromKrypton is 28 feet greater than that ofIntimidator 305.68.790021605740The difference in diameter of Earth and themoon is 5740 miles.70.a.Blue: 275,0005000 = 270,000Bowhead: 60,0008500 = 51,500Humpback: 150,00020,000 = 130,000The Blue Whale had the largest decline.b.The total decline is270,000 + 51,500 + 130,000 = 451,50072.Six less thanx:x6Replacexwith 10.x6 = 106 = 4Ifxis equal to 10, six less thanxis equal to 4.Cumulative Review73.5,117,206 > 13,84274.2,386,702 > 117,40175.120135105360+Edward worked 360 hours in the three-monthperiod.76.4303212286508+Drew paid $508 for the dog and all the supplies.

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ISM: PrealgebraChapter 1:Whole Numbers and Introduction to Algebra7Classroom Quiz 1.31.a.A number subtracted from 8: 8nb.Two less than a number:n2c.Four decreased by a number: 4n2.a.11, 0556, 2944, 761Check:6, 2944, 76111, 055+b.502, 401291,632210, 769Check:291, 632210, 769502, 401+3.482237881034The first bid was $1034 greater.1.4Understanding the ConceptMemorizing Multiplication Facts1.a.3(7) = 2(7) + 7 = 14 + 7 = 21b.4(8) = 5(8)8 = 408 = 32c.6(8) = 5(8) + 8 = 40 + 8 = 48d.9(8) = 10(8)8 = 808 = 721.4 Exercises2.a.9x: Nine times a number.b.mn: the product ofmandn4.4 times 3:6.8(34) = (34)8The order of the multiplication is changed. This is the commutative property of multiplication.8.45(3x) = (453)x= 60x10.(4y)32 = 4y32 = (432)y= 24y

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Chapter 1:Whole Numbers and Introduction to AlgebraISM: Prealgebra812.a.WhitePale BlueRoseBeigeBeigeWhiteBeigePale BlueBeigeRoseGrayGrayWhiteGrayPale BlueGrayRoseBlueBlueWhiteBluePale BlueBlueRoseLightBrownLightBrownWhiteLightBrownPale BlueLightBrownRoseb.4(3) = 12 different combinations14.10(5) = 50 different ice cream dishes16.4(7) = 28The factors are 4 and 7. The product is 28.18.7a= 49The factors are 7 anda. The product is 49.20.A number times 5:x5 = 5x22.Double a number: 2x24.The product ofaandb:ab26.Ifab= 0 anda= 10, thenb= 0.28.By the associative and commutative properties of multiplication,b(ac) = (ba)c= (ab)c, so(ab)c= 30.30.(4)(5)(2)(2) = (4)(2)(5)(2) = (42)(52) = (8)(10) = 8032.(5)(4)(3)(2) = (4)(3)(5)(2) = (43)(52) = (12)(10) = 12034.9086 = 036.3245 = (34)(25) = 1210 = 12038.7(5b) = (75)b= 35b40.3(x8) = 3(8x) = (38)x= 24x42.2(a9) = 2(9a) = (29)a= 18a44.5(8x) = (58)x= 40x46.2(3)(5z) = 6(5z) = (65)z= 30z48.0(7)(z8) = 050.4(7)(x1) = 28x

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ISM: PrealgebraChapter 1:Whole Numbers and Introduction to Algebra952.64(3y) = 24(3y) = (243)y= 72y54.(4a)52 = 4a(52) = 4a(10) = (410)a= 40a56.4(3a)5 = (43)a5 = 12a5 = 125a= 60a58.92687408×60.40562430×62.578500289, 000×64.871300261,300×66.81343242432754×68.44683522642992×70.668953 34060 1263, 460×72.322741 28822 5423,828×74.632201632126 40127, 032×76.631201631126 20126,831×78.445657835 648311 922 228 02, 575, 568×80.900256327 006540 124 501 05, 068,126×82.23,109605115 54513 865 4013, 980, 945×84.86, 2462000172, 492, 000×86.45062700×The plane travels 2700 miles.88.12672×John has 72 plants.

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Chapter 1:Whole Numbers and Introduction to AlgebraISM: Prealgebra1090.11691044×The player will gain 1044 rushing yards in theseason.92.12896×Each wall requires 96 tiles.963288×Karen needs 288 tiles for the three walls.24112424264×Karen bought 264 tiles.No, Karen does not have enough tiles tocomplete the job because she needs 288 tiles butonly bought 264.94.a.The bar for Boston is labeled 41. The hightemperature was 41°F.b.The high temperature in Burlington was30°F.30390×The high temperature in Newport Beach was90°F.96.(4x)(2y)(6z) = (426)(xyz) = 48xyz98.2(3x)(3y)(5z) = (2335)(xyz) = 90xyz100.8a(5b)2c= (852)(abc) = 80abcCumulative Review102.426,8622,128428,990+103.70001426858104.826,540Identify the round-off place digit: 826,540.The digit to the right is 5 or more. Increase theround-off place digit by 1. Replace all digits tothe right with zeros.827,000105.168,406,000Identify the round-off place digit: 168,406,000.The digit to the right is 5 or more. Increase theround-off place digit by 1. Replace all digits tothe right with zeros.168,410,000106.1209723The bill was $23 less than the budget allotment.107.920455465Mary Ann must drive 465 miles the second day.Classroom Quiz 1.41.The product of four and a number: 4n2.205110714 357205 10219, 457×3.2x(5y)(4) = (254)(xy) = 40xy1.5Understanding the ConceptThe Commutative Property and Division1.a÷b=b÷awhenaandbare equal.1.5Understanding the ConceptConclusions and Inductive Reasoning1.1, 1, 2, …Notice that 1 + 0 = 1 and 1 + 1 = 2. If we followa pattern of adding consecutive whole numbers(0, 1, 2, …) to the preceding number, the nextnumber is 2 + 2 = 4.Notice that 11 = 1 and 12 = 2. If we follow apattern of multiplying the preceding number byconsecutive counting numbers (1, 2, 3, …), thenext number is 23 = 6.

