CChapter 1 hapter 1 RResource Mastersesource Masters

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Chapter 1 Chapter 1 Resource MastersResource Masters

ContentsChapter Resources• Family Letter • Are You Ready Worksheets• Diagnostic Test • Pretest

Language Arts Resources• Student Glossary

Practice and Reinforcement• Facts Practice

Leveled Lesson Resources• Explore• Reteach• Skills Practice• Homework Practice• Problem-Solving Practice• Enrich

Technology Resources• Graphing Calculator Activity• Scientific Calculator Activity• Spreadsheet Activity

Assessment Resources• Reflecting on the Chapter• Chapter Quizzes• Vocabulary Test• Chapter Tests• Standardized Test Practice• Extended-Response Test• Student Recording Sheet• Chapter Project Rubric

Answer Pages

ChapterResource Masters

are provided forevery chapter in both

print and digitalformats.

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Copyright © by the McGraw-Hill Companies, Inc. All rights reserved. Permission is granted to reproduce the material contained herein on the condition that such materials be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Math Connects, Course 3. Any other reproduction, for use or sale, is expressly prohibited without prior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

ISBN: 978-0-07-892300-5MHID: 0-07-892300-X Math Connects, Course 3

Printed in the United States of America.

2 3 4 5 6 7 8 9 10 032 18 17 16 15 14 13 12 11 10 09

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CONTENTSCONTENTSTeacher’s Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Chapter 1 ResourcesFamily Letter . . . . . . . . . . . . . . . . . . . . . . 1Are You Ready?

AL Practice Worksheet . . . . . . . . . . . . . . . . . 5

Review Worksheet . . . . . . . . . . . . . . . . . . . . . . 6

BL Apply Worksheet . . . . . . . . . . . . . . . . . . . 7

Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . 8

Pretest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Language Arts ResourcesStudent Glossary . . . . . . . . . . . . . . . . . . . . . . 10

Practice and Reinforcement Facts Practice . . . . . . . . . . . . . . . . . . . . . . . . . 11

Lesson Resources

A Rational NumbersAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 12

Skills Practice . . . . . . . . . . . . . . . . . . . . . . 13Homework Practice . . . . . . . . . . . . . . . . . . 14Problem-Solving Practice . . . . . . . . . . . . . 15BL Enrich. . . . . . . . . . . . . . . . . . . . . . . . . 16

B Add and Subtract Rational NumbersAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 17


C Multiply Rational NumbersAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 22

Skills Practice . . . . . . . . . . . . . . . . . . . . . . 23Homework Practice . . . . . . . . . . . . . . . . . . 24

Problem-Solving Practice . . . . . . . . . . . . . 25BL Enrich. . . . . . . . . . . . . . . . . . . . . . . . . 26

D Divide Rational NumbersAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 27


Lesson Resources

A PSI: Look for a PatternAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 32

Skills Practice . . . . . . . . . . . . . . . . . . . . . . 33Homework Practice . . . . . . . . . . . . . . . . . . 34Problem-Solving Practice . . . . . . . . . . . . . 35

B Compare Rational NumbersAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 36


C Algebra: The Percent Proportion and EquationAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 41


TI-84 Plus Activity . . . . . . . . . . . . . . . . . . 46

AL = Approaching Level BL = Beyond Level

Lesson

1-1

Lesson

1-2

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Lesson Resources

A Discount, Markup, and Sales TaxAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 47


TI-73 Activity . . . . . . . . . . . . . . . . . . . . . 52

B Financial Literacy: InterestAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 53


TI-73 Activity . . . . . . . . . . . . . . . . . . . . . 58

D Percent of ChangeAL Reteach . . . . . . . . . . . . . . . . . . . . . . . 59


Assessment ResourcesReflecting on Chapter 1 . . . . . . . . . . . . . . . . 64

Chapter Quizzes . . . . . . . . . . . . . . . . . . . . . . 65

Vocabulary Test . . . . . . . . . . . . . . . . . . . . . . . 68

Chapter Tests

AL 1A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

AL 1B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

2A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

2B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

BL 3A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

BL 3B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Standardized Test Practice . . . . . . . . . . . . . . 81

Extended-Response Test . . . . . . . . . . . . . . . . 83

Extended-Response Rubric . . . . . . . . . . . . . . 84

Student Recording Sheet . . . . . . . . . . . . . . . 85

Chapter Project Rubric . . . . . . . . . . . . . . . . . 86

Answers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .A1

Lesson

1-3

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Teacher’s Guide to Using theChapter 1 Resource Masters

The Chapter 1 Resource Masters includes the core materials needed forChapter 1. These materials include information for families, student worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing from the online Teacher Edition.

Family ResourcesFamily Introduction to Course 3 (Available in Chapter 0)

• Talks about the focus of the grade level • Gives Web site information.

Family Letter • English and Spanish • Overview of the chapter • Key vocabulary • Provides at-home activities

Chapter ResourcesAre You Ready Worksheets • Use after the Are You Ready section in the Student Edition. • AL Review: Approaching-level students • Practice: On-level students • BL Apply: Beyond-level students

Chapter Diagnostic Test • Use to test skills needed for success in the upcoming chapter. • Retest approaching-level students after the Are You Ready? worksheets.

Chapter Pretest • Quick check of the upcoming chapter’s concepts to determine pacing • Use before the chapter to gauge students’ skill level. • Use to determine class grouping.

NAME ________________________________________ DATE _____________ PERIOD _____

Chapter 1 1

Course 3

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Family Letter1Chapter

Key Vocabulary

Dear Parent or Guardian:

Today we began Chapter 1: Rational Numbers and Percent. In this chapter, your student will learn how to add, subtract, multiply, and divide positive and negative fractions. Also, we will be applying percents to find discount, markup, and sales tax. Included in this letter are key vocabulary words and activities you can do with your student. You may also wish to log on to glencoe.com for other study help. If you have any questions or comments, feel free to contact me at school.

Sincerely,

_____________________

Rational Numberslike fractions Fractions that have the same denominator.

multiplicative inverses Two numbers with a product of 1.

rational numbers Any number that can be written as a fraction.

Percentcompound interest Interest paid on the initial principal and on interest earned in the past.

discount A decrease in price from the original price.

markup The increase in the wholesale price of an item sold.

percent of change The percent that an amount changes from its original amount.

simple interest The amount of money earned or paid on the initial principal of a savings account or loan.

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NAME ________________________________________ DATE _____________ PERIOD _____

Chapter 1 14

Course 3

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1-1A

Write each fraction or mixed number as a decimal. 1. 3 − 5 2. 5 − 8 3. 9 − 20

4. 37 − 50 5. - 11 − 16 6. - 9 − 32

7. 3 1 − 5 8. 4 3 − 8 9. 5 − 33

10. - 7 − 9 11. -8 11 − 18 12. -9 11 − 30

Write each decimal as a fraction or mixed number in simplest form. 13. -0.8 14. 0.44 15. -1.35

16. 0. − 8 17. -1. − 5 18. 4. −− 45

19. POPULATION Refer to the table at the right. a. Express the fraction for Asian as a decimal.

b. Find the decimal equivalent for the fraction of the population that is African American.

c. Write the fraction for Hispanic as a decimal.

20. MEASUREMENTS Use the figure at the right. a. Write the width of the jellybean as a fraction. b. Write the width of the jellybean as a decimal.

Homework PracticeRational Numbers

in. 1

Population of Florida by RaceRace Fraction of

Total PopulationAsian 1 − 50

African American 4 − 25

Hispanic 1 − 5

Get ConnectedGet Connected For more examples, go to glencoe.com.


12/18/08 2:49:11 PM

Language Arts ResourcesStudent Glossary • Includes key vocabulary terms from the chapter • Students record definitions and/or examples for each term. • Students can use the page as a bookmark as they study the chapter

Practice and ReinforcementFacts Practice • Quick recall of concepts needed in the upcoming chapter • Use as a timed test to gauge student mastery of prior concepts.

Lesson Resources

Reteach • Provides vocabulary, key concepts, additional worked-out

examples, and exercises • Use for students who have been absent.

Skills Practice • Focuses on the computational nature of the lesson • Use as an additional practice. • Use as homework for second-day teaching.

Homework Practice • Mimics the types of problems found in the Practice

and Problem Solving of the Student Edition • Use as an additional practice. • Use as homework for second-day teaching.

Problem-Solving Practice • Includes word problems that apply the concepts of the lesson • Use as an additional practice. • Use as homework for second-day teaching.

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Enrich • Provides an extension of the concepts, offers a

historical or multicultural look at the concepts, or widens students’ perspectives on the mathematics

• For use with all levels of students

Technology Activities • Presents ways in which technology can be used with the

concepts in some of the lessons • Use as an alternative approach to teaching the concept. • Use as part of the lesson presentation.

Assessment Resources

Reflecting on Chapter 1 • Three open-ended questions • Allows students to write about mathematics

Chapter Quizzes • Free-response questions • One quiz for each multi-part lesson

Vocabulary Test • Includes a list of vocabulary words and questions to assess students’ knowledge of

those words • Use in conjunction with one of the Chapter Tests.

Chapter Tests • AL 1A-1B Approaching-level students Contains multiple choice questions • 2A-2B On-level students Contains both multiple-choice and free-response questions • BL 3A-3B Beyond-level students Contains free-response questions • Tests A and B are the same format with different numbers. Use when students are absent or for different rows.

Standardized Test Practice • Test is cumulative. • Includes multiple-choice and short-response questions

NAME ________________________________________ DATE _____________ PERIOD _____

SCORE _____

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1Chapter

Chapter 1 81

Course 3

Read each question. Then fill in the correct answer. 1. Write –5 7 − 8 as a decimal. A. –0.875 B. –4.125 C. –4.375 D. –5.875 2. Write –2.18 as a fraction in simplest form. F. –2 18 − 100 G. –2 9 − 50 H. –1 41 − 50 I. –1 82 − 100 3. Find –4 3 − 5 – (–4 3 − 5 ). Write in simplest form. A. 9 1 − 5 B. 0 C. –1 1 − 5 D. –8 2 − 5 4. Find 2 − 5 + 3 − 8 . Write in simplest form. F. 1 − 8 G. 3 − 20 H. 5 − 13 I. 31 − 40 5. GEOMETRY Find the area of a square with sides that measure 1 3 − 8 inches. A. 1 9 − 64 in2 B. 1 57 − 64 in2 C. 2 3 − 4 in2 D. 5 1 − 2 in2

6. A number cube is rolled twice. Find P(odd and even). F. 1 G. 1 − 2 H. 1 − 4 I. 1 − 8 7. What is the multiplicative inverse of 11 − 7 ? A. 7 − 11 B. – 7 − 11 C. – 11 − 7 D. –77 8. BAKING Jose needs 1 2 − 3 cups of flour for a cake recipe. How many cakes can he make for the school carnival if he has 15 cups of flour? F. 25 G. 16 2 − 3 H. 13 1 − 3 I. 9 9. Write 98% as a decimal.

