Practical math applications 3e by burton

Practical math applications 3e by burton Practical math applications 3e by burton Practical math applications 3e by burton Practical math applications 3e by burton Practical math applications 3e by burton Practical math applications 3e by burton Practical math applications 3e by burton Practical math applications 3e by burton Practical math applications 3e by burton v

Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States

Sharon Burton

Brookhaven College Dallas, Texas

Nelda Shelton

Tarrant County College Fort Worth, Texas

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Chapter 1 Basic Math Functions 2

Chapter 8 Invoices and Discounts 260

Chapter 10 Interest 324

Chapter 12 Metrics and Currency 392

Answers to Selected Exercises 424

Index 444

III

Focus on the Basics

Practical Math Applications, 3e applies a straightforward, easy-to-understand

approach to reviewing basic math competencies necessary for life and work This new edition has a brand new look that will engage students right from the start and keep them focused on the essential objectives

Math @ Work features an interview with a career professional that connects math concepts to the real world

Apply Math @ Work activities provide real world connections and practical applications

Chapters are divided into bite-size sections

298

M t W r

Courtesy o

f Kevin Ne

ihaus

Kevin Neiihaus is an accounting associate in the evin Nei

ng and Communications department at a Marketin

’s hospital It is his responsibility to forecast,

e expenses of his department, creating new

be projecting the olicies and procedures, working with vendor departmental po rs,, rove processes that his department uses in d

or trying to imp prove processes that his department uses in d daiily dai operation He sa aid, “It is my goal to make sure my department en runs well, and w we have money to do what needs to be done.”

Kevin know ws that hearing the term “accounting” makes people think of

ng oversitting at a desk doing the same thing over a d and over He said, “M My job is actually filled with changing variablees ble

i

I often have to cconsider many different possibilities and

condi-en tions to formula ate an idea of how the money will be or has bee spent Every day y brings something new.”

How Math is Used in Accounting

a budget, Kevin uses equations to create and When planning

artment’s future expenses This allows him project the depa

much money his department will need in the

to predict how m evin also uses math to calculate exactly how coming year Ke

much a newslett ter his department is creating will cost He said d,

“It is important to know how much each copy of the newslette to know how much each copy of the newslette er

d will cost Addin ng up the costs of producing the newsletter and

t dividing them b by the number we are producing tells me what

a single print wiill cost I then multiply that figure with the number of newssletters we plan on producing to estimate how

to much I should b budget This planning allows my department t produce great publications that patients and families want to read while stayiing within our budget.”

What Do You Think?

What skills do y you need to improve in order to work in accounting?

Math Skills Used

Ad ddition Subtraction

Mu ultiplication Sta atistics Perrcents

Other Skills Needed

Co ommunication Intterpersonal skills

Mu ulti-tasking Org ganizational skills

ACCO U N T I N G

A S S O C I AT E

299

A P P LY ACCO U N T I N G M t W r A S S O C I AT E Math is used in various ways by store owners and their accountants, managers, retail buyers and other retail employees Consider that people working in retail need to know basic skills, such as addition, subtraction, multiplication and division However, more complex tasks in retail require more advanced math skills, such as using equations and formulas to calculate gross profit margins, cash flow, and profitability

You are a new accounting associate and have been asked to apply markdown in the following situation Your store received 150 vests Toward the end of the season, 137 vests had been sold at

$32.00 It has been decided to mark down the remaining vests to $24.99 Suppose that within two weeks, the remaining vests sold at $24.99, the reduced price Calculate the percent of expected total sales the markdown cost the store.

1 Calculate the expected total sales.

2 Determine the markdown for 13 vests.

3 Calculate the percent of expected total sales the markdown cost the store.

IV

Strong, well-defi ned organization brings key concepts and ideas to students’ attention

Chapters are divided into bite-sized sections

Exercises apply key concepts immediately, giving students feedback and building confi dence along the way

Worked out, clear examples

build student confi dence

by illustrating step-by-step procedures

Terms are highlighted and defi ned

Objectives are clearly stated to guide learning

Selling price(also ( l retail price il i ) is what the customer pays The ) i h h Th cost is what i h

he retailer pays to the manufacturer The difference between the cost and the t

selling price is

(also

an item may be marked up by $23.67 or by 30% The markup rate can be calculated either on the selling price or on the cost.

b ic c c pri pr pri r cin c in g v g vari ari ables e es es s s s.

3 Cal Calcul cul cu cul culate ate ate th th th t e s e s sell ell el l ing ing pri

price, ce, ce ma ma ma marku rkup a p a p p mou m o nt tt, t,

or r

or cos co t w w hen an a y t y wo w

or or o

or cos o t w w hen hen an an an y t y two wo wo wo o

n.

of

of the tth th th th h ree ree e ar ar ar ar are k e k e now no n

OBJECTIVE 3 C C alculate t t t he s s s el e el e ling p p ri r ri r ce c ce , ma rk rk k up a a mo m mo unt, t t, t

or o

or c c os o os t t when e a a a a ny n ny t t t tt wo o o o f the e th th th h h re r e e e e are e known n n.

Calculating Selling Price

Add cost and markup to obtain selling price.

Cost + Markup = Selling Price

$17.40 + $8.00 = $25.40 selling price

OBJECTIVE 2

The fundamental purpose of a business is to make a profit A retail business

sells goods and services for an acceptable price that is sufficient to cover all

expenses and to provide the company with a reasonable profit Pricing goods

is based on an equation that the selling price of an item is equal to the cost

NEW Four Step Problem Solving Plan helps students solve word problems.

Abundant Exercises for Each Concept

Example

Phillip Fontano earns $2,345 a month He spends one-fifth of his monthly

salary for rent How much does he pay each month for rent?

Steps

When a math problem uses the word of, as in “He spends one-fifth of ff

his monthy salary,” the word of means to multiply f

Problem Solving Plan

To determine the rent, multiply 1 @

5 2,345 1

1 @= $469 Conclusion Did you answer

the question the problem is asking?

