Business math demystified

BUSINESS MATH
DEMYSTIFIED


Demystified Series
Accounting Demystified
Advanced Statistics Demystified
Algebra Demystified
Anatomy Demystified
asp.net 2.0 Demystified
Astronomy Demystified
Biology Demystified
Biotechnology Demystified
Business Calculus Demystified
Business Math Demystified
Business Statistics Demystified
C++ Demystified
Calculus Demystified
Chemistry Demystified
College Algebra Demystified
Corporate Finance Demystified
Data Structures Demystified
Databases Demystified
Differential Equations Demystified
Digital Electronics Demystified
Earth Science Demystified
Electricity Demystified
Electronics Demystified
Environmental Science Demystified
Everyday Math Demystified

Forensics Demystified
Genetics Demystified
Geometry Demystified
Home Networking Demystified
Investing Demystified
Java Demystified
JavaScript Demystified
Linear Algebra Demystified
Macroeconomics Demystified

Management Accounting Demystified
Math Proofs Demystified
Math Word Problems Demystified
Medical Terminology Demystified
Meteorology Demystified
Microbiology Demystified
Microeconomics Demystified
Nanotechnology Demystified
OOP Demystified
Options Demystified
Organic Chemistry Demystified
Personal Computing Demystified
Pharmacology Demystified
Physics Demystified
Physiology Demystified
Pre-Algebra Demystified
Precalculus Demystified
Probability Demystified
Project Management Demystified
Psychology Demystified

Quality Management Demystified
Quantum Mechanics Demystified
Relativity Demystified
Robotics Demystified
Six Sigma Demystified
sql Demystified
Statistics Demystified
Technical Math Demystified
Trigonometry Demystified
uml Demystified
Visual Basic 2005 Demystified
Visual C# 2005 Demystified
xml Demystified


BUSINESS MATH
DEMYSTIFIED

ALLAN G. BLUMAN

McGRAW-HILL
New York Chicago San Francisco Lisbon London
Madrid Mexico City Milan New Delhi San Juan
Seoul Singapore Sydney Toronto


Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved. Manufactured in the United States of America. Except
as permitted under the United States Copyright Act of 1976, no part of this publication may be reproduced or distributed in any form
or by any means, or stored in a database or retrieval system, without the prior written permission of the publisher.
0-07-148711-5

The material in this eBook also appears in the print version of this title: 0-07-146470-0.
All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps.
McGraw-Hill eBooks are available at special quantity discounts to use as premiums and sales promotions, or for use in corporate
training programs. For more information, please contact George Hoare, Special Sales, at or (212)
904-4069.
TERMS OF USE
This is a copyrighted work and The McGraw-Hill Companies, Inc. (“McGraw-Hill”) and its licensors reserve all rights in and to the
work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and
retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works
based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill’s prior consent. You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right
to use the work may be terminated if you fail to comply with these terms.
THE WORK IS PROVIDED “AS IS.” McGRAW-HILL AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES
AS TO THE ACCURACY, ADEQUACY OR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE
WORK, INCLUDING ANY INFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIA HYPERLINK OR OTHERWISE, AND EXPRESSLY DISCLAIM ANY WARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO
IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. McGraw-Hill and its
licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will
be uninterrupted or error free. Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error
or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill and/or its licensors be liable for any
indirect, incidental, special, punitive, consequential or similar damages that result from the use of or inability to use the work, even
if any of them has been advised of the possibility of such damages. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.
DOI: 10.1036/0071464700


Professional

Want to learn more?
We hope you enjoy this
McGraw-Hill eBook! If
you’d like more information about this book,
its author, or related books and websites,

please click here.


