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Chapter 2Resource Masters

Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.

Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7

ANSWERS FOR WORKBOOKS The answers for Chapter 2 of these workbookscan be found in the back of this Chapter Resource Masters booklet.

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.

Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027

ISBN: 0-07-827726-4 Algebra 1Chapter 2 Resource Masters

2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03

© Glencoe/McGraw-Hill iii Glencoe Algebra 1

Contents

Vocabulary Builder . . . . . . . . . . . . . . . . vii

Lesson 2-1Study Guide and Intervention . . . . . . . . . 75–76Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 77Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Reading to Learn Mathematics . . . . . . . . . . . 79Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 80




Lesson 2-5Study Guide and Intervention . . . . . . . . 99–100Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 101Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Reading to Learn Mathematics . . . . . . . . . . 103Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 104



Chapter 2 AssessmentChapter 2 Test, Form 1 . . . . . . . . . . . . 117–118Chapter 2 Test, Form 2A . . . . . . . . . . . 119–120Chapter 2 Test, Form 2B . . . . . . . . . . . 121–122Chapter 2 Test, Form 2C . . . . . . . . . . . 123–124Chapter 2 Test, Form 2D . . . . . . . . . . . 125–126Chapter 2 Test, Form 3 . . . . . . . . . . . . 127–128Chapter 2 Open-Ended Assessment . . . . . . 129Chapter 2 Vocabulary Test/Review . . . . . . . 130Chapter 2 Quizzes 1 & 2 . . . . . . . . . . . . . . . 131Chapter 2 Quizzes 3 & 4 . . . . . . . . . . . . . . . 132Chapter 2 Mid-Chapter Test . . . . . . . . . . . . 133Chapter 2 Cumulative Review . . . . . . . . . . . 134Chapter 2 Standardized Test Practice . . 135–136

Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1

ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A32

© Glencoe/McGraw-Hill iv Glencoe Algebra 1

Teacher’s Guide to Using theChapter 2 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 2 Resource Masters includes the core materials neededfor Chapter 2. These materials include 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 in theAlgebra 1 TeacherWorks CD-ROM.

Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.

WHEN TO USE Give these pages tostudents before beginning Lesson 2-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.

Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.

WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.

Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.

WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.

Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.

WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.

WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.

Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.

© Glencoe/McGraw-Hill v Glencoe Algebra 1

Assessment OptionsThe assessment masters in the Chapter 2Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions

and is intended for use with basic levelstudents.

• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.

• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.

All of the above tests include a free-response Bonus question.

• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.

• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.

Intermediate Assessment• Four free-response quizzes are included

to offer assessment at appropriateintervals in the chapter.

• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.

Continuing Assessment• The Cumulative Review provides

students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.

• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questionsthat appear in the Student Edition onpages 116–117. This improves students’familiarity with the answer formats theymay encounter in test taking.

• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided forthe assessment masters in this booklet.

Reading to Learn MathematicsVocabulary Builder

NAME ______________________________________________ DATE ____________ PERIOD _____

22

© Glencoe/McGraw-Hill vii Glencoe Algebra 1

Voca

bula

ry B

uild

erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 2.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.

Vocabulary Term Found on Page Definition/Description/Example

absolute value

additive inverses

A·duh·tihv

equally likely

frequency

integers

irrational number

ih·RA·shuh·nuhl

line plot

measures of central tendency

natural number

odds

(continued on the next page)

© Glencoe/McGraw-Hill viii Glencoe Algebra 1

Vocabulary Term Found on Page Definition/Description/Example

opposites

perfect square

principal square root

probability

PRAH·buh·BIH·luh·tee

rational number

RA·shuh·nuhl

real number

sample space

simple event

square root

stem-and-leaf plot

whole number

Reading to Learn MathematicsVocabulary Builder (continued)

NAME ______________________________________________ DATE ____________ PERIOD _____

22

Study Guide and InterventionRational Numbers on the Number Line

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

© Glencoe/McGraw-Hill 75 Glencoe Algebra 1

Less

on

2-1

Graph Rational Numbers The figure at the right is part of a number line. A number line can be used to show the sets of natural numbers, whole numbers, and integers. Positive numbers, are located to the right of 0,and negative numbers are located to the left of 0.

Another set of numbers that you can display on a number line is the set of rational numbers. A rational number can

be written as , where a and b are integers and b � 0. Some

examples of rational numbers are , , , and .12��3

�7��8

�3�5

1�4

a�b

10�1�2�3�4 2 3

Natural Numbers

Positive NumbersNegative Numbers

4

Whole Numbers

Integers

Name the coordinates of thepoints graphed on each number line.

a.

The dots indicate each point on the graph.The coordinates are {�3, �1, 1, 3, 5}

b.

The bold arrow to the right means the graphcontinues indefinitely in that direction. Thecoordinates are {2, 2.5, 3, 3.5, 4, 4.5, 5, …}.

32.521.51 3.5 4 4.5 5

10�1�2�3 2 3 4 5

Graph each set ofnumbers.

a. {…, �3, �2, �1, 0, 1, 2}

b. �� , 0, , �12–

31–30�1–

3�2–3

4–3

5–3 2

2�3

1�3

1�3

10�1�2�3�4 2 3 4

Example 1Example 1 Example 2Example 2

ExercisesExercises

Name the coordinates of the points graphed on each number line.

1. 2.

3. 4.

Graph each set of numbers.

5. {�3, �1, 1, 3} 6. {�5, �2, 1, 2} 7. {integers less than 0}

8. {…, �2, �1, 0, 1} 9. ��2 , �1 , � , � 10. {…, �4, �2, 0, 2, …}

�3�4�5�6 �2 �1 0 1 2�21–2�3 �2�11–

2�1 �1–2 0 1–

2 1�3�4 �2 �1 0 1 2 3 4

1�2

1�2

1�2

1�2

�3�4 �2 �1 0 1 2 3 4�3�4�5 �2 �1 0 1 2 3�3�4 �2 �1 0 1 2 3 4

�3�4 �2 �1 0 1 2 3 4�1–4�1–

2 0 1–4

1–2

3–4 1 5–

43–2

0�1 1 2 3 4 5 6 70�1�2 1 2 3 4 5 6


Absolute Value On a number line, �3 is three units from zero in the negative direction, and 3 is three units from zero in the positive direction. The number line at the right illustrates the meaning of absolute value. Theabsolute value of a number n is the distance from zero on a number line and is represented n. For this example,�3 � 3 and 3 � 3.

10�1�2�3�4�5 2 3

3 units 3 units

� direction� direction4 5

Study Guide and Intervention (continued)

Rational Numbers on the Number Line

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

Find each absolute value.

a. �6�6 is six units from zero in the negativedirection.�6 � 6

b. is three halves units from zero in the

positive direction.

�3�2

3�2

3�2

3�2

Evaluate 4 � x � 2 if x � 5.

4 � x � 2 � 4 � 5 � 2 Replace x with 5.

� 4 � 3 5 � 2 � 3

� 4 � 3 3 � 3

� 7 Simplify.


ExercisesExercises


1. 2 2. �5 3. �24

4. �1.3 5. � 6. Evaluate each expression if a � 5, b � , x � 8, and y � 2.5.

7. 18 � 4 � y 8. x � 8 � 12 9. x � 2 � 8.2

10. 2 � x � 5 11. 2.5 � y � 12 12. 23 � x � 9

13. x � 6 � 4.5 14. 10 � a � 2 15. 6 � b �

16. � b � � 17. 3 � b � a 18. �b � 1 1�2

1�2

1�4

1�2

1�4

35�41

2�3

Skills PracticeRational Numbers on the Number Line

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1


Less

on

2-1


1. 2.

3. 4.


5. {�8, �5, �3, 0, 2} 6. {�9, �6, �4, �3, �1}

7. {�3, �2, �1, 0, …} 8. {…, �1, 0, 1, 2, 3}

9. �� , 0, , 1, � 10. {…, �3, �2.5, �2, �1.5, �1}


11. �9 12. 15 13. �30

14. � 15. 2.4 16. Evaluate each expression if a � 3, b � �10, c � , x � 9, y � 1.5, and z � 12.

17. 26 � x � 6 18. 11 � 10 � x

19. 12 � a � 5 20. a � 20 � 4

21. 4.5 � y 22. z � 7 � 5

23. 14 � b 24. b � 2

25. c � � 2 26. 9 � 3.5 � y1�2

1�2

9�11

5�7

�3 �2 �1 0 1 2�1 �1–2 0 1–

2 1 3–2 2 5–

2 3 7–2 4

5�2

1�2

1�2

�1 0 1 2 3 4 5 6 7 8 9�10 �9 �8 �7 �6 �5 �4 �3 �2 �1 0

�5�6�7�8�9�10 �4 �3 �2 �1 0�5�6�7�8 �4 �3 �2 �1 0 1 2

1.41.31.21.11.0 1.5 1.6 1.7 1.8 1.9 2.03210�1�2�3 4 5 6 7

10�1�2�3�4�5�6�7 2 310�1�2�3�4�5�6 2 3 4



1. 2.


3. �…, � , � , �1, � , � � 4. {integers less than �4 or greater than 2}


5. �11 6. 100 7. �0.35 8. � Evaluate each expression if a � 4, b � , c � , x � 14, y � 2.4, and z � �3.

9. 41 � 16 � z 10. 3a � 20 � 15 11. 2x � 4 � 6 12. 2.5 � 3.8 � y

13. �b � � � � 14. � b � 15. c � 1 � 16. �c �

ASTRONOMY For Exercises 17–19, use the following information.

The absolute magnitude of a star is how bright the star would appear from a standard distance of 10 parsecs, or 32.6 light years.The lower the number, the greater the magnitude, or brightness,of the star. The table gives the magnitudes of several stars.

17. Use a number line to order the magnitudes from least to greatest.

18. Which of the stars are the brightest and the least bright?

19. Write the absolute value of the magnitude of each star Source: www.astro.wisc.edu

20. CLIMATE The table shows the mean wind speeds in miles per hour at DaytonaBeach, Florida. Source: National Climatic Data Center

Graph the wind speeds on a number line. Which month has the greatest mean wind speed?

7 7.5 8 8.5 9 9.5 10 10.5

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

9.0 9.7 10.1 9.7 9.0 7.9 7.4 7.1 8.3 9.1 8.7 8.5

�6�7�8

� � � �

�9 �5 �4 �3 �2 �1 0 1 2 3

Star Magnitude

Altair 2.3

Betelgeuse �7.2

Castor 0.5

Deneb �4.7

Pollux 0.7

Regulus �0.3

Rigel �8.1

Sirius 1.4

3�4

1�3

2�5

2�15

3�10

1�5

3�2

3�5

28�53

� � � � � ��7–5 �6–

5 �1 �3–5�4–

5 �2–5 �1–

51–5

2–5

3–50

3�5

4�5

6�5

7�5

0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4�7–4 �3–

2 �5–4 �1 �3–

4 �1–2 �1–

41–4

1–2

3–40

Practice Rational Numbers on the Number Line

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

Reading to Learn MathematicsRational Numbers on the Number Line

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1


Less

on

2-1

Pre-Activity How can you use a number line to show data?

Read the introduction to Lesson 2-1 at the top of page 68 in your textbook.

In the table, what does the number �0.2 tell you?

Reading the Lesson

1. Refer to the number line on page 68 in your textbook. Write true or false for each of thefollowing statements.

a. All whole numbers are integers.

b. All natural numbers are integers.

c. All whole numbers are natural numbers.

d. All natural numbers are whole numbers.

e. All whole numbers are positive numbers.

2. Use the words denominator, fraction, and numerator to complete the following sentence.

You know that a number is a rational number if it can be written as a

that has a and that are integers, where the denominator is not equal to zero.

3. Explain why , 0.6�, and 15 are rational numbers.

Helping You Remember

4. Connecting a mathematical concept to something in your everyday life is one way ofremembering. Describe a situation or setting in your life that reminds you of absolutevalue.

�3�7


Intersection and UnionThe intersection of two sets is the set of elements that are in both sets.The intersection of sets A and B is written A � B. The union of two setsis the set of elements in either A, B, or both. The union is written A � B.

In the drawings below, suppose A is the set of points inside the circleand B is the set of points inside the square. Then, the shaded areasshow the intersection in the first drawing and the union in the seconddrawing.

Write A � B and A � B for each of the following.

1. A � {p, q, r, s, t}B � {q, r, s}

2. A � {the integers between 2 and 7}B � {0, 3, 8}

3. A � {the states whose names start with K}B � {the states whose capitals are Honolulu or Topeka}

4. A � {the positive integer factors of 24}B � {the counting numbers less than 10}

Suppose A � {numbers x such that x � 3}, B � {numbers x such as x � �1}, and C � {numbers x such that x � 1.5}. Graph each of the following.

5. A � B 6. A � B

7. B � C 8. B � C

9. (A � C) � B 10. A � (B � C)

�2 �1�4 �3 0 1 2 3 4�2 �1�4 �3 0 1 2 3 4

�2 �1�4 �3 0 1 2 3 4�2 �1�4 �3 0 1 2 3 4

�2 �1�4 �3 0 1 2 3 4�2 �1�4 �3 0 1 2 3 4

Intersection A � B

A B

Union A � B

A B

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-12-1

Study Guide and InterventionAdding and Subtracting Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-22-2


Less

on

2-2

Add Rational Numbers

Adding Rational Numbers, Add the numbers. If both are positive, the sum is positive; if both are negative, Same Sign the sum is negative.

Adding Rational Numbers,Subtract the number with the lesser absolute value from the number with the

Different Signsgreater absolute value. The sign of the sum is the same as the sign of the numberwith the greater absolute value.

Use a number line tofind the sum �2 � (�3).

Step 1 Draw an arrow from 0 to �2.Step 2 From the tip of the first arrow, draw

a second arrow 3 units to the left torepresent adding �3.

Step 3 The second arrow ends at the sum�5. So �2 � (�3) � �5.

10�1�2�3�4�5�6�7�8�9 2 3

�3 �2

Find each sum.

a. �8 � 5�8 � 5 � �(�8 � 5)

� �(8 � 5)� �3

b. � ��

� ��

1�4

2�4

3�4

2�4

3�4

2�4

3�4

1�2

3�4

1�2

3�4


ExercisesExercises

Find each sum.

1. 12 � 24 2. �6 � 14 3. �12 � (�15)

4. �21.5 � 34.2 5. 8.2 � (�3.5) 6. 23.5 � (�15.2)

7. 90 � (�105) 8. 108 � (�62) 9. �84 � (�90)

10. � 11. � 12. � �

13. � � �� 14. � � 15. � � ��

16. � � �� 17. �1.6 � (�1.8) 18. �0.008 � (�0.25)5�6

3�5

10�20

18�40

7�11

1�5

1�4

2�3

3�5

4�9

6�17

3�14

1�3

5�7


Subtract Rational Numbers Every positive rational number can be paired with anegative rational number so that their sum is 0. The numbers, called opposites, areadditive inverses of each other.

Additive Inverse Property For every number a, a � (�a) � 0.

To subtract a rational number, add its inverse and use the rules for addition given on page 81.

Subtraction of Rational Numbers For any numbers a and b, a � b � a � (�b).

Find 8.5 � 10.2.

8.5 � 10.2 � 8.5 � (�10.2) To subtract 10.2, add its inverse.

� �(�10.2 � 8.5) �10.2 is greater, so the result is negative.

� �1.7 Simplify.

Find each difference.

1. 11 � 41 2. 15 � (�21) 3. �33 � (�17)

4. 18 � (�12) 5. 15.5 � (�2.5) 6. 65.8 � (�23.5)

7. 90 � (�15) 8. �10.8 � (6.8) 9. �84 � (�72)

10. 58.8 � (�11.2) 11. �18.2 � 3.2 12. �9 � (�5.6)

13. � � �� 14. � � �� 15. �

16. � �� 17. � � �� 18. �

19. Sanelle was playing a video game. Her scores were �50, �75, �18, and �22. What washer final score?

20. The football team offense began a drive from their 20-yard line. They gained 8 yards, lost12 yards and lost 2 yards before having to kick the ball. What yard line were they onwhen they had to kick the ball?

18�20

24�10

3�9

7�8

1�2

12�23

5�9

9�4

4�7

1�5

3�4

1�3


Adding and Subtracting Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-22-2

ExampleExample

ExercisesExercises

Skills PracticeAdding and Subtracting Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-22-2


Less

on

2-2

Find each sum.

1. 28 � 13 2. 18 � 54 3. �6 � 15

4. �12 � 25 5. �14 � 11 6. �42 � 18

7. �19 � (�3) 8. �9 � (�17) 9. 25 � (�30)

10. 16 � (�20) 11. � �� 12. �2.5 � 3.2


13. 31 � 12 14. 53 � 47 15. 17 � 20

16. 28 � 39 17. �15 � 65 18. �27 � 13

19. �11 � (�12) 20. �25 � (�36) 21. �9 � (�7)

22. �14 � (�8) 23. �1.5 � 1 24. 3.6 � 4.8

25. � � �� 26. � � 27. � �

28. WEATHER At 6:00 P.M., the temperature in North Fork was 28 degrees Fahrenheit.Shortly afterward, a strong cold front passed through, and the temperature dropped 36 degrees by 8:00 A.M. the next morning. What was the temperature at 8:00 A.M.?

3�2

3�4

1�6

1�3

1�2

1�2

3�4

1�4


Find each sum.