Solve Perform the steps in the action plan

Clues Look for facts What is the problem asking or what are you trying to fi nd?

Action Plan Identify the steps

to take in the appropriate sequence

D Solve the following word problems Round answers to the nearest cent OBJECTIVES 1, 2, 3

29.You are asked to verify an invoice that totals $718.12 before your company pays

it The net price of the merchandise is $635.29; the sales tax rate is 6.5%; and the shipping charge is $39.

a Is the invoice amount correct?

b If not, what error was made, and what should the total amount be?

c.What was the amount of the sales tax?

30.In Exercise 29, the terms of payment are 2/10, n/30.

a What is the amount of the cash discount if paid within the discount

period?

b What is the total payment amount?

31.You are preparing an invoice for a customer whose purchase lists for $337.50.

The customer is entitled to a trade discount of 10/5; the payment terms are 3/15, n/45; and the sales tax rate is 6% What should be the total amount

of the invoice?

32.Marisa Tallifero bought a cordless phone priced at $49.99 It was subject to 8.75% sales tax What was the sales tax?

What was the total amount Marisa paid for the phone?

33.Jerry Hutchins purchased an assortment of holiday paper His purchases the sales tax?

34.Penny Holcomb purchased pen and pencil gift sets to give to her employees for the holidays The total bill was $103.92, which included the sales tax

of 6.5% How much was the actual selling price?

What was the amount of the sales tax?

35.For his party, Bobby bought 4 cans of gourmet popcorn and paid $19.96

The tax was 6.2% How much was the actual selling price?

What was the amount of the sales tax?

36.The amount of a sale is $479.50 and the sales tax rate is 7.25% How much is the sales tax?

What is the total selling price?

37.A printer is priced at $524 If a sales tax of 8 1 @

2 % is charged on the printer, what is the total selling price?

8.5 Sales Tax 285

DirectionsSolve the following problems.

A Complete the following OBJECTIVE 1

1 A sales tax is calculated on all sales True or False?

2 When calculating a cash discount, you multiply the total amount of the invoice by the discount rate True or False?

B Find the sales tax and the total amount due on these invoices OBJECTIVE 1 Round answers to the nearest cent.

VI

Conceptsprovide specifi c steps and examples for easy review

Key Termsare listed for ready reference

Quiz is a quick

meaningful review for the chapter test

Review Exercises

focus on each objective

Chapter Review and Assessment

KEY TERMS

adjusted gross income adjustments to income alternative minimum tax assessed rate assessed value assessor earned income tax credit escrow account estimated tax payments exemptions

Federal Unemployment Tax Act (FUTA)

Health Savings Account (HSA) individual retirement account (IRA)

itemized deductions levied market value mill personal property

property tax real property standard deduction State Unemployment Tax Act (SUTA)

tax tax credits tax rate taxable income total income

6.1 Calculate the tax levied on property based

on the assessed value.

Dollars per $100

1 Multiply the market value of the property by the

assessed rate.

2 Determine the number of $100s in the assessed value.

3 Multiply the number of $100s by the tax rate to determine

the amount of tax due.

Dollars per $1,000

Mills per dollar of assessed value

1 Convert mills to dollars.

2 Multiply the assessed value by the tax rate in dollars.

Assessed value is 60% of market value; Tax rate is

$3.80 per $100; Market value is $130,000.

$130,000 × 60% = $78,000 assessed value

$78,000 ÷ $100 = 780

780 × $3.80 = $2,964 property tax due

Dollars per $1,000 works the same, except determine the number of $1,000s in the market value instead of the number of $100s and then follow the steps above.

Assessed value is $126,000; Tax rate is 32 mills.

32 mills ÷ $1,000 = $0.032

$126,000 × $0.032 = $4,032 property tax due

6.1 Calculate the tax rate levied on property based on the assessed value.

1 Determine the amount of money needed.

2 Divide the amount of money needed by the total

assessed value.

$50,000,000 Assessed value: $5,000,000,000

$50 million ÷ $5 billion = 0.01 or 1%

224 CHAPTER 6 TAXES

Chapter 6 Review Exercises

DirectionsWrite your answers in the blanks provided Round dollar amounts to the nearest hundredth.

A Determine the amount of tax due in the following problems 6.1 OBJECTIVE 2

Market Value Assessed Value Tax Rate Tax Due

1. $80,000 75% $2.95 per $1,000

2. $110,000 60% $5.45 per $100

3. $200,000 100% 12 mills

B Complete the following problems to compute the tax rates Round your 6.1 OBJECTIVE 3

answers to the nearest whole percent.

Money Needed Assessed Value Tax Rate

4. $5,500,000 $225,000,000

5. $946,245 $19,050,000

C Complete the following problems to compute state unemployment tax 6.2 OBJECTIVE 2

for one employee Assume a tax rate of 3% on the first $9,000.

6. $4,300 gross wages tax due 7 $12,000 gross wages tax due

8. $15,825 gross wages tax due 9 $8,900 gross wages tax due

D Compute federal unemployment tax Use 0.8% as the tax rate Assume all 6.2 OBJECTIVE 3

wages subject to tax.

10. $42,000 gross earnings tax due 11 $58,942 gross earnings tax due

12. $18,296 gross earnings tax due 13 $96,500 gross earnings tax due

E Compute federal income tax as you would on Form 1040EZ 6.3 OBJECTIVES 2,3

JoAnn White is single and earned $19,500 in wages and $560 in interest from her savings account JoAnn has no exemptions other than herself Compute JoAnn’s tax.

