Math for the automotive trade

Math

for the

Automotive Trade

FOURTH EDITION

Math

for the

Automotive Trade

FOURTH EDITION

John c. Peterson

Professor of Mathematics (retired)

Chattanooga State Technical Community College

Chattanooga, Tennessee

W illiam J. deKryger

Professor of Automotive Technology

Central Michigan University

Mount Pleasant, Michigan

T H O I V I S O N

DEUVIAR LEARNING

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and Trades:

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T H O I V I S O N

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Matb for the AiitDinotive Tni4e. «h tẩi6om

John c. Peterson and William J. deKryger

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^Contents

P refa ce ..................................................................................................................................................

1 Whole N um bers................................................................................................................ 1

Adding W hole N u m b ers........................................................................................................................................ 1

Subtracting W hole Numbers .............................................................................................................................. 9

M ultiplying W hole Numbers .............................................................................................................................. 15

Dividing W hole N u m b ers..................................................................................................................................... 21

E stim a tin g ................................................................................................................................................................ 21

D iv id in g ..................................................................................................................................................................... 21

Remainders .............................................................................................................................................................. 22

2 Decimals............................................................................................................................ 27

Estim ating Sum s .................................................................................................................................................... 27

Adding D e c im a ls .................................................................................................................................................... 27

k Estim ating D ifferen ces.......................................................................................................................................... 35

" Subừacting D e c im a ls............................................................................................................................................ 35

Estim ating P ro d u c ts ............................................................................................................................................... 39

M ultiplying Decimals .......................................................................................................................................... 39

Dividmg D e c im a ls................................................................................................................................................. 43

3 Fractions .......................................................................................................................... 47

M ixed N u m b e rs ...................................................................................................................................................... 47

Equivalent F ractio n s............................................................................................................................................... 48

M aking Equivalent Fractions .............................................................................................................................. 49

Reducing Fractions ............................................................................................................................................... 49

Comparing Fractions .................................................................................................................... 50

Changing Fractions to D ecim als......................................................................................................................... 50

Addition o f F ra ctio n s............................................................................................................................................ 55

Com mon D en o m in ato rs........................................................................................................................................ 55

Adding F ra c tio n s .................................................................................................................... 55

Subtraction o f F ra ctio n s........................................................................................................................................ 59

M ultiplication o f F ra ctio n s................................................................................................................................... 63

Changing W hole Numbers to Fractions ..................................................................................................... 63

Changing M ixed Numbers to Fractions ................................................................................. 63

Changing Decimals to F ractio n s......................................................................................................................... 63

^ M ultiplying F ractio n s..................................................................................................... 64

Rules for M ultiplying witti Negative N u m b e rs.............................................................................................. 64

Division o f Fractions ............................................................................................................................................. 69 .

Reciprocals .............................................................................................................................................................. 69 f

Dividing F ra c tio n s .................................................................................................................................................. 69

Rules for Dividing with Negative Numbers ................................................................................................... 70

4 Geometry, Angle Measurement, and the Metric System .............................................. 73

A n g le s ........................................................................................................................................................................ 73

D e g r e e s ..................................................................................................................................................................... 73

M easuring Angles ................................................................................................................................................. 74

Fractional Degrees and M in u te s......................................................................................................................... 75

Adding Angular M easurements ......................................................................................................................... 76

Subtracting Angular Measurements ................................................................................................................. 76

Cừcular Measures ................................................................................................................................................. 81

C ircum ference........................................................................................................................................................ 81

Arc L engứ i................................................................................................................................................................ 82

A r e a ............................................................................................................................................................................ 82

C y lin d e rs.................................................................................................................................................................. 82

Volume .................................................................................................................................................................... 83

The Mettic S y stem ................................................................................................................................................. 87

Units of M e a su re ................................................................................................................................................... 87

W iitmg M e ttle s ...................................................................................................................................................... 88

Changing Between the Mettic and Customary S y s te m ............................................................................... 88 ^

5 Integers and Signed Numbers......................................................................................... 95

Adding Signed Numbers .................................................................................................................................... 95

Subtracting Signed Numbers ............................................................................................................................. 103

6 Ratios, Proportions, and Percentages............................................................................. 107

Ratios ...................................................................................................................................................................... 107

SimpUfying R a tio s ................................................................................................................................................. 107

Rates ......................................................................................................................................................................... 109