For more information about this title, click here

CONTENTS

Preface

xi

CHAPTER 1

Fractions—Review
Basic Concepts
Operations with Fractions
Operations with Mixed Numbers
Quiz

1
1
4
7
10

CHAPTER 2

Decimals—Review
Rounding Decimals
Addition of Decimals

Subtraction of Decimals
Multiplication of Decimals
Division of Decimals
Comparing Decimals
Changing Fractions to Decimals
Changing Decimals to Fractions
Quiz

17
17
19
20
20
21
24
25
27
29

CHAPTER 3

Percent—Review
Basic Concepts
Changing Percents to Decimals
Changing Decimals to Percents
Changing Fractions to Percents
Changing Percents to Fractions
Three Types of Percent Problems

32

32
32
34
36
38
39
v


CONTENTS

vi

Word Problems
Quiz

43
45

CHAPTER 4

Formulas—Review
Introduction
Exponents
Order of Operations
Formulas
Quiz

49
49

50
51
55
58

CHAPTER 5

Checking Accounts
Introduction
Recording the Transactions
Reconciling a Bank Statement
Summary
Quiz

61
61
61
67
73
73

CHAPTER 6

Payroll and Commission
Introduction
Yearly Salary
Hourly Wages
Piecework Wages
Commission
Payroll Deductions

Summary
Quiz

76
76
76
78
80
82
85
87
88

CHAPTER 7

Markup
Introduction
Markup on Cost
Markup on Selling Price
Relationships Between the Markups
Markdown and Shrinkage
Summary
Quiz

91
91
92
97
103
106

113
113

CHAPTER 8

Discounts
Introduction

116
116


CONTENTS

vii

Trade Discounts
Trade Discount Series
Cash Discounts
Discounts and Freight Terms
Summary
Quiz

117
121
126
132
135
136

CHAPTER 9

Simple Interest and Promissory Notes
Introduction
Simple Interest
Finding the Principal, Rate, and Time
Exact and Ordinary Time
Promissory Notes and Discounting
Summary
Quiz

138
138
139
145
149
157
164
164

CHAPTER 10

Compound Interest
Introduction
Compound Interest
Effective Rate
Present Value
Summary
Quiz

167
167
167
173
175
179
180

CHAPTER 11

Annuities and Sinking Funds
Introduction
Annuities
Sinking Funds
Summary
Quiz

182
182
183
188
191
192

CHAPTER 12

Consumer Credit
Introduction
Installment Loans
Annual Percentage Rate

Rule of 78s
Credit Cards

194
194
194
198
202
207


CONTENTS

viii

Summary
Quiz

213
214

CHAPTER 13

Mortgages
Introduction
Fixed-Rate Mortgage
Finding Monthly Payments
Amortization Schedule
Summary
Quiz

216
216
217
220
224
228
229

CHAPTER 14

Insurance
Introduction
Fire Insurance
Automobile Insurance
Life Insurance
Summary
Quiz

231
231
231
238
240
243
244

CHAPTER 15

Taxes

Introduction
Sales Tax
Property Tax
Income Tax
Summary
Quiz

246
246
246
249
252
255
255

CHAPTER 16

Stocks and Bonds
Introduction
Stocks
Bonds
Summary
Quiz

257
257
258
265
269
269

CHAPTER 17

Depreciation
Introduction
The Straight-Line Method

272
272
273


CONTENTS

ix

Sum-of-the-Years-Digits Method
Declining-Balance Method
The Units-of-Production Method
The MACRS Method
Summary
Quiz

276
281
285
287
287
287

CHAPTER 18

Inventory
Introduction
Cost of Goods Sold
The Retail Inventory Method
Inventory Turnover Rate
Summary
Quiz

291
291
291
300
303
308
308

CHAPTER 19

Financial Statements
Introduction
The Balance Sheet
Income Statements
Summary
Quiz

312
312
313

319
322
322

CHAPTER 20

Statistics
Introduction
Frequency Distributions
Measures of Average
Measures of Variability
Summary
Quiz

325
325
325
334
337
343
343

CHAPTER 21

Charts and Graphs
Introduction
The Bar Graph and Pareto Graph
The Pie Graph
The Time Series Graph
The Scatter Diagrams