Total income $19,500

14. Adjusted gross income

Less standard deduction (single) $ 5,450 15. Taxable income

16. Federal income tax (single, from tax table)

Income tax withheld $ 1,005 17. Federal income tax due

226 CHAPTER 6 TAXES Name Date Score DirectionsSolve the following problems Place your answers in the blanks provided. A Compute the amount of property tax due Round dollar amounts to 6.1 OBJECTIVE 2 the nearest hundredth Market Value Assessed Value Tax Rate Tax Due 1. $145,000 65% $2.35 per $1,000 = 2. $90,000 80% $3.35 per $100 = 3. $365,000 100% 9 mills per dollar = B Compute the property tax rate 6.1 OBJECTIVE 3 Money Needed Assessed Value Tax Rate 4. $240,000 $1,500,000 = 5. $7,500,000 $250,000,000 = C Complete the following problems to compute state unemployment tax 6.2 OBJECTIVE 2 for one employee Assume a tax rate of 3% on the first $9,000 6. $10,356 gross wages = tax due 7. $6,555 gross wages = tax due D Compute federal unemployment tax Use 0.8% as the tax rate Assume 6.2 OBJECTIVE 3 all wages subject to tax Round dollar amounts to the nearest hundredth 8. $6,123 gross wages = tax due 9. $18,752 gross wages = tax due E Compute federal income tax as you would on Form 1040EZ Kristen is 6.3 OBJECTIVES 2,3 single Her total income was $21,000 in wages and $350 in interest from her savings account Kristen has no exemptions other than herself Compute her tax. Total income $21,000 Plus interest income (savings account) $350

10. Adjusted gross income

Less exemptions (1)

11. Taxable income

12. Federal income tax (single, from tax table)

$1,709 13. Federal income tax due/Refund due

Q U I Z

232 CHAPTER 6 TAXES

VII

Crunch the Numbers Makes Calculations Easy

common consumer issues and helps students understand the math

Write about Math provides opportunities to write about math concepts students are studying

How much do you really know about your bank account?

1 What service charge amounts are charged, if

any, on a personal checking account? If there are choices or conditions, indicate what they are.

2 What does the bank charge for an

insufficient-funds check? What rules are followed, if any?

3 How can a customer get a copy of a check if the

bank doesn’t return checks and is there a charge?

9 Doe

Wha com prov

10 Doe

acco num Wh

How your checking account works is one of the first things you should learn when you open your account

For instance, you need to learn how to write paper checks, make cash withdrawals at the bank or from an automated teller machine (ATM), or pay with a debit card Your paycheck might go by “direct deposit” into your account, or you might deposit checks at the bank’s teller window, through drive-through banking, or at an ATM You also need to learn how to deposit funds, how

to get additional funds when you make a purchase, how

to pay a bill, how to monitor your account, and how to avoid overdrafts You might already know the basics;

however, there is more information you need to know about your banking experience that will save you money.

Call a local bank (main bank or any branch), savings &

loan, or credit union and obtain the following mation about their checking accounts You may find the bank will mail you a brochure that has most of the information in it, or you may visit the bank and pick up the information Answer the following questions

infor-nager and are considering opening a small retail store Last week you attended a seminar for potential small business retailers and were presented with the following questions that are related to price-setting To develop your own understanding for price-setting, answer the following questions

1.When pricing, what operating costs must you consider? In addition to your earnings and your employees’ earnings, identify other operating costs?

2.When marking up your merchandise, will you use markup based on cost or markup based on selling price?

Compare the two methods presented in section 9.3 Also, consider the following: which one is larger—a 35%

markup on cost or a 30% markup on selling price Determine the price and cost of an item and work the math

3.Will your customers consider your prices fair? What does fair mean to you as a customer? From an owner’s tive, what does fair mean?

perspec-4.Will you allow customers to bargain over the prices of any items? What if a customer brings in an ad that reads “we’ll meet competitors’ prices”? Will you meet competitors’ prices?

Suppose you have been working in retail since you were a teen

Calculating with a percent is a two-step process You must change the percent to a decimal by dividing by 100 Then, use that decimal as a factor for multiplication All and memory keys, and calculate a percent in a single step.

When you use a percent key on a calculator, it serves as the equal key, while at the same time divides by 100 Percent problems are presented in two formats:

t
UIF
XIPMF
BNPVOU
BOE
UIF
QFSDFOU
BSF
HJWFO
⇒ multiply to find the part of the whole amount.

t
UIF
QBSU
BOE
UIF
QFSDFOU
BSF
HJWFO
⇒ divide to find the whole amount.

For most calculators, the [%] is used in place of the [=] key

Example

The numbers given in the problem are the whole amount and the percent

Multiply the whole amount by the percent Use the [%] key.

The number shown is 6.25% of $70 You need to round the number in the display to the nearest cent The sales tax on the $70 coat was $4.38.

Example

The % Key on a Calculator

A spreadsheet is a software application that contains worksheets with colu based on formulas built into the program and also formulas created by the Columns are labeled with letters, and rows are labeled with numbers T

intersection of a column and row is a cell, which is identified by the letter o

column and number of the row

A spreadsheet is useful for business-related tasks such as calculating w employees at a company By changing a formula or by changing the data u formula, you can quickly calculate large quantities of data

The following will guide you through the steps to create a spreadshee computing hourly wages

Open a new spreadsheet Click in cell A1 and type Name Use the arrow

to cell B1, and type Hourly Rate In cell C1 type Hours, and in cell D1, type Gro Enter the name of four employees in cells A2 through A5: Jane, Tyrone, Si, an

Payroll On a Spreadsheet

Press [M+] to save this number in the memory

Notice the M on the left side of the display

[179452] [–] [MRC] [=] The display will show The amount of donations in May total $164,916.39.

Perfo rfo rm th rm e indicate cate d operat ra tio n Round t o the nearest cent.

5.$1,34 1.82 1 is wh h at pe at percent rcent of $ o 2,738.40? 6 $9,792 is 15% of w what?

7.$580 80 is 37 is 3 % of what? hat? 8 $99 is what perceent of $113.85?

9 160% % of $1 of $ 5,899 is w w hat? 10 8.75% of $199 is wwha t?

