Prealgebra and Introductory Algebra 1st Edition Solution Manual

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1Chapter 1Whole NumbersAre You Prepared?Section 1.1Study TipsGroup Activity: Becoming a Successful Student1.Answers will vary.2.Answers will vary.3.Answers will vary.4.Answers willvary.5.Problem Recognition Exercises: page 114Chapter Summary: page 123Chapter Review Exercises: page 125Chapter Test: page 128Cumulative Review Exercises: page 1296.Answers will vary.7.Answers will vary.8.Answers will vary.9.Answers will vary.10.Answers will vary.Section 1.2Introduction to Whole NumbersSection 1.2Practice Exercises1.Answers will vary.2.(a)Adigitis one of the numbers 0, 1,2, 3, 4, 5, 6, 7, 8, 9.(b)A number is written instandardformif the position of each digitdetermines the place value of thedigit.(c)Periodsare groups of three digitsseparated by commas in a largenumber.(d)A number is written inexpandedformif each digit is written with itsplace value units.3.8,213,4577: ones

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Chapter 1Whole Numbers25: tens4: hundreds3: thousands1: ten-thousands2: hundred-thousands8: millions4.103,5966: ones9: tens5: hundreds3: thousands0: ten-thousands1: hundred-thousands5.321tens6.689tens7.214ones8.738ones9.8710hundreds10.2293hundreds11.1430thousands12.3101thousands13.452,723hundred-thousands14.655,878hundred thousands15.1,023,676,207billions16.3,111,901,211billions17.22,422ten-thousands18.58,106ten-thousands19.51,033,201millions20.93,971,224millions21.10,677,881ten-millions22.31,820mi2thousands23.7,653,468,440billions24.31,000 ftten-thousands25.5 tens + 8 ones26.7 tens + 1 one27.5 hundreds + 3 tens + 9 ones28.3 hundreds + 8 tens + 2 ones29.5 thousands + 2 hundreds + 3 ones30.7 thousands + 8 tens + 9 ones31.1 ten-thousand + 2 hundreds + 4 tens +1 one32.2 ten-thousands + 8 hundreds + 7 tens +3 ones33.52434.31835.15036.62037.1,90638.4,20139.85,00740.26,00241.ones, thousands, millions, billions42.ones, tens, hundreds, thousands43.Two hundred forty-one44.Three hundred twenty-seven45.Six hundred three46.One hundred eight47.Thirty-one thousand, five hundred thirty48.Fifty-two thousand, one hundred sixty49.One hundred thousand, two hundredthirty-four50.Four hundred thousand, one hundredninety-nine

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Section 1.2Introduction to Whole Numbers351.Nine thousand, five hundred thirty-five52.One thousand, three hundred seventy-seven53.Twenty thousand, three hundred twenty54.One thousand, eight hundred55.Five hundred ninety thousand, sevenhundred twelve56.Sixty million57.600558.400459.672,00060.248,00061.1,484,25062.2,647,52063.64.65.Counting on a number line, 10 is 4 units tothe right of 6.66.Counting on a number line, 3 is 8 units tothe left of 11.67.Counting on a number line, 4 is 3 units tothe left of 7.68.Counting on a number line, 5 is 5 units tothe right of 0.69.8 > 28 is greater than 2, or 2 is less than 8.70.6 < 116 is less than 11, or 11 is greater than 6.71.3 < 73 is less than 7, or 7 is greater than 3.72.14 > 1214 is greater than 12, or 12 is less than 14.73.6 < 1174.14 > 1375.21 > 1876.5 < 777.3 < 778.14 < 2479.95 > 8980.28 < 3081.0 < 382.8 > 083.90 < 9184.48 > 4785.False; 12 is made up of the digits 1 and 2.86.False; 26 is made up of the digits 2 and 6.87.9988.99989.There is no greatest whole number.90.0 is the least whole number.91.10,000,0007 zeros92.100,000,000,00011 zeros93.96494.840Section 1.3Addition and Subtraction of Whole Numbers andPerimeter

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Chapter 1Whole Numbers4Section 1.3Practice Exercises1.Answers willvary.2.(a)Asumis the result of an additionproblem.(b)Theaddendsare the numbers beingadded.(c)Apolygonis a flat figure formed byline segments connected at their ends.(d)Theperimeterof a polygon is thedistance around the outside of thefigure.(e)Thedifferenceis the result of asubtraction problem.(f)Thesubtrahendis the number beingsubtracted.(g)Theminuendis the number beingsubtracted from.(h)Avariableis a letter or symbol thatrepresents a number.3.3 hundreds + 5 tens + 1 one4.20045.40126.62067.Fill in the table. Use the number line if necessary.+0123456789001234567891123456789102234567891011334567891011124456789101112135567891011121314667891011121314157789101112131415168891011121314151617991011121314151617188.11 +10 = 21Addends: 11, 10Sum: 219.1 + 13 + 4 = 18Addends: 1, 13, 4Sum: 1810.5 + 8 + 2 = 15Addends: 5, 8, 2Sum: 1511.424 tens2 ones333 tens3 ones757 tens5 ones=++=+=+12.212 tens1 one535 tens3 ones747 tens4 ones=++=+=+13.121 ten2 ones151 ten5 ones323 tens2 ones595 tens9 ones=+=++=+=+14.101 ten0 ones80 tens8 ones303 tens0 ones484 tens8 ones=+=+=+=+