1. A B C D

2. F G H I

3. A B C D

4. F G H I

5. A B C D

6. F G H I

7. A B C D

8. F G H I

9.

Standardized Test Practice(Chapter 1)

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Chapter 1 64

Course 3

1. Write about one new thing you learned in this chapter.

2. Create a problem in which an item is advertised as being on sale. Then explain how to find the percent of change in the price.

3. Write about the concepts of markup, discount, and selling price. Provide real-world examples of where these concepts are used.

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1-1A

A Triangular Line DesignConnect each pair of equivalent rational numbers with a straight line segment. Although you will draw only straight lines, the finished design will appear curved!

722 13

16 711

120

118

112

116

130

513

13 3

7 38

19

18

341

4

59

78

16

23

12

15

17

0.03

0.428571

0.318

0.333

0.666

0.166

0.875

0.5

0.8125

0.11

0.384615

0.375

0.142857

0.6363

0.083

0.05

0.2

0.250.05

0.750.125

0.06250.5

Enrich

Chapter 1 16

Course 3


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Extended-Response Test • Contains performance-assessment tasks • Sample answers are included.

Extended-Response Rubric • The scoring rubric for the Extended-Response Test

Student Recording Sheet • Corresponds with the Test Practice at the end of the

Student Edition chapter

Chapter Project Rubric • The scoring rubric for the Chapter Project found in the

Teacher Edition

Answers

Chapter and Lesson Resources • Chapter Resources, Facts Practice, and Lesson Resources are provided as reduced

pages with answers appearing in black.

Assessments • Full-size answer keys are provided for the assessment masters.

NAME ________________________________________ DATE _____________ PERIOD _____

SCORE _____

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1Chapter

Chapter 1 85

Course 3

Student Recording Sheet

Use this recording sheet with pages 86-87 of the Student Edition.Fill in the correct answer. For gridded-response questions, write your answers in the boxes on the answer grid and fill in the bubbles to match your answers.

1. A B C D

2.

3. F G H I

4. A B C D

5. F G H I

6. A B C D

7.

8. F G H I

9.

10. A B C D

11.

12. F G H I

Extended ResponseRecord your answers for Exercise 13 on the back of this paper.

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NAME ________________________________________ DATE _____________ PERIOD _____

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Chapter 1 1 Course 3

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.Family Letter1

Chapter

Key Vocabulary

Dear Parent or Guardian:

Today we began Chapter 1: Rational Numbers and Percent. In this chapter,

your student will learn how to add, subtract, multiply, and divide positive and

negative fractions. Also, we will be applying percents to find discount, markup,

and sales tax. Included in this letter are key vocabulary words and activities

you can do with your student. You may also wish to log on to glencoe.com

for other study help. If you have any questions or comments, feel free to

contact me at school.

Sincerely,

_____________________

Rational Numbers

like fractions Fractions that have the same denominator.

multiplicative inverses Two numbers with a product of 1.

rational numbers Any number that can be written as a fraction.

Percentcompound interest Interest paid on the initial principal and on interest earned in the past.

discount A decrease in price from the original price.

markup The increase in the wholesale price of an item sold.

percent of change The percent that an amount changes from its original amount.

simple interest The amount of money earned or paid on the initial principal of a savings

account or loan.

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NAME ________________________________________ DATE _____________ PERIOD _____

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Chapter

Materials: paper, pencil, ruler, four household items such as a paperclip, spoon, etc.

• Divide the paper into four pieces.

• Write the name of one of the household items on each.

• Measure one dimension of each item to the nearest 1 − 8 inch and write the length on the corresponding piece of paper.

• Order the household items from smallest to largest based on the length measured.

• Place the corresponding pieces of paper in the same order and compare the fractions.

• Choose three pages from the newspaper.

• For each page, write a percent that represents the amount of space used for advertising and a percent for the amount of space used for the articles.

• Write each percent as a fraction. Then add the pair of fractions for each page.

• Discuss what you find for each page.

Real-World Activity

Hands-On Activity

At-Home Activities

1 in.18

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NOMBRE ______________________________________ FECHA ____________ PERÍODO ____

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.Carta a la familia1

CapÍtulo

CapÍtulo 1 3 Course 3

Estimado padre o apoderado:

Hoy comenzamos el Capítulo 1: Números racionales y porcentaje. En este

capítulo, su estudiante aprenderá a sumar, restar, multiplicar y dividir

fracciones positivas y negativas. Además, aplicaremos porcentajes para calcular

descuentos, márgenes de utilidad e impuestos sobre las ventas. En esta carta

se incluyen palabras del vocabulario clave y actividades que pueden realizar

con su estudiante. Si desean obtener más ayuda para el estudio, visiten

glencoe.com. Si tienen alguna pregunta o desean hacer algún comentario,

pueden contactarme en la escuela.

Sinceramente,

Vocabulario clave

Números racionales

fracciones semejantes Fracciones que tienen el mismo denominador.

inversos multiplicativos Dos números cuyo producto es 1.

números racionales Cualquier número que se puede escribir como fracción.

Porcentajesinterés compuesto Interés que se paga sobre el capital inicial y sobre los intereses ganados

en el pasado.

descuento Disminución del precio original.

margen de utilidad Aumento sobre el precio al mayor de un artículo vendido.

porcentaje de cambio Porcentaje en que cambia una cantidad a partir de la cantidad

original.

interés simple Cantidad de dinero ganada o pagada sobre el capital inicial de una cuenta de

ahorros o de un préstamo.

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CapÍtulo

CapÍtulo 1 4 Course 3

Actividades para el hogar

Actividad manual

Materiales: papel, lápiz, regla, cuatro artículos del hogar como un clip, una cuchara, etc.

• Dividan el papel en cuatro trozos.

• Escriban el nombre de cada uno de los artículos del hogar en cada papel.

• Midan las dimensiones de cada artículo al 1 − 8 de pulgada más cercano y escriban la longitud en el papel correspondiente.

• Ordenen los artículos de menor a mayor según las longitudes medidas.

• Coloquen los trozos de papel correspondientes en el mismo orden y comparen las fracciones.

Actividad concreta

• Elijan tres páginas de un periódico.

• Para cada página, escriban un porcentaje que represente la cantidad de espacio empleado en promociones y un porcentaje de la cantidad de espacio empleado en artículos.

• Escriban cada porcentaje como fracción y luego sumen el par de fracciones de cada página.

• Comenten sus cálculos para cada página.

1 in.18

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Mercado fresco

FresasfrescasFresasfrescas


NAME ________________________________________ DATE _____________ PERIOD _____

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Are You ReadyAre You Readyfor Chapter 1?for Chapter 1?

Practice


Add, subtract, multiply, or divide.

1. –22 + 35

2. 44 – (–12)

3. –11(–12)

4. –33 ÷ (–11)

5. FOOTBALL Milo is a running back on his middle school football team. On his first running play he netted –8 yards, and on his second running play he netted –6 yards. What is the average of his two carries?

6. TEMPERATURE The high temperature for the day was 77° while the low was 52°. What is the difference between the high and low temperature for the day?

Solve each proportion.

7. - 6 − 7 = m −

21

8. 10 − n = 2 − 3

9. 18 − 24

= p −

4

10. 12 − p = 1 − 3

11. 12 − 4 = 75 − n

12. 64 − 48

= 36 − y

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.


NAME ________________________________________ DATE _____________ PERIOD _____

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Review• To add integers with the same sign, add the absolute value of each number. The sum has the sign of

the integers.• To add integers with different signs, find the difference of their absolute values. The sum has the sign

of the integer with the greater absolute value.

Example 1

Find -22 + (-33).

–22 + (–33) = -55 |- 22| + |- 33| = 55

The sum is negative because both integers are negative.

Example 2

Find -41 + 20.

− 41 + 20 = -21 |- 41| - |20| = 21

The sum is negative because |- 41| > |20|.

Exercises

Add the integers with the same sign.

1. 147 + 13

2. -55 + (-31)

3. 18 + 71

Add the integers with different sign.

4. -14 + 21

5. 12 + (-56)

6. -4 + 18

Add the integers.

7. -31 + (-17)

8. 72 + (-22)

9. 47 + 23

1.

2.

3.

4.

5.

6.

7.

8.

9.


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Apply 1. AUTOMOBILES Killian’s tire is leaking

air. The change in the amount of air is –2 cubic inches per minute. At this rate, how many minutes will it be before the total change is –16 cubic inches?

2. STOCKS Helen owns stock in the Do Well company. Over the past 4 days, the value of her stock fell $5 each day. What is the total change in the price of her stock during these four days?

3. TENNIS Louis played tennis while in middle school. The table shows the number of wins and losses he had in each of the three years. How many matches did Louis win during his middle school career?

Grade Wins Losses6th 12 37th 9 88th 11 2

4. DEBT Kenneth wanted to buy a skateboard but found that he did not have enough money. To make his purchase, he borrowed $5 from Dontrell, $2 from Serena, and $27 from Linda. If he did not owe any money to start with, what is the total change in his debt?

5. TEMPERATURE During the course of a 6-hour period the temperature dropped 18°. What was the average change in temperature per hour?

6. SCIENCE A microscope slide shows 35 red blood cells out of 60 blood cells. Write and solve a proportion to find how many red blood cells would be expected in a sample of the same blood that has 840 blood cells.


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Chapter

Diagnostic Test

Add, subtract, multiply, or divide.

1. 15 + (-3)

2. 21 - (-6)

3. -5(13)

4. -25 ÷ 5

5. BALLOON RIDES Dakota is taking a balloon ride. The balloon first ascends to 850 feet and then descends 75 feet. What is the current height of the balloon?

6. SHOPPING Toni had $45 dollars to spend. She bought a book for $13 and then found a ten dollar bill on her way home. How much money did she have when she got home?

Solve each proportion.

7. 3 − 7 = 9 − w

8. p −

8 = 5 −

4

9. 25 − 60

= t − 12

10. 35 − 50

= y −

10

11. 7 − 9 = 70 − m

12. 64 − n = 16 − 4

13. 45 − 60

= n − 12

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.


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.1

Chapter

Pretest

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Add, subtract, multiply, or divide. Write in simplest form.

1. - 3 − 4 · 8 −

9

2. - 2 − 5 + 4 −

5

3. 3 1 − 3 ÷ 5 −

6

4. 1 − 6 - (- 1 −

3 )

5. Write 13.1% as a decimal.

6. 17 is what percent of 68?

7. BUSINESS A paint store buys a gallon of paint at a wholesale price and then prices it to sell at a 50% markup. If a gallon of paint costs the store $16, what is the selling price of the gallon of paint?

8. SPORTS A sporting goods store is advertising a 30% off sale on soccer balls. Panna wants to buy a soccer ball that originally costs $44.50. Find the sale price of the soccer ball.

9. ANIMALS Dorie’s kitten weighed 14 ounces when she brought it home. One year later that same kitten weighed 30 ounces. Find the percent of change in the kitten’s weight. Round to the nearest tenth.