Crunch the Numbersincludes activities for handheld and online calculators and for spreadsheets to provide students information about using calculation tools

Numbers on a Calculator 46Fractions on a Calculator 92The % Key on a Calculator 126Balance Your Checkbook Online 156Payroll on a Spreadsheet 194The IRS Website 230

Life Insurance Estimator 256Purchase Orders and Invoices 294Markups and Markdowns 320Simple, Ordinary, and Exact Interest 358Mortgage Calculator 388

Convert Units of Measure 420

VIII

NEW CourseMaster for Practical Math Applications

CourseMaster for Practical Math Applications is an online homework

product that increases your student’s engagement in your course through motivating, interactive features Feedback is instantly available

to keep students motivated, moving forward, and well on their way to successfully mastering the concepts

CourseMaster for Practical Math Applications includes:

Interactive online eHomework solution or grader

• Interactive eBook

•

www.cengage.com/businessmath/burton/pma3e

Practical Math Applications 3e off ers a feature-packed website with

tools and activities that will enhance the mastery of basic math competencies

Student Resources

FlashcardsCrossword puzzlesChapter quizzesWeb linksand more

Instructor Resources

PowerPoint slidesTest bankswww.cengage.com/burton/businessmath/burton/pma3

IX

Chapter 1 Basic Math Functions 2

1.1 Numbers 4 Objectives: Identify terms used with the decimal number system 4 |

Exercises 7

1.2 Addition 9 Objectives: Identify terms used with addition 9 | Align numbers correctly for

1.3 Subtraction 17 Objectives: Identify terms used with subtraction 17 | Subtract vertically 17 |

1.4 Multiplication 25 Objectives: Identify terms used with multiplication 25 | Multiply whole

Exercises 29

1.5 Division 32 Objectives: Identify terms used with division 32 | Divide whole numbers 32 |

Chapter 2 Fractions 50

2.1 Fractions and Mixed Numbers 52

Objectives : Identify terms used with fractions 52 | Distinguish between

X

Add and subtract like fractions 65 | Find the least common denominator 66 |

2.3 Multiply and Divide Fractions and Mixed Numbers 76

Objectives: Multiply fractions 76 | Use cancellation 77 | Multiply whole

Chapter Review and Assessment 84 Key Terms 84 | Concepts and Examples 84 | Review Exercises 87 | Quiz 94

Features

Math @ Work: Chef 51 | Apply Math@Work: Chef 90 | Write about Math 90 |

Personal Finance: Do you use your budget to manage your money? 91 | Crunch the Numbers: Fractions on a Calculator 92

3.1 Introduction to Percents 98

Objectives: Identify terms used with percents 98 | Write a percent as a

3.2 Part, Rate, and Base 103

Objectives: Identify the terms part, rate, and base 103 | Find the part 104 |

3.3 Percent of Increase and Decrease 111

Objectives: Identify terms used with percent of increase and percent of

Chapter Review and Assessment 118 Key Terms 118 | Concepts and Examples 118 | Review Exercises 121 | Quiz 128

Features

Math @ Work: Real Estate Agent 97 | Apply Math@Work: Real Estate Agent 124 |

Write about Math 124 | Personal Finance: How much are higher prices costing you? 125 | Crunch the Numbers: The % Key on a Calculator 126

XI

Objectives : Identify terms used with checking accounts 132 | Identify checking

Exercises 140

4.2 Bank Statement Reconciliation 143 Objectives : Understand why a checking account must be reconciled 143 |

Chapter Review and Assessment 150 Key Terms 150 | Concepts and Examples 150 | Review Exercises 151 | Quiz 158

Features

Math @ Work: Bank Services 131 | Apply Math@Work: Bank Services 154 | Write about Math 154 | Personal Finance: How much do you really know about your bank account? 155 | Crunch the Numbers: Balance Your Checkbook Online 156

Chapter 5 Payroll 160

5.1 Gross Earnings 162

Objectives : Identify terms used for computing gross earnings 162 | Calculate

5.2 Gross Pay for Various Compensation Methods 167

Objectives : Identify terms used for various compensation methods 167 |

Exercises 169

5.3 Payroll Deductions 171

Objectives : Identify terms used for payroll deductions 171 | Calculate

5.4 Employee’s Earnings Record and Payroll Register 181

Objectives : Create an employee’s earnings record 181 | Create a payroll

XII

6.1 Property Tax and Property Tax Rate 200

Objectives : Identify terms used with property tax and property tax rates 200 |

Exercises 203

6.2 State and Federal Unemployment Tax 205

Objectives : Identify terms used with state unemployment tax (SUTA) and federal

6.3 Federal Income Tax 208

Objectives : Identify terms used with federal income tax 208 | Collect

7.1 Health and Life Insurance 236

Objectives : Identify terms used with health and life insurance 236 | Determine

7.2 Motor Vehicle and Property Insurance 243

Objectives : Identify terms used with motor vehicle and property insurance 243 |

Exercises 248

Chapter Review and Assessment 250 Key Terms 250 | Concepts and Examples 250 | Review Exercises 251 | Quiz 258

Features

Math @ Work: Insurance Agent 235 | Apply Math@Work: Insurance Agent 254 |

Write about Math 254 | Personal Finance: Are you knowledgeable enough to make decisions about buying insurance? 255 | Crunch the Numbers: Life Insurance Estimator 256

XIII

Objectives : Describe the purchasing cycle 262 | Identify terms used with

8.2 Cash Discounts 268 Objectives : Identify terms used with cash discounts 268 | Calculate cash

Find total amount due after cash discount is subtracted and other charges are

Exercises 273

8.3 Trade Discounts 274 Objectives : Calculate trade discounts and net prices 274 | Apply a trade

8.4 Series Discounts 278 Objectives : Calculate series discounts and net prices 278 | Exercises 280

8.5 Sales Tax 281 Objectives : Calculate sales tax 281 | Prepare an invoice 282 | Verify an

9.1 Concepts Used in Pricing Merchandise 300 Objectives : Identify terms used with pricing merchandise 300 | Distinguish

9.2 Markup on Cost 303 Objectives : Calculate the markup amount and the rate based on cost 303 |

Calculate the cost when the markup amount and the markup rate based on cost

XIV

Calculate the selling price when cost and markup rate based on selling price

9.4 Markdown 311 Objectives : Determine markdown sale price 311 | Calculate markdown rate 312 |

Exercises 313

Chapter Review and Assessment 314 Key Terms 314 | Concepts and Examples 314 | Review Exercises 316 | Quiz 322

