Business math demystified

Business Calculus DemystifiedBusiness Math Demystified Business Statistics Demystified C++ Demystified Calculus Demystified Chemistry Demystified College Algebra Demystified Corporate Finance D

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

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ALLAN G BLUMAN

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Finding the Principal, Rate, and Time 145

CONTENTS ix

The Stem and Leaf Plot 363

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-to-understand 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

con-cepts 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

mathemat-ics for business with topmathemat-ics 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

recom-mended 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

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 Anyresemblance 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

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

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

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An improper fraction is a fraction whose numerator is greater than or equal

to its denominator; for example, 185,8

3, and 7

7 are improper fractions A mixed number is a whole number and a fraction; 634, 31

9, and 27

8 are mixed numbers

To change an improper fraction to a mixed number, divide the numerator bythe denominator and write the remainder as the numerator of a fraction whosedenominator is the divisor Reduce the fraction if possible

428

6 = 44

6 = 423

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 thenumerator 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 themixed number

1 Reduce to lowest terms: 1030

2 Reduce to lowest terms: 4548

3 Reduce to lowest terms: 2733

4 Change 34 to 28ths

CHAPTER 1 Fractions—Review 3

5 Change 58 to 72nds

6 Change 109 to 40ths

7 Change 2115 to a mixed number

8 Change 136 to a mixed number

9 Change 537 to an improper fraction

10 Change 918 to an improper fraction

2 45

48 = 45÷ 3

48÷ 3 =

1516

3 27

33 = 27÷ 3

33÷ 3 =

911

4 3

4 = 3× 7

4× 7 =

2128

5 5

8 = 5× 9

8× 9 =

4572

6 9

10 = 9× 4

10× 4 =

3640

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 16,2

3, and7

9 is 18 since 18 can be divided evenly by 3, 6, and 9 Thereare several mathematical methods for finding the LCD; however, we will usethe 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 mathematicalmethod to find the LCD

To add or subtract fractions

1 Find the LCD

2 Change the fractions to higher terms

3 Add or subtract the numerators Use the LCD

4 Reduce or simplify the answer if necessary

8 = 924+5

6 = 202437

−7

9= 2836536

To divide two fractions, invert (turn upside down) the fraction after the ÷sign and multiply.

7 1

8× 45

8 7

8× 3

5× 47

9 2

3÷ 59

10 8

9÷ 23

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

5= 6 820

1423

20 = 15 3

20

To subtract mixed numbers, borrow if necessary, subtract the fractions, and

then subtract the whole numbers Simplify the answer when necessary

81324

No borrowing is necessary here

When borrowing is necessary, take one away from the whole number and add

it to the fraction For example,

To multiply or divide mixed numbers, change the mixed numbers to improperfractions and then multiply or divide as shown before.

PRACTICE:

Perform the indicated operations

1 15

6+ 238

2 121

9+ 323

3 41

5+ 52

3 + 3910

Calculator Tip

Almost all of the new scientific calculators have a fraction key With thiskey, all of the operations with fractions can be performed on the calcula-tor Since various brands of calculators perform operations with fractionsdifferently, it is necessary that you read the instruction manual in order tolearn how to use the fraction key Although it is not absolutely necessarythat you know how to use a calculator to do fractions for this book, it willsave you time if you are able to use the calculator

Quiz

1 Reduce36

45.(a) 23(b) 34(c) 45(d) 78

2 Reduce15

60.

(a) 15(b) 23(c) 34(d) 14

6 Write 73

4as an improper fraction.

(a) 314(b) 254(c) 1414(d) 313

7 Change15

6 to a mixed number.

(a) 156(b) 213(c) 116(d) 212

8 Change12

7 to a mixed number.