1. �82 � 14 2. �33 � 47 3. �17 � (�39)

4. 8 � (�11) 5. �1.7 � 3.2 6. �13.3 � (�0.9)

7. �51.8 � 29.7 8. 7.34 � (�9.06) 9. �

10. � � 11. � � �� 12. � ��


13. 65 � 93 14. �42 � (�17) 15. 13 � (�19)

16. �8 � 43 17. 82.8 � (�12.4) 18. 1.27 � 2.34

19. �9.26 � 12.05 20. �18.1 � (�4.7) 21. � �

22. � 23. � � �� 24. � ��

FINANCE For Exercises 25–27, use the following information.

The table shows activity in Ben’s checking account. The balance before the activity was$200.00. Deposits are added to an account and checks are subtracted.

Number Date Transaction Amount Balance

5/2 deposit 52.50 252.50

101 5/10 check to Castle Music 25.50 ?

102 6/1 check to Comp U Save 235.40 ?

25. What is the account balance after writing check number 101?

26. What is the account balance after writing check number 102?

27. Realizing that he has just written a check for more than is in the account, Benimmediately deposits $425. What will this make his new account balance?

28. CHEMISTRY The melting points of krypton, radon, and sulfur in degrees Celsius are�156.6, �61.8, and 112.8, respectively. What is the difference in melting points betweenradon and krypton and between sulfur and krypton?

5�6

1�8

3�7

5�2

5�6

4�3

2�3

1�5

2�3

3�8

3�5

3�4

2�3

3�5

5�6

5�9

Practice Adding and Subtracting Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-22-2

Reading to Learn MathematicsAdding and Subtracting Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-22-2


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Pre-Activity How can a number line be used to show a football team’s progress?


Use positive or negative to complete the following sentences.

The five-yard penalty is shown by the number �5.

The 13-yard pass is shown by the number 13.

Reading the Lesson

1. To add two rational numbers, you can use a number line. Each number will berepresented by an arrow.

a. Where on the number line does the arrow for the first number begin?

b. Arrows for negative numbers will point to the (left/right). Arrows for

positive numbers will point to the (left/right).

2. Two students added the same pair of rational numbers. Both students got the correctsum. One student used a number line. The other student used absolute value. Then theycompared their work.

a. How do the arrows show which number has the greater absolute value?

b. If the longer arrow points to the left, then the sum is (positive/negative). If the longer arrow points to the right, then the sum is

(positive/negative).

3. If two numbers are additive inverses, what must be true about their absolute values?

4. Write each subtraction problem as an addition problem.

a. 12 � 4 b. �15 � 7

c. 0 � 9 d. �20 � 34


5. Explain why knowing the rules for adding rational numbers can help you to subtractrational numbers.


Rounding FractionsRounding fractions is more difficult than rounding whole numbers or

decimals. For example, think about how you would round inches to

the nearest quarter-inch. Through estimation, you might realize that

is less than . But, is it closer to or to ?

Here are two ways to round fractions. Example 1 uses only thefractions; Example 2 uses decimals.

1�4

1�2

1�2

4�9

4�9

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-22-2

Subtract the fraction twice. Use the twonearest quarters.

� � � �

Compare the differences.

�

The smaller difference shows you whichfraction to round to.

rounds to .1�2

4�9

7�36

1�18

7�36

1�4

4�9

1�18

4�9

1�2

Change the fraction and the two nearestquarters to decimals.

� 0.44�, � 0.5, � 0.25

Find the decimal halfway between the twonearest quarters.

(0.5 � 0.25) � 0.375

If the fraction is greater than the halfwaydecimal, round up. If not, round down.

0.44� � 0.3675. So, is more than half way

between and .

rounds to .1�2

4�9

1�2

1�4

4�9

1�2

1�4

1�2

4�9


Round each fraction to the nearest one-quarter. Use either method.

1. 2. 3. 4.

5. 6. 7. 8.

Round each decimal or fraction to the nearest one-eighth.

9. 0.6 10. 0.1 11. 0.45 12. 0.85

13. 14. 15. 16. 5�9

23�25

3�20

5�7

23�30

9�25

31�50

7�20

4�15

7�11

3�7

1�3

Study Guide and InterventionMultiplying Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-32-3


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Multiply Integers You can use the rules below when multiplying integers and rationalnumbers.

Multiplying Numbers with the Same Sign The product of two numbers having the same sign is positive.

Multiplying Numbers with Different Signs The product of two numbers having different signs is negative.

Find each product.

a. �7(6)The signs are different, so the product isnegative.�7(6) � �42

b. �18(�10)The signs are the same, so the product ispositive.�18(�10) � 180

Simplify the expression(�2x)5y.

(�2x)5y � (�2)(5)x y Commutative Property ()

� (�2 5)xy Associative Property

� �10xy Simplify.


ExercisesExercises

Find each product.

1. 11(4) 2. �5(�3) 3. (�24)(�2)

4. (60)(�3) 5. (�2)(�3)(�4) 6. 8(�15)

7. �15(3) 8. (12)(�10) 9. (�22)(�3)(2)

10. (5)(�5)(0)(4) 11. (�15)(45) 12. (�12)(�23)

Simplify each expression.

13. 4(�2x) � 8x 14. 6(�2n ) � 10n 15. 6(3y � y)

16. �3(3d � 2d) 17. �2x(2) � 2x(3y) 18. 4m(�2n) � 2d(�4e)

19. �5(2x � x) � 3(�xy) 20. (2)(�4x � 2x) 21. (�3)(�8n � 6m)


Multiply Rational Numbers Multiplying a rational number by �1 gives you theadditive inverse of the number.

Multiplicative Property of �1The product of any number and �1 is

(�1)(5) � 5(�1) � �5 its additive inverse.


Multiplying Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-32-3

Evaluate a3b2 if a � �2and b � �5.

a3b2 � (�2)3(�5)2 Substitution

� (�8)(25) (�2)3 � �8 and (�5)2 � 25

� �200 different signs → negative product

Evaluate n2�� if n � � .

n2�� 2�� Substitution

� � �� 2

� �� or

� � different signs → negative product3

�20

1�4

1�2

1�2

1�2

3�5

1�4

3�5

1�2

3�5

1�2

3�5


ExercisesExercises

Find each product.

1. (�12) 2. �� 3. ��

4. (6.0)(�0.3) 5. �� 6. 8(�15)

7. �15(�4) 8. � �(�10) 9. �� (�3)� �

10. � �(�2)(0)� � 11. �� 12. ��1 ��2 �

Evaluate each expression if a � �2.5, b � 4.2, c � 5.5, and d � �0.2.

13. �2a2 14. 5(�2b) 15. �6(cd)

16. �2(3d � 2c) 17. �ad � 3c 18. b2(c � 2d)

19. �5bcd 20. �3d2 � 4 21. (�3)(�8a � 2b)

1�3

1�2

4�5

1�3

1�4

4�5

2�3

2�5

1�2

3�4

1�3

1�2

2�5

2�7

2�3

1�5

1�4

Skills PracticeMultiplying Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-32-3


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on

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Find each product.

1. 9(17) 2. �8(�7)

3. 5(�7) 4. �4(11)

5. �6(�12) 6. 7(�25)

7. � �� 8. ��

9. �� 10. � ��

11. �� 12. (1.5)(2.2)

13. (�2.8)(0.5) 14. (2.4)(�0.6)

15. (�4.7)(�1.3) 16. (1.1)(�1.2)


17. 5(�2a) � 8a 18. �6(3x) � 12x

19. 3(4n � n) 20. �4(2d � d)

Evaluate each expression if a � �1.2, b � 0.5, c � , and d � � .

21. �4ab 22. �3b2

23. �2a2 24. c2��

25. d2 26. �3cd

27. STAIRCASES A staircase in an office building starts at ground level. Each step downlowers you by 7.5 inches. What is your height in relation to ground level after descending20 steps?

1�8

1�3

2�3

1�2

2�3

5�6

5�8

3�4

1�2

3�8

1�6

3�5

2�3

1�2


Find each product.

1. 42(7) 2. �28(�17) 3. 15(�34)

4. �� 5. �� 6. � �� 7. ��3 ��2 � 8. ��2 ��1 � 9. �1 ��1 �

10. (1.5)(8.8) 11. (6.8)(�1.3) 12. (�0.2)(2.8)

13. (�3.6)(�0.55) 14. 6.3(�0.7) 15. (�4)(9)


16. 5(�3a) � 18a 17. �8(4c) � 12c 18. �9(2g � g)

19. 7(2b � 4b) 20. �4x(2y) � (�3b)(�2d) 21. �5p(�3q) � (4m)(�6n)

Evaluate each expression if a � � , b � , c � �3.4, and d � 0.7.

22. b2�� 23. 4ab 24. 5a2(�b)

25. �6d2 26. cd � 3 27. c2(�5d)

28. RECIPES A recipe for buttermilk biscuits calls for 3 cups of flour. How many cups of

flour do you need for the recipe?

COMPUTERS For Exercises 29 and 30, use the following information.

Leeza is downloading a file from a Web site at 47.3 kilobytes per second.

29. How many kilobytes of the file will be downloaded after one minute?

30. How many kilobytes will be downloaded after 4.5 minutes?

CONSERVATION For Exercises 31 and 32, use the following information.

A county commission has set aside 640 acres of land for a wildlife preserve.

31. Suppose of the preserve is marshland. How many acres of the preserve are

marshland?

32. If the forested area of the preserve is 1.5 times larger than the marshland, how manyacres of the preserve are forested?

2�5

1�2

1�3

2�3

3�4

4�5

2�3

1�5

1�4

1�6

2�3

1�2

1�4

5�7

9�10

5�6

4�5

7�8

3�4

Practice Multiplying Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-32-3

Reading to Learn MathematicsMultiplying Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-32-3


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on

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Pre-Activity How do consumers use multiplication of rational numbers?


• How is the amount of the coupon shown on the sales slip?

• Besides the amount, how is the number representing the coupon differentfrom the other numbers on the sales slip?

Reading the Lesson

1. Complete: If two numbers have different signs, the one number is positive and the other

number is .

2. Complete the table.

Multiplication Are the signs of the numbers the same Is the product positive or negative?Example or different?

a. (�4)(9)

b. (�2)(�13)

c. 5(�8)

d. 6(3)

3. Explain what the term “additive inverse” means to you. Then give an example.


4. Describe how you know that the product of �3 and �5 is positive. Then describe howyou know that the product of 3 and �5 is negative.


Compound InterestIn most banks, interest on savings accounts is compounded at set timeperiods such as three or six months. At the end of each period, thebank adds the interest earned to the account. During the next period,the bank pays interest on all the money in the bank, including interest.In this way, the account earns interest on interest.

Suppose Ms. Tanner has $1000 in an account that is compoundedquarterly at 5%. Find the balance after the first two quarters.

Use I � prt to find the interest earned in the first quarter if p � 1000 and r � 5%. Why is t equal to ?

First quarter: I � 1000 0.05

I � 12.50

The interest, $12.50, earned in the first quarter is added to $1000.The principal becomes $1012.50.

Second quarter: I � 1012.50 0.05

I � 12.65625

The interest in the second quarter is $12.66.

The balance after two quarters is $1012.50 � 12.66 or $1025.16.

Answer each of the following questions.

1. How much interest is earned in the third quarter of Ms. Tanner’saccount?

2. What is the balance in her account after three quarters?

3. How much interest is earned at the end of one year?

4. What is the balance in her account after one year?

5. Suppose Ms. Tanner’s account is compounded semiannually. Whatis the balance at the end of six months?

6. What is the balance after one year if her account is compoundedsemiannually?

1�4

1�4

1�4

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-32-3

Study Guide and InterventionDividing Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-42-4


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Divide Integers The rules for finding the sign of a quotient are similar to the rules forfinding the sign of a product.

Dividing Two Numbers with the Same Sign The quotient of two numbers having the same sign is positive.

Dividing Two Numbers with Different Signs The quotient of two numbers having different signs is negative.

Find each quotient.

a. �88 (�4)�88 � (�4) � 22 same signs → positive quotient

b.

� �8 different signs → negative quotient�64�8

�64�8

Simplify .

� .

�

�

� �8

32��4

32��3 � (�1)

�4(�8)��3 � (�1)

�4(�10 � 2)��

�3 � (�1)

�4(�10 � 2)��

�3 � (�1)Example 1Example 1 Example 2Example 2

ExercisesExercises

Find each quotient.

1. �80 � (�10) 2. �32 � 16 3. 80 � 5

4. 18 � (�3) 5. �12 � (�3) 6. 8 � (�2)

7. �15 � (�3) 8. 121 � (�11) 9. �24 � 1.5

10. 0 � (�8) 11. �125 � (�25) 12. �104 � 4

Simplify.

13. 14. 15.

16. 17. 18. 4(�12 � 4)��

�2(8)�4(�8 � (�4))��

�3 � (�3)�12(2 � (�3))��

�4 � 1

�6(�6 � 2)��10 � (�2)

5(�10 � (�2))��

�2 � 1�2 � (�4)��(�2) � (�1)


Divide Rational Numbers The rules for division with integers also apply to division

with rational numbers. To divide by any nonzero number, , multiply by the reciprocal of

that number, .

Division of Rational Numbers � � d�c

a�b

c�d

a�b

d�c

c�d


Dividing Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-42-4

a. Find �5 8.

�5 � 8 � � �

� �

� � or �

b. Find .

� 12.3�83.64�

�6.8

�83.64�

�6.8

2�3

16�24

1�8

16�3

8�1

16�3

1�3

1�3

Simplify .

� (�20a � 15) � 5

� (�20a � 15)� �� 20a� � � 15� �� 4a � 3

1�5

1�5

1�5

�20a � 15��5

�20a � 15��5


ExercisesExercises

Find each quotient.

1. � � 2 2. �32 � 3. � �

4. 1.8 � (�3) 5. �12.9 � (�0.3) 6. � �� 7. � � �� 8. 52.5 � (�4.2) 9. � �

10. 105 � (�1.5) 11. �12.5 � (�2.5) 12. � �


13. 14. 15.

16. 17. 18.

Evaluate each expression if a � �6, b � 2.5, c � �3.2, and d � 4.8.

19. 20. 21. a � 2b�c � d

a � d�b

ab�d

57y � 12��3

36a � 12��12

18a � 6b��

�3

�144a�6

16x�2

�44a�4

4�3

1�4

5�3

8�15

3�10

15�32

2�3

3�8

1�5

2�5

1�4

1�8

Skills PracticeDividing Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-42-4


Less

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Find each quotient.

1. �32 � (�4) 2. �28 � 7

3. �45 � (�15) 4. 39 � (�3)

5. �56 � 14 6. 62 � (�4)

7. �23 � (�5) 8. 52 � (�8)

9. �90 � 12 10. �16.5 � 11

11. �1.44 � 1.2 12. �16.2 � (�0.4)

13. 6 � �� 14. � �

15. � � �� 16. �


17. 18.

19. 20.

Evaluate each expression if g � �4, h � 2.5, k � 1.4, and m � �0.8. Round to thenearest hundredth.

21. 22.

23. 24. hk � gm

25. km � gh 26. k � m�g

hk�m

hm�g

gh�m

�54z � 18��

�916c � 4�

�4

216x�12

27a�3

2�3

1�2

1�4

2�3

1�2

3�4

2�9


Find each quotient.

1. 75 � (�15) 2. �323 � (�17) 3. �88 � 16

4. 65.7 � (�9) 5. �36.08 � 8 6. �40.05 � (�2.5)

7. �9 � 8. � � �� 9. � ��


10. 11. 12.

13. 14. 15.

Evaluate each expression if p � �6, q � 4.5, r � 3.6, and s � �5.2. Round to thenearest hundredth.

16. 17. 18. ps � qr

19. rs � pq 20. 21.

22. EXERCISE Ashley walks 2 miles around a lake three times a week. If Ashley walks

around the lake in hour, what is her rate of speed? (Hint: Use the formula r � ,

where r is rate, d is distance, and t is time.)

23. PUBLICATION A production assistant must divide a page of text into two columns. If

the page is 6 inches wide, how wide will each column be?

ROLLER COASTERS For Exercises 24 and 25, use the following information.

The formula for acceleration is a � , where a is acceleration, f is final speed, s is starting speed, and t is time.

24. The Hypersonic XLC roller coaster in Virginia goes from zero to 80 miles per hour in 1.8 seconds. What is its acceleration in miles per hour per second to the nearest tenth?Source: www.thrillride.com

25. What is the acceleration in feet per second per second? (Hint: Convert miles to feet andhours to seconds, then apply the formula for acceleration. 1 mile � 5280 feet)

f � s�t

3�4

d�t

3�4

1�2

r � s�q

p � q�r

rs�q

qr�p

�4c � (�16d)��4

8k �12h��4

18x � 12y��

�6

3t � 12�

�325 � 5x�5

168p��14

49�54

14�63

3�8

5�6

3�5

Practice Dividing Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-42-4

Reading to Learn MathematicsDividing Rational Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-42-4


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on

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Pre-Activity How can you use division of rational numbers to describe data?


• What is meant by the term mean?

• In the expression , will the numerator be positive or negative?

Reading the Lesson

1. Explain what the term inverse operations means to you.

2. Write negative or positive to describe the quotient. Explain your answer.

Expression Negative or Positive? Explanation

a.

b.

c.


3. Explain how knowing the rules for multiplying rational numbers can help you rememberthe rules for dividing rational numbers.

(�5.6)(�2.4)��

1.92

�78��13

35��7

(�127) � 54 � (�65)��3


Other Kinds of MeansThere are many different types of means besides the arithmeticmean. A mean for a set of numbers has these two properties:

a. It typifies or represents the set.b. It is not less than the least number and it is not greater than the

greatest number.

Here are the formulas for the arithmetic mean and three other means.