Features

Math @ Work: Accounting Associate 299 | Apply Math@Work: Accounting Associate 318 |

Write about Math 318 | Personal Finance: How are everyday markups eating away your pay check? 319 | Crunch the Numbers: Markups and Markdowns 320

Chapter 10 Interest 324

Objectives : Identify terms used for calculating simple interest 326 | Calculate

Exercises 333

10.2 Promissory Notes and Discounting 334

Objectives : Identify terms used with promissory notes 334 | Discount notes 335 |

Exercises 338

Objectives : Identify terms used for compounding interest 340 | Calculate

Chapter Review and Assessment 352 Key Terms 352 | Concepts and Examples 352 | Review Exercises 354 | Quiz 360

Features

Math @ Work: Small Business Owner 325 | Apply Math@Work: Small Business Owner 356 | Write about Math 356 | Personal Finance:What interest are you earning? 357 | Crunch the Numbers: Simple, Ordinary, and Exact Interest 358

XV

Objectives : Identify terms used with open-end credit 364 | Calculate fi nance

Objectives : Identify terms used with closed-end credit 370 | Calculate

Objectives : Identify terms used with mortgage loans 376 | Determine monthly

Chapter Review and Assessment 380 Key Terms 380 | Concepts and Examples 380 | Review Exercises 383 | Quiz 390

Features

Math @ Work: Mortgage Loan Offi cer 363 | Apply Math@Work: Mortgage Loan

Offi cer 386 | Write about Math 386 | Personal Finance: Do you use credit cards wisely? 387 | Crunch the Numbers: Mortgage Calculator 388

Chapter 12 Metrics and Currency 392

Objectives : Identify terms used in metrics 394 | Use metric prefi xes 395 |

Exercises 396

Objectives : Convert metric measures to larger or smaller units 397 | Convert

Objectives : Convert English measures to metric measures for weight 402 |

Objectives : Calculate foreign currency exchange 408 | Exercises 409

XVI

Features

Math @ Work: Travel Agent 393 | Apply Math@Work: Travel Agent 418 | Write about Math 418 | Personal Finance: How much do you know about traveling to Alaska

by car? 419 | Crunch the Numbers: Convert Units of Measure 420

Answers to Selected Exercises 424

Glossary 437

Index 444

About the Authors

Sharon Burton is a professor in the Business Studies Division at Brookhaven College, Dallas (Texas)

Community College District (DCCCD) She has 25+ years experience in community college teaching

Recently, she has been coordinating the medical offi ce program at Brookhaven College Sharon teaches

Microsoft software, communications, and medical offi ce classes on campus as well as online She has

a BBA from Lamar University and an MBE from University of North Texas

Nelda Shelton received her BS and MBE degrees from the University of North Texas, Denton, Texas

She is an associate professor at Tarrant County College, South Campus, Fort Worth, Texas, in the

Business and Offi ce Administration Departments Her teaching experience includes business math,

business communications, offi ce procedures, and introduction to accounting both in the classroom

and distance learning via the Internet She has worked part time for the U.S Offi ce of Personnel

Management as a trainer and as an independent contractor and for Dallas County Community College

District as a part-time instructor She has coauthored several textbooks in the business and offi ce

administration areas

The study of business math is a practical approach to learning math In studying business math, you learn basic math skills that will be useful throughout your life Checking a sales slip, balancing

a checking account, and understanding the various ways interest

is charged on loans are just a few of the many practical skills you will learn in the coming chapters You will begin your study

of business math with an explanation of the decimal number system—the number system most used in the United States.

Medical assistant Audra Puckett is the ultimate

multi-tasker A typical day in her doctor’s offi ce job includes answering the phone, scheduling appointments, fi ling medical records, and communicating with insurance companies

And those are just her administrative duties She also checks patients’ fi les to discern the reason for their visits, greets them, and guides them from the waiting room into the examination area

“I measure each patient’s height and weight and show each into

an examining room,” Audra says “There, I measure their pulse and respirations and ask about any new medications I prepare the vials and needles for injections I also prepare prescriptions and administer medications as instructed by the doctor, and I direct the patients to the front desk after their visits for payment and rescheduling.”

People skills are a must “I interact one-on-one with every patient,” Audra says “When I make time to start a conversation and show interest in each individual, the patients feel more comfortable, and it refl ects well on the whole offi ce This job can

be exhausting, both physically and mentally, and you can tell who

is in it just for the money—their work suffers, and the patients notice But the workers who are in it to care for people and who are driven to help the doctor make an accurate diagnosis—they’re the ones who truly succeed.”

How Math is Used in Health Sciences

Audra uses multiplication when she converts drug dosages from milliliters to liters and when she calculates how many blood vials are required for the particular test a patient is undergoing She also uses multiplication when taking vital signs “A person’s pulse rate

is measured in beats per minute, but I only track the pulse for

15 seconds Then I multiply the number of heartbeats by four to get the pulse rate,” she explains “This is a huge timesaver I’d be lost without this skill because it would take four times as long to take each pulse, which would slow down everything else in the offi ce!”

What Do You Think?