Proportions ............................................................................................................................................................. 113

Solving P ro p o rtio n s.............................................................................................................................................. 113

Dừect Proportions ................................................................................................................................................. 113

Inverse or Indữect Proportions........................................................................................................................... 114

Percentages ............................................................................................................................................................. 11 7

Changing Percents to Decimals ........................................................................................................................ 11 7

Changing Decimals to Percents ........................................................................................................................ 11 7

Changing Percentages 10 F ractions.................................................................................................................... 118

Changing Fractions to P ercentages.................................................................................................................... 118

Solving Percentage P ro b lem s........................................................................................................................ 118

D iscounts............................................................................................................................................................... 125

Profit. I.OSS. and rnm m kiinnc n o ể

Contents vií

Interest and Payments ...........................................................................................................................................

In te rest........................................................................................................................................................................

P a y m e n ts...................................................................................................................................................................

139 T a x e s ...........................................................................................................................................................................

Em ployee T a x e s .......................................................................................................................................................

Em ployer T a x e s .......................................................................................................................................................

Property T a x e s ......................................................................................................................................................... 140

7 Completing Repair O rd e rs..............................................................................................

8 The Automobile E ngine.................................................................................................... 153

9 Automobile Engine Systems ............................................................................................

10 Automobile Electrical Systems ........................................................................................ 187

11 The Automobile Drive T ra in ............................................................................................ 201

12 The Automobile Chassis .................................................................................................. 215

13 Automobile Heating, Ventilation, and Air Conditioning .............................................. 233

14 Measurement T ools.......................................................................................................... 247

Digital M eters ......................................................................................................................................................... 247

Scale M easurement ............................................................................................................................................... 253

Analog M e te r s ......................................................................................................................................................... 259

Dial In d ic a to rs......................................................................................................................................................... 265

M icrom eters.............................................................................................................................................................. 271

Drill Sizes ................................................................................................................................................................ 277

Appendix A — Pages from Specification M anuals............................................................... 283

Buick Specifications ............................................................................................................................................. 283

Nissan Specifications............................................................................................................................................. 284

Ford Specifications ............................................................................................................................................... 286

Dodge S pecifications............................................................................................................................................. 288

Porsche S p ecificatio n s.......................................................................................................................................... 291

Corvette Flat Rate M a n u a l................................................................................................................................... 296

Appendix B — Summary of Formulas in this Text-Workbook.......................................... 315

Appendix c — Answers to Odd-Numbered Practice Problems ........................................ 319

Index .................................................................................................................................................... 333

Math fo r the Automotive Trades, 4th Edition, is a text-woikbook ứiat provides the automotive technology student with

examples and problems encountered in this occupation. This edition has been revised to reflect technological require￾ments of workers in automotive technology. The text has three parts. The first part. Chapters 1-6, reviews basic mathe￾matics and measurement skills. The second part. Chapters 7-13, applies the basic mathematics skills to specific auto￾motive situations. This part begũis with a chapter OD “Completing Repaữ Orders.” Repaứ orders are used throughout

the remaining chapters. The thữđ part. Chapter 14, examples measurement aspects of both analog and digital measure￾ment tools used in the automotive trades.

Changes specific to this revision are as follow:

• Applications and examples were updated to reflect changes in automotive technology. In particular, some of the

information about analog meters was either reduced or eliminated and the carburetor specification charts were

deleted.

• The chapter “Geometry, Angle Measurement, and the Metric System” was moved from Chapter 13 to Chapter 4.

• More iníonnatíon on circular measures, cừcumíerence, area of a ckcle, and volume of a cylinder, have been added

to the Geometry chapter.

• Four sections dealing with personal and business finance were introduced in Chapter 6. These four sections are

Discounts

Profit, Loss, and Commissions

Interest and Payments

I Taxes

• The appendices have been changed by adding the following:

New pages from the Corvette flat-rate manual

New and/or revised tables from auto manuals

• Critical thinking skills have been woven into the lessons.

• Additional chapter tests are included in the Instructor’s Guide.

