Wiley Pathways Business Math, 1E - Brossura

Slavin, Steve

Brossura

ISBN 10: 0470007192 ISBN 13: 9780470007198

Casa editrice: JW, 2011

Riassunto

You can get there

Where do you want to go? You might already be working in a business setting. You may be looking to expand your skills. Or, you might be setting out on a new career path.

Wherever you want to go, Business Math will help you get there. Easy-to-read, practical, and up-to-date, this text not only helps you learn fundamental mathematical concepts needed for business, it also helps you master the core competencies and skills you need to succeed in the classroom and beyond. The book's brief, modular format and variety of built-in learning resources enable you to learn at your own pace and focus your studies.

With this book, you will be able to:
* Understand the business uses of percent calculations.
* Solve business problems using algebraic equations.
* Learn why stores markup and markdown their inventory.
* Calculate different types of discounts.
* Examine different banking options.
* Compare personal, sales, and property taxes and the implications of taxing income, property, and retail sales.
* Calculate simple and compound interest and learn how each affects the future value of money.
* Explore the uses of promissory notes, mortgages, and credit cards and how to calculate the cost of each.
* Learn different ways to determine the loss of value of business property and equipment, and the effect of depreciation on taxes.
* Examine financial statements and learn how to read the income statement and the balance sheet.
* Learn how to calculate the mean, median, mode, and range of data.

Wiley Pathways helps you achieve your goals

When it comes to learning about business, not everyone is on the same path. But everyone wants to succeed. The new Wiley Pathways series in Business helps you achieve your goals with its brief, inviting format, clear language, and focus on core competencies and skills.

The books in this series--Finance, Business Communication, Marketing, Business Math, and Real Estate--offer a coordinated curriculum for learning business. Learn more at www.wiley.com/go/pathways.

Su questo libro

Informazioni sull?autore

Steve Slavin, Ph. D., is professor emeritus of economics at Union County College in Cranford, New Jersey. He is the author of several textbooks and self-teaching guides, including Quick Business Math, Math for Your First- and Second- Grader, All the Math You'll Ever Need, , and Economics.

Dalla quarta di copertina

You can get there

Where do you want to go? You might already be working in a business setting. You may be looking to expand your skills. Or, you might be setting out on a new career path.

Wherever you want to go, Business Math will help you get there. Easy-to-read, practical, and up-to-date, this text not only helps you learn fundamental mathematical concepts needed for business, it also helps you master the core competencies and skills you need to succeed in the classroom and beyond. The book’s brief, modular format and variety of built-in learning resources enable you to learn at your own pace and focus your studies.

With this book, you will be able to:

• Understand the business uses of percent calculations.
• Solve business problems using algebraic equations.
• Learn why stores markup and markdown their inventory.
• Calculate different types of discounts.
• Examine different banking options.
• Compare personal, sales, and property taxes and the implications of taxing income, property, and retail sales.
• Calculate simple and compound interest and learn how each affects the future value of money.
• Explore the uses of promissory notes, mortgages, and credit cards and how to calculate the cost of each.
• Learn different ways to determine the loss of value of business property and equipment, and the effect of depreciation on taxes.
• Examine financial statements and learn how to read the income statement and the balance sheet.
• Learn how to calculate the mean, median, mode, and range of data.

Wiley Pathways helps you achieve your goals

When it comes to learning about business, not everyone is on the same path. But everyone wants to succeed. The new Wiley Pathways series in Business helps you achieve your goals with its brief, inviting format, clear language, and focus on core competencies and skills.

The books in this series––Finance, Business Communication, Marketing, Business Math, and Real Estate––offer a coordinated curriculum for learning business. Learn more at www.wiley.com/go/pathways.

Estratto. © Ristampato con autorizzazione. Tutti i diritti riservati.

Wiley Pathways Business Math

By Steve Slavin Tere Stouffer

John Wiley & Sons

Copyright © 2006 Steve Slavin
All right reserved.
ISBN: 978-0-470-00719-8

Chapter One

CALCULATING PERCENTAGES

Converting Decimals and Fractions

Starting Point

Go to www.wiley.com/college/slavin to assess your knowledge of calculating percentages.

Determine where you need to concentrate your effort.