What skills do you need to improve for a career in health sciences?

y

Math Skills Used

AdditionSubtractionMultiplicationDivision

Other Skills Needed

CommunicationOrganizationMultitaskingProblem Solving

H E A LT H S C I E N C E S

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3

The decimal number system (also called the Hindu-Arabic system) is a number system using base 10 It is the most universally used number system

this system are as follows:

1, 2, 3, 4, 5, 6, 7, 8, 9, and 0

point, separates the whole number part from the decimal part Figure 1-1 shows the names of the digits to the left and right of the decimal point—

Notice that commas are used to the left of the decimal point to separate each group of three digits Digits to the left of the decimal point form the

whole number part Digits to the right of the decimal point form the

decimal part

To read a decimal number, begin by reading the whole-number part, say

“and” to indicate the decimal point, and then read the decimal part

OBJECTIVE 2 Convert numbers to or from amounts in

word forms.

form as shown on the next page When an amount is written in word form,

the decimal point is represented by the word and For example, 15.78 is

written fi fteen and seventy-eight hundredths

OBJECTIVE 1 Identify terms used with the decimal number

Billions Comma Hundred millions Ten millions Millions Comma Hundred thousands Ten thousands Thousands Comma Hundreds Tens Units

numbers

, 5 1 2 ,,

Trillions Comma Hundred billions Ten billions

Figure 1-1

Decimal Number System

39.06 thirty-nine and six hundredths

PAY TO THE ORDER OF

DOLLARS

$

For Classroom Use Only

Grand West Bank

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065000883072276790031

DATE

14-88 650

Jẩđảfiắ PãẩđỦ Féợù

say Ềninety-eight thousand, seven hundred sixty-fi ve hundred thousandths.Ể

A common use for word forms is in writing checks The bank requires

a payer to write the amount in both number and word form, as shown in

Figure 1-2 Notice that the fraction of a dollar 50/100 is written as a fraction

along with the word form

Examples

rather than give an exact amount For example, suppose you purchased a portable DVD player and a digital photo frame for $219.95 If a friend asks what you paid for them, you might say $220

You rounded up the amount to the nearest whole dollar (unit position) rather than saying the actual dollars and cents If you had paid $219.05, you might have rounded down to the nearest whole dollar and said $219 Study the following examples

TIPS

When rounding a number,

look at the fi rst digit to

the right of the digit being

rounded Do not look

beyond this digit.

Portable DVD player and digital photo frame cost $219.95, or approximately $220

Portable DVD player and digital photo frame cost $219.05, or approximately $219

If you understand approximation and positions (places), you will

Rules for Rounding

Example 6.8 rounds up to 7 (8 is more than 5)

digits from that position to the right.

Example 6.4 rounds to 6 (4 is less than 5)

You can easily round to any position by looking at the number to its right and applying Rule 2 or Rule 3 given above

Examples

When a number in the round-off position is 9, as in 0.98, and the digit to the right is 5 or more, round up by adding 1 to the 9 even though a decimal number may change to a whole number

Examples

is 358.860

Notice that all digits to the right of the hundreds place are changed to zeros

Name Date

Directions Complete the following problems.

A Write the numeral and the position the underlined digits represent OBJEC TIVE 1

B Write numerals for the following word forms OBJEC TIVE 2

21 One hundred thirty

22 Ninety-fi ve thousand two hundred twenty

23 Seventy-three and sixty-fi ve hundredths

24 Six million three thousand twenty-one

25 Five thousand six hundred and thirty-four thousandths

26 Three hundred eleven

27 One thousand two

28 Nine hundred six

31 Three billion, thirty-four million, six thousand forty

32 Fifty-one and six thousandths

33 One hundred nine and four tenths

34 Seven thousand, four hundred, sixty-two and three hundredths

35 Five hundred and eighteen hundredths

7

E Round the following numbers to the place indicated OBJEC TIVE 3

56 Round $5,267.82 to the nearest ten

57 Round 269.5 to the nearest hundred

58 Round 422.35 to the nearest unit

59 Round 9,742 to the nearest thousand

60 Round 4.2354 to the nearest tenth

61 Round 9.4603 to the nearest hundredth

62 Round 249.9573 to the nearest thousandth

63 Round 7.2468901 to the nearest ten thousandth

64 Round 4.006 to the nearest tenth

65 Round 19,999 to the nearest thousand

66 Round 3,611.875 to the nearest ten

1. Identify terms used with addition.

2. Align numbers correctly for adding.

3. Align decimal points in addition.

OBJECTIVE 1 Identify terms used with addition.

Quick, correct addition

of numbers is a useful

math skill you can

acquire Like any other

skill, addition requires

practice Some everyday

uses of addition are

counting money, keeping

score in a game, and

making purchases You

must be familiar with the

terms used in addition

Addition is the process of combining two

or more numbers and arriving at a larger number Each number is called an

addend The solution is called the sum, total, or amount

plus sign → + 27 ← addend

OBJECTIVE 2 Align numbers correctly for adding.

To prevent errors in adding, it is necessary to align the digits in columns so units

are above units, tens are above tens, hundreds are above hundreds, and so on

When adding numbers with decimals, it is important that you align the decimal points This will ensure the proper placement of digits in the appro-priate column The number of decimal places in the answer is determined by the addend with the largest number of decimal places.

Example

5,146.11 61.044 10.07 694.081

OBJECTIVE 4 Add mentally.

The more skillful you become at adding any two or more combinations of numbers in columns, the more accurately and rapidly you will be able to

of two or more numbers within the column being added Follow these steps when adding a column mentally

Steps

1 Add down the right column (units position) by thinking

10, 16, 19, 22, 23(7 + 3 is 10, + 6 is 16, + 3 is 19, + 3 is 22, + 1 is 23)

2 Write the number 3 in the units position of the answer

Write the number 2, which is to be carried, over the 9 in the tens column

3 Add down the middle column (tens position) by thinking

11, 15, 16, 24, 28(2 + 9 is 11, + 4 is 15, + 1 is 16, + 8 is 24, + 4 is 28)

4 Write the number 8 in the tens position in the answer

Write the number 2, which is to be carried, over the 3 in the hundreds column

5 Add down the left column (hundreds position) by thinking

5, 14, 17, 21, 23, 32(2 + 3 is 5, + 9 is 14, + 3 is 17, + 4 is 21, + 2 is 23, + 9 is 32)

6 Write the number 32 with a comma after the 3 to make it easier to distinguish the thousands position from the hundreds position in the answer

3,283

22 397 + 943 + 306 + 413 + 283 + 941 3,283

10 16 19 22 23

CALCULATOR TIP

Calculators automatically place

the decimal point in the fi nal

CALCULATOR TIP

Check how your calculator works by adding a problem you can mentally add For instance, add 5 + 6 Enter the 5, enter the + sign, enter the 6, enter the + again The answer is shown in the display.