Enrichment

NAME ______________________________________________ DATE______________ PERIOD _____

2-42-4

Arithmetic Mean

Add the numbers in the set. Then dividethe sum by n, the number of elements inthe set.

Harmonic Mean

Divide the number of elements in the set bythe sum of the reciprocals of the numbers.

Geometric Mean

Multiply all the numbers in the set. Thenfind the nth root of their product.

n�x1 � x2� � x3 ��… � xn�

Quadratic Mean

Add the squares of the numbers. Dividetheir sum by the number in the set.Then, take the square root.

��x12 � x2

2 � x32 � … � xn

2

��n

n��x1

1� � �x

1

2� � �x

1

3� � … � �x

1

n�

x1 � x2 � x3 � … � xn��n

Find the four different means to the nearest hundredth for each set of numbers.

1. 10, 100 2. 50, 60

A � 55 G � 31.62 A � 55 G � 54.77

H � 18.18 Q � 71.06 H � 54.55 Q � 55.23

3. 1, 2, 3, 4, 5, 4. 2, 2, 4, 4

A � 3 G � 2.61 A � 3 G � 2.83

H � 2.19 Q � 3.32 H � 2.67 Q � 3.16

5. Use the results from Exercises 1 to 4 to compare the relative sizesof the four types of means.From least to greatest, the means are the harmonic, geometric,arithmetic, and quadratic means.

Study Guide and InterventionStatistics: Displaying and Analyzing Data

NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5


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Create Line Plots and Stem-and-Leaf Plots One way to display data graphicallyis with a line plot. A line plot is a number line labeled with a scale that includes all thedata and s placed above a data point each time it occurs in the data list. The s representthe frequency of the data. A stem-and-leaf plot can also be used to organize data. Thegreatest common place value is called the stem, and the numbers in the next greatest placevalue form the leaves.

Draw a line plot for the data.�3 3 4 7 9 10 �2 3

6 4 3 9 �1 �2 4 2

Step 1 The value of the data ranges from�3 to 10, so construct a number linecontaining those points.

Step 2 Then place an above the numbereach time it occurs.

76543210�1�2�3

8 9 10

76543210�1�2�3 8 9 10

Use the data below tocreate a stem-and-leaf plot.62 74 89 102 92 65 68 98 78 6578 80 83 93 87 89 104 109 104 68 97 68 64 98 93 90 102 104

The greatest common place value is tens, sothe digits in the tens place are the stems.Thus 62 would have a stem of 6 and 104would have a stem of ten. The stem-and-leafplot is shown below.Stem | Leaf

6 | 2 4 5 5 8 8 87 | 4 8 88 | 0 3 7 9 99 | 0 2 3 3 7 8 8

10 | 2 2 4 4 4 9 62 � 62


ExercisesExercises

Use the table at the right for Exercises 1–3.

1. Make a line plot representing the weights of the wrestlers shown in the table at the right.

2. How many wrestlers weigh over 140 lb?

3. What is the greatest weight?

Use each set of data to make a stem-and-leaf plot.

4. 32 45 41 29 30 30 31 34 38 5. 102 104 99 109 108 112 115 120 36 32 34 41 40 42 41 29 30 112 114 98 94 96 101 100 102

200190180170160150140130120110100

Weights of Junior Varsity Wrestlers (pounds)

170 160 135 135 160 122 188 154108 135 140 122 103 190 154


Analyze Data Numbers that represent the centralized, or middle, value of a set of dataare called measures of central tendency. Three measures of central tendency are themean, median, and mode.

Definition Example

MeanSum of the data values divided by the

Data: 24, 36, 21, 30, 21, 30; � 27number of values in the data set.

The middle number in a data set when the numbers are arranged in numerical

Median order. If there is an even number of Data: 21, 21, 25, 30, 31, 42; � 27.5values, the median is halfway between the two middle values.

ModeThe number or numbers that occur

Data: 21, 21, 24, 30, 30, 36; 21 and 30 are modesmost often in the set of data.

Which measure of central tendency best represents the data?

Find the mean, median, and mode.

Mean � 105

Median � 102

Modes � 99 and 112

The median best represents the center of the data since the mean is too high.

Find the mean, median, and mode for each data set. Then tell which bestrepresents the data.

1. 2. 3.

4. 5.

3210

4 5 6 7

Month Days above 90�

May 4

June 7

July 14

August 12

September 8

Stem | Leaf

5 | 0 1 96 | 2 2 5 57 | 1 3 58 | 0 3 7 7 5 |0 � 50

Stem | Leaf

9 | 0 0 1 3 910 | 2 2 511 |12 | 0 3 3 8 8 9 9 |0 � 90

Stem | Leaf

2 | 4 7 73 | 1 2 6 6 6 94 | 05 | 8 8 9 2 |4 � 24

Stem | Leaf

9 | 4 6 8 9 910 | 0 1 2 4 8 911 | 2 212 | 0 1 9 |4 �

25 � 30�

2

24 � 36 � 21 � 30 � 21 � 30��

6


Statistics: Displaying and Analyzing Data

NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5

ExampleExample

ExercisesExercises

Skills PracticeStatistics: Displaying and Analyzing Data

NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5


Less

on

2-5

Use each set of data to make a line plot.

1. 59 39 50 60 45 39 59 45 31 59 2. 5 �2 4 0 7 4 3 7 �1 455 43 39 42 59 35 31 55 43 52 �2 5 2 2 3 4 5 0 �2 2

INCOME For Exercises 3–5, use the list that shows the income from each assignment for a private investigator for a year.

3. Make a line plot of the data.

4. What was the median income per assignment for the investigator?

5. Does the median best represent the data?


6. 52 68 40 74 65 68 59 75 67 73 7. 1.5 2.3 1.7 3.0 4.1 5.3 4.755 63 39 42 59 35 31 59 63 42 1.9 2.2 2.8 4.3 5.2 4.1 2.2

EMPLOYMENT For Exercises 8–10, use the list that shows the ages of employees at Watson &Sterling Publications.

8. Make a stem-and-leaf plot of the data.

9. Which age occurs most frequently?

10. Does the mode best represent the data?Explain.

Stem | Leaf

||||

20 52 21 39 40 58 27 48 36 20 51 2645 30 49 22 59 50 33 35 28 43 55 20

Stem | Leaf

|||||

Stem | Leaf

|||||

5000 5500 6000 6500 7000 7500 8000

6300 6100 78005600 7800 51006000 7200 63005100 6100 7800

76543210�1�2

30 35 40 45 50 55 60


Use each set of data to make a line plot.

1. 72 47 62 78 49 67 80 2. �2 �1.3 1.5 0.1 �1.7 0.4 1.554 47 72 55 62 47 54 1 �1.3 �2 �2.9 0.1 1.3 1.262 80 47 78 72 46 �2.6 1.2 0.2 �1.3 �2.6

HEALTH For Exercises 3 and 4, use the list that shows the grams of saturated fat in a serving of a variety of grains such as bread, cereal, crackers, and pasta.

3. Make a line plot of the data.

4. Which measure of central tendency best describes the data? Explain.


5. 41 53 22 50 41 27 36 57 20 31 6. 4.1 7.3 6.9 5.7 4.8 7.3 5.628 52 41 33 28 27 41 52 22 30 6.0 4.4 7.5 4.6 7.9 5.1 7.7

EMPL0YMENT For Exercises 7–10, use the lists that show survey results ofstudents’ time spent on the Internet and on the telephone for a month.

7. Make a stem-and-leaf plot to compare the data.

8. Which value appears most frequently in each set of data?

9. Is the mode the best measure to compare the data?

10. Overall, did students spend more time on the Internet or the telephone?

Internet | Stem | Telephone

| || || || || || |

Internet Telephone

42 19 28 8 35 42 20 18 36 52 40 28 43 24 8 53

51 4 7 29 14 22 6 41 26 48 35 58 8 4

Stem | Leaf

||||

Stem | Leaf

||||

0 0.5 1 1.5 2 2.5 3

0.3 1.2 0.1 0.3 0.40.4 0.5 0.1 0.4 0.40.1 1.2 2.8 1.3 1.5

�3 �2.5 �2 �1.5 �1 �0.5 0 0.5 1 1.5

45 50 55 60 65 70 75 80

Practice Statistics: Displaying and Analyzing Data

NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5

Reading to Learn MathematicsStatistics: Displaying and Analyzing Data

NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5


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Pre-Activity How are line plots and averages used to make decisions?


• What was the number one name for boys in all five decades?

• Look at the decade in which you were born. Is your name or the names ofany of the other students in your class in the top five for that decade?

Reading the Lesson

1. Use the line plot shown below to answer the questions.

a. What are the data points for the line plot?

b. What do the three ’s above the 6 represent?

2. Explain what is meant by the frequency of a data number.

3. Use the stem-and-leaf plot shown at the right.

a. How is the number 758 represented on the plot?

b. Explain how you know there are 23 numbers in thedata.


4. Describe how you would explain the process of finding the median and mode from astem-and-leaf plot to a friend who missed Lesson 2-5.

Stem | Leaf

72 | 0 1 1 2 573 | 2 2 2 7 9 974 | 1 3 375 | 6 6 8 976 | 0 1 8 8 8 742 � 742

76543210�1�2�3�4�5�6


Runs Created In The 1978 Bill James Baseball Abstract, the author introduced the “runs created” formula.

R � where for each player h � number of hits

w � number of walks,

t � number of total bases,

b � number of at-bats, and

R � approximate number of runs a team scores due to this player’s actions

1. As of June 29, 2001, Roberto Alomar of the Cleveland Indians and Seattle Marinersplayer Ichiro Suzuki were tied with the highest American League batting average at.351. Find the number of runs created by each player using the data below.

h w t b Runs Created

Alomar 97 37 145 276

Suzuki 121 13 159 345

Based on this information, who do you think is the more valuable American Leagueplayer? Why?

2. Carlos Lee of the Chicago White Sox and New York Yankee Bernie Williams were bothbatting .314. Find the number of runs created by each player using the data below.

h w t b Runs Created

Lee 81 13 141 258

Williams 74 31 123 236

3. Why would baseball teams want to calculate the number of runs created by each of theirplayers?

(h + w)t�(b + w)

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-52-5

Study Guide and InterventionProbability: Simple Probability and Odds

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2-62-6


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Probability The probability of a simple event is a ratio that tells how likely it is thatthe event will take place. It is the ratio of the number of favorable outcomes of the event tothe number of possible outcomes of the event. You can express the probability either as afraction, as a decimal, or as a percent.

Probability of a Simple Event For an event a, P(a) � .number of favorable outcomes��number of possible outcomes

Mr. Babcock chooses 5 out of 25 students in his algebra classat random for a special project. What isthe probability of being chosen?

P(being chosen) �

The probability of being chosen is or .1�5

5�25

number of students chosen��total number of students

A bowl contains 3 pears,4 bananas, and 2 apples. If you take apiece of fruit at random, what is theprobability that it is not a banana?

There are 3 � 4 � 2 or 9 pieces of fruit.There are 3 � 2 or 5 pieces of fruit that arenot bananas.

P(not banana) �

�

The probability of not choosing a banana is .5�9

5�9

number of other pieces of fruit��total number of pieces of fruit


ExercisesExercises

A card is selected at random from a standard deck of 52 cards. Determine eachprobability.

1. P(10) 2. P(red 2) 3. P(king or queen)

4. P(black card) 5. P(ace of spades) 6. P(spade)

Two dice are rolled and their sum is recorded. Find each probability.

7. P(sum is 1) 8. P(sum is 6) 9. P(sum is less than 4)

10. P(sum is greater than 11) 11. P(sum is less than 15) 12. P(sum is greater than 8)

A bowl contains 4 red chips, 3 blue chips, and 8 green chips. You choose one chipat random. Find each probability.

13. P(not a red chip) 14. P(red or blue chip) 15. P(not a green chip)

A number is selected at random from the list {1, 2, 3, …, 10}. Find each probability.

16. P(even number) 17. P(multiple of 3) 18. P(less than 4)

19. A computer randomly chooses a letter from the word COMPUTER. Find the probabilitythat the letter is a vowel.


Odds The odds of an event occurring is the ratio of the number of ways an event can occur(successes) to the number of ways the event cannot occur (failures).

Odds

A die is rolled. Find the odds of rolling a number greater than 4.

The sample space is {1, 2, 3, 4, 5, 6}. Therefore, there are six possible outcomes. Since 5 and6 are the only numbers greater than 4, two outcomes are successes and four are failures.

So the odds of rolling a number greater than 4 is , or 1:2.

Find the odds of each outcome if the spinner at the right is spun once.

1. multiple of 4 2. odd number

3. even or a 5 4. less than 4

5. even number greater than 5

Find the odds of each outcome if a computer randomly chooses a number between1 and 20.

6. the number is less than 10 7. the number is a multiple of 4

8. the number is even 9. the number is a one-digit number

A bowl of money at a carnival contains 50 quarters, 75 dimes, 100 nickels, and 125 pennies. One coin is randomly selected.

10. Find the odds that a dime will not be chosen.

11. What are the odds of choosing a quarter if all the dimes are removed?

12. What are the odds of choosing a penny?

Suppose you drop a chip onto the grid at the right. Find the odds of each outcome.

13. land on a shaded square

14. land on a square on the diagonal

15. land on square number 16

16. land on a number greater than 12

17. land on a multiple of 5

1

5

9

13

2

6

10

14

3

7

11

15

4

8

12

16

129

4

38

7

10

56

2�4

number of successes��

number of failures


Probability: Simple Probability and Odds

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6

ExampleExample

ExercisesExercises

Skills PracticeProbability: Simple Probability and Odds

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One chip is randomly selected from a jar containing 8 yellow chips, 10 blue chips,7 green chips, and 5 red chips. Find each probability.

1. P(blue) 2. P(green)

3. P(yellow or green) 4. P(blue or yellow)

5. P(not red) 6. P(not blue)

Find the probability of each outcome if the spinner is spun once.

7. P(multiple of 3) 8. P(less than 7)

9. P(odd or 2) 10. P(not 1)

A person is born in the month of June. Find each probability.

11. P(date is a multiple of 6) 12. P(date is before June 15)

13. P(before June 7 or after June 24) 14. P(not after June 5)

Find the odds of each outcome if a computer randomly picks a letter in the nameThe Petrified Forest.

15. the letter f 16. the letter e

17. the letter t 18. a vowel

CLASS SCHEDULES For Exercises 19–22, use the following information.

A student can select an elective class from the following: 3 in music, 5 in physical education,2 in journalism, 8 in computer programming, 4 in art, and 6 in drama. Find each of the oddsif a student forgets to choose an elective and the school assigns one at random.

19. The class is computer programming.

20. The class is drama.

21. The class is not physical education.

22. The class is not art.

18

456 3

7 2


One chip is randomly selected from a jar containing 13 blue chips, 8 yellow chips,15 brown chips, and 6 green chips. Find each probability.

1. P(brown) 2. P(green)

3. P(blue or yellow) 4. P(not yellow)

A card is selected at random from a standard deck of 52 cards. Find eachprobability.

5. P(heart) 6. P(black card)

7. P(jack) 8. P(red jack)

Two dice are rolled and their sum is recorded. Find each probability.

9. P(sum less than 6) 10. P(sum less than 2)

11. P(sum greater than 10) 12. P(sum greater than 9)

Find the odds of each outcome if a computer randomly picks a letter in the nameThe Badlands of North Dakota.

13. the letter d 14. the letter a

15. the letter h 16. a consonant

CLASS PROJECTS For Exercises 17–20, use the following information.

Students in a biology class can choose a semester project from the following list: animalbehavior (4), cellular processes (2), ecology (6), health (7), and physiology (3). Find each ofthe odds if a student selects a topic at random.

17. the topic is ecology

18. the topic is animal behavior

19. the topic is not cellular processes

20. the topic is not health

SCHOOL ISSUES For Exercises 21 and 22, use the following information.

A news team surveyed students in grades 9–12 on whether to change the time school begins. One student will be selected atrandom to be interviewed on the evening news. The table gives the results.

21. What is the probability the student selected will be in the

9th grade?

22. What are the odds the student selected wants no change?

Grade 9 10 11 12

No change 6 2 5 3

Hour later 10 7 9 8

Practice Probability: Simple Probability and Odds

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6

Reading to Learn MathematicsProbability: Simple Probability and Odds

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6


Less

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Pre-Activity Why is probability important in sports?


Look up the definition of the word probability in a dictionary. Rewrite thedefinition in your own words.

Reading the Lesson

1. Write whether each statement is true or false. If false, replace the underlined word ornumber to make a true statement.

a. Probability can be written as a fraction, a decimal, or a percent.

b. The sample space of flipping one coin is heads or tails.

c. The probability of an impossible event is 1.

d. The odds against an event occurring are the odds that the event will occur.

2. Explain why the probability of an event cannot be greater than 1 while the odds of anevent can be greater than 1.


3. Probabilities are usually written as fractions, decimals, or percents. Odds are usuallywritten with a colon (for example, 1:3). How can the spelling of the word colon helpremember this?


Geometric ProbabilityIf a dart, thrown at random, hits the triangular board shown at the right, what is the probability that it will hit the shaded region? Thiscan be determined by comparing the area of the shaded region to thearea of the entire board. This ratio indicates what fraction of the tosses should hit in the shaded region.

�

� or

In general, if S is a subregion of some region R, then the probability, P(S), that a point,chosen at random, belongs to subregion S is given by the following:

P(S) �

Find the probability that a point, chosen at random, belongs to the shadedsubregions of the following figures.

1. 2. 3.

4. 5. 6.