10. COAT Lorrene bought a coat for $67.20 that was on sale for 20% off. What was the original price of the coat?

11. PET FOOD The pet store’s food stock went from 1,500 cans of food to 1,200 cans in one week. What was the percent of decrease?


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Chapter

Student Glossary

This is an alphabetical list of new vocabulary terms you will learn in Chapter 1. Fold the page vertically and use it as a bookmark. As you study the chapter, write each term’s definition or description in as few words as possible.

Vocabulary Word Definition/Description/Example

compound interest

discount

like fractions

markup

multiplicative inverses

percent equation

percent of change

percent proportion

rational number

simple interest

Fold over


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Chapter

Facts Practice

Write each fraction as a percent.

1. 7 − 8 2. 3 −

4 3. 1 −

10 4. 3 −

11

5. 7 − 20

6. 5 − 8 7. 1 −

5 8. 1 −

3

9. 5 − 16

10. 9 − 40

11. 3 − 8 12. 4 −

9

13. 7 − 50

14. 11 − 25

15. 7 − 15

16. 4 − 25

17. 13 − 50

18. 11 − 12

19. 1 − 100

20. 7 − 16


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AReteachRational Numbers

To express a fraction as a decimal, divide the numerator by the denominator.

Write 3 − 4 as a decimal.

3 − 4 means 3 ÷ 4.

The fraction 3 − 4 can be written as 0.75, since 3 ÷ 4 = 0.75.

Write -0.16 as a fraction in simplest form.

-0.16 = - 16 − 100

0.16 is 16 hundredths.

= - 4 − 25

Simplify.

The decimal -0.16 can be written as - 4 − 25

.

Write 8. − 2 as a mixed number in simplest form.

Assign a variable to the value 8. − 2 . Let N = 8.222… . Then perform the operations on N to determine its value.

N = 8. − 2 or 8.222… .

10(N) = 10(8.222) Multiply each side by 10 because 1 digit repeats.

10N = 82.222… Multiplying by 10 moves the decimal point 1 place to the right.

-N = 8.222… Subtract N = 8.222… to eliminate the repeating part.

9N = 74 10N - 1N = 9N

9N − 9 = 74 −

9 Divide each side by 9.

N = 8 2 − 9 Simplify.

The decimal 8. − 2 can be written as 8 2 − 9 .

Exercises Write each fraction or mixed number as a decimal.

1. 2 − 5 2. 3 −

10 3. 7 −

8 4. 2 16 −

25

5. - 2 − 3 6. -1 2 −

9 7. 6 2 −

3 8. -4 3 −

11

Write each decimal as a fraction or mixed number in simplest form.

9. 0.8 10. -0.15 11. 0. − 1 12. 1. − 7

Example 1

Example 2

Example 3


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.1-1

ASkills PracticeRational Numbers

Write each fraction or mixed number as a decimal.

1. 1 − 10

2. 1 − 8

3. - 3 − 4 4. - 4 −

5

5. 21 − 50

6. -3 9 − 20

7. 4 9 − 25

8. 7 − 9

9. -1 1 − 6 10. -2 4 −

15

11. 5 − 33

12. 7 3 − 11


13. 0.9 14. 0.7

15. 0.84 16. -0.92

17. -1.12 18. -5.05

19. -2.35 20. 8.85

21. -0. − 1 22. 4. − 8

23. 6. − 7 24. -8. − 4


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A

Write each fraction or mixed number as a decimal.

1. 3 − 5 2. 5 −

8 3. 9 −

20

4. 37 − 50

5. - 11 − 16

6. - 9 − 32

7. 3 1 − 5 8. 4 3 −

8 9. 5 −

33

10. - 7 − 9 11. -8 11 −

18 12. -9 11 −

30


13. -0.8 14. 0.44 15. -1.35

16. 0. − 8 17. -1. − 5 18. 4. −− 45

19. POPULATION Refer to the table at the right.

a. Express the fraction for Asian as a decimal.

b. Find the decimal equivalent for the fraction of the population that is African American.

c. Write the fraction for Hispanic as a decimal.

20. MEASUREMENTS Use the figure at the right.

a. Write the width of the jellybean as a fraction.

b. Write the width of the jellybean as a decimal.

Homework PracticeRational Numbers

in. 1

Population of Florida by Race

Race Fraction of Total Population

Asian 1 − 50

African American 4 − 25

Hispanic 1 − 5



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.1-1

AProblem-Solving PracticeRational Numbers

1. ASTRONOMY The pull of gravity on the surface of Mars is 0.38 that of Earth. Write 0.38 as a fraction in simplest form.

2. ENERGY Nuclear power provided 78% of the energy used in France in 2005. Write 0.78 as a fraction in simplest form.

3. WEIGHTS AND MEASURES One pint is

about 5 − 9 liter. Write 5 −

9 liter as a decimal.

4. WEIGHTS AND MEASURES One inch is 25.4 millimeters. Write 25.4 millimeters as a mixed number in simplest form.

5. EDUCATION A local middle school has 47 computers and 174 students. What is the number of students per computer at the school? Write your answer as both a mixed number in simplest form and a decimal rounded to the nearest tenth.

6. BASEBALL In the 2008 season, the Florida Marlins won 84 out of 162 games. What was the ratio of wins to total games? Write your answer as both a fraction in simplest form and a decimal rounded to the nearest thousandth.

7. COLLEGES AND UNIVERSITIES Recently, a small college had an enrollment of 1,342 students and a total of 215 faculty. What was the student-faculty ratio for this college? Write your answer as both a mixed number in simplest form and a decimal rounded to the nearest hundredth.

8. BASKETBALL In the 2007–2008 season, Dwayne Wade made 439 field goals out of 937 attempts. What was Dwayne Wade’s ratio of successful field goals to attempts? Write your answer as both a fraction in simplest form and a decimal rounded to the nearest thousandth.


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A

A Triangular Line DesignConnect each pair of equivalent rational numbers with a straight line segment. Although you will draw only straight lines, the finished design will appear curved!

722

1316

711

120

118

112

116

130

513

13

37

38

19

18

34

14

59

78

16

23

12

15

17

0.03

0.428571

0.318

0.333

0.666

0.166

0.875

0.5

0.8125

0.11

0.384615

0.375

0.142857

0.6363

0.083

0.05

0.2

0.25 0.05 0.750.1250.0625 0.5

Enrich



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.1-1

Fractions that have the same denominator are called like fractions. To add or subtract like fractions, add or subtract the numerators and write the result over the denominator.

Example 1 Find 1 − 5 + (- 4 −

5 ) . Write in simplest form.

1 − 5 + (- 4 −

5 ) = 1 + (-4) −

5 Add the numerators. The denominators are the same.

= -3 − 5 or - 3 −

5 Simplify.

Fractions with unlike denominators are called unlike fractions. To add or subtract unlike fractions, rename the fractions using prime fractors to ! nd the least common denominator. Then add or subtract as with like fractions.

Example 2 Find -3 1 − 2 -1 5 −

6 . Write in simplest form.

-3 1 − 2 -1 5 −

6 = - 7 −

2 - 11 −

6 Write the mixed numbers as improper fractions.

= - 7 − 2 · 3 −

3 - 11 −

6 The LCD is 2 · 3 or 6.

= - 21 − 6 - 11 −

6 Rename - 7 −

2 using the LCD.

= -21 -11 − 6 Subtract the numerators.

= - 32 − 6

= - 16 − 3 or -5 1 −

3 Simplify.

Exercises

Add or subtract. Write in simplest form.

1. 4 − 7 + 2 −

7 2. 1 −

10 + 5 −

10 3. 5 −

9 + (- 1 −

9 )

4. 1 − 6 + (- 5 −

6 ) 5. - 3 −

8 + 7 −

8 6. 5 −

11 - (- 4 −

11 )

7. - 7 − 10

- (- 1 − 2 ) 8. 2 1 −

4 + 1 3 −

8 9. 3 3 −

4 -1 1 −

3

10. -1 1 − 5 - 2 1 −

4 11. -2 4 −

9 - (-1 1 −

3 ) 12. 3 3 −

5 -2 2 −

3

BReteachAdd and Subtract Rational Numbers


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1. 7 − 12

+ 5 − 12

2. 1 − 9 + (- 4 −

9 ) 3. - 5 −

7 + (- 3 −

7 )

4. - 9 − 16

+ (- 3 − 16

) 5. 5 − 8 - 3 −

8 6. 13 −

19 - 6 −

19

7. 3 − 13

- (- 11 − 13

) 8. 2 3 − 7 + 1 2 −

7 9. 1 4 −

15 + 4 8 −

15

10. 5 6 − 7 - 3 2 −

7 11. 6 7 −

12 - 3 1 −

12 12. -2 5 −

11 - 7 1 −

11

13. 7 − 8 + 1 −

4 14. 3 −

4 + 2 −

3 15. 6 −

7 - 3 −

14

16. 4 − 5 - 1 −

3 17. 1 −

4 - 5 −

6 18. - 3 −

5 + 1 −

4

19. 3 1 − 6 + 4 1 −

4 20. 1 1 −

2 + (-1 1 −

5 ) 21. 2 3 −

4 + (-6 3 −

8 )

22. 5 1 − 4 + (-2 2 −

3 ) 23. -5 1 −

12 - 3 2 −

3 24. -3 3 −

5 - 9 −

10

BSkills PracticeAdd and Subtract Rational Numbers


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.1-1 Homework Practice

Add and Subtract Rational Numbers


1. - 1 − 4 + 3 −

4 2. - 3 −

8 + (- 1 −

8 ) 3. - 8 −

11 + 10 −

11

4. - 5 − 7 - 4 −

7 5. 11 −

12 - 7 −

12 6. 2 −

15 - (- 7 −

15 )

7. 4 1 − 5 + 6 3 −

4 8. 1 7 −

10 + (-5 3 −

5 ) 9. 7 3 −

5 - (-5 1 −

3 )

10. -3 2 − 3 - 4 5 −

9 11. -4 3 −

5 - 5 9 −

10 12. -18 5 −

12 + 14 3 −

4

13. POPULATION About 1 − 5 of the world’s population lives in China, and about 1 −

6 of the world’s

population lives in India. What fraction of the world’s population lives in other

countries?

ALGEBRA Evaluate each expression for the given values.

14. r + s if r = 8 4 − 5 and s = -3 2 −

5 15. j - k if j = - 5 −

9 and k = 4 5 −

6

GEOMETRY Find the missing measure for each figure.

16. 3

5

3 1 x

4 1

in. in.

in.

17. 10

17

2 1

x

4 3

in.

14 8 5 in.in.

in.

perimeter = 12 23 − 24

in. perimeter = 59 1 − 4 in.

B



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Add and Subtract Rational NumbersB

1. MEASUREMENTS Tate fills a 13 1 − 3 -ounce

glass from a 21 2 − 3 -ounce bottle of juice.

How much juice is left in the bottle?