To add more accurately and rapidly, you can memorize the number

combinations that total 10

Instead of adding down a column, learn to recognize these groups of tens

to increase your speed in adding At fi rst, this method may appear to take too

much time However, with practice, you will gain speed

Example

5311,3653248+ 1792,155

In business, it is common for numbers to be written horizontally across a page rather than in vertical columns Examples are invoices, checkbooks, and inventory reports You could rewrite the numbers in a column and add vertically, but it is more effi cient to add horizontally.

Example

$698.11 + $47.88

Steps

1 Add the hundredths column, 1 + 8, and write the answer,

2 Add the tenths column, 1 + 8, and write the answer,

4 Add the units, tens, and hundreds columns following

OBJECTIVE 7 Use the Four Step Problem Solving Plan.

Solving problems is a critical skill Knowing what to look for and what dures to apply are very important To identify what procedures to use, you should

proce-be familiar with the problem situation, proce-be able to collect the appropriate tion, identify an action plan, perform the action plan, and draw conclusions

informa-Four Step Problem Solving Plan

1 Clues

• Read the problem slowly and carefully Reading aloud may help

• Ask yourself if you’ve seen a problem similar to the one you are reading

• What facts are relevant or what facts are you expected to know?

• What is the problem asking or what are you trying to fi nd?

• Underline clue words, such as the ones shown in the following table

Sample Clue Words Addition Subtraction Multiplication Division

sumtotal

in addition, in allwhole

diff erencehow much moreremainderminus

producttotalareatimes

sharedistributequotientaverage

TIPS

Add horizontally by

add-ing the positions from

right to left.

Problem Solving Plan

You have 16,452 miles

You have earned extra

miles since your

statement

You need 20,000 miles

for a free ticket

To determine total miles, add the recently earned miles to the balance on your statement

16,452

345 280 500 190 + 310 18,077

Conclusion

You need 20,000 miles and only have 18,077 miles You do not have enough for a free

ticket at this time

or other illustrations

• Determine how the known and unknown facts are related

• Identify the steps to take in the appropriate sequence

3 Solve

Perform the steps in the action plan

4 Conclusion

• Does it seem reasonable?

• Did you answer the question the problem is asking?

• Did you answer using the language in the question?

Use the Four Step Problem Solving Plan to solve a word problem involving addition

Example

As a member of a frequent fl yer program, you receive one mile for each mile you fl y, miles for staying in certain hotels, and miles for shopping at certain stores When you have accumulated enough miles, you can obtain a free airline ticket You have a balance on your frequent fl yer statement of 16,452 miles You have earned the following miles this month that have not been posted on your monthly statement: 345, 280, 500, 190, 310 You want to know how many miles you now have to see if you have enough for a free ticket

You need 20,000 miles for the free ticket

13

Name Date

Directions Complete the following problems.

A Rewrite and add the following problems in the space provided to OBJEC TIVES 2, 3

practice aligning and adding columns of numbers Show maximum

B Fill in the blanks with the numbers you think as you mentally add OBJEC TIVE 4

down each column of fi gures.

C Fill in the blanks with the numbers you think as you mentally add OBJEC TIVE 5

down each column of fi gures by tens.

E Complete the following problems by adding horizontally Write your answers, OBJEC TIVE 6

showing maximum decimals, in the blanks provided.

51 Carlota played 9 holes of golf She scored the following on each hole: 5, 5, 4,

6, 4, 4, 3, 5, and 4 Total all 9 scores and determine her total score for 9 holes

of golf

52 Maria checked her grocery receipt to determine whether the amounts paid

for each of her ten purchases had been added correctly The following numbers appeared on her slip: $1.98, $0.89, $3.29, $2.76, $4.11, $1.19, $0.79,

$0.84, $1.00, $3.25 Add the numbers and determine the total

53 Rafael Molina decided to increase his investment portfolio to include small

cap technology stocks He purchased 100 shares each of Robotic Visions, Inc., costing $298; DSL.net, Inc., costing $320; and Secure Blue, costing $225 What was Rafael’s total investment?

54 Roscoe purchased four new CDs for his blues collection He paid $15.00,

$14.95, $12.95, and $15.00 Tax on the purchase was $4.56 How much was Roscoe’s purchase?

55 Bryan, the offi ce manager for Bailey & Gorman law fi rm, decided to redecorate

the fi rm’s client waiting area He purchased a library table for $375, a lamp for $99, a picture for $24.95, a fl ower arrangement for $69.95, and a mantel clock for $389 How much money did Bryan spend?

56 Khan decided to carpet his house He wanted to estimate the amount of carpet

he would need before he went shopping The square footage for each room in the house was 205, 90, 900, 300, 250, 275, and 200 How many square feet of carpet must Khan buy in order to carpet his entire house?

57 For Memorial Day, Dos Rios Campgrounds rented these campsites: 39 tent-only

campsistes, 86 water and electricity campsites, and 110 full-hookup campsites

Forty-fi ve campsites were not rented How many total campsites at Dos Rios were available for rental?