7. 8. 9.2

2

4 48

4

4

4

4 4

6

6

66

66

6��3 6��3

5

5

55 55

6

6

4

4

4 4

4

6

44 4

6 63 3

5

5

area of subregion S��area or region R

1�2

12�24

�12

�(4)(6)��12

�(8)(6)

area of shaded region��area of triangular board

6

44

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6

Study Guide and InterventionSquare Roots and Real Numbers

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2-72-7


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Square Roots A square root is one of two equal factors of a number. For example, thesquare roots of 36 are 6 and �6, since 6 6 or 62 is 36 and (�6)(�6) or (�6)2 is also 36. Arational number like 36, whose square root is a rational number, is called a perfectsquare.The symbol �� is a radical sign. It indicates the nonnegative, or principal, square root of the number under the radical sign. So �36� � 6 and ��36� � �6. The symbol ��36�represents both square roots.

Find �� .

� represents the negative square root of .

� � �2→ � � �

5�7

25�49

5�7

25�49

25�49

25�49

25�49 Find ��0.16.

��0.16� represents the positive andnegative square roots of 0.16.0.16 � 0.42 and 0.16 � (�0.4)2

��0.16� � �0.4


ExercisesExercises

Find each square root.

1. �64� 2. ��81� 3. �16.81�

4. ��100� 5. � 6. ��121�

7. � 8. � 9. �

10. ��3600� 11. ��6.25� 12. ��0.000�4�

13. 14. � 15. ��1.21�36�49

144�196

121�100

25�16

25�144

4�25


Classify and Order Numbers Numbers such as �2� and �3� are not perfect squares.Notice what happens when you find these square roots with your calculator. The numberscontinue indefinitely without any pattern of repeating digits. Numbers that cannot bewritten as a terminating or repeating decimal are called irrational numbers. The set ofreal numbers consists of the set of irrational numbers and the set of rational numberstogether. The chart below illustrates the various kinds of real numbers.

Natural Numbers {1, 2, 3, 4, …}

Whole Numbers {0, 1, 2, 3, 4, …}

Integers {…, �3, �2, �1, 0, 1, 2, 3, …}

Rational Numbers {all numbers that can be expressed in the form , where a and b are integers and b � 0}

Irrational Numbers {all numbers that cannot be expressed in the form , where a and b are integers and b � 0}

Name the set or sets of numbers to which each real number belongs.

a. Because 4 and 11 are integers, this number is a rational number.

b. �81� Because �81� � 9, this number is a natural number, a whole number, an integer,and a rational number.

c. �32� Because �32� � 5.656854249…, which is not a repeating or terminating decimal,this number is irrational.


1. 2. � 3. 4. �54�natural, whole, rational rational irrationalinteger, rational

5. 3.145 6. �25� 7. 0.62626262… 8. �22.51�rational natural, whole, rational irrational

integer, rational

Write each set of numbers in order from least to greatest.

9. � , �5, �25�, 10. �0.09�, �0.3131…, 11. �1.2�5�, 0.05, � , �5�

�5, � , , �25� �0.3131…, �0.09�, �1.2�5�, � , 0.05, �5�

12. , �2, �124�, �3.11 13. ��1.44�, �0.35 14. 0.3�5�, 2 , � , �5�

�3.11, �2, , �124� ��1.44�, �0.35, � , 0.3�5�, �5�, 2 1�3

9�5

1�5

5�4

9�5

1�3

1�5

5�4

1�4

3�5

7�4

3�4

1�4

3�5

7�4

3�4

2�3

6�7

84�12

4�11

a�b

a�b


Square Roots and Real Numbers

NAME ______________________________________________ DATE______________ PERIOD _____

2-72-7

ExampleExample

ExercisesExercises

Skills PracticeSquare Roots and Real Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-72-7


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Find each square root. If necessary, round to the nearest hundredth.

1. �144� 2. ��36�

3. ��0.25� 4. �5. ��17� 6. �2.25�


7. � 8. �

9. �29� 10. �196�

11. 12. �1.8�

Graph each solution set.

13. x � �1 14. x 1

15. x � 1.5 16. x � �2.5

Replace each ● with �, , or � to make each sentence true.

17. ● 0.4� 18. 0.0�9� ●

19. 6.2�3� ● �39� 20. ●


21. �5�, 2.3�6�, 22. , 0.2�1�, �0.05�

23. ��12�, �3.4�8�, ��11� 24. 0.4�3�, , 3�7

�6��5

2�9

7�3

1��8�

1�8

1�90

4�9

�2 �1�4 �3 0 1 2 3 4�2 �1�4 �3 0 1 2 3 4

�2 �1�4 �3 0 1 2 3 4�2 �1 0 1 2 3 4 5 6

9�13

5�6

28�7

49�100


Find each square root. If necessary, round to the nearest hundredth.

1. �324� 2. ��62� 3. ��25� 4. ��84�

5. � 6. � 7. ��0.081� 8. ��3.06�


9. �93� 10. ��0.062�5� 11. 12. �

Graph each solution set.

13. x � �0.5 14. x � �3.5

Replace each ● with �, , or � to make each sentence true.

15. 0.9�3� ● �0.93� 16. 8.1�7� ● �66� 17. ●


18. �0.03�, , 0.1�7� 19. � , ��8�, � 20. ��8.5�, � , �2

21. SIGHTSEEING The distance you can see to the horizon is given by the formula d � �1.5h�, where d is the distance in miles and h is the height in feet above the horizon line. Mt. Whitney is the highest point in the contiguous 48 states. Its elevation is 14,494 feet. The lowest elevation, at �282 feet, is located near Badwater, California.With a clear enough sky and no obstructions, could you see from the top of Mt. Whitneyto Badwater if the distance between them is 135 miles? Explain.

22. SEISMIC WAVES A tsunami is a seismic wave caused by an earthquake on the oceanfloor. You can use the formula s � 3.1�d�, where s is the speed in meters per second and d is the depth of the ocean in meters, to determine the speed of a tsunami. If anearthquake occurs at a depth of 200 meters, what is the speed of the tsunami generatedby the earthquake?

19�20

�35��2

�7��8

84�30

�2��8

�5��6

5�6

�2 �1�4 �3 0 1 2 3 4�2 �1�4 �3 0 1 2 3 4

144�3

8�7

7�12

4�289

Practice Square Roots and Real Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-72-7

Reading to Learn MathematicsSquare Roots and Real Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-72-7


Less

on

2-7

Pre-Activity How can using square roots determine the surface area of thehuman body?


The expression �3600� is read, “the square root of 3600.” How would youread the expression �64�?

Reading the Lesson

Complete each statement below.

1. The symbol �� is called a and is used to indicate anonnegative or principal square root of the expression under the symbol.

2. A of an irrational number is a rational number that is closeto, but not equal to, the value of the irrational number.

3. The positive square root of a number is called the squareroot of the number.

4. A number whose positive square root is a rational number is a .

5. Write each of the following as a mathematical expression that uses the �� symbol.

a. the positive square root of 1600

b. the negative square root of 729

c. the principal square root of 3025

6. The irrational numbers and rational numbers together form the set of numbers.


7. Use a dictionary to look up several words that begin with “ir-”. What does the prefix “ir-”mean? How can this help you remember the meaning of the word irrational?


Scale DrawingsThe map at the left below shows building lots for sale. The scale ratiois 1:2400. At the right below is the floor plan for a two-bedroomapartment. The length of the living room is 6 m. On the plan theliving room is 6 cm long.

Answer each question.

1. On the map, how many feet are represented by an inch?

2. On the map, measure the frontage of Lot 2 on Sylvan Road in inches. What is the actualfrontage in feet?

3. What is the scale ratio represented on the floor plan?

4. On the floor plan, measure the width of the living room in centimeters. What is theactual width in meters?

5. About how many square meters of carpeting would be needed to carpet the living room?

6. Make a scale drawing of your classroom using an appropriate scale.

7. Use your scale drawing to determine how many square meters of tile would be needed toinstall a new floor in your classroom.

Closet

Closet

Closet

Closet

Kitchen

BedroomBedroom Bath

Dining Area

Living Room

Lot 3

Lot 2

Lot 1

Suns

hine

Lak

e

Sylv

an R

oad

Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-72-7

Chapter 2 Test, Form 1

NAME DATE PERIOD

SCORE


Write the letter for the correct answer in the blank at the right of each question.

1. What set of numbers is graphed below?

A. {2, 4} B. {–4, –2, 2, 4}C. {�4, �3, �2, �1, 0, 1, 2, 3, 4} D. {0} 1.

2. Find � �10 �.A. �10 B. 0 C. 10 D. 10 or �10 2.

3. Evaluate � x � � 2 if x � �3.A. 1 B. �5 C. �1 D. 5 3.

For Questions 4–6, find each sum, difference, or product.

4. �4 � (�5)A. 9 B. �9 C. 1 D. �1 4.

5. �2 � (�7)A. 9 B. �5 C. �9 D. 5 5.

6. (6)(�12)A. �6 B. �72 C. �18 D. �62 6.

7. Simplify the expression �3(2n) � 4n.A. �18n B. 10n C. �2n D. �n 7.

8. Evaluate 6x � 3y if x � �23� and y � ��

13�.

A. 5 B. 1 C. 3 D. 4 8.

9. Find �9 � �34�.

A. �247� B. ��

247� C. ��

34� D. �12 9.


10. ��6

��4

14�

A. �2 B. �5 C. 2 D. 5 10.

11. �12x

4� 8�

A. 12x � 2 B. �12x � 2 C. 3x � 2 D. �3x � 2 11.

�1�2�3�4 0 1 2 43

22

Ass

essm

ent


Chapter 2 Test, Form 1 (continued)

For Questions 12–14, use the list that shows the number of gold medals won by 11 countries in the 2000 Summer Olympic Games. Source: World Almanac

40, 32, 28, 16, 14, 13, 13, 11, 11, 11, 812. To create a line plot of this data, how many �’s would be placed above the

number line between 10 and 15?A. 3 B. 6 C. 7 D. 4 12.

13. Which value occurs most frequently?A. 40 B. 13 C. 11 D. 8 13.

14. Which measure of central tendency best describes the data?A. 40 B. mean C. mode D. median 14.

15. A 6-sided die is rolled one time. Find P(5).

A. �56� B. �

12� C. �

16� D. �

15� 15.

16. A bowl contains 2 red chips, 3 blue chips, and 1 green chip. One chip is randomly drawn. Find P(green).

A. �16� B. �

13� C. �

15� D. �

12� 16.

17. The probability that an event will occur is �35�. What are the odds that the

event will occur?A. 5 : 3 B. 3 : 5 C. 2 : 3 D. 3 : 2 17.

18. Find ��36�.A. 6 B. �18 C. �6 D. 18 18.

19. Name the set or sets of numbers to which the real number �23� belongs.

A. rational numbersB. irrational numbersC. natural numbers, rational numbersD. natural numbers, irrational numbers 19.

20. Write 0, ��12�, �

12�, �

13�, �1 in order from least to greatest.

A. 0, ��12�, �

13�, �

12�, �1 B. �1, ��

12�, 0, �

13�, �

12�

C. �12�, �

13�, 0, ��

12�, �1 D. ��

12�, �1, 0, �

12�, �

13� 20.

Bonus Find �25� � � �4 �. B:

NAME DATE PERIOD

22

Chapter 2 Test, Form 2A

NAME DATE PERIOD

SCORE




A. {0, 1, 2, 3, 4} B. {…, 0, 1, 2, 3, 4}C. {�4, �3, �2, �1, 0, 1, 2, 3, 4} D. {0, 1, 2, 3, 4, …} 1.

2. Evaluate 8 � � 16 � y � if y � 11.A. �19 B. 35 C. 3 D. 13 2.

3. Find ��45� � �

37�.

A. ��1335�

B. ��12� C. 1�3

85�

D. ��112�

3.

For Questions 4 and 5, find each difference.

4. �9 � (�21)A. �30 B. 12 C. �12 D. 30 4.

5. �7.9 � 4.3A. �12.2 B. �3.6 C. 12.2 D. 3.6 5.

6. Find ��56��2

35��.

A. ��321�

B. ��129�

C. ��381�

D. ��110�

6.

7. Simplify 4m(�2n) � 6mn.A. 0 B. 8mn C. �2mn D. 12mn 7.

8. Evaluate m2 � 2nm if m � 4.2 and n � 1.5.A. 0.7 B. 5.04 C. �10.35 D. 30.24 8.

9. Find �158� � ��

23��.

A. �2�25� B. ��

35� C. ��

1165�

D. �5�25� 9.


10. �2(��

24

�� 1

53)

�

A. 6 B. ��178� C. �

131� D. �

53� 10.

11. ��3x

��6

12�

A. �12�x � 2 B. ��

12�x � 2 C. 3x � 2 D. �3x � 2 11.

�1�2�3�4 0 1 2 43

22

Ass

essm

ent


Chapter 2 Test, Form 2A (continued)

For Questions 12–14, use the list that shows the total number of medals won by 15 countries in the 2000 Summer Olympic Games. Source: World Almanac

57, 17, 18, 97, 28, 59, 88, 26, 38, 58, 34, 25, 23, 28, 2912. To create a stem-and-leaf plot of this data, what values would be used for

the stems?A. 10, 20, 30, 40, 50, 60, 70, 80, 90 B. 17, 23, 34, 57, 88, 97C. 1, 2, 3, 4, 5, 6, 7, 8, 9 D. 3, 4, 5, 6, 7, 8, 9 12.

13. How many countries won more than 42 medals?A. 6 B. 4 C. 5 D. 7 13.

14. Which measure of central tendency best describes the data?A. median B. mean C. mode D. 42 14.

15. A computer randomly selects an integer between 5 and 9. Find P(2).

A. 1 B. �13� C. �

15� D. 0 15.

For Questions 16 and 17, a bowl contains 8 red chips, 7 blue chips, and 10 green chips. One chip is randomly drawn.

16. Find P(red or blue).

A. �185�

B. �35� C. �

32� D. �1

15�

16.

17. Find the odds of drawing a green chip.A. 2 : 3 B. 2 : 5 C. 1 : 10 D. 1 : 15 17.

18. Find ��0.81�.A. 0.9 B. �0.9 C. 0.09 D. �0.09 18.

19. Name the set or sets of numbers to which the real number ��25� belongs.A. natural numbers, irrational numbersB. whole numbers, integers, rational numbersC. integers, rational numbersD. irrational numbers 19.

20. Write �3�, �13�, 0.3, �1

31�, 1 in order from least to greatest.

A. �131�

, 0.3, �13�, 1, �3� B. �3�, 1, 0.3, �1

31�, �

13�

C. �13�, 0.3, �1

31�, 1, �3� D. 0.3, �

13�, �1

31�, �3�, 1 20.

Bonus Evaluate 3a � 8b � �49� if a � 4.1 and b � �34�. B:

NAME DATE PERIOD

22

Chapter 2 Test, Form 2B

NAME DATE PERIOD

SCORE




A. {�5, �4, �3, �2, �1, 0, 1, 2, 3} B. {�5, �4, �3, �2, �1, 0}C. {… , �5, �4, �3, �2, �1, 0} D. {�5, �4, �3, �2, �1, 0, …} 1.

2. Evaluate 25 � � 9 � a � if a � 12.A. 4 B. 28 C. 22 D. 46 2.

3. Find 32.5 � (�11.2).A. 41.3 B. 43.7 C. 20.7 D. 21.3 3.

For Questions 4 and 5, find each difference.

4. �12 � (�11)A. �23 B. 1 C. �1 D. 23 4.

5. �45� � �

23�

A. �28� B. �1

25�

C. 1 D. ��185�

5.

6. Find ��13��

67��.

A. �170�

B. ��170�

C. ��27� D. �

27� 6.

7. Simplify �5x(3y) � 7xy.A. �8xy B. 5xy C. �xy D. �22xy 7.

8. Evaluate 3ab � b2 if a � 3.7 and b � 2.1.A. 4.6 B. 18.9 C. 9.62 D. 19.11 8.

9. Find ��34� � �

65�.

A. ��190�

B. �230�

C. ��110�

D. ��58� 9.


10. ��3(

25

��

63)

�

A. �54� B. �6 C. �3 D. 2 10.

11. �24

�k

4� 8�

A. �6k � 8 B. �6k � 2 C. �24k � 2 D. 24k � 2 11.

�1�2�3�4�5 0 1 2 3

22

Ass

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ent


Chapter 2 Test, Form 2B (continued)

For Questions 12–14, use the list which shows the number of 300 games bowled by15 women as sanctioned by the Women’s International Bowling Congress.Source: World Almanac

20, 16, 23, 18, 21, 17, 27, 14, 23, 17, 21, 17, 24, 16, 19

12. To create a stem-and-leaf plot of this data, what values would be used for leaves for the stem value 2?A. 0, 1, 1, 3, 3, 4, 7 B. 20, 21, 22, 23, 24, 25, 26, 27C. 0, 1, 2, 3, 4, 5, 6, 7 D. 20, 21, 21, 23, 23, 24, 27 12.

13. How many of these women bowled more than twenty 300 games?A. 8 B. 7 C. 4 D. 6 13.

14. Which measure of central tendency best describes the data?A. mean B. mode C. median D. mean or

median 14.

15. A computer randomly selects an integer between 1 and 7. Find the probabilityof selecting a number less than 9.

A. 1 B. �17� C. �

19� D. 0 15.

For Questions 16 and 17, a bowl contains 14 red chips, 9 blue chips, and 12 green chips. One chip is randomly drawn.

16. Find P(blue or green).

A. �211�

B. �47� C. �

32� D. �

35� 16.