2. DECORATING Jeri has two posters. One is 4 7 −

10 feet wide and the other is 5 1 −

10

feet wide. Will the two posters fit beside each other on a wall that is 10 feet wide? Explain.

3. HUMAN BODY Tom’s right foot measures 10 2 −

5 inches, while Randy’s

right foot measures 9 4 − 5 inches. How

much longer is Tom’s foot than Randy’s foot?

4. COMPUTERS Trey has two data files on his computer that he is going to combine. One file is 1 4 −

9 megabytes,

while the other file is 3 8 − 9 megabytes.

What will be the size of the resulting file?

5. PETS Laura purchased two puppies from a litter. One of the puppies weighs 4 5 −

6 pounds and the other puppy

weighs 5 1 − 2 pounds. How much more

does the second puppy weigh than the first?

6. AGE Alma is 6 3 − 4 years old, while her

brother David is 3 5 − 6 years old. What

is the sum of the ages of Alma and David?

7. MEASUREMENT Ned pours 7 2 − 5 ounces

of water from a beaker containing 10 1 − 4

ounces. How much water is left in the beaker?

8. GEOMETRY A triangle has sides of 1 1 − 6

inches, 1 1 − 3 inches, and 1 2 −

3 inches. What

is the perimeter of the triangle?


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.1-1

BEnrich

Magic SquaresA magic square is an arrangement of numbers such that the rows, columns, and diagonals all have the same sum. In this magic square, the magic sum is 15.

Find the magic sum for each square in Exercises 1–5. Then fill in the empty cells.

1. 2. 3.

22 3

21 3

23

98

34

54

14

12

2

-2

1

12

4. 5.

14

23

1

1

1

1

112

712

13

112

16

13

381

34

14

116

916

18

1316

12

6. Arrange these numbers to make a magic square.

1 − 2 1 −

3 2 −

3 1 −

4 3 −

4

1 − 6 1 −

12 5 −

12 7 −

12

8

5

27

613

49Column Row

Diagonal


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Multiply 3 − 8 . 4 −


3 − 8 · 4 −

11 = 3 −

8 · 4 −

11 Divide 8 and 4 by their GCF, 4.

= 3 · 1 − 2 · 11

or 3 − 22

Multiply. Then simplify.

To multiply mixed numbers, first rename them as improper fractions.

Multiply -2 1 − 3 · 3 3 −


-2 1 − 3 · 3 3 −

5 = - 7 −

3 · 18 −

5 Rename -2 1 −

3 as 7 −

3 and 3 3 −

5 as 18 −

5 .

= - 7 − 3 · 18 −

5 Divide out common factors.

= - 7 · 6 − 1 · 5

or - 42 − 5 Multiply. Then simplify.

= -8 2 − 5 Write the result as a mixed number.

What is the probability of tossing heads on a coin and rolling a 4 on a number cube?

P(tossing heads) = 1 − 2

P(rolling a 4) = 1 − 6

P(tossing heads and rolling a 4) = 1 − 2 · 1 −

6 or 1 −

12

Exercises

Multiply. Write in simplest form.

1. 2 − 3 · 3 −

5 2. - 1 −

2 · 7 −

9 3. 9 −

10 · 2 −

3

4. - 4 − 7 · (- 2 −

3 ) 5. 2 2 −

5 · 1 −

6 6. -3 1 −

3 · 1 1 −

2

7. 3 3 − 7 · 2 5 −

8 8. -1 7 −

8 · (- 2 2 −

5 ) 9. 2 2 −

3 · 2 3 −

7

10. What is the probability of rolling an even number on a number cube and tossing tails on a coin?

To multiply fractions, multiply the numerators and multiply the denominators.

ReteachMultiply Rational Numbers

Example 1

Example 2

C

Example 3

1

//2

/1

6/


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.1-1 Skills Practice

Multiply Rational NumbersC


1. 1 − 8 · 2 −

3 2. 2 −

9 · 7 −

8 3. 5 −

6 · 3 −

11

4. - 4 − 7 · 3 −

10 5. 2 −

9 · (- 3 −

8 ) 6. - 3 −

5 · -5 −

9

7. 1 3 − 4 · 2 −

3 8. 4 −

5 · 4 3 −

8 9. - 2 −

15 · 5 5 −

6

10. -1 3 − 7 · 1 1 −

5 11. -2 1 −

4 · 1 2 −

3 12. 1 9 −

16 · 2 4 −

5

13. -3 1 − 7 · (-1 2 −

11 ) 14. 2 2 −

3 · (-2 1 −

4 ) 15. (- 4 −

5 ) (- 4 −

5 )

ALGEBRA Evaluate each expression if r = 5 − 6 , s = - 1 −

3 , t = 4 −

5 , and v = - 3 −

4 .

16. rv 17. st 18. rs

19. stv 20. rst 21. rtv

PROBABILITY A number cube is rolled twice. Find each probability.

22. P(2 and 3) 23. P(5 and odd) 24. P(even and prime)


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1. 1 − 4 · 4 −

5 2. 6 −

7 · 1 −

2 3. 3 −

10 · 2 −

3

4. - 15 − 16

· 4 − 5 5. (- 8 −

25 ) 15 −

16 6. (- 7 −

8 ) (- 1 −

7 )

7. 1 1 − 4 · 1 −

5 8. 1 1 −

4 · 1 1 −

5 9. -2 2 −

3 · (- 1 −

4 )

10. 1 − 4 · (- 4 −

15 ) · 5 −

7 11. 2 2 −

5 · 2 1 −

3 · 2 12. 10 · 8.56 · 1 −

2

ALGEBRA Evaluate each expression if a = - 1 − 5 , b = 2 −

3 , c = 7 −

8 , and d = - 3 −

4 .

13. bc 14. ab 15. abc 16. abd

17. COOKING A recipe calls for 2 1 − 4 cups of flour. How much flour would you need

to make 1 − 3 of the recipe?

18. FARMING A farmer has 6 1 − 2 acres of land for growing crops. If she plants corn

on 3 − 5 of the land, how many acres of corn will she have?

PROBABILITY The spinner at the right is spun and a number cube is rolled. Find each probability.

19. P(spinning an odd number)

20. P(rolling a 2)

21. P(spinning an odd number and rolling a 2)

1

2

3

22. P(spinning a 2 or 3 and rolling a number greater than 4)



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.1-1 Problem-Solving Practice


1. NUTRITION Maria’s favorite granola bar has 230 Calories. The nutrition label

states that 7 − 8 of the Calories come from

fat. How many Calories in the granola bar come from fat?

2. ELECTIONS In the last election, 3 − 8 of the

voters in Afton voted for the incumbent mayor. If 424 people voted in Afton in the last election, how many voted for the incumbent mayor?

3. HOBBIES Jerry is building a 1 − 9 scale

model of a race car. If the tires on the actual car are 33 inches in diameter, what is the diameter of the tires on the model?

4. COOKING Enola’s recipe for cookies calls

for 2 1 − 2 cups of flour. If she wants to

make 3 − 4 of a batch of cookies, how much

flour should she use?

5. TRANSPORTATION Hana’s car used 3 − 4 of a

tank of gas to cross Arizona. The gas

tank on her car holds 15 1 − 2 gallons. How

many gallons of gas did it take to cross

Arizona?

6. GEOMETRY The area of a rectangle is found by multiplying its length times its width. What is the area of a

rectangle with a length of 2 1 − 4 inches

and a width of 1 5 − 9 inches?

7. MIDDLE SCHOOL Use the table and information below. There are 480 students enrolled in a middle school located in southern Florida.

a. How many students are enrolled in English?

b. Are more students enrolled in math or science? Explain.

Class

Fraction of

Students Enrolled

English 7 − 8

Math 3 − 4

Art 1 − 5

Science 3 − 5


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Rational Numbers as Ordered PairsIf you think of a rational number as an ordered pair, it

4 n2

2

4

d

0

can be located on a coordinate system. The example graph shows the number 1 −

3 . The horizontal axis is used for the

numerator and the vertical axis for the denominator.

Graph the rational numbers as ordered pairs.

1. 1 − 2 , 2 −

4 , 3 −

6 , 4 −

8 2. 4 −

3 , 8 −

6 , 12 −

9 , 16 −

12 , 20 −

15

4 10862

2

4

6

8d

n0

8 2016124

4

8

12

16d

n0

3. -3 − 2 , -6 −

4 , 3 −

-2 , 6 −

-4 4. -5 −

2 , -10 −

4 , 5 −

-2 , 10 −

-4 , 15 −

-6

4 62-2-4-6

2

-2

4

-4

d

nO

8 12 164-4-8-12 nO

4

8d

-4

-8

5. Complete this generalization: A rational number a − b is shown on a coordinate system

using the ordered pair (a, b). Using this model, equivalent rational numbers will

.

6. Show that this generalization is false: A rational number a − b is shown on a coordinate

system using the ordered pair (a, b). All ordered pairs on the same line stand for equivalent rational numbers.

CEnrich


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DReteachDivide Rational Numbers

Two numbers with a product of 1 are multiplicative inverses, or reciprocals, of each other.

Write the multiplicative inverse of -2 3 − 4 .

-2 3 − 4 = - 11 −

4 Write -2 3 −

4 as an improper fraction.

Since - 11 − 4 (- 4 −

11 ) = 1, the multiplicative inverse of -2 3 −

4 is - 4 −

11 .

Find 3 − 8 ÷ 6 −


3 − 8 ÷ 6 −

7 = 3 −

8 · 7 −

6 Multiply by the multiplicative inverse of 6 −

7 , which is 7 −

6 .

= 3 − 8 · 7 −

6 Divide 6 and 3 by their GCF, 3.

= 7 − 16

Multiply.

Exercises

Write the multiplicative inverse of each number.

1. 3 − 5 2. - 8 −

9 3. 1 −

10 4. - 1 −

6

5. 2 3 − 5 6. -1 2 −

3 7. -5 2 −

5 8. 7 1 −

4

Divide. Write in simplest form.

9. 1 − 3 ÷ 1 −

6 10. 2 −

5 ÷ 4 −

7

11. - 5 − 6 ÷ 3 −

4 12. 1 1 −

5 ÷ 2 1 −

4

13. 3 1 − 7 ÷ (- 3 2 −

3 ) 14. - 4 −

9 ÷ 2

15. 6 − 11

÷ (-4) 16. 5 ÷ 2 1 − 3

Example 1

To divide by a fraction, multiply by its multiplicative inverse.

