Solution Manual for Practical Problems in Mathematics for Electricians, 9th Edition

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’s Guide to AccompanyPractical Problems in Mathematicsfor ElectriciansNinthEdition

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CONTENTSTo thevSection 1Whole NumbersUnit 1Addition of Whole Numbers1Unit 2Subtraction of Whole Numbers1Unit 3Multiplication of Whole Numbers2Unit 4Division of Whole Numbers3Unit 5Combined Operations with Whole Numbers4Section 2Common FractionsUnit 6Addition of Common Fractions5Unit 7Subtraction of Common Fractions5Unit 8Multiplication of Common Fractions6Unit 9Division of Common Fractions7Unit 10Combined Operations with Common Fractions7Section 3Decimal FractionsUnit 11Addition of Decimal Fractions9Unit 12Subtraction of Decimal Fractions9Unit 13Multiplication of Decimal Fractions10Unit 14Division of Decimal Fractions11Unit 15Decimal and Common Fraction Equivalents12Unit 16Combined Operations with Decimal Fractions12Section 4Percents, Averages, and EstimatesUnit 17Percent and Percentage13Unit 18Interest13Unit 19Discount14Unit 20Averages and Estimates14Unit 21Combined Problems on Percents, Averages, and Estimates15Section 5Powers and RootsUnit 22Powers16Unit 23Roots17Unit 24Combined Operations with Powers and Roots17Unit 25Metric Measure and Scientific Notation18Section 6MeasureUnit 26Length Measure18Unit 27Area Measure19Unit 28Volume and Mass Measure20Unit 29Energy and Temperature Measure21Unit 30Combined Problems on Measure22Section 7Ratio and ProportionUnit 31Ratio23Unit 32Proportion24Unit 33Combined Operations with Ratio and Proportion24

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Section 8FormulasUnit 34Representation in Formulas25Unit 35Rearrangement in Formulas25Unit 36General Simple Formulas26Unit 37Ohm’s Law Formulas27Unit 38Power Formulas28Unit 39Combined Problems on Formulas28Section 9TrigonometryUnit 40Right Triangles29Unit 41Trigonometric Functions30Unit 42Plane Vectors30Unit 43Rotating Vectors31Unit 44Combined Problems in Trigonometry32Unit 45Number Systems32Achievement ReviewsAchievement Review A33Achievement Review B35Answers to Achievement Review A38Answers to Achievement Review B39ivContents

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SECTION 1WHOLE NUMBERSUNIT 1Addition of Whole Numbers1.1,1652.5673.5564.4835.$9516.2,577 ft7.2,380 ft8.840 hp9.615 lb10.4,760 kW • h11.14,839 W12.$20713.47314.350 W15.1,05216.22,750 ft17.3,706 ft1.1,161 ft2.$1523.4554.720 ft5.137 ft6.319 lb7.305 ft8.$2579.20010.289 lb11.1,372 kW • h12.65513.6514.815.221 ft16.127 mi17.10 MΩ18.88 cm’s Guide11.176+264+375+234+116=1,1652.124+72+36+92+38+64+74+67=5673.68+58+89+84+72+59+69+57=5564.56+9+86+36+93+105+42+56=4835.$118+$38+$64+$88+$73+$26+$153+$112+$215+$64=$9516.500 ft+1,200 ft+250 ft+90 ft+38 ft+65 ft+84 ft+225 ft+125 ft=2,577 ft7.625 ft+785 ft+75 ft+140 ft+310 ft+325 ft+120 ft=2,380 ft8.75 hp+30 hp+200 hp+40 hp+25 hp+15 hp+5 hp+125 hp+150 hp+175 hp=840 hp9.35 lb+40 lb+125 lb+200 lb+75 lb+90 lb+20 lb+30 lb=615 lb10.450 kW • h+400 kW • h+420 kW • h+380 kW • h+370 kW • h+320 kW • h+310 kW • h+330 kW • h+380 kW • h+400 kW • h+420 kW • h+580 kW • h=4,760 kW • h11.545 W+650 W+750 W+1,820 W+2,462 W+2,571 W+1,360 W+1,540 W+793 W+1,225 W+330 W+793 W=14,839 W12.$58+$55+$51+$19+$24=$20713.325+45+18+25+30+24+6=47314.150 W+125 W+75 W=350 W15.250+125+65+36+48+96+92+28+42+106+140+24=1,05216.7,500 ft+10,750 ft+4,500 ft=22,750 ft17.1,200 ft+1,150 ft+1,076 ft+180 ft+100 ft=3,706 ftUNIT 2Subtraction of Whole Numbers1.500 ft+250 ft+750 ft=1,500 ft1,500 ft – 339 ft=1,161 ft2.$598 – $263 – $173 – $10=$1523.145 – 35=110565 – 110=4554.45 ft+45 ft+45 ft+65 ft+65 ft+65 ft=330 ft1,050 ft – 330 ft=720 ft5.30 ft+15 ft+8 ft+25 ft+15 ft+20 ft=81 ft250 ft – 113 ft=137 ft6.365 lb+422 lb=787 lb1,106 lb – 787 lb=319 lb7.1,365 ft+830 ft=2,195 ft2,500 ft – 2,195 ft=305 ft8.$76+$105=$181$438 – $181=$2579.59+69+72=200400 – 200=20010.15 lb+6 lb+24 lb+12 lb+3 lb+8 lb+17 lb+32 lb+16 lb+13 lb=146 lb435 lb – 146 lb=289 lb11.1,876 kW • h – 504 kW • h=1,372 kW • h