17. Find the odds of drawing a red chip.A. 2 : 5 B. 2 : 3 C. 1 : 14 D. 1 : 21 17.

18. Find ��28516�.

A. �196�

B. ��196�

C. �34� D. ��

34� 18.

19. Name the set or sets of numbers to which the real number �27� belongs.A. natural numbers, irrational numbersB. rational numbersC. irrational numbersD. natural numbers, rational numbers 19.

20. Write ��5�, �0.5, ��15�, ��1

51�

, �1 in order from least to greatest.

A. �0.5, ��15�, ��1

51�

, �1, ��5� B. ��5�, �1, �0.5, ��151�

, ��15�

C. ��15�, ��1

51�

, �0.5, �1, ��5� D. �1, �0.5, ��15�, ��1

51�

, ��5� 20.

Bonus Evaluate � x � � �xzy� if x � �4, y � 3, and z � 6. B:

NAME DATE PERIOD

22

Chapter 2 Test, Form 2C


1. Name the coordinates of the points graphed on the 1.number line.

2.

Graph each set of numbers.3.

2. ��52�, ��

12�, �

32�, 2� 3. {1, 3, 5, …}

Evaluate each expression if x � �5 and y � 4. 4.

4. � x � � 10 5. 10 � � 3 � y � 5.

Find each sum. 6.

6. �13 � 24 7. �10.5 � (�2.4) 7.

8. �34� � ��1

72�� 8.

Find each difference. 9.

9. 4.32 � (�3.79) 10. ��59� � �

23� 10.

For Questions 11 and 12, find each product. 11.

11. 16(�4) 12. ��47��

25�� 12.

13. Simplify 5(�7a) � 12a. 13.

Evaluate each expression if m � �3.2 and n � 7.1. 14.

14. �3mn 15. m(n � 5) 15.

Find each quotient. 16.

16. �44 � 5 17. ��67� � ��

29�� 17.

For Questions 18 and 19, simplify each expression. 18.

18. �6�(53

��

1112)

� 19. �30w

��6

18� 19.

20. Evaluate �4sts�

if s � 1.3 and t � �5.2. 20.

�2�1�3�4 0 1 2 4 53

NAME DATE PERIOD

SCORE 22

Ass

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ent

0 1 32�3 �2 �1

�1�2 0 1 2 4 5 63


Chapter 2 Test, Form 2C (continued)

Use the list that shows the number of touchdowns scored by NFC teams during the first 7 weeks of the 2001 football season. Source: www.nfl.com

2, 3, 1, 5, 2, 0, 4, 3, 4, 3, 3, 4, 6, 3, 2

21. Make a line plot of the data. 21.

22. What is the median of the data? 22.

23. Which values occur least frequently? 23.

24. How many of the teams have made more than 24.3 touchdowns?

25. Does the mean, median, or mode best represent the data? 25.Explain.

For Questions 26–28, a bowl contains 12 red chips,9 blue chips, and 15 green chips. One chip is randomly drawn.

26. Find P(red or green). 26.

27. Find P(blue). 27.

28. Find the odds of drawing a red chip 28.

29. The probability that an event will not occur is �152�

. 29.

What are the odds that the event will occur?

30. Find ��1.21�. 30.

31. Name the set or sets of numbers to which the real number 31.

�231� belongs.

32. Graph the solution set x 2.5. 32.

33. Write ��29�, 0.25, ��

19�, �1

21�

, 0 in order from least to greatest. 33.

Bonus Most historical records do not include a year zero. B:Thus, the year before A.D. 1 is labeled 1 B.C., not 0 B.C.If Rome celebrated its 1000th anniversary in A.D. 248,when was Rome founded?

�1�2�3 0 1 2 3

1 2 3 4 5 60

NAME DATE PERIOD

22

Chapter 2 Test, Form 2D


1. Name the coordinates of the points graphed on the 1.number line.

Graph each set of numbers. 2.

2. ��23�, 0, �

13�, �

43�� 3. {… , �4, �2, 0} 3.

Evaluate each expression if a � �4 and b � 7. 4.

4. 13 � � a � 5. 14 � � b � 2 � 5.

Find each sum. 6.

6. 27 � (�14) 7. �15.3 � (�3.6) 7.

8. ��49� � �

23� 8.

Find each difference. 9.

9. �7.63 � 5.18 10. �38� � ��

34�� 10.

For Questions 11 and 12, find each product. 11.

11. (�15)(7) 12. ��56��

27�� 12.

13. Simplify �4b � 3(6b). 13.

Evaluate each expression if x � 4.3 and y � �2.7. 14.

14. xy � 6 15. x(y � 3) 15.

Find each quotient. 16.

16. 76 � (�8) 17. ��45� � �

83� 17.

For Questions 18 and 19, simplify each expression. 18.

18. ��8(4�

�13

16� 7)

� 19. ��12�w

2� 10� 19.

20. Evaluate �2nm� if m � �3.6 and n � 4.8. 20.

�1�2�3�4 0 1 2 43

0 1 2�1

�1�2�3�5�4 0 1 2 63 4 5

NAME DATE PERIOD

SCORE 22

Ass

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ent


Chapter 2 Test, Form 2D (continued)

Use the list that shows the number of touchdowns scored by AFC teams during the first 7 weeks of the 2001 football season. Source: www.nfl.com

4, 1, 4, 4, 4, 3, 2, 1, 4, 3, 4, 5, 5, 5, 3, 2

21. Make a line plot of the data. 21.

22. What is the median of the data? 22.

23. Which values occur least frequently? 23.

24. How many of the teams made fewer than 3 touchdowns? 24.

25. Does the mean best describe the set of data? Explain. 25.

For Questions 26–28, a bowl contains 8 red chips,16 blue chips, and 10 green chips. One chip is randomly drawn.

26. Find P(red or blue). 26.

27. Find P(green). 27.

28. Find the odds of drawing a blue chip. 28.

29. The probability that an event will not occur is �59�. 29.

What are the odds that the event will not occur?

30. Find ��13669�. 30.

31. Name the set or sets of numbers to which the real number 31.��49� belongs.

32. Graph the solution set x �1. 32.

33. Write ��49�, �

47�, ��

38�, 0.4, 0 in order from least to greatest.

33.

Bonus In a local raffle the odds of winning any prize is 1 : 3, B:and the odds of winning the grand prize is 1 : 999.What is the ratio of grand prizes to the total number of prizes.

�1�2�3�4 0 1 2 43

1 2 3 4 5 60

NAME DATE PERIOD

22

Ass

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ent

Chapter 2 Test, Form 3


1. Name the coordinates of the points graphed on the number line. 1.

For Questions 2 and 3, graph each set of numbers.

2. {… , �5, �3, �1, 1, 3, 5, …} 2.

3. {integers less than �2 or greater than 3} 3.

4. Evaluate � 2 � b � � a if a � �23� and b � ��

19�. 4.

5. Find the sum of �3�16� and 1�

23�. 5.

6. The highest point of elevation in the state of California is 6.14,494 feet at Mount Whitney. The lowest point is �282 feet at Death Valley. What is the difference in elevation of these two points?

7. Find �45 � (�91) � 23. 7.

8. Find ��37��

65��. 8.

9. A bank in Los Angeles, California is a 40-story building. 9.The average height of each story is 12.9 feet. How tall is the bank?

Evaluate each expression if w � 12, x � �7,

y � �34�, and z � ��

56�.

10. 4x2 � 3w 10.

11. xyz � 5yz 11.

For Questions 12 and 13, simplify each expression.

12. �5�(�

6(173

��

1112))� 12.

13. �24x �6

42y� 13.

14. Evaluate �(a �c

b)� if a = �6.3, b = 20.7, and c = 4.5. 14.

0 1 2�1

NAME DATE PERIOD

SCORE 22


Chapter 2 Test, Form 3 (continued)

Use the list that shows the number of silver medals won by 15 countries participating in the 1998 Winter Olympic Games. Source: World Almanac

9, 10, 6, 5, 5, 3, 4, 4, 1, 6, 1, 6, 2, 1, 115. Make a line plot of the data. 15.

16. Which measure of central tendency best describes the data? 16.Explain.

Use the list that shows the height in meters of the winning high jump for women in the Summer Olympic Games from 1936 to 2000. Source: World Almanac 17.

1.60, 1.68, 1.67, 1.76, 1.85, 1.90, 1.82, 1.92,1.93, 1.97, 2.02, 2.03, 2.02, 2.05, 2.01

17. Make a stem-and-leaf plot of the data.


For Questions 19–21, a state lottery game uses ping pong balls numbered 0–39. Balls with the numbers 20, 8, 7,and 1 have already been selected in the weekly drawing.

19. Find the probability of drawing a ball with a number less 19.than 10 as the fifth ball.

20. Find the odds of drawing a ball with a number between 20.10 and 30 as the fifth ball.

21. Find the probability of drawing a ball with the number 21.42 as the fifth ball.

22. The probability that an event will occur is 30%. What are 22.the odds that the event will not occur?

23. Find ��61265��. 23.

24. Name the set or sets of numbers to which the real number 24.

��346�� belongs.

25. Write ��29�, ��1

21�

, �0.2, ��116��, �1 in order from least to greatest. 25.

Bonus Simplify �2�.25((46..94

��

84))�. B:

NAME DATE PERIOD

22

Chapter 2 Open-Ended Assessment


Demonstrate your knowledge by giving a clear, concise solutionto each problem. Be sure to include all relevant drawings andjustify your answers. You may show your solution in more thanone way or investigate beyond the requirements of the problem.

1. a. Explain what a point on a number line represents, and howthe coordinate of the point is different from the point.

b. Describe how to graph the set {3, 4, 5, …} on a number line.

2. a. Use a number line to determine if �4 � 3 is greater than 4 � (�3). Explain your reasoning.

b. Explain how subtracting a number can be done with addition,and give an example.

3. Let x and y be any real numbers. List the conditions under which

the quotient �xy� is positive. Give examples to support your answer.

4. a. Construct a set of eleven numbers with a median of 10 and amean that is less than 10. What is the mean and mode of yourdata?

b. Make a stem-and-leaf plot of the data created for part a.

5. a. Explain why the probability that an event will occur willnever equal 2.

b. The odds that an event will occur are 1 : 1. Explain why the

probability that the event will occur is �12� and not 1.

6. a. Explain why ��49� � ��49�.b. Give a list of six real numbers ordered from least to greatest

such that the first number is a rational number, the secondnumber is an integer, the third number is an irrationalnumber, the fourth number is negative, the fifth number is anatural number, and the sixth number is a whole number.

NAME DATE PERIOD

SCORE 22

Ass

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Chapter 2 Vocabulary Test/Review

Write the letter of the term that best matches each phrase.

1. a number that can be written in the

form �ab�, where a and b are integers

and b � 0

2. a number and its opposite

3. the number of times a data item occurs in a set

4. often used to describe sets of data because they represent a centralized or “middle”value

5. all possible outcomes of an event

6. outcomes for which the probabilities are equal

7. the ratio that compares the number of ways an event can occur to the number of ways it cannot occur

8. one of two equal factors of a number

9. a number that cannot be written in the form �ab�

where a and b are integers and b � 0

10. the set of irrational numbers and rational numbers

In your own words—Define each term.

11. absolute value

12. opposites

absolute valueadditive inversesback-to-back stem-and-leaf plot

Completeness Propertycoordinateequally likelyfrequency

graphinfinityintegersirrational numberline plotmeasures of central tendency

natural number

negative numberoddsoppositesperfect squarepositive numberprincipal square rootprobabilityradical sign

rational approximationrational numberreal numbersample spacesimple eventsquare rootstem-and-leaf plotwhole number

NAME DATE PERIOD

SCORE 22

a. frequency

b. measures of centraltendency

c. equally likely

d. odds

e. rational number

f. square root

g. irrational number

h. additive inverses

i. real numbers

j. sample space

Chapter 2 Quiz (Lessons 2–1 and 2–2)

22


1. Name the coordinates of the points graphed on the number 1.line.

2. Graph {�5, 2, 4}.

For Questions 3 and 4, find each absolute value.

3. � �72 � 4. � 4.9 �

5. Evaluate �� 17 � y � if y � 13.

Find each sum.

6. 5 � (�2) 7. �51 � 47

8. �12� � �

13�


9. �54 � 23 10. 3.1 � 1.7

�1�2�3�4 0 1 2 43

NAME DATE PERIOD

SCORE


For Questions 1 and 2, find each product.

1. 7(�31) 2. ��23��

67��

3. Simplify 4(7a) � 3a.

4. Evaluate xy � 3 if x � �1.2 and y � �2.3.

Find each quotient.

5. �42 � 6 6. �95� � �

32�


7. ��5(217

��4

13)� 8. ��9x

��3

15y�

Evaluate each expression if n � �2, m � 3.5, and p � �34�.

9. �n4p�

10. �8 �

nm

�

NAME DATE PERIOD

SCORE 22

Ass

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ent

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

�2�1�3�4�5 0 1 2 43

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.


For Questions 1–3, the heights (in inches) of the students in Mrs. Graham’s class are 60, 75, 58, 73, 59, 74, 59, 61, 59, 63, 62,and 61.

1. Draw a line plot for the data. 1.

2. Which height occurs most frequently? 2.


4. One shirt is randomly selected from a drawer containing 4.5 red shirts, 6 blue shirts, and 3 yellow shirts. Find P(red).

5. A weather forecast states that the probability of snow the 5.next day is 75%. What are the odds that it will snow?

55 60 65 70 75

Chapter 2 Quiz (Lesson 2–7)

Find each square root.

1. ��49� 2. �0.36� 3. ��12251

��For Questions 4 and 5, name the set or sets of numbers to which each real number belongs.

4. �248� 5. ��13�

6. Graph the solution set x 1.3.

For Questions 7 and 8, replace � with �, �, or � to make each sentence true.

7. 0.6 � �23� 8. �11� � 3.3�1�

9. Write ��13�, �

�110��, 0.3, ��

49� in order from least to greatest.

10. Standardized Test Practice Which of the following is a true statement?

A. ��13��

��12��

B. �5� �7� C. ��12��

� �2� D. �9� � �8�

NAME DATE PERIOD

SCORE


22

NAME DATE PERIOD

SCORE

22

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

�1�2�3�4 0 1 2 43

Ass

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ent

Chapter 2 Mid-Chapter Test (Lessons 2–1 through 2–4)



1. What set of numbers is graphed at the right?

A. {�2, �1, 0, 1, 2, 3, 4} B. {… , �2, �1, 0, 1, 2, 3, 4}C. {�2, �1, 0, 1, 2, 3, 4, …} D. {0, 1, 2, 3, 4} 1.

2. Evaluate 15 � � a � if a � �6.A. 21 B. �21 C. �9 D. 9 2.

3. Find �1.07 � 0.12.A. �1.19 B. �0.95 C. 1.19 D. 0.95 3.

4. Find ��14� � �

38�.

A. ��58� B. ��

18� C. �

18� D. �

58� 4.

5. Simplify the expression �2(�7m) � 3m.A. �11m B. �6m C. 12m D. 17m 5.

6. Evaluate x2 � 3y if x � ��12� and y � ��

56�.

A. �3�12� B. 1�

16� C. �2�

14� D. 2�1

52�

6.

7. Simplify �6r��

618

�.

A. �r � 18 B. �r � 3 C. �18r D. 6r � 3 7.

8. Graph {integers less than or equal to �2}. 8.

9. Find �61 � 18. 9.

10. Find �15� � �

12�. 10.

11. Find �6(�12). 11.

12. Find �92� � ��

43��. 12.

For Questions 13 and 14, evaluate each expression if u � �7, and v � 3.9

13. �2u8� � (�2) 13.

14. uv 14.

15. Evaluate � z � � 0.13 if z � �0.45. 15.

�1�2�3�5�6�7 �4 0 1 2 3 4

Part I

NAME DATE PERIOD

SCORE 22

Part II


Chapter 2 Cumulative Review (Chapters 1–2)

1. Write an algebraic expression for the verbal expression 1.seven more than the square of a number. (Lesson 1–1)

2. Evaluate 3a(a � b) if a � 4 and b � 3. (Lesson 1–2) 2.

For Questions 3 and 4, simplify each expression.

3. 6a � 11a � 3 4. 2(4 � 2x) � 6(Lesson 1–5) (Lesson 1–6)

5. Identify the hypothesis and conclusion of the statement.Then write the statement in if-then form. I’ll go to the store when I finish my homework. (Lesson 1–7) 5.

6. As the weather gets warmer, the beaches become more 6.crowded. Draw a reasonable graph that shows the number of people at the beach as the temperature increases. Let the horizontal axis show the temperature and the vertical axis show the number of people. (Lesson 1–8)

7. Name the coordinates of the points graphed on the number line. (Lesson 2–1) 7.

8. Evaluate 12 � �x � 11�, if x � 13. (Lesson 2–1) 8.

9. Find 32.4 � (�14.6). (Lesson 2–2) 9.

10. Find 31 � 17. (Lesson 2–2) 10.

11. Find ��25��

37��. (Lesson 2–3) 11.

12. Simplify �12t6� 18�. (Lesson 2–4) 12.

13. Use the data to make a line plot. (Lesson 2–5) 13.46 42 45 41 42 40 44 46 42 40 47

14. A card is selected from a standard deck of cards. 14.Determine P(black ace). (Lesson 2–6)

15. Write ��5�, �5275�

, � �94�, 2.2�4� in order from least to 15.

greatest. (Lesson 2–7)

NAME DATE PERIOD

22

�1�2�3�5�4 0 1 2 63 4 5

3.

4.