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Section 1.3Addition and Subtraction of Whole Numbers and Perimeter515.890107997+16.444354798+17.413102119+18.112215237+19.17645121+20.1255984+21.18724111+22.13877115+23.658231889+24.1642295937+25.1 1152549701+26.1 1462388850+27.1 17911212203+28.1 162907341003+29.1149801022315, 203+30.1 12311289224,00431.1 1 1Ź10 22325 7824 98040,98532.11 1 192 3775 62234 659132,65833.101 + 44 = 44 + 10134.8 + 13 = 13 + 835.x+y=y+x36.t+q=q+t37.(23 + 9) + 10 = 23 + (9 + 10)38.7 + (12 + 8) =(7 + 12) + 839.r+ (s+t) = (r+s) +t

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Chapter 1Whole Numbers640.(c+d) +e=c+ (d+e)41.The commutative property changes theorder of the addends, and the associativeproperty changes the grouping.42.The sum of any number and 0 is thatnumber.(a)423 + 0 =423(b)0 + 25 = 25(c)67 + 0 = 67(d)0 +x=x43.12−8 = 4minuend: 12subtrahend: 8difference: 444.963−minuend: 9subtrahend: 6difference: 345.27−9 = 18 because 18 + 9 = 27.46.20−8 = 12 because 12 + 8 = 20.47.102−75 = 27 because 27 + 75 = 102.48.211−45 = 166 because 166 + 45 = 211.49.8−3 = 5Check:5+ 3 = 850.7−2 = 5Check:5+ 2 = 751.4−1 = 3Check:3+ 1 = 452.9−1 = 8Check:8+ 1 = 953.13472211126−Check:1126+2211347✓54.48657134152−Check:4152+7134865✓55.14,35613, 2531,103−Check:1 103+13 25314,356✓56.34,550−31,4503100Check:3 100+31 45034,550✓57.6 16765917−Check:117+5976✓58.5 14644816−Check:116+4864✓59.106 0 107 1 01 8 95 2 1−Check:1 1521+189710✓60.4 1085 0−30 3547Check:1547+303850✓61.995 10 10126 0 0 21 2 3 84 7 6 4−Check:1 1 14764+12386002✓62.99210 10103 0 0 02 3 5 66 4 4−Check:1 1 1644+23563000✓63.0 1010 ,425−9 0221, 403Check:1 403+9 02210,425✓64.91 13 8 10 112 3, 9 0 1−80 6 415 ,8 3 7Check:11 115 837+8 06423,901✓

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Section 1.3Addition and Subtraction of Whole Numbers and Perimeter765.115 1 1062 08859 8712, 217−Check:112 217+59 87162,088✓66.11 10 102 10 01232 , 1 1 2−28, 3 3 43 7 7 8Check:1 1 113 778+28 33432,112✓67.16 92 6 10 1037 0 0−29 8 77 1 3Check:1 1 1713+29873700✓68.9 97 10 10 108 0 0 0−3 7 8 84 2 1 2Check:1 1 14212+37888000✓69.1313 1332 , 4 39−14 9830 ,9 41Check:1130 941+1 49832,439✓70.1 1121 3354 12317, 212−Check:117 212+4 12321,335✓71.97 10102 148, 0 07, 23 42, 3 45,11 55, 6 62,11 9−Check:1 115 662 119+2 345 1158,007,234✓72.92 10144 163 0 45 5 671 8 71 4 951, 1 74,0 72−Check:111 174 072+1 871 4953,045,567✓73.The expression 7−4 means 7 minus 4,yielding a difference of 3. The expression4−7 means 4 minus 7 which results in adifference of−3.74.Subtraction is not associative. Forexample, 10−(6−2) = 10−4 = 6, and(10−6)−2 = 4−2 = 2. Therefore10−(6−2) does not equal (10−6)−2.75.13 + 7113720+76.100 + 4210042142+77.7 + 45174552+78.23 + 812381104+79.18 + 5118523+80.76 + 276278+81.1523 + 901Ź1523+90161382.1320 + 4481320+448176883.5 + 39 + 81153981125+