58 Johnson’s Gourmet Sandwich Shop sold 86 Cucumber and Apricot sandwiches,

63 Focaccia Turkey Club sandwiches, 110 South of the Border sandwiches,

120 Monte Cristo sandwiches, 75 Grilled Tofu sandwiches, and 91 Eggplant sandwiches How many sandwiches were sold?

59 Cory drove a cab part time while in college on weekends For regular fares,

the meter tracks the total fares and miles; however, the local hospital provides vouchers for patients who need transportation to and from therapy Cory’s total vouchers were $322.50 and his total credit card receipts were $205.90

What was his total for the vouchers and credit card receipts?

60 Steamboat Springs Properties rented 48 condos during their early season

(November 26–December 12), 92 during preholiday (December 13–19), and

225 during the holiday season (December 20–January 4) How many condos were rented?

Subtraction, like addition, is a basic math skill used in business Subtraction is

might say, “9 minus 5,” “9 take away 5,” “9 subtract 5,” “5 subtracted from 9,”

or “the difference between 9 and 5.”

A negative number results when you subtract a larger number from a smaller number Negative numbers are often expressed by enclosing the number

within angle brackets, such as 〈29〉 They may also be enclosed within

paren-theses, expressed with a minus sign before the number (–29), or printed in red

OBJECTIVE 2 Subtract vertically.

To subtract vertically, work from right to left, subtracting the bottom number

from the top

Example

36

Steps

1 Align the minuend, 36, over the subtrahend, 15

2 Working from right to left, subtract the units position, 6 − 5 = 1

Write the difference, 1, beneath the 5 in the units position

3 Subtract the tens position, 3 − 1 = 2 Write the difference, 2, under the 1 in the tens position

4 The solution is 21

OBJECTIVE 1 Identify terms used with subtraction.

1. Identify terms used with subtraction.

2. Subtract vertically.

3. Check subtraction by addition.

4. Regroup in subtraction.

5. Solve problems with zeros in regrouping in subtraction.

6. Subtract horizontally.

7. Express negative numbers.

8. Add negative numbers.

9. Combine addition and subtraction.

17

Subtraction is based on addition Therefore, you can check your solutions

to problems by adding the difference and the subtrahend The result is the minuend Study the following problem and check the answer

OBJECTIVE 4 Regroup in subtraction.

Regrouping, or borrowing as it is sometimes called, should not be diffi cult for you In the example below, the number has been rewritten to show the positions or places to help you learn how to borrow

Example

Steps

1 Working from right to left, subtract the units position Because the

9 cannot be subtracted from the 5, you must borrow 10 from the tens position and add it to the 5 to make 15 In doing so, you are reducing the tens position by 1, leaving 6 tens Draw a line through the 7 and write a 6 above it to help you remember that you have reduced the 7 to a 6 when you begin subtracting the tens position

You can now subtract the units position, 15 − 9 = 6

2 Subtract the tens position, 6 − 3 = 3

Always check your answer by adding the subtrahend and the difference.

OBJECTIVE 5 Solve problems with zeros in regrouping in

subtraction.

Many students have diffi culty with borrowing when subtraction problems

contain zeros The following steps will be helpful to you

8 hundreds + 10 tens + 0 units

9 0 0– 1 8

8 1 0

← 1 hundred = 10 tens

Now you can borrow 1 from the tens position, as shown here

8 hundreds + 9 tens + 10 units

9 0 0– 1 82

8 1 0 10 9

← 1 ten = 10 units

Subtract the units position, 10 − 8 = 2

2 Remember, the tens position has been reduced by 1 because you borrowed 1 It is now 9 Subtract the tens position

9 0 0– 1 8

8 2

8 1 0 10 9

3 Subtract the hundreds position, 8 − 0 = 8

9 0 0– 1 8

8 8 2

8 1 0 10 9

19

In business it often becomes necessary to subtract a problem that is written across the page horizontally rather than vertically You should learn to subtract horizontally rather than take the time to rewrite the problem Follow these steps to subtract horizontally.

Example

$334.92 − $12.41

Steps

1 Subtract the hundredths position, 2 − 1, and write the

2 Subtract the tenths position, 9 − 4, and write the

3 Place the decimal point next to the 5 Subtract theunits position, 4 − 2, and write the answer, 2, next

4 Subtract the tens position, 3 − 1, and write the

5 There is no number to subtract from the hundredsposition Write the number 3 to the left of the 2that is in the tens position in the blank Add the

OBJECTIVE 7 Express negative numbers.

A negative number results when a larger number is subtracted from a smaller number To subtract a larger number from a smaller number, reverse the numbers and subtract You must remember to place a negative sign before the answer, or the answer will be incorrect

Example

− 48 subtrahend (larger) 48

check your answer by

adding the subtrahend

and the diff erence.

When the temperature drops below zero, negative numbers are used to describe

the temperature in degrees Numbers above zero are positive numbers Notice

that the negative sign often resembles a minus sign, which indicates subtraction

Another example of negative numbers is when you write a check for more money than you have deposited in the bank If the bank honors the

check, it will notify you that you have a negative balance

OBJECTIVE 8 Add negative numbers.

You may be required to add a column of negative numbers, as in the

OBJECTIVE 9 Combine addition and subtraction.

You may be required to complete calculations on the job that combine

pos-itive and negative numbers, resulting in a negative or a pospos-itive number

Example

+25+13

−88+07

−26

Total the positive numbers (+) 25, 13, 7 Total the negative numbers (−) 88, 26

Then subtract the two sums If the total of the positive numbers is the greater

of the two, the answer is a positive number If the total of the negative

numbers is the greater of the two, the answer is a negative number

Total positive numbers → + 25 + 13 + 7 = +45Total negative numbers → − 88 − 26 = −114

Subtract → −114

+45Solution → −69

TIPS

A negative sign, a number

in red, or a number placed

in parentheses or brackets might indicate that the number is negative.

It is often necessary to compare or convert Fahrenheit to Celsius You can fi nd online calculators

to do these conversions.

21

Name Date

Directions Solve the following problems Write your answers in the blanks provided Place commas and dollar signs in

answers where appropriate.

A Subtract the numbers vertically; regroup Then check your OBJEC TIVES 2, 3, 4, 5