Standardized Test Practice (Chapters 1–2)


1. Evaluate x2 � y2 � z, if x � 7, y � 6, and z � 4. (Lesson 1–2)

A. 17 B. 101 C. 89 D. 59 1.

2. Find the solution set for 5(7 � x) � 18 if the replacement set is {0, 1, 2, 3, 4, 5, 6}. (Lesson 1–3)

E. {4, 5, 6} F. {0, 1, 2, 3} G. {2, 3, 4} H. {5, 6} 2.

3. Using the Distributive Property to find 9�5�23�� would give which

expression? (Lesson 1–5)

A. 9(5) � �23� B. 9��

137�� C. 9(5) � 9��

23�� D. 9(5)��

23�� 3.

4. Identify the conclusion of the statement. (Lesson 1–7)

If you are at the Grand Canyon, then you are in Arizona.E. you are at the Grand Canyon F. you are in AmericaG. you are not in Arizona H. you are in Arizona 4.

5. Evaluate �26 � r� � 7 if r � 9. (Lesson 2–1)

A. 45 B. 10 C. 22 D. 24 5.

6. Simplify 6a(�4b). (Lesson 2–3)

E. 2ab F. �24ab G. �2a H. 24b 6.

7. Simplify �17 �8

15�. (Lesson 2–4)

A. �167� � �

185� B. 4 C. 3�

58� D. �

383� 7.

8. Which set of data was used to make the stem-and-leaf plot? (Lesson 2–5)

E. 14, 245, 36 F. 4, 4, 5, 6G. 14, 24, 25, 36 H. 1.4, 2.4, 2.5, 3.6 8.

9. What is the probability that a number chosen at random from the domain {�3, �2, �1, 0, 1, 2, 3} will satisfy the inequality 3 � 2x � 5? (Lesson 2–6)

A. {0, 1, 2, 3} B. �37� C. �

47� D. �

57� 9.

10. Which number is greater than �3� and less than 1.9? (Lesson 2–7)

E. 1.72 F. �1.8�2� G. �95� H. �

3290�

10. HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

NAME DATE PERIOD

22

Ass

essm

ent

Stem Leaf

123

44 56

1 4 � 14

Part I: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.


Standardized Test Practice (continued)

11. Evaluate 123. (Lesson 1–1) 11. 12.

12. Evaluate 3.7 � 7.4 � 8.6 � 2.3. (Lesson 1–6)

13. Kendrick needs to mix two types of flour for 13. 14.

his secret cookie dough. If he adds �34� cup of

one type of flour to �18� cup of the second type

of flour, how much flour in cups does he have? (Lesson 2–2)

14. Dalila ran 5.3 miles yesterday, but only ran 3.7 miles this morning. How far must she run this afternoon to run the same distance today as she ran yesterday? (Lesson 2–2)

Column A Column B

15. 15.

(Lesson 1–2)

16. 16.

(Lesson 1–4)

17. 17.

(Lesson 2–1)

DCBA� �6 � � � �3 �� 10 �

DCBA8 � �18

� � 2 � 08 � 0 � 2 � �12

�

DCBA4(3) � 2 � 24(3 � 2) � 2

Part 3: Quantitative Comparison

Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

NAME DATE PERIOD

22

NAME DATE PERIOD

A

D

C

B

Part 2: Grid In

Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.

Standardized Test PracticeStudent Record Sheet (Use with pages 116–117 of the Student Edition.)

© Glencoe/McGraw-Hill A1 Glencoe Algebra 1

Select the best answer from the choices given and fill in the corresponding oval.

1 4 7

2 5 8

3 6 9

Solve the problem and write your answer in the blank.

For Questions 11 and 12, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.

10 11 12

11 (grid in)

12 (grid in)

13

14

Select the best answer from the choices given and fill in the corresponding oval.

15

16

17

18

Record your answers for Questions 19–20 on the back of this paper.

DCBA

DCBA

DCBA

DCBA

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

DCBADCBADCBA

DCBADCBADCBA

DCBADCBADCBA

NAME DATE PERIOD

22

An

swer

s

Part 2 Short Response/Grid InPart 2 Short Response/Grid In

Part 3 Quantitative ComparisonPart 3 Quantitative Comparison

Part 4 Open-EndedPart 4 Open-Ended

Part 1 Multiple ChoicePart 1 Multiple Choice

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1

Ab

solu

te V

alu

eO

n a

nu

mbe

r li

ne,

�3

is t

hre

e u

nit

s fr

om z

ero

in t

he

neg

ativ

e di

rect

ion

,an

d 3

is t

hre

e u

nit

s fr

om z

ero

in t

he

posi

tive

dir

ecti

on.T

he

nu

mbe

r li

ne

at

the

righ

t il

lust

rate

s th

e m

ean

ing

of a

bso

lute

val

ue.

Th

eab

solu

te v

alu

e of

a n

um

ber

nis

th

e di

stan

ce f

rom

zer

o on

a

nu

mbe

r li

ne

and

is r

epre

sen

ted

n.

For

th

is e

xam

ple,

�3

�3

and

3

�3.

10

�1

�2

�3

�4

�5

23

3 un

its3

units

� d

irect

ion

� d

irect

ion

45

Stu

dy G

uid

e a

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nte

rven

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(c

onti

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)

Rat

ion

al N

um

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s o

n t

he

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ine

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ME

____

____

____

____

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____

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____

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2-1

2-1

Fin

d e

ach

ab

solu

te v

alu

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a.�

6�

6 is

six

un

its

from

zer

o in

th

e n

egat

ive

dire

ctio

n.

�6

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b.

is t

hre

e h

alve

s u

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s fr

om z

ero

in t

he

posi

tive

dir

ecti

on.

�

3 � 23 � 2

3 � 2

3 � 2

Eva

luat

e 4

�x

�2

if

x�

5.

4 �

x�

2�

4 �

5 �

2R

epla

ce x

with

5.

�4

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5

�2

�3

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3

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Sim

plify

.

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ple1

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ple2

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cises

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ach

ab

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1.2

2

2.�

55

3.�

24

24

4.�

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1.3

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6.

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luat

e ea

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n i

f a

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b�

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d y

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19.5

8.x

�8

�12

289.

x �

2

�8.

214

.2

10.2

�x

�5

511

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5 �

y�

1217

12.

23 �

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96

13.

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6.5

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0 �

a�

27

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6 �

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3 �

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a8

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�1

13 � 4

1 � 21 � 4

1 � 21 � 4

3 � 41 � 2

1 � 4

35 � 4135 � 41

2 � 32 � 3


Stu

dy G

uid

e a

nd I

nte

rven

tion

Rat

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al N

um

ber

s o

n t

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Nu

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ME

____

____

____

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2-1

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Lesson 2-1

Gra

ph

Rat

ion

al N

um

ber

sT

he

figu

re a

t th

e ri

ght

is

part

of

a n

um

ber

lin

e.A

nu

mbe

r li

ne

can

be

use

d to

sh

ow

the

sets

of

nat

ura

l n

um

ber

s,w

hol

e n

um

ber

s,an

d in

tege

rs.P

osit

ive

nu

mb

ers,

are

loca

ted

to t

he

righ

t of

0,

and

neg

ativ

e n

um

ber

sar

e lo

cate

d to

th

e le

ft o

f 0.

An

oth

er s

et o

f n

um

bers

th

at y

ou c

an d

ispl

ay o

n a

nu

mbe

r li

ne

is t

he

set

of r

atio

nal

nu

mb

ers.

A r

atio

nal

nu

mbe

r ca

n

be w

ritt

en a

s ,w

her

e a

and

bar

e in

tege

rs a

nd

b�

0.S

ome

exam

ples

of

rati

onal

nu

mbe

rs a

re

,,

,an

d .

12 � �3

�7

� �8

�3

�5

1 � 4

a � b

10

�1

�2

�3

�4

23

Natu

ral N

umbe

rs

Posi

tive

Num

bers

Nega

tive

Num

bers

4

Who

le N

umbe

rs

Inte

gers

Nam

e th

e co

ord

inat

es o

f th

ep

oin

ts g

rap

hed

on

eac

h n

um

ber

lin

e.

a.

Th

e do

ts i

ndi

cate

eac

h p

oin

t on

th

e gr

aph

.T

he

coor

din

ates

are

{�

3,�

1,1,

3,5}

b.

Th

e bo

ld a

rrow

to

the

righ

t m

ean

s th

e gr

aph

con

tin

ues

in

defi

nit

ely

in t

hat

dir

ecti

on.T

he

coor

din

ates

are

{2,

2.5,

3,3.

5,4,

4.5,

5,…

}.

32.

52

1.5

13.

54

4.5

5

10

�1

�2

�3

23

45

Gra

ph

eac

h s

et o

fn

um

ber

s.

a.{…

,�3,

�2,

�1,

0,1,

2}

b.��

,0,

,�

12 – 3

1 – 30

�1 – 3

�2 – 3

4 – 35 – 3

2

2 � 31 � 3

1 � 3

10

�1

�2

�3

�4

23

4

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

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e th

e co

ord

inat

es o

f th

e p

oin

ts g

rap

hed

on

eac

h n

um

ber

lin

e.

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{�2,

0,2,

4,6}

{1,3

,5,7

,…}

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,,

,,1

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3,�

,,2

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1,2}

7.{i

nte

gers

les

s th

an 0

}

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9.��

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1,�

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…,�

4,�

2,0,

2,…

}

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�4

�5

�6

�2

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01

2�

21 – 2�

3�

2�11 – 2

�1

�1 – 2

01 – 2

1�

3�

4�

2�

10

12

34

1 � 21 � 2

1 � 21 � 2

�3

�4

�2

�1

01

23

4�

3�

4�

5�

2�

10

12

3�

3�

4�

2�

10

12

34

1 � 31 � 2

3 � 41 � 2

1 � 41 � 4

�3

�4

�2

�1

01

23

4�

1 – 4�

1 – 20

1 – 41 – 2

3 – 41

5 – 43 – 2

0�

11

23

45

67

0�

1�

21

23

45

6

Answers (Lesson 2-1)


An

swer

s

Skil

ls P

ract

ice

Rat

ion

al N

um

ber

s o

n t

he

Nu

mb

er L

ine

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

2-1

2-1

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Lesson 2-1

Nam

e th

e co

ord

inat

es o

f th

e p

oin

ts g

rap

hed

on

eac

h n

um

ber

lin

e.

1.2.

{�5,

�1,

0,2,

4}{�

6,�

5,�

4,�

1,0,

2}

3.4.

{…,�

3,�

2,�

1,0,

1}{1

.4,1

.5,1

.6,1

.7,1

.8,1

.9,2

.0,…

}

Gra

ph

eac

h s

et o

f n

um

ber

s.

5.{�

8,�

5,�

3,0,

2}6.

{�9,

�6,

�4,

�3,

�1}

7.{�

3,�

2,�

1,0,

…}

8.{…

,�1,

0,1,

2,3}

9.��

,0,

,1,

�10

.{…

,�3,

�2.

5,�

2,�

1.5,

�1}

Fin

d e

ach

ab

solu

te v

alu

e.

11.

�9

912

.15

15

13.

�30

30

14. �

15

.2.

42.

416

.

Eva

luat

e ea

ch e

xpre

ssio

n i

f a

�3,

b�

�10

,c�

,x�

9,y

�1.

5,an

d z

�12

.

17.2

6 �

x�

611

18.1

1 �

10

�x

12

19.

12 �

a�

514

20.

a�

20

�4

19

21.4

.5 �

y

322

.z

�7

�5

10

23.1

4 �

b

424

.b

�2

8

25. c

��

23

26.9

�3

.5 �

y11

1 � 2

1 � 2

9 � 119 � 11

5 � 75 � 7

�3

�2

�1

01

2�

1�

1 – 20

1 – 21

3 – 22

5 – 23

7 – 24

5 � 21 � 2

1 � 2

�1

01

23

45

67

89

�10

�9

�8

�7

�6

�5

�4

�3

�2

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0

�5

�6

�7

�8

�9

�10

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�3

�2

�1

0�

5�

6�

7�

8�

4�

3�

2�

10

12

1.4

1.3

1.2

1.1

1.0

1.5

1.6

1.7

1.8

1.9

2.0

32

10

�1

�2

�3

45

67

10

�1

�2

�3

�4

�5

�6

�7

23

10

�1

�2

�3

�4

�5

�6

23

4

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Nam

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e co

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inat

es o

f th

e p

oin

ts g

rap

hed

on

eac

h n

um

ber

lin

e.

1.2.

�…,�

,�,�

,�1,

��

{2.4

,2.8

,3.2

,3.6

,4,…

}

Gra

ph

eac

h s

et o

f n

um

ber

s.

3.�…

,�,�

,�1,

�,�

�4.

{in

tege

rs l

ess

than

�4

or g

reat

er t

han

2}

Fin

d e

ach

ab

solu

te v

alu

e.

5.�

11

116.

100

10

07.

�0.

35

0.35

8.�

E

valu

ate

each

exp

ress

ion

if

a�

4,b

�,c

�,x

�14

,y�

2.4,

and

z�

�3.

9.41

�16

�z

22

10.

3a�

20

�15

1711

.2x

�4

�6

2612

.2.5

�3

.8 �

y1.

1

13. �b

��

�14

.�

b�

15

.c

�1

�16

.�

c�

AST

RO

NO

MY

For

Exe

rcis

es 1

7–19

,use

th

e fo

llow

ing

info

rmat

ion

.

Th

e ab

solu

te m

agn

itu

de

of a

sta

r is

how

bri

ght

the

star

wou

ld

appe

ar f

rom

a s

tan

dard

dis

tan

ce o

f 10

par

secs

,or

32.6

lig

ht

year

s.T

he

low

er t

he

nu

mbe

r,th

e gr

eate

r th

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agn

itu

de,o

r br

igh

tnes

s,of

th

e st

ar.T

he

tabl

e gi

ves

the

mag

nit

ude

s of

sev

eral

sta

rs.

17.U

se a

nu

mbe

r li

ne

to o

rder

th

e m

agn

itu

des

from

lea

st

to g

reat

est.

18.W

hic

h o

f th

e st

ars

are

the

brig

hte

st a

nd

the

leas

t br

igh

t?b

rig

hte

st:

Rig

el;

leas

t b

rig

ht:

Alt

air

19.W

rite

th

e ab

solu

te v

alu

e of

th

e m

agn

itu

de o

f ea

ch s

tar

2.3,

7.2,

0.5,

4.7,

0.7,

0.3,

8.1,

1.4

Sour

ce:w

ww.as

tro.w

isc.ed

u

20.C

LIM

ATE

Th

e ta

ble

show

s th

e m

ean

win

d sp

eeds

in

m

iles

per

hou

r at

Day

ton

aB

each

,Flo

rida

.So

urce

:Nat

iona

l Clim

atic

Data

Cen

ter

Gra

ph t

he

win

d sp

eeds

on

a n

um

ber

lin

e.W

hic

h

mon

th h

as t

he

grea

test

mea

n w

ind

spee

d?M

arch

7.1

7.4

7.9

8.3

8.7

9.1�

2�

2

9.7

10.1

77.

58

8.5

99.

510

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____

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____

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____

____

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2-1

2-1



Readin

g t

o L

earn

Math

em

ati

csR

atio

nal

Nu

mb

ers

on

th

e N

um

ber

Lin

e

NA

ME

____

____

____

____

____

____

____

____

____

____

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2-1

2-1

©G

lenc

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cGra

w-H

ill79

Gle

ncoe

Alg

ebra

1

Lesson 2-1

Pre-

Act

ivit

yH

ow c

an y

ou u

se a

nu

mb

er l

ine

to s

how

dat

a?

Rea

d th

e in

trod

uct

ion

to

Les

son

2-1

at

the

top

of p

age

68 i

n y

our

text

book

.

In t

he

tabl

e,w

hat

doe

s th

e n

um

ber

�0.

2 te

ll y

ou?

Th

e le

vel o

f th

e B

razo

s R

iver

incr

ease

d b

y 0.

2 fo

ot

in

24 h

ou

rs.

Rea

din

g t

he

Less

on

1.R

efer

to

the

nu

mbe

r li

ne

on p

age

68 i

n y

our

text

book

.Wri

te t

rue

or f

alse

for

each

of

the

foll

owin

g st

atem

ents

.

a.A

ll w

hol

e n

um

bers

are

in

tege

rs.

tru

e

b.

All

nat

ura

l n

um

bers

are

in

tege

rs.

tru

e

c.A

ll w

hol

e n

um

bers

are

nat

ura

l n

um

bers

.fa

lse

d.

All

nat

ura

l n

um

bers

are

wh

ole

nu

mbe

rs.

tru

e

e.A

ll w

hol

e n

um

bers

are

pos

itiv

e n

um

bers

.fa

lse

2.U

se t

he

wor

ds d

enom

inat

or,f

ract

ion

,an

d n

um

erat

orto

com

plet

e th

e fo

llow

ing

sen

ten

ce.

You

kn

ow t

hat

a n

um

ber

is a

rat

ion

al n

um

ber

if i

t ca

n b

e w

ritt

en a

s a

that

has

a

and

that

are

in

tege

rs,w

her

e th

e de

nom

inat

or i

s n

ot e

qual

to

zero

.

3.E

xpla

in w

hy

,0.6 �

,an

d 15

are

rat

ion

al n

um

bers

.

Eac

h n

um

ber

is in

or

can

be

wri

tten

in t

he

form

,w

her

e a

and

bar

e

inte

ger

s an

d b

�0.

0.6�

can

be

wri

tten

as

,an

d 1

5 ca

n b

e w

ritt

en a

s .