What You'll Learn in This Chapter

* How to convert decimals and fractions to percentages

* The definition of percentage, rate, and base

* How to calculate percentage increase and percentage decrease

* How to find a percentage distribution

After Studying This Chapter, You'll Be Able To

* Apply the methods for converting decimals and fractions to percentages

* Examine the relationship between percentage, rate, and base

* Calculate percentage increase and percentage decrease

* Compare the uses of percentage distribution

Goals and Outcomes

* Master the terminology, understand the procedures/perspectives, and recognize the tools used in calculating percentages

* Understand the business uses of percentage calculations

* Use tools and technique to analyze percentage changes and distributions

INTRODUCTION

Much of the business world requires a thorough understanding of percentages. Percentages are really decimals and fractions (see Chapters 1 and 2) dressed up to look a little different. When you learn how to convert percentages into decimals or fractions and vice versa, solving percentage problems is a snap, including those tricky "30% off" and "50% increase" problems.

3.1 Writing Decimals and Fractions as Percentages

The first step in solving any percentage problem is to understand the connection between percentages and decimals (or fractions). Any percentage can be expressed as a fraction or as a decimal, and any decimal or fraction can be expressed as a percentage.

3.1.1 Converting Decimals to Percentages

To convert a decimal to a percentage, you move the decimal place two places to the right and add a percent sign (%). For example, to convert the decimal 0.255, you move the decimal point two places to the right and add a percent sign, to get 25.5%. (Keep in mind that with a whole number such as 25, you don't need the decimal point at the end [i.e., 25.] because a decimal point at the end of any whole number is implied.)

Try converting these decimals to percentages:

1. 0.32

2. 0.835

3. 1.29

4. 0.03

5. 0.41

How do you convert the decimal 1.2? In this case, you simply add a 0 to the end of the number so that you can move the decimal point two places: 1.20 = 120%. You can add a zero if doing so doesn't change the value of the number. So, you can't add a zero to 30, because the new value would be 300. But you can add a zero to 1.2, because 1.2 and 1.20 are the same number.

How would you convert the decimal 5? To figure this one out, you place the implied decimal point at the end of the number (i.e., 5.) and add two zeros (i.e., 5.00). Then you move the decimal two places, and you get 500%.

You would follow the same procedure for 82 or 306. You simply add the implied decimal point and any zeros, as needed, and move the decimal two places: 82.00 = 8200% and 306.00 = 30600%.

3.1.2 Converting Percentages to Decimals

To change a percentage to a decimal, you simply reverse the process: Move the decimal point two places to the left. For example, 78% = 78.0% = 0.78.

Try converting the following percentages to their decimal equivalents:

1. 25%

2. 33%

3. 45.2%

4. 82.25%

5. 600%

6. 42%

7. 326.9%

8. 7.125%

9. 82% 10. 500%

3.1.3 Converting Fractions to Percentages

To convert a fraction to a percentage, you must first convert the fraction to a decimal (i.e., divide the numerator by the denominator) and then use the procedure described in Section 3.1.1. See Chapter 2 for information on converting fractions to decimals.

Let's take a closer look at the relationship among decimals, fractions, and percentages. We'll begin with the fraction 1/100. How much is 1/100 as a percentage? It's 1%. How much is the decimal? It's 0.01. So,

1/100 = 0.01 = 1%

In fact, any time you have a fraction with 100 in the denominator, the percentage will be the numerator. For this reason, if you can get 100 in the denominator (e.g., by multiplying), you can easily find the percentage.

For example, suppose you are given 1/50 and asked to find the percentage. You want to get 100 in the denominator, so you multiply both the numerator and denominator by 2, as follows:

1/50 x 2/2 = 2/100 = 2%

If you have 2/20, you multiply both the numerator and the denominator by 5, as follows:

2/20 x 5/5 = 10/100 = 10%

This is a simple shortcut that prevents you from having to divide the numerator by the denominator, as you are instructed to do in Chapter 2. Hint: This works only if the denominator is a factor of 100, such as 2, 4, 5, 10, 20, 40, or 50.

Try converting the following fractions to percentages:

1. 1/25

2. 7/25

3. 40/80

4. 3 1/2

5. 4/50

6. 2/30

7. 4 1/5

8. 9/10

9. 45/90

10. 16/32

FOR EXAMPLE

Why Do We Need to Know Percentages?