The authors wish to thank the following people for theừ contributions and guidance:

Randy Bealt, Service Dữector, Beaty Chevrolet Co., Knoxville, TN

R. A. Buckholz, Pinelias Vocational Technical Institute

Carl w. Cavilo, Consumnes River College

Dell Cooper, Skyline College

Robert w. Hawfield, Chattanooga State Technical Community College

Edna Mosley, Lincoln Technical Institute

Ed Peữunak, New Castle School of Trades

Pat Peinardy, Chippewa Valley Technical CoUege

Roger E. Shanks, John H. Hinds Vocational/Technical School

Charles Statz, Temple Junior College

This edition is the product of refinement over the course of three previous editions plus ửiẾ eflforts of the reviewers who

made specific suggestions for improvÌDg the fouiứỉ edition. The authors would like to thank all of the reviewers, stu- M

dents, and insứuctors who have commented on the previous edition, and especially the followmg individuals who con* "

tiibuted ứieữ time aod effort to ửie fourth editíon:

Gabriel Murphy Mark Robinson

Triton College Triton College

River Grove, niinois River Grover, Illinois

Brian Campbell Jack Cheek

Iowa Lakes Community College Lancaster City School

Emmetsburg, Iowa Lancaster, Ohio

Anthony Allegro

Lincoln Technical Institute

Union, New Jersey

Additional thanks are extended to those individuals whose thorough review of the manuscript helped create a textbook

that is both technically accurate and complete:

Linda WiUey

Clifton Pari^ NY

About the Authors

John c . PetersoD is retired from Chattanooga State Technical Community College (CSTCC), Chattanooga, Tennessee,

where he was a Professor of Maihematics. Earlier in his career he was a Senior Research Specialist al the National Center

for Research in Vocational Education at The Ohio State University. In his professional dudes he has served as a Vice ấ

President of the American Mathematical Association of Two-Year Colleges (AMATYC) and is cuưeDtly the Production *

0Ĩ The AMATYC Review. In 1995 he received the Teaching Excellence Award from CSTCC. He has had over 80

articles published in various professional journals and has authored or co-authored several college-level texd>ooks.

WiUiam J. deKryger is ASE certified as ã Master Technician and is a member of the Society of Automotive Engineers.

He began his career working as a professional technidan in Grand Rapids, Michigan, Hollywood, CaUfomia, and

Honolulu, Hawaii. He is currently a member of ứie Department of Engmeering and Technology and the Professor of

Automotive Technology at Central Michigan University. Oứier professional responsibilities include: Expert Witness for

automotive cases; Automotive A ib itr^ r for ứie National Center for Dispute Settlement; annual Study Abroad Group

Leader to Vladimữ State University, Vladiimr, Russia; and annual Visiting Professor of Automotive Technology to

Instituto Tecnologico Y de Estudios Superiores de Monterrey. Campus Toluca, Mexico.

If you have any comments or coưectioDs, you may contact the auửiors at MaihAutnTrarift@cnmcasLneL

Whole Numbers

Objectives: After studying this chapter, you should be able to

• Add, subtract, multiply, and divide whole numbers.

• Apply the basic mathematics operations of whole numbers to solve practical problems.

• Determine total costs related to repair and maintenance.

• Calculate trip distance, fuel consumption, and fuel economy.

• Determine costs related to buying, selling, and insuring a car.

• Determine component inventory volume and production requừements.

I • Determine weights of automobiles and automotive components.

W

hole numbers are numbers such as 14, 57,

and 832. Each digit has a different value

depending on its location in the whole num￾ber. In the whole numbers 14, 57, and 832,

the 4,7, and 2 are in the ones’ place of each number. In a

decimal, such as 23.47, the number just to the left of the

decũnal point is in the ones’ place. You could write each

whole number with a decimal point. Therefore, you could

have written 14., 57., and 832. for the above numbers.

The position just to the left of the ones’ place is the

tens’ place. In the numbers 14, 57, and 832, the 1, 5, and

3 are all ÍD the tens’ place.

The thừd position left of the decimal place is the hun￾dreds’ place. The 8 in the number 832 is in the hundreds’

place.

Each digit in a whole number has a place value. The

chart below shows some of the names of the places for a

whole number with 7 digits.

7. 9

Large numbers may be written either with a space or

a comma separating every third numeral. Hence, the

number above could have been written as 7 984 365 or

as 7,984,365. Large Dumbers are usually written with

spaces instead of commas when the metric system of

measurement is used.

Adding Whole Numbers

In order to answer a question like the following, you must

be able to add whole numbers.

A new automobile has a basic price of $14,674. For

power sunroof, add $732; for California emission con￾ưol, add $93; for a cellular phone, add $434. Destination

charges are $525. What is the total price of the new car

before taxes?