Hel

pin

g Y

ou

Rem

emb

er

4.C

onn

ecti

ng

a m

ath

emat

ical

con

cept

to

som

eth

ing

in y

our

ever

yday

lif

e is

on

e w

ay o

fre

mem

beri

ng.

Des

crib

e a

situ

atio

n o

r se

ttin

g in

you

r li

fe t

hat

rem

inds

you

of

abso

lute

valu

e.

Sam

ple

an

swer

:Th

e d

ista

nce

fro

m e

ach

go

al li

ne

to t

he

50-y

ard

lin

e is

50

yard

s.

15 � 12 � 3

a � b

�3

�7

den

om

inat

or

nu

mer

ato

rfr

acti

on

©G

lenc

oe/M

cGra

w-H

ill80

Gle

ncoe

Alg

ebra

1

Inte

rsec

tio

n a

nd

Un

ion

The

inte

rsec

tion

of

two

sets

is t

he s

et o

f el

emen

ts t

hat

are

in b

oth

sets

.T

he in

ters

ecti

on o

f se

ts A

and

B is

wri

tten

A �

B.T

he u

nion

of

two

sets

is t

he s

et o

f el

emen

ts in

eit

her

A,B

,or

both

.The

uni

on is

wri

tten

A �

B.

In t

he

draw

ings

bel

ow,s

upp

ose

A i

s th

e se

t of

poi

nts

in

side

th

e ci

rcle

and

B i

s th

e se

t of

poi

nts

in

side

th

e sq

uar

e.T

hen

,th

e sh

aded

are

assh

ow t

he

inte

rsec

tion

in

th

e fi

rst

draw

ing

and

the

un

ion

in

th

e se

con

ddr

awin

g.

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te A

�B

an

d A

�B

for

eac

h o

f th

e fo

llow

ing.

1.A

�{p

,q,r

,s,t

}A

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�{q

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}B

�{q

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}A

�B

�{p

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,s,t

}

2.A

�{t

he

inte

gers

bet

wee

n 2

an

d 7}

A �

B �

{3}

B �

{0,3

,8}

A �

B �

{0,3

,4,5

,6,8

}

3.A

�{t

he

stat

es w

hos

e n

ames

sta

rt w

ith

K}

A �

B �

{Kan

sas}

B �

{th

e st

ates

wh

ose

capi

tals

are

Hon

olu

lu o

r T

opek

a}A

�B

�{H

awai

i,K

ansa

s,K

entu

cky}

4.A

�{t

he

posi

tive

in

tege

r fa

ctor

s of

24}

A �

B �

{1,2

,3,4

,6,8

}B

�{t

he

cou

nti

ng

nu

mbe

rs l

ess

than

10}

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{1,2

,3,4

,5,6

,7,8

,9,1

2,24

}

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pp

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{nu

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hat

x�

3},B

�{n

um

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s x

such

as

x

�1}

,an

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x

1.5}

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6.A

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7.B

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8.B

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.A �

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C)

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A �

B

AB

Unio

nA

� B

AB

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

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AT

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____

____

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ER

IOD

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2-1

2-1



An

swer

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

Add

ing

an

d S

ub

trac

tin

g R

atio

nal

Nu

mb

ers

NA

ME

____

____

____

____

____

____

____

____

____

____

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AT

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ER

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2-2

2-2

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Alg

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1

Lesson 2-2

Ad

d R

atio

nal

Nu

mb

ers

Ad

din

g R

atio

nal

Nu

mb

ers,

Add

the

num

bers

. If

both

are

pos

itive

, th

e su

m is

pos

itive

; if

both

are

neg

ativ

e,

Sam

e S

ign

the

sum

is n

egat

ive.

Ad

din

g R

atio

nal

Nu

mb

ers,

Sub

trac

t th

e nu

mbe

r w

ith t

he le

sser

abs

olut

e va

lue

from

the

num

ber

with

the

Dif

fere

nt

Sig

ns

grea

ter

abso

lute

val

ue. T

he s

ign

of t

he s

um is

the

sam

e as

the

sig

n of

the

num

ber

with

the

gre

ater

abs

olut

e va

lue.

Use

a n

um

ber

lin

e to

fin

d t

he

sum

�2

�(�

3).

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p 1

Dra

w a

n a

rrow

fro

m 0

to

�2.

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p 2

Fro

m t

he

tip

of t

he

firs

t ar

row

,dra

wa

seco

nd

arro

w 3

un

its

to t

he

left

to

repr

esen

t ad

din

g �

3.S

tep

3T

he

seco

nd

arro

w e

nds

at

the

sum

�5.

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�(�

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10

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ple1

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362.

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258

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7 � 453 � 5

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86 � 17

3 � 141 � 21

22 � 211 � 3

5 � 7

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lenc

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Gle

ncoe

Alg

ebra

1

Sub

trac

t R

atio

nal

Nu

mb

ers

Eve

ry p

osit

ive

rati

onal

nu

mbe

r ca

n b

e pa

ired

wit

h a

neg

ativ

e ra

tion

al n

um

ber

so t

hat

th

eir

sum

is

0.T

he

nu

mbe

rs,c

alle

d op

pos

ites

,are

add

itiv

e in

vers

esof

eac

h o

ther

.

Ad

dit

ive

Inve

rse

Pro

per

tyF

or e

very

num

ber

a, a

�(�

a) �

0.

To s

ubtr

act

a ra

tion

al n

umbe

r,ad

d it

s in

vers

e an

d us

e th

e ru

les

for

addi

tion

giv

en o

n pa

ge 8

1.

Su

btr

acti

on

of

Rat

ion

al N

um

ber

sF

or a

ny n

umbe

rs a

and

b, a

�

b�

a�

(�b)

.

Fin

d 8

.5 �

10.2

.

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sub

trac

t 10

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add

its in

vers

e.

��

(�

10.2

�

8.5

)�

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is

gre

ater

, so

the

res

ult

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egat

ive.

��

1.7

Sim

plify

.

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fin

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core

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85

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he

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ball

tea

m o

ffen

se b

egan

a d

rive

fro

m t

hei

r 20

-yar

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ne.

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ey g

ain

ed 8

yar

ds,l

ost

12 y

ards

an

d lo

st 2

yar

ds b

efor

e h

avin

g to

kic

k th

e ba

ll.W

hat

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ne

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e th

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nw

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th

ey h

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-yar

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ne

1 � 23 � 2

13 � 241 � 46

47 � 46

18 � 2024 � 10

3 � 97 � 8

1 � 212 � 23

25 � 3661 � 36

13 � 355 � 12

5 � 99 � 4

4 � 71 � 5

3 � 41 � 3

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Add

ing

an

d S

ub

trac

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g R

atio

nal

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mb

ers

NA

ME

____

____

____

____

____

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____

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____

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AT

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____

____

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ER

IOD

____

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2-2

2-2

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

Add

ing

an

d S

ub

trac

tin

g R

atio

nal

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mb

ers

NA

ME

____

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____

____

____

____

____

____

____

____

____

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AT

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____

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ER

IOD

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2-2

2-2

©G

lenc

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ncoe

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ebra

1

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d e

ach

su

m.

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6 �

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00 P

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the

tem

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th F

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28

degr

ees

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ren

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hor

tly

afte

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pass

ed t

hro

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d th

e te

mpe

ratu

re d

ropp

ed

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egre

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y 8:

00 A

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orn

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at w

as t

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pera

ture

at

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1

Fin

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1 � 55 � 25

nu

mbe

r of

stu

den

ts c

hos

en�

��

�to

tal

nu

mbe

r of

stu

den

ts

A b

owl

con

tain

s 3

pea

rs,

4 b

anan

as,a

nd

2 a

pp

les.

If y

ou t

ake

ap

iece

of

fru

it a

t ra

nd

om,w

hat

is

the

pro

bab

ilit

y th

at i

t is

not

a b

anan

a?

Th

ere

are

3 �

4 �

2 or

9 p

iece

s of

fru

it.

Th

ere

are

3 �

2 or

5 p

iece

s of

fru

it t

hat

are

not

ban

anas

.

P(n

ot b

anan

a)� �

The

pro

babi

lity

of

not

choo

sing

a b

anan

a is

.5 � 9

5 � 9nu

mbe

r of

oth

er p

iece

s of

fru

it�

��

�to

tal

nu

mbe

r of

pie

ces

of f

ruit

Exam

ple1

Exam

ple1

Exam

ple2

Exam

ple2

Exer

cises

Exer

cises

A c

ard

is

sele

cted

at

ran

dom

fro

m a

sta

nd

ard

dec

k o

f 52

car

ds.

Det

erm

ine

each

pro

bab

ilit

y.

1.P

(10)

2.P

(red

2)

3.P

(kin

g or

qu

een

)

4.P

(bla

ck c

ard)

5.P

(ace

of

spad

es)

6.P

(spa

de)

Tw

o d

ice

are

roll

ed a

nd

th

eir

sum

is

reco

rded

.Fin

d e

ach

pro

bab

ilit

y.

7.P

(su

m i

s 1)

08.

P(s

um

is

6)9.

P(s

um

is

less

th

an 4

)

10.P

(su

m i

s gr

eate

r th

an 1

1)11

.P(s

um

is

less

th

an 1

5)12

.P(s

um

is

grea

ter

than

8)

1

A b

owl

con

tain

s 4

red

ch

ips,

3 b

lue

chip

s,an

d 8

gre

en c

hip

s.Y

ou c

hoo

se o

ne

chip

at r

and

om.F

ind

eac

h p

rob

abil

ity.

13.P

(not

a r

ed c

hip

)14

.P(r

ed o

r bl

ue

chip

)15

.P(n

ot a

gre

en c

hip

)

A n

um

ber

is

sele

cted

at

ran

dom

fro

m t

he

list

{1,

2,3,

…,1

0}.F

ind

eac

h p

rob

abil

ity.

16.P

(eve

n n

um

ber)

17.P

(mu

ltip

le o

f 3)

18.P

(les

s th

an 4

)

19.A

com

pute

r ra

ndo

mly

ch

oose

s a

lett

er f

rom

th

e w

ord

CO

MP

UT

ER

.Fin

d th

e pr

obab

ilit

yth

at t

he

lett

er i

s a

vow

el.

3 � 8

3 � 103 � 10

1 � 2

7 � 157 � 15

11 � 15

5 � 181 � 36

1 � 125 � 36

1 � 41 � 52

1 � 2

2 � 131 � 26

1 � 13

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lenc

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w-H

ill10

6G

lenc

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Od

ds

Th

e od

ds o

f an

eve

nt

occu

rrin

g is

th

e ra

tio

of t

he

nu

mbe

r of

way

s an

eve

nt

can

occ

ur

(su

cces

ses)

to

the

nu

mbe

r of

way

s th

e ev

ent

can

not

occ

ur

(fai

lure

s).

Od

ds

A d

ie i

s ro

lled

.Fin

d t

he

odd

s of

rol

lin

g a

nu

mb

er

grea

ter

than

4.

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e sa

mpl

e sp

ace

is {

1,2,

3,4,

5,6}

.Th

eref

ore,

ther

e ar

e si

x po

ssib

le o

utc

omes

.Sin

ce 5

an

d6

are

the

only

nu

mbe

rs g

reat

er t

han

4,t

wo

outc

omes

are

su

cces

ses

and

fou

r ar

e fa

ilu

res.

So

the

odds

of

roll

ing

a n

um

ber

grea

ter

than

4 i

s ,o

r 1:

2.

Fin

d t

he

odd

s of

eac

h o

utc

ome

if t

he

spin

ner

at

the

righ

t is

sp

un

on

ce.

1.m

ult

iple

of

41:

42.

odd

nu

mbe

r1:

1

3.ev

en o

r a

53:

24.

less

th

an 4

3:7

5.ev

en n

um

ber

grea

ter

than

53:

7

Fin

d t

he

odd

s of

eac

h o

utc

ome

if a

com

pu

ter

ran

dom

ly c

hoo

ses

a n

um

ber

bet

wee

n1

and

20.

6.th

e n

um

ber

is l

ess

than

10

9:11

7.th

e n

um

ber

is a

mu

ltip

le o

f 4

1:3

8.th

e n

um

ber

is e

ven

1:1

9.th

e n

um

ber

is a

on

e-di

git

nu

mbe

r9:

11

A b

owl

of m

oney

at

a ca

rniv

al c

onta

ins

50 q

uar

ters

,75

dim

es,1

00 n

ick

els,

and

12

5 p

enn

ies.

On

e co

in i

s ra

nd

omly

sel

ecte

d.

10.F

ind

the

odds

th

at a

dim

e w

ill

not

be

chos

en.

11:3

11.W

hat

are

th

e od

ds o

f ch

oosi

ng

a qu

arte

r if

all

th

e di

mes

are

rem

oved

?2:

9

12.W

hat

are

th

e od

ds o

f ch

oosi

ng

a pe

nn

y?5:

9

Su

pp

ose

you

dro

p a

ch

ip o

nto

th

e gr

id a

t th

e ri

ght.

Fin

d t

he

odd

s of

eac

h o

utc

ome.

13.l

and

on a

sh

aded

squ

are

1:1

14.l

and

on a

squ

are

on t

he

diag

onal

1:1

15.l

and

on s

quar

e n

um

ber

161:

15

16.l

and

on a

nu

mbe

r gr

eate

r th

an 1

21:

3

17.l

and

on a

mu

ltip

le o

f 5

3:13

1 5 9 13

2 6 10 14

3 7 11 15

4 8 12 16

12

9

4

38 7

10

56

2 � 4

num

ber

of s

ucce

sses

��

�nu

mbe

r of

fai

lure

s

Stu

dy G

uid

e a

nd I

nte

rven

tion

(c

onti

nued

)

Pro

bab

ility

:Sim

ple

Pro

bab

ility

an

d O

dds

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

2-6

2-6

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

Pro

bab

ility

:Sim

ple

Pro

bab

ility

an

d O

dds

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

2-6

2-6

©G

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7G

lenc

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lgeb

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Lesson 2-6

On

e ch

ip i

s ra

nd

omly

sel

ecte

d f

rom

a j

ar c

onta

inin

g 8

yell

ow c

hip

s,10

blu

e ch

ips,

7 gr

een

ch

ips,

and

5 r

ed c

hip

s.F

ind

eac

h p

rob

abil

ity.

1.P

(blu

e)�

33%

2.P

(gre

en)

�23

%

3.P

(yel

low

or

gree

n)

�50

%4.

P(b

lue

or y

ello

w)

�60

%

5.P

(not

red

)�

83%

6.P

(not

blu

e)�

67%

Fin

d t

he

pro

bab

ilit

y of

eac

h o

utc

ome

if t

he

spin

ner

is

spu

n o

nce

.

7.P

(mu

ltip

le o

f 3)

�25

%8.

P(l

ess

than

7)

�75

%

9.P

(odd

or

2)�

62.5

%10

.P(n

ot 1

)�

87.5

%

A p

erso

n i

s b

orn

in

th

e m

onth

of

Ju

ne.

Fin

d e

ach

pro

bab

ilit

y.

11.P

(dat

e is

a m

ult

iple

of

6)12

.P(d

ate

is b

efor

e Ju

ne

15)

�17

%�

47%

13.P

(bef

ore

Jun

e 7

or a

fter

Ju

ne

24)

14.P

(not

aft

er J

un

e 5)

�40

%�

17%

Fin

d t

he

odd

s of

eac

h o

utc

ome

if a

com

pu

ter

ran

dom

ly p

ick

s a

lett

er i

n t

he

nam

eT

he

Pet

rifi

ed F

ores

t.

15.t

he

lett

er f

2:1

6 o

r 1

:816

.th

e le

tter

e4

:14

or

2:7

17.t

he

lett

er t

3:1

5 o

r 1

:518

.a v

owel

7:1

1

CL

AS

S S

CH

ED

UL

ES

For

Exe

rcis

es 1

9–22

,use

th

e fo

llow

ing

info

rmat

ion

.

A s

tude

nt

can

sel

ect

an e

lect

ive

clas

s fr

om t

he

foll

owin

g:3

in m

usi

c,5

in p

hys

ical

edu

cati

on,

2 in

jou

rnal

ism

,8 i

n c

ompu

ter

prog

ram

min

g,4

in a

rt,a

nd

6 in

dra

ma.

Fin

d ea

ch o

f th

e od

dsif

a s

tude

nt

forg

ets

to c

hoo

se a

n e

lect

ive

and

the

sch

ool

assi

gns

one

at r

ando

m.

19.T

he

clas

s is

com

pute

r pr

ogra

mm

ing.

8:2

0 o

r 2

:5

20.T

he

clas

s is

dra

ma.

6:2

2 o

r 3

:11

21.T

he

clas

s is

not

ph

ysic

al e

duca

tion

.23

:5

22.T

he

clas

s is

not

art

.24

:4 o

r 6

:1

1 � 62 � 5

7 � 151 � 6

7 � 85 � 8

3 � 41 � 4

18

45

63

72

2 � 35 � 6

3 � 51 � 2

7 � 301 � 3

©G

lenc

oe/M

cGra

w-H

ill10

8G

lenc

oe A

lgeb

ra 1

On

e ch

ip i

s ra

nd

omly

sel

ecte

d f

rom

a j

ar c

onta

inin

g 13

blu

e ch

ips,

8 ye

llow

ch

ips,

15 b

row

n c

hip

s,an

d 6

gre

en c

hip

s.F

ind

eac

h p

rob

abil

ity.

1.P

(bro

wn

)�

36%

2.P

(gre

en)

�14

%

3.P

(blu

e or

yel

low

)�

50%

4.P

(not

yel

low

)�

81%

A c

ard

is

sele

cted

at

ran

dom

fro

m a

sta

nd

ard

dec

k o

f 52

car

ds.