Example 2

1/

/2


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DSkills PracticeDivide Rational Numbers


1. 2 − 3 2. - 4 −

7 3. - 1 −

12

4. 22 5. 9 − 35

6. - 14 − 17

7. 1 5 − 7 8. -1 3 −

13 9. -31

10. -3 6 − 11

11. 4 8 − 15

12. 5 3 − 5


13. 3 − 7 ÷ 3 −

5 14. 2 −

7 ÷ 6 −

7

15. - 5 − 8 ÷ 3 −

4 16. 7 −

9 ÷ (- 14 −

15 )

17. - 4 − 5 ÷ 8 −

9 18. 2 −

11 ÷ 4 −

9

19. 1 3 − 4 ÷ 2 1 −

2 20. -2 3 −

5 ÷ 1 3 −

10

21. -3 4 − 7 ÷ (-1 1 −

14 ) 22. 10 −

11 ÷ 5

23. -4 ÷ 3 − 5 24. 3 4 −

15 ÷ 4 2 −

3

25. 9 1 − 3 ÷ 5 3 −

5 26. -12 3 −

4 ÷ (-2 5 −

6 )

27. 2 4 − 9 ÷ (-6 2 −

7 ) 28. -11 1 −

5 ÷ 3 1 −

9


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1. 4 − 5 2. - 7 −

12 3. -20 4. -5 3 −

8


5. 1 − 5 ÷ 1 −

4 6. 2 −

5 ÷ 5 −

6 7. 3 −

7 ÷ 6 −

11

8. 3 − 10

÷ 4 − 5 9. 3 −

8 ÷ 6 10. 6 −

7 ÷ 3

11. 4 − 5 ÷ 10 12. 6 −

11 ÷ (-8) 13. - 4 −

5 ÷ 5 −

6

14. 5 − 12

÷ (- 3 − 5 ) 15. - 3 −

10 ÷ (- 2 −

5 ) 16. - 13 −

18 ÷ (- 8 −

9 )

17. 4 1 − 5 ÷ 1 3 −

4 18. 8 1 −

3 ÷ 3 3 −

4 19. -10 1 −

2 ÷ 2 1 −

3

20. OFFICE SUPPLIES A regular paper clip is 1 1 − 4 inches long, and a jumbo paper clip is 1 7 −

8

inches long. How many times longer is the jumbo paper clip than the regular paper clip?

21. STORAGE The ceiling in a storage unit is 7 2 − 3 feet high. How many boxes may be stacked

in a single stack if each box is 3 − 4 foot tall?

ALGEBRA Evaluate each expression for the given values.

22. r ÷ s if r = - 7 − 20

and s = 7 − 15

23. m ÷ n if m = 4 − 9 and n = 11 −

12

Homework PracticeDivide Rational NumbersD



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Divide Rational NumbersD

1. CONTAINER GARDENING One bag of

potting soil contains 8 1 − 4 quarts of soil.

How many clay pots can be filled from one bag of potting soil if each pot holds 3 −

4 quart?

2. MUSIC Doug has a shelf 9 3 − 4 inches long

for storing CDs. Each CD is 3 − 8 inch

wide. How many CDs will fit on one shelf?

3. SERVING SIZE A box of cereal contains

15 3 − 5 ounces of cereal. If a bowl holds

2 2 − 5 ounces of cereal, how many bowls

of cereal are in one box?

4. HOME IMPROVEMENT Lori is building a path in her backyard using square

paving stones that are 1 3 − 4 feet on each

side. How many paving stones placed end-to-end are needed to make a path that is 21 feet long?

5. GEOMETRY Given the length of a rectangle and its area, you can find the width by dividing the area by the

length. A rectangle has an area of

6 2 − 3 square inches and a length of

2 1 − 2 inches. What is the width of the

rectangle?

6. GEOMETRY Given the length of the base b of a parallelogram and its area, you can find its height h by dividing the area by the base. The

parallelogram shown has an area of

9 9 − 10

square inches. What is its

height?

7. HOBBIES Dena has a picture frame that

is 13 1 − 2 inches wide. How many pictures

that are 3 3 − 8 inches wide can be placed

beside each other within the frame?

8. YARD WORK Leon is mowing his yard,

which is 21 2 − 3 feet wide. His lawn

mower makes a cut that is 1 2 − 3 feet wide

on each pass. How many passes will Leon need to finish the lawn?

h

in.4 12b =


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.1-1

Continued FractionsThe expression at the right is an example of a 1 + 1 −

1 + 1 − 1 + 1 −

9

continued fraction. The example shows how to change an improper fraction into a continued fraction.

Write 72 − 17

as a continued fraction.

72 − 17

= 4 + 4 − 17

= 4 + 1 − 17 − 4

= 4 + 1 − 4 + 1 −

4

Exercises

Change each improper fraction to a continued fraction.

1. 13 − 10

2. 17 − 11

3. 25 − 13

4. 17 − 6

Write each continued fraction as an improper fraction.

5. 1 + 1 − 1 + 1 −

1 + 1 − 2 6. 1 + 1 −

1 + 1 − 1 + 1 −

3 7. 1 + 1 −

1 + 1 − 1 + 1 −

5

EnrichD

Example

Notice that each fraction must have a numerator of 1 before the process is complete.


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AReteachProblem-Solving Investigation: Look for a Pattern

You may need to look for a pattern to solve a problem.

Understand Determine what information is given in the problem and what you need to ! nd.

Plan Select a strategy including a possible estimate.

Solve Solve the problem by carrying out your plan.

Check Examine your answer to see if it seems reasonable.

Example 1

The Ferris wheel located at Navy Pier in Chicago stands 150 feet tall and can

carry 240 people. It takes 7 1 − 2 minutes to make one revolution, 15 minutes to make

two revolutions, and 22 1 − 2 minutes to make three revolutions. If this pattern

continues, how many minutes will it take to make six revolutions?

Understand You know the time it takes to make the first three revolutions.

Plan Look for a pattern in the number of minutes. Then continue the pattern to find how many minutes it takes to make six revolutions.

Solve Complete the information for the first, second, and third revolutions. Continue the pattern to solve the problem.

First Revolution

SecondRevolution

ThirdRevolution

FourthRevolution

FifthRevolution

SixthRevolution

7 1 − 2 min 15 min 22 1 −

2 min 30 min 37 1 −

2 min 45 min

It takes 45 minutes to make six revolutions.

Check Check your pattern to make sure the answer is correct.

Exercises

Look for a pattern. Then use the pattern to solve each problem.

1. COOKING A muffin recipe calls for 2 1 − 2 cups of flour for every 2 −

3 cup of sugar. How many

cups of flour should be used when 4 cups of sugar are used?

2. FUNDRAISER There were 256 people at a fundraiser. When the event was over, half of the people who remained left every 5 minutes. How long after the event ended did the last person leave?

1-2

"

+ 7 1 − 2

"

+ 7 1 − 2

"

+ 7 1 − 2

"

+ 7 1 − 2

"

+ 7 1 − 2


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ASkills PracticeProblem-Solving Investigation: Look for a Pattern

Look for a pattern in Exercises 1–6.

1. YARN A knitting shop is having a yarn sale. One skein sells for $1.00, 2 skeins sell for $1.50, and 3 skeins sell for $2.00. If this pattern continues, how many skeins of yarn can you buy for $5.00?

2. BIOLOGY Biologists place sensors in 8 concentric circles to track the movement of grizzly bears throughout Yellowstone National Park. Four sensors are placed in the inner circle. Eight sensors are placed in the next circle. Sixteen sensors are placed in the third circle, and so on. If the pattern continues, how many sensors are needed in all?

3. HONOR STUDENTS A local high school displays pictures of the honor students from each school year on the office wall. The top row has 9 pictures displayed. The next 3 rows have 7, 10, and 8 pictures displayed. The pattern continues to the bottom row, which has 14 pictures in it. How many rows of pictures are there on the office wall?

4. EARNING MONEY Penny is holding a car wash. The table

shows what part of a car she can wash in 1 − 4 hour. How many

cars can she wash in 3 hours?

5. GEOMETRY Find the perimeters of the next two figures in the pattern. The length of each side of each small square is 3 feet.

6. HOT TUBS A hot tub holds 520 gallons of water when it is full. A hose fills

the tub at a rate of 6 1 − 2 gallons every five minutes. How long will it take to

fill the hot tub?

1-2

Time(h)

Cars Washed

1 − 4 1 −

3

1 − 2 2 −

3

3 − 4 1


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A

Look for a pattern in Exercises 1 and 2.

1. GEOMETRY Draw the next two angles in the pattern.

10°20°

30° 40°

a.

c.

b.

d.

2. ANALYZE TABLES A falling object continues to fall faster until it hits the ground. How far will an object fall during the fifth second?

Time Period Distance Fallen

1st Second 16 feet

2nd Second 48 feet

3rd Second 80 feet

4th Second 112 feet

Use any strategy to solve Exercises3–6. Some strategies are shown below.

PROBLEM-SOLVING STRATEGIES • Look for a pattern • Work backward • Guess, check, and revise • Choose an operation

3. YARD WORK Denzel can mow 1 − 8 of his

yard every 7 minutes. If he has 40 minutes to mow 3 −

4 of the yard, will he

have enough time?

4. READING Ling read 175 pages by 1:00 P.M., 210 pages by 2:00 P.M., and 245 pages by 3:00 P.M. If she continues reading at this rate, how many pages will Ling have read by 4:00 P.M.?

5. MOVIES The land area of Alaska is about 570 thousand square miles. The land area of Washington, D.C., is

about 3 − 50

square mile. How many times

larger is Alaska than Washington, D.C.?

6. U.S. PRESIDENTS President Clinton served 5 two-year terms as governor of Arkansas and 2 four-year terms as President of the United States. How many total years did he serve in these two government offices?

Homework PracticeProblem-Solving Investigation: Look for a Pattern

1-2



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AProblem-Solving PracticeProblem Solving Investigation: Look for a Pattern

Look for a pattern. Then use the pattern to solve each problem.

ENTERTAINMENT For Exercises 1 and 2, use the information at the right, which shows the ticket prices at a skating rink.

Number of People in

Group

Total Cost per Group

1 $1.002 $2.003 $2.904 $3.705 $4.40

1. Describe the pattern used to calculate the cost for a group after 2 people.

2. If the pattern continues, what would the cost be for a group of 8 skaters?

3. RUNNING Evie wants to train to run a marathon. For the first four weeks, she ran 3, 6, 9, and 12 miles. If the pattern continues, how many miles will she run in the 6th week of training?

4. AGRICULTURE In a vegetable garden, the second row is 8 inches from the first row, the third row is 10 inches from the second row, the fourth row is 14 inches from the third row, and the fifth row is 20 inches from the fourth row. If the pattern continues, how far will the eighth row be from the seventh row?

5. GEOMETRY Draw the next two figures in the pattern.

6. BIOLOGY A newborn seal pup weighs 4 pounds at the end of the first week, 8 pounds at the end of the second week, 16 pounds at the end of the third week, and 32 pounds at the end of the fourth week. If this growth pattern continues, how many weeks old will the seal pup be before it weighs over 100 pounds?

1-2


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BReteachCompare Rational Numbers

• To write a percent as decimal, divide by 100 and remove the percent symbol.

• To write a decimal as a percent, multiply by 100 and add the percent symbol.

• To express a fraction as a percent, you can solve a proportion or you can write the fraction as a decimal and then write the decimal as a percent.

Write 56% as a decimal.