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ISM: PrealgebraChapter 1:Whole Numbers and Introduction to Algebra111.5 Exercises2.There are 320÷20 rows.4.Each person paidn÷7.6.(b) and (c) are correct.8.Eight divided by a number: 8÷a10.Sixty-three jelly beans divided equally amongthree children: 63÷312.The quotient of forty-four and eleven: 44÷1114.The quotient of eleven and forty-four: 11÷4416.25÷25 = 118.0099=20.45÷0undefined22.60÷9 = 6 R 669 60546Check: 6(9) + 6 = 54 + 6 = 6024.3726÷6 = 6216216 3726361212660Check: 6(621) = 372626.4046÷6 = 674 R 26746 404636444226242Check: 6(674) + 2 = 4044 + 2 = 404628.1863÷20 = 93 R 39320 186318063603Check: 20(93) + 3 = 1860 + 3 = 186330.783÷20 = 39 R 33920 783601831803Check: 20(39) + 3 = 780 + 3 = 78332.6436÷32 = 201 R 420132 64366436324Check: 32(201) + 4 = 6432 + 4 = 643634.1301÷24 = 54 R 55424 1301120101965Check: 24(54) + 5 = 1296 + 5 = 130136.1350÷16 = 84 R 68416 135012870646Check: 16(84) + 6 = 1344 + 6 = 1350

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Chapter 1:Whole Numbers and Introduction to AlgebraISM: Prealgebra1238.12,854÷42 = 306 R 230642 128541262542522Check: 42(306) + 2 = 12,852 + 2 = 12,85440.37,780÷118 = 320 R 20320118 3778035423823620Check: 118(320) + 20 = 37,760 + 20 = 37,78042.123,264÷136 = 906 R 48906136 123264122486481648Check: 136(906) + 48 = 123,216 + 48 = 123,26444.21,945÷29 = 756 R 2175629 2194520316414519517421Check: 29(756) + 21 = 21,924 + 21 = 21,94546.321 756312The remainder is 12, so 12 tickets were donatedto the homeless shelter.48.2365 14951301951950The ticket price should be $23.50.625250 1562501500625500125012500The rancher should allow 625 cows on the field.52.714 98980The pattern is 7 inches wide.54.a.1415 2181568608He can completely fill 14 cases.b.After filling 14 cases, he will have 8 carsleft to give to his brother.56.4, 16, 64, 256, ...Each number after the first is the precedingnumber multiplied by 4. The next number is4×256 or 1024.58.0, 2, 6, 12, 20, ...Add 2 to the first number to obtain the second.Add 4 to the second number to obtain the third.Add 6, and then add 8. The next number is20 + 10 or 30.60.1, 6, 8, 13, 15, 20, ...Alternate adding 5 and adding 2 to the precedingnumber. The next number is 20 + 2 or 22.

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ISM: PrealgebraChapter 1:Whole Numbers and Introduction to Algebra1362.1, 4, 8, ...Alternate multiplying the preceding number by 4and multiplying the preceding number by 2. Thenext number is 4(8) = 32.Add 3 to the first number to obtain the second.Add 4 to the second number to obtain the third.Add 5 to the third number to obtain the fourth:The next number is 8 + 5 or 13.64.a.(48÷6)÷2 = 8÷2 = 4b.48÷(6÷2) = 48÷3 = 16c.The property does not apply to division.Cumulative Review65.Seven plusx: 7 +x66.106011494667.40312028 062806 20814, 262×68.556,432Identify the round-off place: 556,432.The digit to the right is less than 5. Do notchange the round-off digit. Replace all digits tothe right with zeros.556,00069.1389430959959495464Leo must drive 464 miles the third day.70.29, 5996, 20023,39923,3995, 50017,899The balance is $17,899.Classroom Quiz 1.51.a.The quotient of twenty and two: 20÷2b.The quotient of two and twenty: 2÷202.10,577÷35 = 302 R 730235 10577105777073.12450005 622500051210222025250Each investor will pay $1,245,000.1.6 Exercises2.What number squared is equal to 81?4.49 9 9 99=6.2b bb=8.1=zz10.37 7 77=12.238 88=xxxx14.243 33y y y yy=16.226 66=xy yxy18.52257 77or 7=xxxxxxx20.a.677 7 7 7 7 7=b.2xx x=22.333 3 327==24.266 636==
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