Fin

d e

ach

pro

bab

ilit

y.

5.P

(hea

rt)

�25

%6.

P(b

lack

car

d)�

50%

7.P

(jac

k)�

8%8.

P(r

ed ja

ck)

�4%

Tw

o d

ice

are

roll

ed a

nd

th

eir

sum

is

reco

rded

.Fin

d e

ach

pro

bab

ilit

y.

9.P

(su

m l

ess

than

6)

�28

%10

.P(s

um

les

s th

an 2

)0

�0%

11.P

(su

m g

reat

er t

han

10)

�8%

12.P

(su

m g

reat

er t

han

9)

�17

%

Fin

d t

he

odd

s of

eac

h o

utc

ome

if a

com

pu

ter

ran

dom

ly p

ick

s a

lett

er i

n t

he

nam

eT

he

Ba

dla

nd

s of

Nor

th D

ak

ota

.

13.t

he

lett

er d

3:2

1 o

r 1

:714

.th

e le

tter

a4

:20

or

1:5

15.t

he

lett

er h

2:2

2 o

r 1

:11

16.a

con

son

ant

16:8

or

2:1

CLA

SS P

RO

JEC

TSF

or E

xerc

ises

17–

20,u

se t

he

foll

owin

g in

form

atio

n.

Stu

den

ts i

n a

bio

logy

cla

ss c

an c

hoo

se a

sem

este

r pr

ojec

t fr

om t

he

foll

owin

g li

st:a

nim

albe

hav

ior

(4),

cell

ula

r pr

oces

ses

(2),

ecol

ogy

(6),

hea

lth

(7)

,an

d ph

ysio

logy

(3)

.Fin

d ea

ch o

fth

e od

ds i

f a

stu

den

t se

lect

s a

topi

c at

ran

dom

.

17.t

he

topi

c is

eco

logy

6:1

6 o

r 3

:8

18.t

he

topi

c is

an

imal

beh

avio

r4

:18

or

2:9

19.t

he

topi

c is

not

cel

lula

r pr

oces

ses

20:2

or

10:1

20.t

he

topi

c is

not

hea

lth

15:7

SC

HO

OL

IS

SU

ES

For

Exe

rcis

es 2

1 an

d 2

2,u

se t

he

foll

owin

g in

form

atio

n.

A n

ews

team

su

rvey

ed s

tude

nts

in

gra

des

9–12

on

wh

eth

er t

o

chan

ge t

he

tim

e sc

hoo

l be

gin

s.O

ne

stu

den

t w

ill

be s

elec

ted

atra

ndo

m t

o be

in

terv

iew

ed o

n t

he

even

ing

new

s.T

he

tabl

e gi

ves

the

resu

lts.

21.W

hat

is

the

prob

abil

ity

the

stu

den

t se

lect

ed w

ill

be i

n t

he

9th

gra

de?

�32

%

22.W

hat

are

th

e od

ds t

he

stu

den

t se

lect

ed w

ants

no

chan

ge?

16:3

4 o

r 8

:17

8 � 25

Gra

de

910

1112

No

ch

ang

e6

25

3

Ho

ur

late

r10

79

8

1 � 61 � 12

5 � 18

1 � 261 � 13

1 � 21 � 4

17 � 211 � 2

1 � 75 � 14

Pra

ctic

e (

Ave

rag

e)

Pro

bab

ility

:Sim

ple

Pro

bab

ility

an

d O

dds

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

2-6

2-6



An

swer

s

Readin

g t

o L

earn

Math

em

ati

csP

rob

abili

ty:

Sim

ple

Pro

bab

ility

an

d O

dd

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

AT

E__

____

____

__P

ER

IOD

____

_

2-6

2-6

©G

lenc

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cGra

w-H

ill10

9G

lenc

oe A

lgeb

ra 1

Lesson 2-6

Pre-

Act

ivit

yW

hy

is p

rob

abil

ity

imp

orta

nt

in s

por

ts?

Rea

d th

e in

trod

uct

ion

to

Les

son

2-6

at

the

top

of p

age

96 i

n y

our

text

book

.

Loo

k u

p th

e de

fin

itio

n o

f th

e w

ord

prob

abil

ity

in a

dic

tion

ary.

Rew

rite

th

ede

fin

itio

n i

n y

our

own

wor

ds.

Sam

ple

an

swer

:th

e lik

elih

oo

d o

f so

met

hin

g h

app

enin

g

Rea

din

g t

he

Less

on

1.W

rite

wh

eth

er e

ach

sta

tem

ent

is t

rue

or f

alse

.If

fals

e,re

plac

e th

e u

nde

rlin

ed w

ord

orn

um

ber

to m

ake

a tr

ue

stat

emen

t.

a.P

roba

bili

ty c

an b

e w

ritt

en a

s a

frac

tion

,a d

ecim

al,o

r a

perc

ent.

tru

e

b.

Th

e sa

mpl

e sp

ace

of f

lipp

ing

one

coin

is

hea

ds o

r ta

ils.

tru

e

c.T

he

prob

abil

ity

of a

n i

mpo

ssib

le e

ven

t is

1.

fals

e;0

d.

Th

e od

ds a

gain

st a

n e

ven

t oc

curr

ing

are

the

odds

th

at t

he

even

t w

ill

occu

r.fa

lse;

will

no

t

2.E

xpla

in w

hy

the

prob

abil

ity

of a

n e

ven

t ca

nn

ot b

e gr

eate

r th

an 1

wh

ile

the

odds

of

anev

ent

can

be

grea

ter

than

1.

Sam

ple

an

swer

:To

fin

d t

he

pro

bab

ility

of

an e

ven

t,yo

u c

om

par

e a

par

t o

fth

e sa

mp

le s

pac

e to

th

e w

ho

le s

amp

le s

pac

e.W

hen

yo

u f

ind

th

e o

dd

s o

fan

eve

nt,

you

co

mp

are

the

nu

mb

er o

f fa

vora

ble

ou

tco

mes

to

th

e n

um

ber

of

un

favo

rab

le o

utc

om

es.I

n s

om

e si

tuat

ion

s,th

ere

may

be

mo

refa

vora

ble

th

an u

nfa

vora

ble

ou

tco

mes

.

Hel

pin

g Y

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2-6

2-6



Stu

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2-7

2-7

Exam

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Exam

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An

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s gi

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form

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ney

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ney

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ater

if

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dist

ance

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135

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u c

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top

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Mt.

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282

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.

22.S

EISM

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AV

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If a

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200

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wh

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s th

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abo

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2-7

2-7



Readin

g t

o L

earn

Math

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ati

csS

qu

are

Ro

ots

an

d R

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um

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s

NA

ME

____

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2-7

2-7

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Lesson 2-7

Pre-

Act

ivit

yH

ow c

an u

sin

g sq

uar

e ro

ots

det

erm

ine

the

surf

ace

area

of

the

hu

man

bod

y?

Rea

d th

e in

trod

uct

ion

to

Les

son

2-7

at

the

top

of p

age

103

in y

our

text

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.

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e ex

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�36

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wou

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the

squ

are

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din

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he

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on

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ple

te e

ach

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tem

ent

bel

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he

sym

bol

��

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d a

and

is u

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onn

egat

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l sq

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pres

sion

un

der

the

sym

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of

an

irr

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nal

nu

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r is

a r

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at i

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ose

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ut

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of t

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irra

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um

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posi

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root

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a n

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ber

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alle

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uar

ero

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um

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nu

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r w

hos

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rati

onal

nu

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a

.

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rite

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llow

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as a

mat

hem

atic

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xpre

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n t

hat

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00

1600

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729

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729

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the

prin

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l sq

uar

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f 30

25

3025

�

6.T

he

irra

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al n

um

bers

an

d ra

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um

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tog

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er f

orm

th

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t of

n

um

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.

Hel

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g Y

ou

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se a

dic

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to l

ook

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seve

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hat

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in w

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“ir

-”.W

hat

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efix

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nu

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at

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left

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how

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:240

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6 m

.On

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6 cm

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.

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n t

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map

,how

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re r

epre

sen

ted

by a

n i

nch

?20

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on

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van

Roa

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in

ches

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00

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eter

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m

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bou

t h

ow m

any

squ

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met

ers

of c

arpe

tin

g w

ould

be

nee

ded

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arpe

t th

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vin

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om?

24 m

2

6.M

ake

a sc

ale

draw

ing

of y

our

clas

sroo

m u

sin

g an

app

ropr

iate

sca

le.

An

swer

s w

ill v

ary.

7.U

se y

our

scal

e dr

awin

g to

det

erm

ine

how

man

y sq

uar

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eter

s of

til

e w

ould

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nee

ded

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stal

l a

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flo

or i

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our

clas

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s w

ill v

ary.

Clos

et

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et

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et

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et

Kitc

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Bedr

oom

Bedr

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Bath

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rea

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ng R

oom

Lot 3

Lot 2

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Sylvan Road

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

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____

_

2-7

2-7



1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. A

A

D

B

C

D

A

B

A

C

D

1

B

A

C

D

A

C

D

C

B

C

A

D

C

C

B

D

B

D

C

B

Chapter 2 Assessment Answer KeyForm 1 Form 2APage 117 Page 118 Page 119

(continued on the next page)

An

swer

s


12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 2

B

C

A

B

D

A

D

D

A

B

B

D

B

A

D

B

C

D

A

C

13.3

A

C

B

A

B

D

A

C

C

Chapter 2 Assessment Answer KeyForm 2A (continued) Form 2BPage 120 Page 121 Page 122

An

swer

s


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

B: 752 B.c.

��19

��, ��29

�, 0, �121�, 0.25

�1�2�3 0 1 2 3

natural numbers, wholenumbers, integers, and

rational numbers

�1.1

7 : 5

1 : 2

�14

� or 25%

�34

� or 75%

They are all the same, soall of them represent the

data well.

5

0, 1, 5, 6

3

1 2 3 4 5 60

��

��

��

��

�1.3

�5w � 3

�4

�277� or 3�

67

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68.16

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�64

� �191� or �1�

29

�

8.11

�16

�

�12.9

11

3

�5

�1�2 0 1 2 4 5 63

0 1 32�3 �2 �1

{�4, �1, 0, 2, 3, 5}

Chapter 2 Assessment Answer KeyForm 2CPage 123 Page 124


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

B:�2150�

��49

��, ��38

�, 0, 0.4, �47

�

�1�2�3�4 0 1 2 43

integers and rationalnumbers

��163�

5 : 4

8 : 9

�157� or about 29%

�1127� or about 71%

No; the mean is lowerthan the cluster of most

of the values.

4

1, 2

4

1 2 3 4 5 60

��

��

��

��

��

�1.5

6w � 5

�4

��130�

�9.5

�24.51

�5.61

�22b

��251�

�105

�98

� or 1�18

�

�12.81

�29

�

�18.9

13

19

9

�1�2�3�4 0 1 2 43

0 1 2�1

{�5, �1, 0, 1, 3, 4}

Chapter 2 Assessment Answer KeyForm 2DPage 125 Page 126

An

swer

s


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

24.

25.

B: �4.3

�1, ��116��, ��

29

�, �0.2, ��121�

natural numbers,whole numbers,

integers, andrational numbers

��245�

7 : 3

0

1 : 1

�376� or about 19%

Sample answer:Median; the mode

is too high.

Sample answer:Median or mean; the

mode is too low.

2 3 4 5 6 7 8 9 101

��

��

� � ��

��

�

��

� �

3.2

4x � 7y

�4.8

�125� or 7�

12

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160

516 ft

�2375�

�113

14,776 ft

��32

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�

1�29

�

�1�2�3�5�4 0 1 2 63 4 5

�1�2�3�5�4 0 1 2 63 4 5

��1, ��13

�, �23

�, �43

��

Chapter 2 Assessment Answer KeyForm 3Page 127 Page 128

16 � 7 � 1.67

Stem Leaf1617181920

0 7 862 50 2 3 71 2 2 3 5


Chapter 2 Assessment Answer KeyPage 129, Open-Ended Assessment

Scoring Rubric

Score General Description Specific Criteria

• Shows thorough understanding of the concepts ofgraphing rational numbers, adding, subtracting, anddividing rational numbers, displaying and analyzing data,simple probability and odds, square roots, and classifyingand ordering real numbers.

• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.

• Shows an understanding of the concepts of graphingrational numbers, adding, subtracting, and dividing rationalnumbers, displaying and analyzing data, simple probabilityand odds, square roots, and classifying and ordering realnumbers.

• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.

• Shows an understanding of most of the concepts ofgraphing rational numbers, adding, subtracting, anddividing rational numbers, displaying and analyzing data,simple probability and odds, square roots, and classifyingand ordering real numbers.

• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.

• Final computation is correct.• No written explanations or work is shown to substantiate

the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.

• Shows little or no understanding of the concepts ofgraphing rational numbers, adding, subtracting, anddividing rational numbers, displaying and analyzing data,simple probability and odds, square roots, and classifyingand ordering real numbers.

• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.

0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given

1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation

2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem

3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation

4 SuperiorA correct solution that is supported by well-developed, accurateexplanations

Chapter 2 Assessment Answer KeyPage 129, Open-Ended Assessment

Sample Answers


1a. The student should explain that thepoint on a number line representsthe location of a number relative tothe rest of the real numbers. Thecoordinate of a point is the numberthat the point represents.

1b. Sample answer: Draw a number linewith tick marks labeled from –5 to 5.Plot points at 3, 4, and 5. Make theright arrow bold to represent thatthe graph continues indefinitely inthat direction.

2a.

Since �4 � 3 lies to the left of 4 � (�3) on a number line, thenumber �4 � 3 is not greater than 4 � (�3).

2b. The student should explain thatsubtracting a number is the same asadding the opposite of the number,thus making it possible to subtractby adding. Sample answer:2 � 1 � 2 � (�1) � 1

3. If x and y are both positive, then �xy� is

positive: x � 4, y � 2, �xy� � �

42� � 2.

If x and y are both negative, then �xy� is

positive: x � �6, y � �3, ��

63�

� 2.

4a. Sample answer:{1, 1, 2, 4, 5, 10, 11, 12, 13, 14, 15};mean is 8; mode is 1.

4b. The student should use the set ofdata created for part a.Sample answer:

0 � 1 � 01

5a. The probability that an event willoccur is defined to be the number offavorable outcomes divided by thetotal number of possible outcomes.The number of favorable outcomes isalways less than or equal to the totalnumber of possible outcomes. Thus,this quotient is always less than orequal to 1, which means it can neverequal 2.

5b. The odds that an event will occur isthe ratio of the number of ways anevent can occur to the number ofways the event cannot occur. Thetotal number of possible outcomes isthe sum of the number of ways anevent can occur and the number ofways the event cannot occur. Thus,if the odds that an event will occur is 1 : 1, then the probability that the

event will occur is �1 �1

1� � �12�.

6a. The student should recognize that,since there is no real number thatcan be multiplied by itself to producea negative number, ��49� is not areal number. However, ��49� is thenegative square root of 49, or �7.

6b. Sample answer:�2.1, �2, ��2�, �1, 1, 2

�1�2�3

�3

�4

�4

0 1 2 43

�1�2�3

�3

�4

�4

0 1 2 43

In addition to the scoring rubric found on page A28, the following sample answers may be used as guidance in evaluating open-ended assessment items.

An

swer

s

Stem Leaf

01

1 1 2 4 50 1 2 3 4 5


Chapter 2 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 2–1 and 2–2) Quiz (Lessons 2–5 and 2–6)

Page 130 Page 131 Page 132

1. e

2. h

3. a

4. b

5. j

6. c

7. d

8. f

9. g

10. i

11. The absolute valueof any number n isits distance fromzero on the numberline.

12. A pair of numbersconsisting of apositive rationalnumber and anegative rationalnumber with a sumof zero.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lessons 2–3 and 2–4)

Page 131

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

1.

2.

3.

4.

5.

Quiz (Lesson 2–7)

Page 132

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. C

��49

�, ��13

�, 0.3, ��

110��

�

�

�1�2�3�4 0 1 2 43

irrational numbers

natural numbers,whole numbers, integers,and rational numbers

��151�

0.6�7

3 : 1

�154�

Sample answer:Median; the mode istoo low and the meanis too high.

59

55 60 65 70 75

��

� ��

�5.75

��83

� or �2�23

�

3x � 5y

10

�65

� or 1�15

�

�7

�0.24

31a

��47

�

�217

1.4�77

�56

�

�43

�4

4.972

�2�1�3�4�5 0 1 2 43

{…, �4, �3, �2,�1, 0, 1}


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.��

94

�, ��5�, 2.2�4�, �5275�

�216�

40 41 42 43 44 45 46 47

� � ��

��

� ��

2t � 3

��365�

14

17.8

36

�3, �1, 2, 5, 6

Temperature

Peo

ple

Sample answer:

hypothesis: I finish myhomework; conclusion:I’ll go to the store; If Ifinish my homework,

then I’ll go to the store.

4x � 14

17a � 3

84

x2 � 7

0.58

�27.3

�2

��287� or �3�

38

�

72

�170�

�79

�1�2�3�5�4 0 1 2 3

B

C

D

A

B

D

C

Chapter 2 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 133 Page 134

An

swer

s


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11. 12.

13. 14.

15.

16.

17. DCBA

DCBA

DCBA

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

1 . 6

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

87 1

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

2 2

0 0 0

.. ./ /

.

99 9 987654321

87654321

87654321

87654321

1 7 2 8

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

HGFE

DCBA

Chapter 2 Assessment Answer KeyStandardized Test Practice

Page 135 Page 136

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