346
346
347
352
356
359


CONTENTS

x

The Stem and Leaf Plot
Summary
Quiz

363
366
366

Final Exam

368

Answers to Quizzes and Final Exam

382

Index

387


PREFACE

The purpose of this book is to provide the mathematical skills and knowledge
to students who are either entering or are already in the business profession.
This book presents the mathematical concepts in a straightforward, easy-tounderstand way. It does require, however, a knowledge of arithmetic (fractions,
decimals, and percents) and a knowledge of algebra (formulas, exponents, and
order of operations). Chapters 1 through 4 provide a brief review of these concepts. If you need a more in-depth presentation of these topics, you can consult
another one of my books in the series entitled Pre-Algebra Demystified.
This book can be used as a self-study guide or as a supplementary textbook
for those taking a business mathematics course at a junior college, a community
college, a business or technical school, or a 4-year college. It should be pointed
out that this book is not for students taking a high-level course in mathematics for business with topics such as linear programming, quantitative analysis,
elementary functions, or matrices.
It is recommended that you use a scientific calculator for some of the more
complex formulas found in Chapters 10 through 13. Also, some calculators
are not able to handle several nested parentheses; that is, parentheses inside of
parentheses. If you get an error message while trying to do this, it is recommended that you do some of the operations inside the parentheses first and use
these numbers omitting the parentheses.
I hope you will find this book helpful in improving your mathematical skills
in business and enabling you to succeed in your endeavors.
Good luck!
Allan G. Bluman

xi
Copyright © 2006 by The McGraw-Hill Companies, Inc. Click here for terms of use.

PREFACE

xii

Acknowledgments
I would like to thank my editor Judy Bass for her assistance in the publication
of this book and Carrie Green for her helpful suggestions and error checking.
Finally I would like to thank my wife Betty Claire for her proofreading, typing,
and encouragement. Without her, this book would not be possible.
Note: All names of people and businesses in this book are fictitious and
are used to make the concepts presented more business-world oriented. Any
resemblance to actual persons or businesses is purely coincidental.

Copyright © 2006 by The McGraw-Hill Companies, Inc. Click here for terms of use.


BUSINESS MATH
DEMYSTIFIED


This page intentionally left blank


1

CHAPTER

Fractions—Review

Basic Concepts
In a fraction, the top number is called the numerator and the bottom number
is called the denominator.
To reduce a fraction to lowest terms, divide the numerator and denominator
by the largest number that divides evenly into both.
EXAMPLE: Reduce

28
.
36

SOLUTION:
28 ÷ 4
7
28
=
=
36
36 ÷ 4
9
To change a fraction to higher terms, divide the smaller denominator into the
larger denominator, and then multiply the smaller numerator by that answer.

1
Copyright © 2006 by The McGraw-Hill Companies, Inc. Click here for terms of use.


CHAPTER 1

2

EXAMPLE: Change

Fractions—Review

3
to 30ths.
5

SOLUTION:
3
18
Divide 30 ÷ 5 and multiply 3 × 6 = 18. Hence, = . This can be written
5
30
3×6
18
3
as =
= .
5
5×6
30
An improper fraction is a fraction whose numerator is greater than or equal
to its denominator; for example, 18
, 8 , and 77 are improper fractions. A mixed
5 3
number is a whole number and a fraction; 6 34 , 3 19 , and 2 78 are mixed numbers.
To change an improper fraction to a mixed number, divide the numerator by
the denominator and write the remainder as the numerator of a fraction whose

denominator is the divisor. Reduce the fraction if possible.
EXAMPLE: Change

28
to a mixed number.
6

SOLUTION:

4
28
6
24
4

4
2
28
=4 =4
6
6
3

To change a mixed number to an improper fraction, multiply the denominator
of the fraction by the whole number and add the numerator; this will be the
numerator of the improper fraction. Use the same number for the denominator
of the improper fraction as the number in the denominator of the fraction in the
mixed number.
3
EXAMPLE: Change 7 to an improper fraction.

4
SOLUTION:
3
4×7+3
31
7 =
=
4
4
4
PRACTICE:
1.

Reduce to lowest terms:

2.

Reduce to lowest terms:

3.

Reduce to lowest terms:

4.

Change

3
4

to 28ths.

10
.
30
45
.
48
27
.
33


CHAPTER 1
5.

Change

6.

Change

7.

Change

8.

Change

9.

Change

10.

Change

Fractions—Review

5
to 72nds.
8
9
to 40ths.
10
21
to a mixed number.
15
13
to a mixed number.
6
3
5 7 to an improper fraction.
9 18 to an improper fraction.

SOLUTIONS:
1.

10 ÷ 10

1
10
=
=
30
30 ÷ 10
3

2.

45
45 ÷ 3
15
=
=
48
48 ÷ 3
16

3.

27
27 ÷ 3
9
=
=
33
33 ÷ 3
11

4.

3
3×7
21
=
=
4
4×7
28

5.

5×9
45
5
=
=
8
8×9
72

6.

9×4
36
9
=
=
10

10 × 4
40

1
7. 15 21
15
6
2
13
8. 6
12
1

21
6
2
=1 =1
15
15
5

13
1
=2
6
6

9.

7×5+3

38
3
=
5 =
7
7
7

10.

8×9+1
73
1
=
9 =
8
8
8

3


CHAPTER 1

4

Fractions—Review

Operations with Fractions
In order to add or subtract fractions, you need to find the lowest common

denominator (LCD) of the fractions. The LCD of the fractions is the smallest
number that can be divided evenly by all the denominator numbers. For example,
the LCD of 16 , 23 , and 79 is 18 since 18 can be divided evenly by 3, 6, and 9. There
are several mathematical methods for finding the LCD; however, we will use
the guess method. That is, just look at the denominators and figure out the LCD.
If needed, you can look at an arithmetic or prealgebra book for a mathematical
method to find the LCD.
To add or subtract fractions
1.
2.
3.
4.

Find the LCD.
Change the fractions to higher terms.
Add or subtract the numerators. Use the LCD.
Reduce or simplify the answer if necessary.

EXAMPLE: Add

1 3 5
+ + .
3 8 6

SOLUTION:
Use 24 as the LCD.
1
8
=
3 24

9
3
=
8 24
5 20
+ =
6 24
13
37
=1
24
24
EXAMPLE: Subtract

11 7
− .
12 9

SOLUTION:
Use 36 as the LCD.
11 33
=
12 36
7 28
− =
9 36
5
36

CHAPTER 1

Fractions—Review

To multiply two or more fractions, cancel if possible, multiply numerators,
and then multiply denominators.
EXAMPLE: Multiply

9
2
× .
10 3

SOLUTION:
Cancel then multiply.
9
2⁄ 1
3×1
2 9⁄ 3
3
× = 5× 1 =
=
10 3 10
3⁄
5×1
5
⁄
To divide two fractions, invert (turn upside down) the fraction after the ÷
sign and multiply.
EXAMPLE: Divide

2 8
÷ .
3 9

SOLUTION:
1×3
3
2 8
2⁄ 1 9⁄ 3
÷ = 1× 4 =
=
3 9
1×4
4
3⁄
8⁄
PRACTICE:
Perform the indicated operation. Reduce all answers to lowest terms.
1.

5 3
+
8 4

2.

2 3
+
5 8

3.

1 5 5
+ +
2 8 6

4.

2
9
−
10 5

5.

7
1
−
12 8

6.

5 2
×
7 5

5

CHAPTER 1

6

7.

1 4
×
8 5

8.

7 3 4
× ×
8 5 7

9.

2 5
÷
3 9

10.

8 2
÷
9 3

Fractions—Review

SOLUTIONS:
1.

5 3
5 6
11
3
+ = + =
=1
8 4
8 8
8
8

2.

2 3
16 15
31
+ =
+
=
5 8
40 40
40

3.

12 15 20
47

23
1 5 5
+ + =
+
+
=
=1
2 8 6
24 24 24
24
24

4.

2
9
4
5
1
9
− =
−
=
=
10 5
10 10
10
2

5.

1
14
3
11
7
− =
−
=
12 8
24 24
24

6.

5⁄ 1
5 2
1×2
2
2
× =
× 1 =
=
7 5
7
5⁄
7×1
7

7.

4⁄ 1
1
1×1
1
1 4
× = 2×
=
=
8 5
8⁄
5
2×5
10

8.

1×3×1
3
7 3 4
7⁄ 1 3 4⁄ 1
× × = 2× × 1 =
=
8 5 7
8⁄
5 7⁄
2×5×1
10

9.

2 5
2
2×3
6
1
9⁄ 3
÷ = 1×
=
= =1
3 9
3⁄
5
1×5
5
5

10.

4
1
8 2
4×1
8⁄ 4 3⁄ 1
÷ = 3× 1 =
= =1
9 3
9⁄
2⁄
3×1

3
3


CHAPTER 1

Fractions—Review

7

Operations with Mixed Numbers
To add mixed numbers, add the fractions, and then add the whole numbers.
Simplify the answer when necessary.
2
3
EXAMPLE: Add 8 + 6 .
4
5
SOLUTION:

3
15
8 =8
4
20
2
8
+6 = 6
5
20

14

23
3
= 15
20
20

To subtract mixed numbers, borrow if necessary, subtract the fractions, and
then subtract the whole numbers. Simplify the answer when necessary.
EXAMPLE: 15

11
3
−7 .
12
8

SOLUTION:

22
11
= 15
12
24
9
3
−7 = 7
8
24

15

8

13
24

No borrowing is necessary here.
When borrowing is necessary, take one away from the whole number and add
it to the fraction. For example,
5
5
5
6 5
11
9 =9+ =8+1+ =8+ + =8
6
6
6
6 6
6
Another example:
5
5
7 5
12
5
15 = 15 + = 14 + 1 + = 14 + + = 14
7

7
7
7 7
7


CHAPTER 1

8

Fractions—Review

1
3
EXAMPLE: Subtract 9 − 6 .
3
4
SOLUTION:
4
16
1
9 =9 =8
3
12
12
3
9
9
−6 = 6 = 6
4

12
12
7
2
12
To multiply or divide mixed numbers, change the mixed numbers to improper
fractions and then multiply or divide as shown before.
1
5
EXAMPLE: Multiply 5 × 3 .
2
11
SOLUTION:
5
1
11
⁄ 1 38
⁄ 19 19 = 19
5 ×3 = 1 × 1 =
2
11
2⁄
1
11
⁄
1
2
EXAMPLE: Divide 9 ÷ 2 .
3
3

SOLUTION:
2
28 8 28
1
1
⁄ 7 3⁄ 1 7
÷ = 1 × 2 = =3
9 ÷2 =
3
3
3
3
3⁄
8⁄
2
2
PRACTICE:
Perform the indicated operations.
5
3
1. 1 + 2
6
8
2.

1
2
12 + 3
9
3

3.

2
9
1
4 +5 +3
5
3
10

4.

15

5.

2
1
23 − 7
6
3

1
11
−8
12
8

CHAPTER 1

Fractions—Review

6.

1
2
1 ×6
2
3

7.

2
1
6 ×2
4
5

8.

1 5
1
2 ×3 ×
8
2 7

9.

1
1
8 ÷2
8
2

10.

1
3
7 ÷4
2
4

SOLUTIONS:
1.

5
3
20
9
29
5
1 +2 =1 +2 =3 =4
6
8
24
24
24
24

2.

1
2
1
6
7
12 + 3 = 12 + 3 = 15
9
3
9
9
9

3.

2
9
6
20
27
53
23
1
4 + 5 + 3 = 4 + 5 + 3 = 12 = 13
5
3
10
30

30
30
30
30

4.

15

5.

2
1
4
7
4
3
1
1
23 − 7 = 23 − 7 = 22 − 7 = 15 = 15
6
3
6
6
6
6
6
2

6.

2
1
3⁄ 1 20
⁄ 10 10 = 10
1 ×6 = 1 × 1 =
2
3
2⁄
3⁄
1

7.

2 25
1
⁄ 5 12⁄ 3 15 = 15
6 ×2 = 1 × 1 =
4
5
4⁄
5⁄
1

8.

1 5
17 7⁄ 1
5
5

85
1
2 ×3 × =
×
× 1 =
=5
8
2 7
8
2
7⁄
16
16

9.

1
65 5 65
1
⁄ 13 2⁄ 1 13 = 3 1
÷ = 4 × 1 =
8 ÷2 =
8
2
8
2
8⁄
5⁄
4
4

10.

1
22
3
19
11
− 8 = 15 − 8 = 7
12
8
24
24
24

3
15 19
15 4⁄ 2
30
11
1
÷
= 1 ×
=
=1
7 ÷4 =
2
4
2
4

2⁄
19
19
19

9