56% = 56% Divide by 100.

= 0.56 Remove the percent symbol.

Write 0.17 as a percent.

0.17 = 0.17 Multiply by 100.

= 17% Add the percent symbol.

Write 7 − 20

as a percent.

Method 1 Use a proportion. Method 2 Write as a decimal.

7 − 20

= x − 100

Write the proportion. 7 − 20

= 0.35 Convert to a decimal by dividing.

7 · 100 = 20 · x Find cross products. = 35% Multiply by 100, and add the percent symbol.

700 = 20x Multiply.

700 − 20

= 20x − 20

Divide each side by 20.

35 = x Simplify.

So, 7 − 20

can be written as 35%.

Exercises

Write each percent as a decimal.

1. 10% 2. 36% 3. 0.8% 4. 49.1%

Write each decimal as a percent.

5. 0.14 6. 0.59 7. 0.932 8. 1.07


9. 3 − 4 10. 7 −

10 11. 9 −

16 12. 1 −

6

Example 1

Example 2

Example 3

""

""

""


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BSkills PracticeCompare Rational Numbers


1. 50% 2. 13% 3. 2%

4. 41% 5. 79% 6. 0.9%

7. 17.5% 8. 33.4% 9. 91.5%

10. 122% 11. 282% 12. 331%


13. 0.6 14. 0.05 15. 0.17

16. 0.38 17. 0.081 18. 0.453

19. 0.572 20. 0.737 21. 0.061

22. 1.19 23. 1.4 24. 2.38


25. 9 − 20

26. 2 − 25

27. 5 − 16

28. 33 − 40

29. 3 − 80

30. 5 − 9

31. 3 − 11

32. 59 − 80

33. 14 − 10

34. 28 − 25

35. 5 − 3 36. 33 −

20


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panies, Inc.Homework PracticeCompare Rational Numbers


1. 70% 2. 40% 3. 135% 4. 369%

5. 0.5% 6. 52.5% 7. 8% 8. 3%


9. 0.73 10. 0.84 11. 0.375 12. 0.232

13. 0.005 14. 1.3 15. 4.11 16. 3.52


17. 13 − 25

18. 19 − 20

19. 5 − 4 20. 9 −

5

21. 3 − 40

22. 7 − 125

23. 5 − 9 24. 1 −

3

Order each set of numbers from least to greatest.

25. 2 − 5 , 0.5, 4%, 3 −

10 26. 0.6, 6%, 3 −

20 , 4 −

25

27. 93%, 0.96, 47 − 50

, 19 − 20

28. 77%, 3 − 4 , 19 −

25 , 0.73

Replace with <, >, or = to make a true statement.

29. 1 − 200

1 − 2 % 30. 2.24 2 2 −

5 % 31. 7 −

8 7 −

8 %

32. TEST SCORES On a science test, Ali answered 38 of the 40 questions

correctly, Jamar answered 9 − 10

of the questions correctly, and Paco

answered 92.5% of the questions correctly. Write Ali’s and Jamar’s scores as percents and list the students in order from the least to the highest score.

1-2B



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.1-2

BProblem-Solving PracticeCompare Rational Numbers

1. BASKETBALL In a recent season, Deanne Nolan of the WNBA team the Detroit Shock made 39% of her 3-point shots. Write this percent as a decimal.

2. POPULATION From 2000 to 2006, the population of New York City increased by 3%. Write this percent as a decimal.

3. BASEBALL Recently, the Chicago White Sox had a team batting average of 0.263. Write this decimal as a percent.

4. POPULATION In 2006, 4.4% of people in the U.S were of Asian descent. Write this percent as a decimal.

5. INTERNET Internet access in the U.S. has increased dramatically in recent years. If 110 out of every 200 households has Internet access, what percent of households has Internet access?

6. VOTING The data below show the rate of voter turnout in three U.S presidential elections. Order the rates from least to greatest as percents.

Year Rate of Turnout

1996 49.1%

2000 0.513

2004 553 − 1,000

7. LAND Florida makes up approximately 0.015 of the land mass of the United States. Write this decimal as a percent.

8. READING Over the summer, Chang

read 7 − 8 of the books that Alaqua read

during the previous school year. Write this fraction as a percent.


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Block Party 1. This model is made up of 27 cubes and has a length of 3 cubes,

a width of 3 cubes, and a height of 3 cubes. The entire model will be painted yellow, then cut apart into individual cubes.

What percent of the cubes will be painted yellow on:

0 sides? 1 side? 2 sides?

3 sides? 4 sides? 5 sides?

6 sides?

2. This model is made up of 64 cubes and has a length of 4 cubes, a width of 4 cubes, and a height of 4 cubes. The entire model will be painted orange, then cut apart into individual cubes.

What percent of the cubes will be painted orange on:



6 sides?

3. This model is made up of 125 cubes and has a length of 5 cubes, a width of 5 cubes, and a height of 5 cubes. The entire model will be painted purple, then cut apart into individual cubes.

What percent of the cubes will be painted purple on:



6 sides?

1-2B

Enrich


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.ReteachAlgebra: The Percent Proportion and EquationC

1-2

In a percent proportion, one ratio compares a part to the whole. The other ratio is the equivalent percent written as a fraction with a denominator of 100.

part −

whole = percent

A percent equation is an equivalent form of a percent proportion in which the percent is written as a decimal.

part = percent • whole

12 is what percent of 60?

METHOD 1 Use the percent proportion.part

whole 12 − 60

= p −

100 } percent Write the percent proportion.

12 • 100 = 60 • p Find the cross products.

1,200 = 60p Multiply.

1200 − 60

= 60p

− 60


20 = p Simplify.

So, 12 is 20% of 60.

METHOD 2 Use the percent equation.


12 = p • 60 Write the percent equation.

12 − 60

= 60p

− 60


0.2 = p Simplify.

Since 0.2 = 20%, 12 is 20% of 60. Note that the answer, a decimal, must be converted to a percent.

Exercises

Solve each problem using a percent proportion. 1. 3 is what percent of 10? 2. What number is 15% of 40?

3. 24 is 75% of what number? 4. 45 is what percent of 60?

Solve each problem using a percent equation. 5. Find 30% of 70. 6. 52 is what percent 65?

7. What percent of 56 is 14? 8. Find 180% of 160.

Example

→→


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panies, Inc.Skills PracticeAlgebra: The Percent Proportion and EquationC

1-2

Solve each problem using a percent proportion.

1. 1 is what percent of 5? 2. What number is 25% of 40?

3. 30 is 60% of what number? 4. What percent of 8 is 6?

5. Find 15% of 20. 6. 33 is 33% of what number?

7. 15 is what percent of 150? 8. What number is 30% of 140?

9. 90 is 60% of what number? 10. What percent of 60 is 42?

11. Find 90% of 40. 12. 21 is 35% of what number?

Solve each problem using a percent equation.

13. Find 50% of 40. 14. What is 90% of 20?

15. What percent of 64 is 16? 16. 24 is what percent of 30?

17. Find 20% of 55. 18. What is 60% of 45?

19. 16 is 40% of what number? 20. 70% of what number is 63?

21. What percent of 84 is 63? 22. 9 is what percent of 30?

23. 35 is 10% of what number? 24. 15% of what number is 24?


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.Homework PracticeAlgebra: The Percent Proportion and Equation

Solve each problem using a percent proportion.

1. 6 is what percent of 24? 2. 125 is what percent of 375?

3. What is 20% of 80? 4. What is 14% of 440?

5. 28 is 35% of what number? 6. 63 is 63% of what number?

7. GAMES Before discarding, Carolee has 4 green cards, 3 red cards, 3 orange cards, and 1 gold card. If she discards the gold card, what percent of her remaining cards are red?

Solve each problem using a percent equation.

8. 4% of what number is 7? 9. 85 is 10% of what number?

10. Find 3 1 − 2 % of 250. 11. What is 7 1 −

4 % of 56?

12. 560 is what percent of 420? 13. 2 1 − 5 % of what number is 44?

14. MUSIC In a recent survey, 47% of teens said they use the Internet to download music. If there were 300 teens surveyed, how many use the Internet to download music?

1-2C



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C

In Exercises 1–4, use a percent proportion. In Exercises 5-8, use a percent equation.

Problem-Solving PracticeAlgebra: The Percent Proportion and Equation

1. DINING OUT Trevor and Michelle’s restaurant bill comes to $35.50. They are planning to tip the waiter 20%. How much money should they leave for a tip?

2. CHESS The local chess club has 60 members. Twenty-four of the members are younger than twenty. What percent of the members of the chess club are younger than twenty?

3. TENNIS In the city of Bridgeport, 75% of the parks have tennis courts. If 18 parks have tennis courts, how many parks does Bridgeport have altogether?

4. COLLEGE There are 175 students in twelfth grade at Silverado High School. A survey shows that 64% of them are planning to attend college. How many Silverado twelfth-grade students are planning to attend college?

5 SPORTS In the 2007-2008 season, the Tampa Bay Buccaneers won 9 out of 16 games in the regular season. What percent of their games did they win? Round to the nearest tenth if necessary.

6. GOLF On a recent round of golf, Shana made par on 15 out of 18 holes. On what percent of holes did Shana make par? Round to the nearest tenth if necessary.

7. DRIVING TEST On the written portion of her driving test, Sara answered 84% of the questions correctly. If Sara answered 42 questions correctly, how many questions were on the driving test?

8. EDUCATION In a certain small town, 65% of the adults are college graduates. How many of the 240 adults living in the town are college graduates?


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The Cost of UsingThe percent proportion can be used to describe the percent by which something depreciates, or loses its value during the course of time.

In 2006, the average purchase price of a new compact automobile was $17,000. One year later, the compact automobile that was purchased new in 2006 typically was worth $11,500. By what percent did the automobile depreciate during the first year of ownership?

First find the amount of decrease.

$17,000 - $11,500 = $5,500

Then write and solve the percent proportion.

$5,500 is what percent of $17,000?

5,500 −

17,000 = r −

100

550,000 = 17,000r

32.4 ≈ r

The automobile depreciated about 32.4%, or about 1 − 3 of its value, during the first year of

ownership.

Exercises

Advertisements such as these regularly appear in the classified pages of newspapers. Find the percent of depreciation in each advertisement. Round to the nearest tenth if necessary.

1. For sale: Venus 2 dr, 5 speed, air, sport wheels, mint. Bought new 8 months ago for $9,600, yours for $7,200. Must sell—baby on way.

2. For sale: Washer/dryer combo. Antique white, electric, like new—18 mos. old. Paid $950, asking $500.

3. For sale: Mars 4 dr, auto, air, ABS, the works. 1 year old—12,400 mi. Purchase price—$16,000. Your price—$12,800 firm.

4. For sale: Dishwasher, 2 racks, full factory warranty. Never used—won in contest. List: $840. I will deliver for $588 cash.

5. For sale: Mountain bike. 20-inch frame. 26 × 1.60 new tires. Used but not abused. Bought last summer for $320. $150 or best offer.