In the business world, the use of percentages, decimals, and fractions is intertwined. Business leaders and others-and even advertisements-talk in terms of percentages when those numbers sound impressive: "300% increase in profits," "200% reduction in defects," "20% more for your money," and "50% off sale." When fractions sound better, those terms are used instead: "One-quarter of our staff," "Three-quarters of those surveyed," and so on. But in order to put a fraction into an equation and make quick calculations, you need to know its decimal equivalent. If you can easily calculate that 300% is 3.0, 20% is 0.20, and three-quarters is 0.75, you can fiddle with-and even question-the numbers you see in corporate reports and in company advertisements.

It is useful to memorize the common percentages and their decimal and fractional equivalents. The following chart lists some of the most common:

Percentage Decimal Fraction

25% .25 1/4

33 1/3% .3333 1/3

50% .50 1/2

12 1/2% .125 1/8

75% .75 3/4

66 2/3% .67 2/3

20% .2 1/5

80% .8 4/5

SELF - CHECK

Describe how to convert decimals to percentages and vice versa.

Review how to convert fractions to decimals.

Draw basic conclusions about the relationship between decimals and percentages.

3.2 Finding the Percentage, Base, and Rate

Percentage (amount), base, and rate are three components involved in calculating percentages. The rate, which is the number of hundredths parts taken, is commonly followed by a percent sign or a decimal; it is a fraction representing a relationship between the percentage and the base. The base is the number on which the rate operates, the starting amount. The percentage is the part of the base determined by the rate. Confused? It's really quite simple if you look at the following equation:

P = B x R

So, for example, in the equation

* 10% is the rate.

* 90 is the base.

* 9 is the percentage.

3.2.1 Finding the Percentage When the Base and Rate Are Known

As mentioned in the preceding section, if you know the base and rate, you can calculate the percentage, by using this formula:

P = B x R

For example, what number is 8% of 65? In this case, the base is 65, and the rate is 8%. To find the percentage, you say "8% of 65 is what?" (Note that of always means "multiply," and is always means "equals.") In this case, you can set up the following equation:

P = B x R

8% x 65 = ?

0.08 x 65 = 3

Therefore, 8% of 65 is 3.

Try finding the percentages for the following:

1. 25% of 100

2. 10% of 300

3. 5% of 25

4. 6% of 9.95

5. 11% of 10

6. 1/2% of 100 7. 400% of 50

8. 2% of 90

9. 1% of 9 10. 20% of 16.95

3.2.2 Finding the Rate When the Base and Percentage Are Known

If you know the base and percentage, you can find the rate, by using this formula:

R = [P/B]

For example, 18 is what percentage of 72? Here, the base is 72, and the percentage is 18. You can make this into a simple equation:

18 = ?% x 72

To find the answer, you divide each side of the equation (that is, each set of numbers on either side of the equals sign) by 72, as follows:

R = [P/B]

18 = [?%/72]

18/72 = ?%/72

0.25 = ?%

= 25%

Chapter 4 discusses this process in more depth.

Try finding the following rates:

1. 60 is what percentage of 600?

2. 15 is what percentage of 150? 3. 700 is what percentage of 70,000?

4. 45 is what percentage of 180?

5. 200 is what percentage of 25?

6. 27 is what percentage of 200? 7. $4 is what percentage of $100?

8. 9 is what percentage of 10?

9. 1,000 is what percentage of 1,200?

10. 82 1/2 is what percentage of 141?

3.2.3 Finding the Base When the Percentage and Rate Are Known

If you know the percentage and rate, you can find the base by again using this formula:

P = R x B

For example, 10 is 25% of what number? In this case, the rate is 25%, and the percentage is 10. To solve this, you make it into a simple equation:

10 = 25% x ?

Then you convert the rate to a decimal, 0.25, and plug that in to the equation:

10 = 0.25% x ?

To find the answer, you divide each side of the equation by 0.25, like this:

10 = 0.25 x ?

10/0.25 = 0.25/0.25 x ?

40 = ?

Try finding the following bases:

1. 10 is 40% of what? 2. 15 is 30% of what?

3. 25 is 4% of what?

4. 40 is 10% of what?

5. 60 is 300% of what?