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Chapter 1Whole Numbers884.78672−85.422100322−86.894247−87.8 10109 07 2101 8−88.0 113111603051−89.4 105 01 33 7−90.405103302−91.9 1310 3−3 56 892.8 119 1−1 47 793.1 2126,548,00026,930,000+20,805,00074,283,000The shows had a total of74,283,000 viewers.94.3 33854446197103+124521521 deliveries weremade.95.1111510493111423+423 desks were delivered.96.1$6082+58$200The total amount is $200.97.1 10 211Ź1020, 320 ft−14, 246 ft6, 074 ftDenali is 6074 ft higher than WhiteMountain Peak.98.4 155 53 91 6−16 DVDs are left.99.997 10 10102 398 0 0 02 390 2 5 27 7 4 8−The difference is 7748 marriages.100.2,398,000−2,248,000150,000The decrease is 150,000 marriages.

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Section 1.3Addition and Subtraction of Whole Numbers and Perimeter9101.133 3 132 4 4 3 4892 2 48 000195, 489−The difference is 195,489 marriages.102.2,398,0002,336,00062,000−The greatest increase occurred between1995−2000; the increase was 62,000marriages.103.1 1 1 1 1100,052675,03845,934821,024+There are 821,024nonteachers.104.1 11$7 3299 5601 2483 500$21,637+The total cost is $21,637.105.6288−20324256Mt. Washington is 4256 ft higher than thePinkham Notch Visitor Center.106.9 133 10 14 134 0 4 3−2 0 6 41 9 7 9The Lion Kinghad been performed 1979more times.107.126,9602 60029,560+Jeannette will pay $29,560 for 1 year.108.11ŹŹ138+96234They are 234 miles apart.109.135 cm35 cm34 cm104 cm+110.127 in.13 in.20 in.60 in.+111.26 yd10 yd11 yd3 yd5 yd7 yd42 yd+112.2 3200 yd136 yd142 yd98 yd58 yd38 yd672 yd+113.94 ft94 ft50 ft50 ft288 ft+114.90 ft90 ft90 ft90 ft360 ft+115.14 m12 m26 m+39 m26 m13 m−The missing length is 13 m.

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Chapter 1Whole Numbers10116.11139 cm87 cm201 cm427 cm+547 cm427 cm120 cm−The missing length is 120 cm.117.45, 41881,9909 063+56,309192,780118.9,300,0507,803,5133, 480,009907,82221, 491,394+119.3,421,019822,7611,003,721+9,6785,257,179120.4,905,620458,3184, 447,302−121.953, 400, 41556,341,902897,058,513−122.82,025,160−79,118,7052,906,455123.103, 718 mi2−54,310 mi249,408 mi2The difference in land area betweenColorado and Wisconsin is49,408 mi2.124.41, 217 mi2−24,078 mi217,139 mi2Tennessee has17,139 mi2more thanWest Virginia.125.22221 045mi41, 217 mi54,310 mi96,572 mi+The combined land area of Rhode Island,Tennessee, and Wisconsin is96,572 mi2.126.2222221 045mi41, 217 mi24,078mi54,310 mi103,718mi224,368 mi+The combined land area of the five statesis224,368 mi2.Section 1.4Rounding and EstimatingSection 1.4Practice Exercises1.Answers will vary2.Roundinga number allows us to give anapproximation of the number to a specificplace value.3.593326−4.0 12 101 3 09 83 2−

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Section 1.4Rounding and Estimating115.1 1 14 009+9985 0076.12,03323,44135,474+7.Ten-thousands8.Hundreds9.If the digit in the tens place is 0, 1, 2, 3, or4, then change the tens and ones digits to0. If the digit in the tens place is 5, 6, 7, 8,or 9, increase the digit in the hundredsplace by 1 and change the tens and onesdigits to 0.10.If the digit in the ones place is 0, 1, 2, 3, or4, then change the ones digits to 0. If thedigit in the ones place is 5, 6, 7, 8, or 9,increase the digit in the tens place by 1and change the ones digit to 0.11.34234012.83483013.72573014.44545015.9384940016.8363840017.8539850018.9817980019.34,99235,00020.76,83177,00021.2578300022.3511400023.998210,00024.7974800025.109,337109,00026.437,208437,00027.489,090490,00028.388,725390,00029.$148431,020$148,000,00030.$33,050$33,00031.238,863 mi239,000 mi32.492,0002m500,0002m33.578221+→→→608020160+34.337841+→→→308040150+35.639−422→→640−42022036.851−399→→850−40045037.892+129→→900+100100038.347+563→→300+60090039.3412−1252→→3400−1300210040.9771−4544→→9800−45005300