(a) 157(b) 227(c) 1 512(d) 114

9 7

10+ 2

3 = ?(a) 913

(b) 1

10

(c) 116(d) 1 310

13 3

4× 5

6× 2

15 = ?(a) 143

60(b) 634(c) 1 710(d) 112

14 31

4+ 52

3 = ?(a) 81112(b) 2 512(c) 8 512(d) 3968

15 19

10 + 52

3+ 31

5 = ?(a) 411

30(b) 102330

24(b) 5117

24(c) 311

24

(b) 113

8

(c) 63104(d) 62324

19 61

5÷ 21

2 = ?(a) 21225(b) 1512(c) 3 710(d) 8 710

20 42

3÷ 21

3 = ?(a) 1089(b) 7

(c) 213(d) 2

For example, in the number 0.8731, the 3 is in the thousandths place The 1

is in the ten-thousandths place

Decimals are rounded to a specific place value as follows: First locate that

place-value digit in the number If the digit to the right is 0, 1, 2, 3, or 4, the

place-value digit remains the same If the digit to the right of the place-value

digit is 5, 6, 7, 8, or 9, add one to the place-value digit In either case, all digits

to the right of the place-value digit are dropped

EXAMPLE: Round 0.16832 to the nearest hundredth.

SOLUTION:

We are rounding to the hundredths place, which is the digit 6 Since the digit to

the right of the 6 is 8, raise the 6 to a 7 and drop all digits to the right of the 6

Hence, the answer is 0.17

17

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

T Hundredths Thousandths T Hundred-thousandths Millionths

Zeros can be affixed to the end of a decimal on the right side of the decimalpoint For example, 0.62 can be written as 0.620 or 0.6200 Likewise, the zeroscan be dropped if they are at the end of a decimal on the right side of the decimalpoint For example, 0.3750 can be written as 0.375

PRACTICE:

1 Round 0.67 to the nearest tenth

2 Round 0.5431 to the nearest hundredth

3 Round 83.2173 to the nearest thousandth

4 Round 3.99999 to the nearest ten-thousandth

5 Round 4.7261 to the nearest one (whole number)

Notes on rounding: If an item sells at a cost of 3/$1.00, and you purchase one

item, the exact cost is $1.00÷ 3 or $0.331

3 Now in the real world, you wouldpay $0.34 for the item In other words, you “pay the extra penny.” However,most business math books, including this one, follow the rounding rules used

CHAPTER 2 Decimals—Review 19

in mathematics; therefore, the cost of an item, if rounded to the nearest cent,

would be $0.33 That is just the way business math books are written

Also, round all answers involving money to the nearest cent following the

rounding rules given in this chapter Percents generally are rounded to one or

two decimal places

Addition of Decimals

In order to add two or more decimals, write the numbers in a column, placing

the decimal points of the numbers in a vertical line Add the numbers and place

the decimal point in the sum directly under the other decimal points above

Subtraction of Decimals

Subtracting decimals is similar to adding decimals To subtract two decimals,write the decimals in a column, placing the decimal points in a vertical line.Subtract the numbers and place the decimal point in the difference directly underthe other decimal points

EXAMPLE: Subtract 156.31− 18.623

SOLUTION:

156.310 (Annex a zero to keep the columns straight.)

−18.623137.687

EXAMPLE: Subtract 28.6− 14.7132

SOLUTION:

28.6000 (Annex zeros to keep the columns straight.)

− 14.713213.8868

CHAPTER 2 Decimals—Review 21

the product and place the decimal point there If there are fewer digits in the

product than are places, prefix as many zeros as needed

front of the product

When dividing two decimals, it is important to find the correct location of the

decimal point in the quotient There are two cases:

Case 1: To divide a decimal by a whole number, divide as though both numberswere whole numbers and place the decimal point in the quotient directly abovethe decimal point in the dividend.

Case 2: When the divisor contains a decimal point, move the point to the right

of the last digit in the divisor Then move the point to the right to the samenumber of places in the dividend Divide and place the point in the quotientdirectly above the point in the dividend

EXAMPLE: Divide 42 by 7.2 and round the answer to the nearest hundredth.

SOLUTION:

7.242Carry the answer to three decimal places (i.e., thousandths), as shown:

EXAMPLE: Which is larger, 0.27 or 0.635?

SOLUTION:

0.27→ 0.270 → 2700.635→ 0.635 → 635Since 635 is larger than 270, 0.635 is larger than 0.27

EXAMPLE: Arrange the decimals 0.84, 0.341, 5.2, and 0.6 in order of size,

smallest to largest

SOLUTION:

0.84→ 8400.341→ 3415.2→ 52000.6→ 600

In order: 0.341, 0.6, 0.84, and 5.2