6. For sale: Personal Computer. Intex processor. 8.0 GB hard drive. 56X CD-ROM drive. 17-inch monitor. Color inkjet printer with lots of software. $2,200 new—yours for $895.

Enrich

Example 1


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On the TI-84 Plus, you can use the equation solver to solve percent proportions. To do this, you first set the equation equal to zero.

Solve x − 300

= 80 − 100

.

First, subtract 80 − 100

from each side to set the equation equal to zero.

So, the new equation is x − 300

- 80 − 100

= 0.

Now use the TI-84 Plus Equation Solver to solve for x.

MATH θ ÷ 300 80 ÷ 100

ALPHA [SOLVE]

So, x = 240.

Exercises

Solve each percent proportion. 1. x −

50 = 70 −

100 2. 40 − x = 50 −

100

3. x − 50

= 20 − 100

4. 3 − 30

= x − 100

5. 25 − 125

= x − 100

6. 9 − x = 18 − 100

7. 45 − x = 15 − 100

8. 12 − 48

= x − 100

TI-84 Plus ActivitySolving Percent Proportions

Example


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Find the Sale Price

SPORTS At Sports You Play, a skateboard that costs $60 is on sale for 20% off. What is the sale price of the skateboard?

Step 1 Find the amount of the discount.

Let d represent the total discount.


d = 0.2 • 60 Write the percent equation.

d = 12 Multiply.

Step 2 Subtract the discount from the original price to find the sale price.

$60 – $12 = $48.

Discount is the amount by which a regular price is reduced.

ReteachDiscount, Markup, and Sales Tax

Sales tax is an additional amount of money charged on certain goods and services.

CLOTHES A sweater costs $30 and the sales tax is 7%. What is the total cost of the sweater?

Step 1 Find the amount of the sales tax.

Let t represent the sales tax.


t = 0.07 • 30 Write the percent equation.

t = 2.10 Multiply.

Step 2 Add the sales tax to the original price to find the total price.

$30 + $2.10 = $32.10.

Exercises

Find the sale price or total cost of each item to the nearest cent.

1. book: $25, 10% discount 2. computer: $900, 20% discount

3. bicycle: $220, 15% discount 4. purse: $70, 35% discount

5. car: $15,000, 7% tax 6. CD: $19.50, 5% tax

7. notebook paper: $2.25, 4% tax 8. shoes: $80, 7% tax

Example 1

Example 2


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ASkills PracticeDiscount, Markup, and Sales Tax

Find the sale price of each item to the nearest cent.

1. guitar: $600, 20% discount 2. slacks: $42, 10% discount

3. bracelet: $45, 15% discount 4. burger: $2.50, 5% discount

5. toaster: $52, 12% discount 6. golf balls: $13, 10% discount

Find the total cost of each item to the nearest cent.

7. winter boots: $85, 7.5% tax 8. blush: $16.50, 8% tax

9. camera: $250, 8.25% tax 10. frozen pizza: $6.25, 5.25% tax

11. tent: $102, 7% tax 12. wrapping paper: $6.50, 4% tax

Find the selling price for each item given the percent of markup.

13. video game: $70, 30% markup 14. frying pan: $35, 10% markup

15. baseball glove: $50, 20% markup 16. skates: $90, 15% markup

17. glasses: $250, 25% markup 18. microwave: $95, 22% markup

Find the total cost of each item to the nearest cent.

19. running outfit: $85, 25% discount, 5% tax

20. softball: $16, 10% discount, 7.5% tax


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AHomework PracticeDiscount, Markup, and Sales Tax

Find the sale price, selling price, or total cost of each item to the nearest cent.

1. earrings: $20, 6% tax 2. snowcone: $2, 30% markup

3. picture frame: $44, 15% discount 4. potato chips: $4.50, 7.4% tax

5. photo album: $25.50, 10% markup 6. yoyo: $4.50, 15% discount

7. lawn chair: $15, 25% off, 6% tax 8. rake: $27, 15% off, 7.5% tax

9. swimsuit: $22, 5% off, 4% tax 10. jeans: $67, 12% off, 8% tax

11. TRAVEL Theodore is staying at the Comfy Hotel. The hotel charges $145 a night for a room.

a. He has a coupon to receive an additional 15% off. What is the cost of the room before tax?

b. After he receives the discount, how much will his total bill be if there is an 8% tax?

12. AUTOMOBILES Tayshia is buying a new car. The sales person tells her she will get a goodwill discount of 5% but then will have to pay an 8.75% sales tax.

a. If the car Tayshia wants to buy costs $35,000 without the discount, what will the cost be after the discount but before the tax?

b. After she receives the discount, how much will her total bill be after taxes?

13. SHOPPING Rosa knows that her mother buys bolts of fabric for her sewing shop wholesale. If a bolt of fabric costs $150 dollars and the markup is 20%, what is the selling price of a bolt of fabric?



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1. SPORTS Hector wants to buy a new football. He initially thought it would cost $36, but when he went to the sporting goods store it was discounted 20%. What is the sale price of the football?

2. RESTAURANT Camilla had lunch with her friend Cleavon. Before tax, the bill is $15.45. How much will the bill be if there is a 7.4% sales tax?

3. PHARMACY At Health First Pharmacy, the wholesale price of an asthma medicine is $126. What is the selling price, if the percentage of markup is 42%?

4. SHOPPING Upon entering EZ-Mart, Kyle sees the following sign. What should he pay for a sweater originally selling for $32.50?

Everything in the store 10% off!

5. CARNIVAL A ride ticket usually costs $1.50, but if you buy 10 tickets, you get a 5% discount. Find the sale price of 10 tickets which would normally cost $15.

6. SURFBOARD A surf board that costs $112 is on sale for 12% off, and the sales tax is 5.5%. What is the total cost of the surf board?

7. TELEVISION At Total Viewing, the wholesale price of a 52-inch television is $1,950. What does it cost to buy the television if the store’s markup is 15% and the sales tax is 7.5%?

8. BAKERY It costs Mr. Goody $0.85 to make a loaf of bread. What does it cost to buy the loaf if Mr. Goody’s markup is 22% and the sales tax is 8%?

Problem-Solving PracticeDiscount, Markup, and Sales Tax


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AEnrich

Party Time!It is football season and you decide to have a party. The table contains a list of items you want to buy for your party. The table also indicates the quantity of each item needed and the unit cost for the item. If there is a * next to the unit price, the item will be discounted 5%. If there is a ** next to the unit price, the item will be discounted 10%.

Use the table to solve each problem.Round all answers to the nearest cent. 1. What is your cost for all of the food items before

tax?

2. What is your cost for all of the non-food items before tax?

3. What is your total cost before tax?

4. Suppose you live on the border between Cook County and Lake County. If the sales tax is 7% for non-food items in Lake County and 10% for non-food items in Cook County, how much will you save if you travel across the border from Cook County to Lake County to buy the party items?

5. Research the sales tax on food in your area. Is the sales tax the same on all items purchased in a supermarket, or does the tax vary depending on the item? Is the sales tax the same throughout your county or state?

Item Quantity Unit Price

Sports Drink 2 $4.00

Milk 1 $2.05Juice 2 $3.85Bottled Water 1 $6.98**

Potato Chips 3 $2.50

Popcorn 1 $3.00Pretzels 2 $2.75Salsa 1 $4.10Dip 2 $3.15Shrimp 1 $9.50Shrimp Sauce 1 $3.75**

Chocolate Bars 10 $0.95

Tablecloth 1 $6.50*Napkins 1 $3.25*Paper Plates 1 $6.00*

Plastic Utensils 1 $3.50

Drink Cups 1 $4.50*


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ATI-73 Activity Discounts

Suppose you are the owner of a shop that sells casual clothes. Your store often has sales where every item is discounted by the same percent. Use your calculator to find the sales price of each item so that you can have new signs printed that show the sale prices.

The Moonlight Madness Sale will offer customers 25% off. Find the sale prices.

Step 1 Store the amount of the discount in the variable x.

25

Step 2 Enter the current price of each item in a list.

Item Regular Price

1 Cotton Sweater 29.99

2 Denim Jacket 36.29

3 Team Sweatshirt 24.89

4 Sport Socks 3-Pack 6.59

5 T-Shirt 7.99

[MEM] 6

In L1 enter each regular price.

Press after each price.

Step 3 Enter a formula in L2 to calculate the sale price.sale price = regular price - (discount %)(regular price)

[TEXT] " Done

[STAT] 1 x

[STAT] 1 [TEXT] " Done

The sale price for each item is displayed in L2.

Use the list of data to answer the questions below.

1. List the sale prices for the Moonlight Madness Sale.

2. Explain why the formula for L2 correctly calculates the sale price.

3. Use the same lists, L1 and L2, to find sale prices when the discount rate is 35%. (Hint: Store a new value in x.)

4. Add a new item: a suede jacket priced at $99.59. What is its sale price when the discount is 35%?

5. Create a new list, L3, to find the amount of the discount for each item at 35% off.

Example


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Financial Literacy: Interest

Find the simple interest for $600 invested at 8.5% for 6 months.

Notice the time is given in months. Six months is 6 − 12

or 1 − 2 year.

I = prt Write the simple interest formula.

I = 600 · 0.085 · 1 − 2 Replace p with 600, r with 0.085, and t with 1 −

2 .

I = 25.50 Simplify.

The simple interest is $25.50.

Find the total amount in an account where $136 is invested at 7.5% compounded annually for 2 years.

First Year


I = 136 · 0.075 · 1 Replace p with 136, r with 0.075, and t with 1.

I = 10.20 Simplify.

136 + 10.20 = 146.20 Add the amount invested and the interest.

Second Year


I = 146.20 · 0.075 · 1 Replace p with 146.20, r with 0.075, and t with 1.

I = 10.97 Simplify.

The amount in the account after two years is $146.20 + $10.97 or $157.17.

Exercises

Find the simple interest to the nearest cent.

1. $300 at 5% for 2 years 2. $650 at 8% for 3 years

3. $575 at 4.5% for 4 years 4. $735 at 7% for 2 1 − 2 years

Find the total amount in each account to the nearest cent, if the interest is compounded annually.


7. $945 at 7.25% for 4 years 8. $2,680 at 9.1% for 2 years

To ! nd simple interest, use the formula I = prt. Interest I is the amount of money paid or earned. Principal p is the amount of money invested or borrowed. Rate r is the annual interest rate expressed as a decimal. Time t is the time in years.

Example 1

Example 2

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3. $350 at 6.2% for 3 years 4. $280 at 5.5% for 4 years

5. $740 at 3.25% for 2 years 6. $1,150 at 7.6% for 5 years

7. $725 at 4.3% for 2 1 − 2 years 8. $266 at 5.2% for 3 years

9. $955 at 6.75% for 3 1 − 4 years 10. $1,245 at 5.4% for 4 years

Find the total amount in each account to the nearest cent if the interest is compounded annually.