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Chapter 1Whole Numbers1241.97,404,57653,695,428+→→197,000,00054,000,000151,000,000+$151,000,000 was brought in by Mars.42.81,296,78454,391,26838,168,580+→→→181,000,00054,000,00038,000,000173,000,000+$173,000,000 was brought in by Hershey.43.71,339,710−59,684,076→→71,000,000−60,000,00011,000,000Neil Diamond earned $11,000,000 more.44.48441190−→→500010004000−4000 more women gave birth.45.$3,316,8973,272,028+3,360,289→→→1$3,300,0003,300,000+3,400,000$10,000,00046.$3,470,2953,173,050+1,970,380→→→$3,500,0003,200,000+2,000,000$8,700,00047.(a)2003; $3,470,295→$3,500,000(b)2005; $1,970,380→$2,000,00048.$3,500,000−2,000,000$1,500,00049.Massachusetts; 78,815→79,000 students50.Vermont; 8059→8000 students51.79,000−8 00071,000The difference is 71,000 students.52.45,879913716,75678,81517, 42213,1728059+→→→→→→→446,0009,00017,00079,00017,00013,000+8 000189,000The total is 189,000 students.53.3045 mm1892 mm3045 mm+ 1892 mm→→→→3000 mm2000 mm3000 mm+ 2000 mm10,000 mm54.1851 cm1782 cm1851 cm+ 1782 cm→→→→2000 cm2000 cm2000 cm+ 2000 cm8000 cm55.105 in.57 in.57 in.105 in.57 in.+ 57 in.→→→→→→2110 in.60 in.60 in.110 in.60 in.+ 60 in.460 in.56.182 ft121 ft182 ft169 ft+ 169 ft→→→→→200 ft100 ft200 ft200 ft+ 200 ft900 ftSection 1.5Multiplication of Whole Numbers and AreaSection 1.5Practice Exercises1.Answers will vary.2.(a)Multiplicationis repeated addition.

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Section 1.5Multiplication of Whole Numbers and Area13(b)The numbers that are multiplied arecalledfactors.(c)The result of multiplication is calledtheproduct.(d)Areameasures the amount of surfacecontained within a region.(e)Thearea of a rectangleis the productof the length and the width.3.1869, 240870,00034,92130,000108,332110,0001,010,000→→+→+4.907,801900,000413,560400,000500,000→−→−5.88218800340134005400→−→−6.01234567890000000000010123456789202468101214161830369121518212427404812162024283236505101520253035404560612182430364248547071421283542495663808162432404856647290918273645546372817.5 + 5 + 5 + 5 + 5 + 5 = 65 = 308.2222222229218++++++++==9.9 + 9 + 9 = 39 = 2710.7 + 7 + 7 + 7 = 47 = 2811.1342 = 546factors: 13, 42; product: 54612.269 = 234factors: 26, 9; product: 23413.352 = 30factors: 3, 5, 2; product: 3014.438 = 96factors: 4, 3, 8; product: 9615.For example: 512; 512; 5(12)16.For example: 2314; 2314; 23(14)17.d18.a19.e20.b21.c22.a23.14 • 8 = 8 •1424.3 • 9 = 9 • 325.6 • (2 • 10) = (6 • 2) • 10

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Chapter 1Whole Numbers1426.(4 • 15) • 5 = 4 • (15 • 5)27.5(7 + 4) = (5 • 7) + (5 • 4)28.3(2 + 6) = (3 • 2) + (3 • 6)29.24624Multiply 64.Multiply 620.120Add.144+30.18540Multiply 58.Multiply 510.50Add.90+31.26212Multiply 26.Multiply 220.40Add.52+32.7133Multiply 31.Multiply 370.210Add.213+33.13155Multiply 51.Multiply 530.150Multiply 5100.500Add.655+34.72531560+21002175Multiply 35.Multiply 320.Multiply 3700.Add.35.344416Multiply 44.Multiply 440.160Multiply 4300.1200Add.1376+36.105945Multiply 95.Multiply 90.00Multiply 9100.900Add.945+37.31410811, 28038.32016612,09639.213312723,18440.44801524,00541.11 342,0149378,12642.451,0068408,04843.3214128320448+44.412141820861+

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Section 1.6Division of Whole Numbers1545.131682427213601632+46.255415522002255+47.7212144720864+48.11134678520598+49.3 214317100114302431+50.1 11 1 1722285 77614 44020, 216+51.14 834919314134906631+52.5123151215 36015,872+53.131511271 0573 02015 10019,177+54.1117031464 21828 12070 300102,638+55.1111 12228412228 880177 600186,702+56.4 35 43875062 3220 000193 500195,822+57.1 13 112 13532601414 12835 320000 00021192 00021, 241, 448+

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