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12.14+75=89804 – 60=744744 – 89=65513.47+65=112112 – 4=108173 – 108=6514.10+12+20+20=6270 – 62=815.250 ft – 29 ft=221 ft16.134 mi – 7 mi=127 mi17.14 MΩ+25 MΩ+11 MΩ=50 MΩ60 MΩ– 50 MΩ=10 MΩ18.189 cm – 101 cm=88 cmUNIT 3Multiplication of Whole Numbers1.a.3×16=48b.3×21=63c.3×11=33d.2×16=32e.2×21=42f.2×11=222.3.4.5.No. (2,860 turns will not satisfy the required 2,900 turns.)6.16×50 W=800 W9×15 W=135 W12×25 W=300 W6×75 W=450 W4×100 W=400 W2,085 W7.10×150 W=1,500 W8×60 W=480 W=1,980 W8.34 boxes – 23 boxes=11 boxes88 holes+161 holes=249 holes9.2’s Guide1.a.48b.63c.33d.32e.42f.222.324,000 r3.16,412 W4.20,855 turns5.No6.2,085 W7.1,980 W8.249 holes9.$19,60010.1,800 W11.1,940 W12.$66713.220 circuits14.3,815 ft7 people×$18×40 hours=$5,04011 people×$20×40 hours=$8,8009 people×$16×40 hours=$5,760$5,040+$8,800+$5,760=$19,600

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1.47 staples2.a.$3b.$63.5,124 W4.21 rolls5.5 outlets6.13 ft7.21 ft8.65 lb9.8 weeks10.10 coils11.36 lamps12.22 ft13.$314.4 ft15.1,320 W16.$37.5017.30 ft10.2 A×120 V=240 W4 A×120 V=480 W6 A×120 V=720 W3 A×70 V=210 W3 A×50 V=150 W240 W+480 W+720 W+210 W+150 W=1,800 W11.23×40 W=920 W40 lamps – 23 lamps=17 lamps17×60 W=1,020 W920 W+1,020 W=1,940 W12.4×$19=$ 7612×$26=$3129×$31=$279$76+$312+$279=$66713.14.UNIT 4Division of Whole Numbers’s Guide321

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4’s GuideUNIT 5Combined Operations with Whole Numbers1.68+87+57+74+49+101+99+56=5912.120′+327′+637′+302′+500′+250′+140′+75′+789′=3,140′3.30 lb+120 lb+37 lb+125 lb+103 lb+33 lb+210 lb+40 lb=698 lb4.2,569 W+1,260 W+1,639 W+563 W+790 W+800 W+1,137 W+250 W+500 W+750 W+1,830 W+2,462 W=14,550 W5.250′+71′+39′+110′+75′+87′+560′=1,192′6.28+250+38+108+92+130+25+36+97+91+65+40=1,0007.498′+103′+78′=679′679′– 27′=652′8.500 – 127=373373+61=4349.$262+$348+$27=$637$875 – $637=$23810.978 ft+1,023 ft=2,001 ft2,500 ft – 2,001 ft=499 ft11.70(100 W)+38(75 W)+10(60 W)+20(40 W)=11,250 W12.5($15)+4($17)+7($16)=$25513.14.5,127 ft÷250 ft/roll=21 rolls15.16.336 ft÷28=12 ft17.18.1,100 lbs÷20 cartons=55 lb/carton19.315×47=14,805or 124 couplings20.12 ft+1 ft+1 ft=14 ft14 ft+1.5 ft=15.5 ft250 ft15.5 ft=16.13 boxes plus one box at the beginning=17 boxes1.5912.3,140 ft3.698 lb4.14,550 W5.1,192 ft6.1,0007.652 ft8.4349.$23810.499 ft11.11,250 W12.$25513.39214.2115.9116.12 ft17.4,000 ft18.55 lb19.124 couplings20.17 boxes21.a.550 boxesb.75 boxesc.400 outletsd.250 switchese.50 switches

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21.a.(16+6)×25=550 single-gang boxesb.3×25=75 two-gang boxesc.16×25=400 outletsd.(6+2+2)×25=250 single-pole switchese.2×25=50 three-way switchesSECTION 2COMMON FRACTIONSUNIT 6Addition of Common Fractions1.a.10⁄32+12⁄32+24⁄32+7⁄32=121⁄32b.2⁄32+24⁄32+28⁄32+31⁄32=221⁄32c.36⁄48+32⁄48+30⁄48+15⁄48=217⁄48d.14⁄20+16⁄20+15⁄20+6⁄20=211⁄202.3⁄48hp+16⁄48hp+16⁄48hp+8⁄48hp=43⁄48hp3.4⁄8hp+4⁄8hp+6⁄8hp+1⁄8hp=17⁄8hp4.15⁄60Ω+50⁄60Ω+40⁄60Ω+20⁄60Ω+50⁄60Ω+36⁄60Ω+24⁄60Ω+12⁄60Ω=47⁄60Ω5.1⁄64in+2⁄64in+1⁄64in+8⁄64in=3⁄16in6.62⁄64in+1⁄64in+1⁄64in=1 in7.52⁄64in+5⁄64in+6⁄64in+8⁄64in=17⁄64in.8.1⁄64in+8⁄64in+8⁄64+4⁄64in+48⁄64in+56⁄64in=161⁄64in9.1⁄64in+1⁄64+1⁄64in+1⁄64in+4⁄64in+4⁄64in+8⁄64in+8⁄64in=7⁄16in10.26⁄8in+5⁄8in+5⁄8in=4 in11.14⁄16in+14⁄16in+312⁄16+13⁄16in=65⁄16in12.96⁄8in+21⁄8+32⁄8in=151⁄8in13.4⁄64in+32⁄64in+8⁄64in+6⁄64in+3⁄64in+12⁄64in=11⁄64in14.4 cuts for 5 pieces=4⁄16in4⁄16in+714⁄16in+34⁄16in+68⁄16in+122⁄16in+243⁄16in=543⁄16in15.4 cuts for 5 pieces=4⁄8in8⁄16in+14⁄16in+32⁄16in+21⁄16in+124⁄16in+1⁄16in=187⁄8in16.410⁄20MΩ+215⁄20MΩ+18⁄20MΩ=83⁄20MΩ17.62⁄10m+89⁄10m+205⁄10m+83⁄10m=439⁄10mUNIT 7Subtraction of Common Fractions1.10⁄8in – (1⁄8in+1⁄8in)=1 in2.32⁄64in –5⁄64in=27⁄64in3.4⁄32in+3⁄32in+16⁄32in=23⁄32in48⁄32in –23⁄32in=25⁄32in4.11⁄16in+2⁄16in+8⁄16in 15⁄16in.18⁄16in – 15⁄16in=3⁄16in5.4⁄32in+1⁄32in=5⁄32in14⁄32in –5⁄32in=9⁄32in6.4⁄1,000in+8⁄1,000in=12⁄1,000in875⁄1,000in –12⁄1,000in=863⁄1,000in7.59⁄8in – 36⁄8in=23⁄8in8.12⁄1,000in+12⁄1,000in+50⁄1,000in+50⁄1,000in=124⁄1,000in500⁄1.000in –124⁄1,000in=376⁄1,000in9.59⁄64in –58⁄64=1⁄64in10.38⁄64in – (3⁄64in+3⁄64in)=31⁄32in11.268⁄64in – (19⁄64+19⁄64in)=215⁄32in12.156⁄64in –49⁄64in=17⁄64in13.510⁄8mA – 43⁄8mA=17⁄8mA14.1994⁄4ft=463⁄4ft=1531⁄4ft1.a. 121⁄32b. 221⁄32c. 217⁄48d. 211⁄202.43⁄48hp3.17⁄8hp4.47⁄60Ω5.3⁄16in6.1 in717⁄64in8.161⁄64in9.7⁄16in10.4 in11.65⁄16in12.151⁄8in13.11⁄64in14.543⁄16in15.187⁄8in16.83⁄20MΩ17.439⁄10m1.1 in2.27⁄64in3.25⁄32in4.3⁄16in5.9⁄32in6.863⁄1,000in7.23⁄8in8.376⁄1,000in9.1⁄64in10.31⁄32in11.215⁄32in12.17⁄64in13.17⁄8mA14.1531⁄4ft’s Guide5

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UNIT 8Multiplication of Common Fractions1.2.3.4.5.6.7.8.9.10.6’s Guide1.79⁄16lb2.$3803.2557⁄12ft4.831⁄2hp5.26311⁄12ft6.923⁄4hr7.269⁄16kW • h8.100 lb9.5⁄12kg10.31⁄8A

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UNIT 9Division of Common Fractions1.2.3.4.5.6.7.8.9.10.UNIT 10Combined Operations with CommonFractions1.6⁄48hp+36⁄48hp+3⁄48hp+24⁄48hp+16⁄48hp+24⁄48hp+16⁄48hp+12⁄48hp=241⁄48hp2.1⁄64″+4⁄64″+2⁄64″+8⁄64″=15⁄64″3.2(1⁄16″)=1⁄8″4⁄32″+4⁄32″+4⁄32″+1⁄32″+8⁄32″=21⁄32″4.20⁄64″+40⁄64″+10⁄64″+5⁄64″=111⁄64″5.4(1⁄32″)+2(1⁄8″)+2(1⁄4″)=7⁄8″6.1⁄64″+2⁄64″+1⁄64″+2⁄64″+8⁄64″+12⁄64″=13⁄32″7.four saw cuts for five pieces4 (1⁄64″)=1⁄16″314⁄16″+58⁄16″+712⁄16″+92⁄16″+6⁄16″+1⁄16″=2611⁄16″8.98⁄16″+1011⁄16″+69⁄16″+78⁄16″+110⁄16″=357⁄8″9.4⁄8″–3⁄8″=1⁄8″1.82.143.141⁄49W4.85.356.1807.113⁄178.309.$410.731⁄3m1.241⁄48hp2.15⁄64in3.21⁄32in4.111⁄64in5.7⁄8in6.13⁄32in7.2611⁄16in8.357⁄8in9.1⁄8in2112427424014279602735 1527350 t2 n1 t0 n2401fifi×=÷=×===’s Guide7

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10.6⁄1,000″+9⁄1,000″=15⁄1,000″875⁄1,000″–15⁄1,000″=860⁄1,000″11.625⁄1,000″– 2(16⁄1,000″+62⁄1,000″)=469⁄1,000″12.58⁄64″–56⁄64″=1⁄32″13.36(61⁄2′)+9(11⁄12′)+4(6⁄12′)+5(18⁄12′)234′+81⁄4′+2′+71⁄2=2513⁄4′14.12(5⁄8lb)=71⁄2lb15.5(31⁄2′)+8(18⁄12′)=6(30⁄12′)171⁄2′+12′+15′=441⁄2′16.3(71⁄2hp)+4(11⁄2hp)+2(1⁄4hp)+3(1⁄2hp)221⁄2hr+6 hp+1⁄2hp+11⁄2hp=301⁄2hp17.18.9 pieces×2=18 pieces19.20.21.22.371⁄2hr÷71⁄2hr=523.24.25.26.27.28.8’s Guide10.860⁄1,000in11.469⁄1,000in12.1⁄32in13.2513⁄4′14.71⁄2lb15.441⁄2ft16.301⁄2hp17.$96018.1819.$320.3521.1,19341⁄60r22.523.3024.11⁄2kW25.5,000 ft26.62⁄3or 6 whole pieces27.4928.65 hr101321012362 3÷=×=/=6 whole pieces

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1.$286.262.0.463 in3.$60.054.3.046 A5.$82.946.0.026 in7.$122.898.$77.169.9.724 A10.$500.9811.2.312 in12.1.8745 in13.7 in14.2.0222 in15.2.6875 in16.4.7575 cm17.4.635 cm18.900 ft1.1,067.35 kW • h2.215.74 V3.9.12 lb4.1.154Ω5.0.6255 in6.0.75 A7.3.375 in8.0.0025 in9.1.25 in10.2.0625 in11.1.0625 in12.0.375 in13.1.0625 in14.0.03992 in15.larger16.0.01489 in17.#1218.0.00025 in19.0.0035 in20.1.187 ASECTION 3DECIMAL FRACTIONSUNIT 11Addition of Decimal Fractions1.$205.50+$48.38+$32.28=$286.262.0.007 in+0.125 in+0.140 in+0.187 in+0.004 in=0.463 in3.$1.50+$0.65+$1.98+$55.92=$60.054.0.208 A+0.834 A+0.334 A+1.670 A=3.046 A5.$3.98+$1.12+$0.49+$0.57+$0.38+$76.40=$82.946.0.002 in+0.006 in+0.010 in+0.008 in=0.026 in7.$1.43+$0.97+$1.89+$118.60=$122.898.$32.65+$12.56+$24.45+$7.50=$77.169.0.834 A+2.97 A+4.17 A+1.75 A=9.724 A10.$45.50+$165.50+$35.20+$42.75+$65.38+$9.85+$45.60+$45.60+$45.60=$500.9811.0.375 in+0.875 in+1.062 in=2.312 in12.0.3125 in+0.500 in+1.062 in=1.8745 in13.0.75 in+0.500 in+2.625 in+3.125 in=7 in14.0.923 in+1.0992 in=2.0222 in15.0.9375 in+0.875 in+0.875 in=2.6875 in16.4.75 cm+0.0075 cm=4.7575 cm17.4.035 cm+0.3 cm+0.3 cm=4.635 cm18.22.5 ft+8 ft+30.25 ft+22.5 ft+816.75 ft=900 ftUNIT 12Subtraction of Decimal Fractions1.6,336.71 kW • h – 5,269 kW • h=1,067.35 kW • h2.219.7 V – 3.96 V=215.74 V3.11.01 lb – 1.89 lb=9.12 lb4.1.25Ω– 0.096Ω=1.154Ω5.1.9375 in – 1.312 in=0.6255 in6.1.87 A – 1.12 A=0.75 A7.3.9375 in – (0.28125 in+0.28125 in)=3.375 in8.0.037 in – 0.0345 in=0.0025 in9.1.875 in – (0.3125 in+0.3125 in)=1.25 in10.3.1875 in – (0.5625 in+0.5625 in)=2.0625 in11.2.1325 in – (0.375 in+0.375 in+0.25 in+0.25 in)=1.0625 in12.3.000 in – (1.750 in+0.875 in)=0.375 in13.3.375 in – (0.250 in+2.0625 in)=1.0625 in14.0.09074 in – 0.05082 in=0.03992 in15.0.10190 in is larger than 0.08081 in16.0.07196 in – 0.05707 in=0.01489 in17.(#12) 0.08081 in – 0.079 in=0.00181 in(#13) 0.079 in – 0.07196 in=0.00704 inIt is closer to #1218.0.0025 in – 0.00225 in=0.00025 in19.1.000 in – 0.9965 in=0.0035 in20.1.76 A – 0.573 A=1.187 A’s Guide9