11. $400 at 3.5% for 2 years 12. $710 at 5% for 4 years

13. $90 at 6.2% for 4 years 14. $870 at 7.4% for 3 years

15. $1,200 at 5.24% for 36 months 16. $65 at 12% for 2 years

17. $540 at 8.6% for 5 years 18. $888 at 2.4% for 24 months

19. $112 at 2% for 36 months 20. $640 at 10% for 4 years

Skills PracticeFinancial Literacy: InterestB


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1. $350 at 5% for 4 years 2. $750 at 6.5% for 3 years

3. $925 at 4.75% for 3 months 4. $2,050 at 7.65% for 36 months

Find the total amount in each account to the nearest cent, assuming simple interest.

5. $1,500 at 6% for 5 years 6. $4,010 at 5.2% for 4 years

7. $16,000 at 3 1 − 4 % for 42 months 8. $3,200 at 6 2 −

3 % for 5 1 −

2 years

Find the total amount in each account to the nearest cent if the interest is compounded annually.

9. $320 at 2.5% for 4 years 10. $1,100 at 5% for 4 years

11. $70 at 6 1 − 4 % for 2 years 12. $470 at 6.6% for 24 months

13. HOUSING Mrs. Landry bought a house for $35,000 in 1975. She sold the house for $161,000 in 2005. Find the simple interest rate for the value of the house.

14. CARS Brent’s older brother took out a 4-year loan for $16,000 to buy a car. If the simple interest rate was 8%, how much total will he pay for the car including interest?

15. SAVINGS What is the total amount of money in an account where $300 is invested at an interest rate of 4.5% compounded annually for 5 years?

16. CREDIT Reed borrowed $3,200 from the credit union at an interest rate of 7%. The interest is compounded annually. Suppose he made no payments, how much does he owe at the end of the 3 years?

Homework PracticeFinancial Literacy: InterestB



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Financial Literacy: Interest

1. SAVINGS ACCOUNT How much interest will be earned in 3 years from $730 placed in a savings account at 6.5% simple interest?

2. INVESTMENTS Salvador’s investment of $2,200 in the stock market earned $528 in two years. Find the simple interest rate for this investment.

3. SAVINGS ACCOUNT Lonnie places $950 in a savings account that earns 5.75% interest compounded annually. Find the total amount in the account after five years.

4. INHERITANCE William’s inheritance from his great uncle came to $225,000 after taxes. If William invests this money in a savings account at 7.3% simple interest, how much will he earn from the account each year?

5. RETIREMENT Han has $410,000 in a retirement account that earns $15,785 each year. Find the simple interest rate for this investment.

6. COLLEGE FUND When Jin was born, her parents put $8,000 into a college fund account that earned 9% interest compounded annually. Find the total amount in the account after 2 years.

7. MONEY Leora won $800,000 in a state lottery. After paying $320,000 in taxes, she invested the remaining money in a savings account at 4.25% interest compounded annually. What is the total amount of money in her account after 4 years?

8. SAVINGS Mona has an account with a balance of $738. She originally opened the account with a $500 deposit and a simple interest rate of 5.6%. If there were no deposits or withdrawals, how long ago was the account opened?

B


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Does Compounding Really Make a Difference?Does it really make a difference whether an investment earns simple interest or compound interest? Suppose you invest $10,000 in a savings account paying 7% interest for 9 years. Using the ideas you have already learned about interest, you can answer the question.

There are formulas for both simple interest and compound interest that will predict the balance in your savings account. For simple interest, the formula is A = p + prt. For compound interest, the formula is A = p(1 + r)t. A is the balance in the account at the end of a given time period, p is the amount of money invested, r is the interest rate expressed as a decimal, and t is the length of time written in years. In the example, p = $10,000, r = 7%, and t = 9 years. Use a calculator with a power key to find the value of A.

Simple Interest Compound Interest

A = p + prt A = p(1 + r)t

A = 10,000 + 10,000(0.07)(9) A = 10,000(1 + 0.07) 9

A = 10,000 + 6,300 A = 10,000(1.07) 9

A = 16,300 A = 18,384.59

Since $18,384.59 − $16,300 = $2,084.59, your investment will earn $2,084.59 dollars more if it earns compound interest.

Find the balance in your account for the given values of p, r, and t using both the simple interest formula and the compound interest formula. Round to the nearest dollar. Then tell how much more interest you will earn on your investment if it earns compound interest.

1. p = $3,000 2. p = $5,000r = 5% r = 6.5%t = 6 years t = 4.5 years

3. p = $400 4. p = $1,600r = 8% r = 3.5%t = 10 years t = 8 years

Enrich


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BTI-73 ActivityThe Percent Key

You can use the percent key, , to solve equations involving simple interest.

Find the simple interest to the nearest cent from $265 invested at 5.15% for 2 years.

Use the formula I = prt: interest = principal × rate × time.

I = $265 × 5.15% × 2

Keys: 265 5.15 2

Display: 265∗5.15%∗2 27.295

The interest is $27.30.

Exercises


1. $1,000 at 6.75% for 5 years 2. $535 at 8.2% for 6 months

3. $257 at 15% for 2.5 years 4. $48.67 at 12.25% for 30 months

5. Terry put $500 in a savings account that earned 5.125% simple interest. She has not made any deposits or withdrawals for 7 years. How much interest has she earned?

6. How much money will be in Terry’s account at the end of 15 years if she does not make any deposits or withdrawals?

7. Suppose you deposit $200 in an account that earns 10% simple interest. How many months will it take to earn $50 in interest?

8. How much money would you have to deposit in an account that earns 8.375% simple interest to earn $1,000 in interest in 18 months?

Example 1


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Percent of Change

Two months ago, the bicycle shop sold 50 bicycles. Last month, 55 bicycles were sold. Find the percent of change. State whether the percent of change is an increase or a decrease.

Step 1 Subtract to find the amount of change.

55 - 50 = 5 final amount - original amount

Step 2 Write a ratio that compares the amount of change to the original number of bicycles. Express the ratio as a percent.

percent of change = amount of change −−

original amount Definition of percent of change

= 5 − 50

Substitution

= 0.1 Divide. Use a calculator.

Step 3 The decimal 0.1 written as a percent is 10%. Since the percent of change is positive, it is a percent of increase.

Exercises

Find each percent of change. Round to the nearest tenth if necessary. State whether the percent of change is an increase or a decrease.

1. original: 4 hours 2. original: 10 bottlesnew: 5 hours new: 13 bottles

3. original: 15 books 4. original: $30new: 12 books new: $18

5. original: 60 days 6. original: 160 milesnew: 63 days new: 136 miles

7. original: 77 years 8. original: $96new: 105 years new: $59

To find the percent of change, first subtract the original amount from the final amount to find the

amount of change. Then write the ratio amount of change

−− original amount

as a decimal. Finally, write the decimal as a percent.

Example

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DSkills PracticePercent of Change


1. original: 4 computers 2. original: $35new: 6 computers new: $28

3. original: 80 days 4. original: 45 hoursnew: 52 days new: 63 hours

5. original: 120 minutes 6. original: 210 milesnew: 132 minutes new: 105 miles

7. original: 84 customers 8. original: $91new: 111 customers new: $77

9. original: 100 bacteria 10. original: 300 studentsnew: 200 bacteria new: 250 students

11. original: 75°F 12. original: 180 housesnew: 60°F new: 270 houses

13. original: $35 14. original: 550 peoplenew: $45 new: 425 people


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Percent of Change


1. original: 20 rooms 2. original: 110 ticketsnew: 15 rooms new: 175 tickets

3. original: $312 4. original: 92 hoursnew: $400 new: 62 hours

5. original: 75 minutes 6. original: 620 milesnew: 45 minutes new: 800 miles

7. POLLS In a presidential poll taken last week, 182 people said they would vote for the democratic candidate. This week, when the poll was taken again, 150 people said they would vote for the democratic candidate. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

8. TRAFFIC The Florida Department of Transportation wanted to know how many vehicles passed through a particular intersection weekly. During the first week, 470 vehicles passed through the intersection. During the second week, 600 vehicles passed through the intersection. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

9. COMMISSION Nino works at a furniture store. Last week he earned $130 in commission. This week he earned $90 in commission. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

D



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Percent of Change

1. CLUBS Last year the chess club had 20 members. This year the club has 15 members. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

2. READING During Todd’s junior year in high school, he read 15 books. In his senior year, he read 18 books. Find the percent of change. Round to the nearest tenth, if necessary. State whether the change is an increase or decrease.

3. INCOME La’Rae earned $612 last week and $820 this week. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

4. SOFTBALL Eileen plays softball. Last year she had 34 extra base hits. This year she had 21. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

5. TRAVEL Micha is on vacation. Yesterday he traveled 512 miles. Today he traveled 212 miles. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

6. GROWTH Last year Becca was 48 inches tall. This year she is 52 inches tall. Find the percent of change. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

7. PRICING The table shows the change in price of three items sold at Eisenbach’s Grocery Store. Find the percent of change in the price of potatoes. Round to the nearest tenth if necessary. State whether the change is an increase or decrease.

Item Old Price New PriceBeans $2.75 per lb $2.20 per lbPotatoes $4.00 per lb $3.30 per lbTomatoes $5.15 per lb $5.00 per lb

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Florida’s Population GrowthThe table to the right shows the estimated population of Florida at the beginning of the indicated decades.

Year Population(millions)

Increase in

Population(millions)

Percent of Change inPopulation

1950 2.771 X X1960 4.9521970 6.7911980 9.7471990 12.9382000 15.982

1. Without doing any calculations, explain how you know that the percent of change in the population from decade to decade is always increasing.

2. Complete the table. Round the percent of change in population to the nearest tenth, if necessary.

3. In which decade did the total population increase the most? In which decade did the total population increase the least?

4. What would you estimate the population of Florida to be in the year 2010 if you knew the percent of change in population was 23.3%? How close is your answer to the actual estimate? Round your answer to the nearest tenth, if necessary.

5. Research and write a few paragraphs explaining why the population of Florida has grown so quickly over the last half of the twentieth century. What do you think will happen over the first half of the twenty-first century? Explain.


NAME ________________________________________ DATE _____________ PERIOD _____

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1. Write about one new thing you learned in this chapter.

2. Create a problem in which an item is advertised as being on sale. Then explain how to find the percent of change in the price.

3. Write about the concepts of markup, discount, and selling price. Provide real-world examples of where these concepts are used.

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Contents Chapter 0 Start Smart Chapter 1 Rational Numbers and Percent Chapter 2 Expressions and Functions Chapter 3 Linear Functions and Systems of Equations Chapter 4 Equations and Inequalities Chapter 5 Operations on Real Numbers Chapter 6 Angles and Lines Chapter 7 Similar Triangles and the Pythagorean Theorem Chapter 8 Data Analysis Chapter 9 Units of Measure Chapter 10 Measurement: Area and Volume Chapter 11 Properties and Multi-Step Equations and InequalitiesChapter 12 Nonlinear Functions and Polynomials

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