When adding whole numbers, first write the num￾bers so that the numbers in the ones’ place are all in the

same column, the numbers in ihe tens’ place are in

the same column, and so on. Then add the numbers in the

ones’ colunm, then ứie numbers in the tens' column, and so

on. The answer to an additional problem is called ữie sum.

1

2 Chapter 1 ■ Whole Numbers

■ EXAMPLE 1-1

Find the sum of 214 + 2 + 53.

2 1 4

2

+ 5 3

Step 1 Write numbers widi digits in the ones’ place in

the same column.

2 1 4

2

+ 5 3

4 5 Ă

+ 2 8 ^

7 3

Step 3 Add the digits in the tens’ column. Thus, the

sum of 45 and 28 is 73.

■ EXAMPLE 1-3

Add 4568 + 927.

Solution

4 5 6 8

+ 9 2 1

Step 2 Add the digits in the ones’ place. Step 1 8 + 7 = 15. Carry the one to the tens’ column.

2 1 4

2

+ 53

6 9

Step 3 Add the digits in the tens’ place.

4568

927

9 5

Step 2 1 + 6 + 2 = 9, so no number needs to be carried.

2 1 4

2

+ 53

2 6 9

Step 4 Add the digits in ứìe hundreds’ place. The sum

is 269.

4 5 6 8

h 9 2 7

Step 3 5 + 9 = 14. Carry the one to the thousands’

column.

If ứie sum of the digits in any colunm is more ứian 9,

you will have to carry part of ứie sum to the next column.

■ EXAMPLE 1-2

Add 45 + 28.

4568

+ 927

Step 4 Add ứie digits in the ữiousands’ column.

Therefore, the sum of 4568 and 927 is 5495.

S te p l

4 5

+ 28

■ EXAMPLE 1-4

Find the sum of 7805 + 2041 + 926.

Solution

45

+ 28

7 8 0 5

2 0 4 1

h 9 2 6

step 2 Since 8 + 5=13, cany the 1 to the tens’ column. Step 1 The sum of the digits in the ones’ column is 12. I

ị 7805

f 204 1

+ 926

7 2

Step 2 l + 0 + 4 + 2 = 7. No number needs to be

carried.

Chapter 1 • Whole Numbers 3

2 1 2

4 3 7

28

7 4 1

+ 2835

404 1

The sum is 4041.

7805

2041

+ 926

772

Step 3 The sum of 8 + 0 + 9 = 17. Caưy die 1 to the

thousands’ column.

■ EXAMPLE 1-6

Find the sum of 25 354 + 48 + 9784 + 129 + 97.

Solution

Remember. 25 354 means the same as 25,354. Here we

wiU write 9784 as 9 784.

7 8 0 5

2041

+ 92 6

1 0 7 7 2

So, the sum is 10,772.

■ EXAMPLE 1-5

Find the sum of 437 + 28 + 741 + 2835.

Solution

2

4 3 7

2 8

7 4 1

+ 2 8 3 5

1

Step 1 The sum of the digits in the ones’ column is 21.

Cany the 2 to the tens’ column.

I 2

4 3 7

28

7 4 1

+ 2835

4 1

Step 2 The sum of the digits in the tens’ column is 14.

Cany the 2 to the hundreds’ column.

2 I 2

4 3 7

28

7 4 1

+ 2835

2 5 354

48

9 7 84

129

+____ ^

2

Step 1 The sum of the digits in the ones’ column is 32.

Carry the 3 to the tens’ colunm.

3 3

2 5 3 5 4

4 8

9 7 8 4

1 2 9

+ 9 7

1 2

Step 2 The sum of the digits in the tens' column is 31.

Carry the 3 to the hundreds’ column.

1 J 3

2 5 3 5 4

4 8

9 7 8 4

1 2 9

+ 9 7

4 1 2

Step 3 The sum of the digits in the hundreds’ column i;

14. Carry the 1 to the thousands’ column.

11 3 3

2 5 3 5 4

4 8

9 7 8 4

1 2 9

+ 9 7

0 4 1

Step 3 The sum of (he digits in the hundreds’ column is

20. Cany the 2 to the thousands’ column.

5 4 12

Step 4 The sum of the digits in the thousands’ column

is 15. Cairy the 1 to the len-ửiousands’ column.