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UNIT 13Multiplication of Decimal Fractions1.2.424.32 lb+37.5 lb=461.82 lb3.3.1416×18.5 in=58.12 in4.3.1416×20 in=62.832 in94.248 ft+1.5 ft=95.748 ft5.3.1416×2.375 in=7.461 in6.7.8.9.8,930 kW • h – 8,749 kW • h=181 kW • h10.11.12.13.14.3.1416×5 in=15.708 in3.1416×30 in=94.248 in94.248 in – 15.708 in=78.54 in15.3.1416×6 in=18.8496 in16.17.18.10’s Guide1.$0.1712.461.82 lb3.58.12 in4.95.748 ft5.7.461 in6.0.7065 lb7.15.3615 lb8.26Ω9.$63.3510.$290.6311.$1,194.0312.$962.5013.$4,149.1814.78.54 in15.31.416 ft/min16.$107.8117.37.125 V18.$16,425.45

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’s Guide11UNIT 14Division of Decimal Fractions1.2.3.4.5.6.7.8.9.10.11.12.13.14.1.$1.0662.1.94 A3.0.00256Ω4.$22.505.$0.866.$847.2.40625 in8.$3.1139.180.82 W10.14.0625 V11.$188.5812.1.375 V13.1,676.75 lb14.$1.22

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12’s GuideUNIT 15Decimal and Common Fraction Equivalents1.13⁄8in=1.375 in1⁄16in=0.0625 in1.375 in – 0.0625 in=1.3125 in2.1⁄4in=0.25 in0.25 in – 0.010 in=0.24 in3.33⁄4lb=3.75 lb29.14 lb – 3.75 lb=25.39 lb4.3⁄32in=0.09375 in5.1⁄8in=0.125 in0.125 in+0.006 in=0.131 in6.1⁄32in=0.03125 in0.4365 in+0.03125 in=0.46775 in7.1625⁄1,000=15⁄8in8.11⁄4in=1.25 in1.25 in – 0.008 in=1.242 in1.242 in+2(0.002 in)=1.246 in9.1.375 in=13⁄8in1.250 in=11⁄4in13⁄8in – 12⁄8in=1⁄8in1.1.3125 in2.0.24 in3.25.39 lb4.0.09375 in5.0.131 in6.0.46775 in7.15⁄8in8.1.246 in9.1⁄8in10.1.49875 in by 0.74875 in11.1.753 in12.1.995 in by 0.610 in13.0.258 in14.1⁄1615.0.4325 in by 0.622 in1.0.535 in2.$67.803.2.171 A4.0.09 in5.2.2175 in6.2.3375 in7.3.86 in8.1.5222 in9.3.555 in10.2.5125 in11.8.375 lb12.0.28125 in13.1.5 A14.72.39 lb15.$40.2416.37.6992 in17.$24.5018.26.55 lb19.7.04 in20.0.125 in10.115⁄32in=1.46875 in1.46875 in+2(0.015 in)=1.49875 in23⁄32in=0.71875 in0.71875+2(0.015 in)=0.74875 in11.13⁄4in=1.75 in1.75 in+0.003 in=1.753 in12.2 in – 0.005 in=1.995 in0.625 in – 0.015 in=0.610 in13.21⁄8in=2.125 in2.125 in – 1.609 in=0.516 in14.625⁄10,000in=1⁄16in15.7⁄16in=0.4375 in5⁄8in=0.625 inW=0.4375 – 0.005 in=0.4325 inH=0.625 – 0.003 in=0.622 inUNIT 16Combined Operations with Decimal Fractions1.0.065″+0.150″+0.130″+0.185″+0.005″=0.535″2.$0.65+$0.98+$1.17+$65=$67.803.0.834 A+0.437 A+0.375 A+0.225 A+0.175A+0.125 A=2.171 A4.0.003″+0.065″+0.015″+0.007″=0.09″5.0.305″+0.870″+1.0425″=2.2175″6.2(0.675″)+0.9875″=2.3375″7.7.025″– 3.165″=3.86″8.2.0222″– 0.500″=1.5222″9.3.860″– 0.305″=3.555″10.3.860″– (0.305″+1.0425″)=2.5125″11.15.625 lb – 7.25 lb=8.375 lb12.(3.9375″– 3.375″)÷2=0.28125″13.8.75 A – 7.25 A=1.5 A14.7(9.36 lb)+6.87 lb=72.39 lb15.16.3.1416(12″)=37.6992″17.$980÷40 hr=$24.5018.19.56″– 5(2.75″)=42.25″42.25″÷6=7.04″20.(1.825″– 1.575″)÷2=0.125″

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