FOR EXAMPLE

Base, Rate, and Percentage in the Real World

Base, rate, and percentage are used extensively in business and personal finance. Suppose you're planning to buy a house that costs $130,000. The mortgage company wants you to put down 20%. In this case, you know the rate (20%) and the base ($130,000). You need to find the percentage to know how much money you need to put down. In words, you say this as "20% of $130,000 is what?" This equates to the simple equation 20% x $130,000 = ? or 0.20 x $130,000 = $26,000. So you need to come up with a $26,000 down payment.

SELF - CHECK

Define base, rate, and percentage.

Describe how these three terms interrelate.

Set up simple equations.

Calculate one quantity when you know the other two.

3.3 Percentage Increases and Decreases

Suppose you were earning $500 per week and got a $20 raise. By what percentage did your salary go up? You use the following equation to find out:

Percentage change = Change/Original number

Your salary is the original number, and your raise is the change:

Percentage change = $20/$500 = 2/50 = 4/100 = 4%

Therefore, the percentage change is an increase of 4%.

Here's an example of a percentage decrease problem: On New Year's Eve, you made a resolution to lose 30 pounds by the end of July. After eating less and exercising five days per week for seven months, your weight dropped from 140 pounds to 110 pounds. By what percentage did your weight decrease? Here's how you figure it out:

Percentage change = Change/Original number

Percentage change = 30/140 = 3/14 = 0.2143 = 21.43%

If you know the original number and the percentage change and want to calculate the amount of the change, you use the following formula:

Change = Original number x Percentage change

For example, say your corporation is giving you a 5% bonus for your excel- lent work on the Alpha Project. If the bonus is based on your current salary of $42, 000, how much is your bonus? Here's how you figure it out:

? = 42,000 x .05 = $2,100.00

If you want to know not just the change but also the new number, you have to add in the original number:

New number = Change + Original number

Here's an example: Your restaurant bill is $40.00, and you would like to leave the service staff a 20% tip. How much cash must you leave? Here's how you figure it out:

New number = (Original number x Percentage change) + Original number

New number = (40 x 20%) + 40

New number = (40 x 0.20) + 40

New number = $8 + $40 = $48

If you're calculating a percentage change that results in a decrease from the original number, you subtract the change from the original number, as follows:

New number = Original number - (Original number x Percentage change)

Try figuring out the following percentage changes:

1. You expect an increase in sales this summer at your water and ice stand, from 150 cups per day to 175. What is the rate of increase?

2. As a result of spending $6 million in additional advertising this year, your local cable provider forecasts new installations to be at a 20% rate of increase over the prior year. If the company installed 30 new cable customers per week in the prior year, how many can be expected per week this year?

3. Say that sales increase by 210 units. What is the rate increase if original sales were 1,415 units? 4. Your salary increases from $435 per week to $497. What is the rate of increase?

For Example

Percentage Change Applications

Not sure where you'll use percentage change in the real world? In business, percentage change comes up all the time. Suppose you manage human resources for a small company. Because the company's profits grew 30% last year, you've been allocated an additional 30% in your annual budget to hire new employees. If last year's budget was $720,000, how much do you have to spend this year? Here's how you figure it out:

New number = (Original number x Percentage change) + Original number

New number = ($720,000 x 30%) + $720,000

New number = ($720,000 x 0.20) + 40

New number = $216,000 + $720,000 = $936,000

SELF - CHECK

Calculate percentage increase, percentage decrease, and percentage change.

Discuss the amount you have left when you experience a 100% decrease.

3.4 Percentage Distribution

A corporate in-service training session is composed of half men and half women. What percentage of the session is men and what percentage is women? The answers are pretty obvious: 50% and 50%. In a nutshell, that's all there is to percentage distribution. Sure, the problems get a little more complex than this, but the totals always add up to 100%.

Suppose one-quarter of the management team is in sales, one-quarter is from the accounting department, and the rest are support staff. What is the team's percentage distribution of sales, accounting, and support staff? Here's how you figure it out:

* Sales are 1/4, or 25%.

* Accountants are also 1/4, or 25%.

* Support staff must be the remaining 50%.

(Continues...)

Excerpted from Wiley Pathways Business Mathby Steve Slavin Tere Stouffer Copyright © 2006 by Steve Slavin. Excerpted by permission.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.

Dettagli dell'edizione

• Editore: JW
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 0470007192
• ISBN 13: 9780470007198
• Rilegatura: Copertina flessibile
• Numero di pagine: 310
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile