Chapter 2 Resource Masters - Math Class · ©Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the Chapter 2 Resource Masters The Fast File Chapter Resource system

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)

⎧ ⎪ ⎨ ⎪ ⎩

⎧ ⎪ ⎨ ⎪ ⎩

Brad and Anissa Stuckey

© 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 # y⏐1"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


Less

on 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


Less

on 2

-3

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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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


Less

on 2

-3

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


Less

on 2

-4

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

on 2

-4

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


Less

on 2

-4

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


Less

on 2

-5

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 6⏐2 $ 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 | Leaf9 | 0 0 1 3 9

10 | 2 2 511 |12 | 0 3 3 8 8 9 9 |0 $ 90

Stem | Leaf2 | 4 7 73 | 1 2 6 6 6 94 | 05 | 8 8 9 2 |4 $ 24

Stem | Leaf9 | 4 6 8 9 9

10 | 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


Less

on 2

-5

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 | Leaf72 | 0 1 1 2 573 | 2 2 2 7 9 974 | 1 3 375 | 6 6 8 976 | 0 1 8 8 8 74⏐2 $ 742

76543210!1!2!3!4!5!6

) ) ) ) ) ) ) ) ) ) ) ) ) )) ) ) ) ) ) ) )

) ))

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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

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6


Less

on 2

-6

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

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10

14

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7

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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

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6


Less

on 2

-6

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

on 2

-6

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

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4

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4

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Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-62-6

Study Guide and InterventionSquare Roots and Real Numbers

NAME ______________________________________________ DATE ____________ PERIOD _____

2-72-7


Less

on 2

-7

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

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25"16

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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

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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


Less

on 2

-7

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

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!2 !1!4 !3 0 1 2 3 4!2 !1 0 1 2 3 4 5 6

9"13

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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?

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144"3

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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.

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Enrichment

NAME ______________________________________________ DATE ____________ PERIOD _____

2-72-7

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tion

Rat

iona

l Num

bers

on

the

Num

ber

Line

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-1

2-1

©G

lenc

oe/M

cGra

w-H

ill75

Gle

ncoe

Alg

ebra

1

Lesson 2-1

Gra

ph R

atio

nal N

umbe

rsT

he f

igur

e at

the

rig

ht is

pa

rt o

f a

num

ber

line.

A n

umbe

r lin

e ca

n be

use

d to

sho

w

the

sets

of n

atu

ral

nu

mbe

rs,w

hol

e n

um

bers

,and

in

tege

rs.P

osit

ive

nu

mbe

rs,a

re lo

cate

d to

the

rig

ht o

f 0,

and

neg

ativ

e n

um

bers

are

loca

ted

to t

he le

ft o

f 0.

Ano

ther

set

of

num

bers

tha

t yo

u ca

n di

spla

y on

a n

umbe

r lin

e is

the

set

of r

atio

nal

nu

mbe

rs.A

rat

iona

l num

ber

can

be w

ritt

en a

s ,w

here

aan

d b

are

inte

gers

and

b%

0.So

me

exam

ples

of

rati

onal

num

bers

are

,

,,a

nd

.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.

The

dot

s in

dica

te e

ach

poin

t on

the

gra

ph.

The

coo

rdin

ates

are

{!3,

!1,

1,3,

5}b.

The

bol

d ar

row

to

the

righ

t m

eans

the

gra

phco

ntin

ues

inde

fini

tely

in t

hat

dire

ctio

n.T

heco

ordi

nate

s ar

e {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

bers

.

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

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.

{!2,

0,2,

4,6}

{1,3

,5,7

,…}

3.4.

!!,0

,,

,,1

"!!3

,!,

,2,3

"G

rap

h e

ach

set

of

nu

mbe

rs.

5.{!

3,!

1,1,

3}6.

{!5,

!2,

1,2}

7.{i

nteg

ers

less

tha

n 0}

8.{…

,!2,

!1,

0,1}

9.!!

2,!

1,!

,"

10.{

…,!

4,!

2,0,

2,…

}

!3

!4

!5

!6

!2

!1

01

2!

21 – 2!

3!

2!11 – 2!

1!

1 – 20

1 – 21

!3

!4

!2

!1

01

23

4

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)


Ans

wer

s

Skil

ls P

ract

ice

Rat

iona

l Num

bers

on

the

Num

ber

Line

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-1

2-1

©G

lenc

oe/M

cGra

w-H

ill77

Gle

ncoe

Alg

ebra

1

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

bers

.

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

abs

olu

te v

alu

e.

11.⏐

!9⏐

912

.⏐15

⏐15

13.⏐

!30

⏐30

14. ⏐!

⏐15

.⏐2.

4⏐2.

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"

6⏐11

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 !

y⏐11

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

!1

0

!5

!6

!7

!8

!9

!10

!4

!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

©G

lenc

oe/M

cGra

w-H

ill78

Gle

ncoe

Alg

ebra

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.

!…,!

,!,!

,!1,

!"

{2.4

,2.8

,3.2

,3.6

,4,…

}

Gra

ph

eac

h s

et o

f n

um

bers

.

3.!…

,!,!

,!1,

!,!

"4.

{int

eger

s le

ss t

han

!4

or g

reat

er t

han

2}

Fin

d e

ach

abs

olu

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 !

y⏐1.

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

.

The

abs

olut

e m

agni

tude

of a

sta

r is

how

bri

ght

the

star

wou

ld

appe

ar f

rom

a s

tand

ard

dist

ance

of

10 p

arse

cs,o

r 32

.6 li

ght

year

s.T

he lo

wer

the

num

ber,

the

grea

ter

the

mag

nitu

de,o

r br

ight

ness

,of

the

sta

r.T

he t

able

giv

es t

he m

agni

tude

s of

sev

eral

sta

rs.

17.U

se a

num

ber

line

to o

rder

the

mag

nitu

des

from

leas

t to

gre

ates

t.

18.W

hich

of

the

star

s ar

e th

e br

ight

est

and

the

leas

t br

ight

?br

ight

est:

Rig

el;l

east

bri

ght:

Alta

ir19

.Wri

te t

he a

bsol

ute

valu

e of

the

mag

nitu

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

The

tab

le s

how

s th

e m

ean

win

d sp

eeds

in

mile

s pe

r ho

ur a

t D

ayto

naB

each

,Flo

rida

.So

urce

:Nati

onal

Clim

atic D

ata C

ente

r

Gra

ph t

he w

ind

spee

ds o

n a

num

ber

line.

Whi

ch

mon

th h

as t

he g

reat

est

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

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

!8.

1!

7.2

!4.

7!

0.3

2.3

1.4

0.5

0.7

!9

!5

!4

!3

!2

!1

01

23

Sta

rM

agni

tude

Alta

ir2.

3

Bet

elge

use

!7.

2

Cas

tor

0.5

Den

eb!

4.7

Pol

lux

0.7

Reg

ulus

!0.

3

Rig

el!

8.1

Siri

us1.

4

3 # 41 # 6

1 # 37 # 10

3 # 41 # 3

2 # 52 # 15

3 # 101 # 5

3 # 23 # 5

28 # 5328 # 53

!6

!5

!4

!3

!2

!1

01

23

4!

7 – 5!

6 – 5!

1!

3 – 5!

4 – 5!

2 – 5!

1 – 51 – 5

2 – 53 – 5

0

3 # 54 # 5

6 # 57 # 5

3 # 45 # 4

3 # 27 # 4

00.

40.

81.

21.

62

2.4

2.8

3.2

3.6

4!

7 – 4!

3 – 2!

5 – 4!

1!

3 – 4!

1 – 2!

1 – 41 – 4

1 – 23 – 4

0

Pra

ctic

e (A

vera

ge)

Rat

iona

l Num

bers

on

the

Num

ber

Line

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-1

2-1



Rea

din

g t

o L

earn

Math

emati

csR

atio

nal N

umbe

rs o

n th

e N

umbe

r Li

ne

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-1

2-1

©G

lenc

oe/M

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

mbe

r li

ne

to s

how

dat

a?

Rea

d th

e in

trod

ucti

on t

o L

esso

n 2-

1 at

the

top

of

page

68

in y

our

text

book

.

In t

he t

able

,wha

t do

es t

he n

umbe

r "

0.2

tell

you?

The

leve

l of

the

Bra

zos

Riv

er in

crea

sed

by 0

.2 fo

ot in

24

hou

rs.

Read

ing

the

Less

on

1.R

efer

to

the

num

ber

line

on p

age

68 in

you

r te

xtbo

ok.W

rite

tru

eor

fal

sefo

r ea

ch o

f th

efo

llow

ing

stat

emen

ts.

a.A

ll w

hole

num

bers

are

inte

gers

.tr

ue

b.A

ll na

tura

l num

bers

are

inte

gers

.tr

ue

c.A

ll w

hole

num

bers

are

nat

ural

num

bers

.fa

lse

d.A

ll na

tura

l num

bers

are

who

le n

umbe

rs.

true

e.A

ll w

hole

num

bers

are

pos

itiv

e nu

mbe

rs.

fals

e

2.U

se t

he w

ords

den

omin

ator

,fra

ctio

n,an

d nu

mer

ator

to c

ompl

ete

the

follo

win

g se

nten

ce.

You

know

tha

t a

num

ber

is a

rat

iona

l num

ber

if it

can

be

wri

tten

as

a

that

has

a

and

that

are

inte

gers

,whe

re t

he d

enom

inat

or is

not

equ

al t

o ze

ro.

3.E

xpla

in w

hy

,0.6 %

,and

15

are

rati

onal

num

bers

.

Eac

h nu

mbe

r is

in o

r ca

n be

wri

tten

in t

he fo

rm

,whe

re a

and

bar

e

inte

gers

and

b%

0.0.

6#ca

n be

wri

tten

as

,and

15

can

be w

ritt

en a

s .

Hel

ping

You

Rem

embe

r

4.C

onne

ctin

g a

mat

hem

atic

al c

once

pt t

o so

met

hing

in y

our

ever

yday

life

is o

ne w

ay o

fre

mem

beri

ng.D

escr

ibe

a si

tuat

ion

or s

etti

ng in

you

r lif

e th

at r

emin

ds y

ou o

f ab

solu

teva

lue.

Sam

ple

answ

er:T

he d

ista

nce

from

eac

h go

al li

ne t

o th

e 50

-yar

d lin

e is

50

yard

s.

15 # 12 # 3

a # b

!3

#7

deno

min

ator

num

erat

orfr

actio

n

©G

lenc

oe/M

cGra

w-H

ill80

Gle

ncoe

Alg

ebra

1

Inte

rsec

tion

and

Uni

onT

he in

ters

ecti

on o

f tw

o se

ts is

the

set

of e

lem

ents

tha

t ar

e in

bot

h se

ts.

The

inte

rsec

tion

of s

ets

A a

nd B

is w

ritt

en A

!B

.The

uni

on o

f tw

o se

tsis

the

set

of e

lem

ents

in e

ithe

r A

,B,o

r bo

th.T

he u

nion

is w

ritt

en A

"B

.

In t

he d

raw

ings

bel

ow,s

uppo

se A

is t

he s

et o

f po

ints

insi

de t

he c

ircl

ean

d B

is t

he s

et o

f po

ints

insi

de t

he s

quar

e.T

hen,

the

shad

ed a

reas

show

the

inte

rsec

tion

in t

he f

irst

dra

win

g an

d th

e un

ion

in t

he s

econ

ddr

awin

g.

Wri

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

#B

"{q

,r,s

}B

${q

,r,s

}A

$B

"{p

,q,r

,s,t

}

2.A

${t

he in

tege

rs b

etw

een

2 an

d 7}

A #

B "

{3}

B $

{0,3

,8}

A $

B "

{0,3

,4,5

,6,8

}

3.A

${t

he s

tate

s w

hose

nam

es s

tart

wit

h K

}A

#B

"{K

ansa

s}B

${t

he s

tate

s w

hose

cap

ital

s ar

e H

onol

ulu

or T

opek

a}A

$B

"{H

awai

i,K

ansa

s,K

entu

cky}

4.A

${t

he p

osit

ive

inte

ger

fact

ors

of 2

4}A

#B

"{1

,2,3

,4,6

,8}

B $

{the

cou

ntin

g nu

mbe

rs le

ss t

han

10}

A $

B "

{1,2

,3,4

,5,6

,7,8

,9,1

2,24

}

Su

pp

ose

A "

{nu

mbe

rs x

such

th

at x

&3}

,B "

{nu

mbe

rs x

such

as

x'

!1}

,an

d

C "

{nu

mbe

rs x

such

th

at x

(1.

5}.G

rap

h e

ach

of

the

foll

owin

g.

5.A

!B

6.A

"B

7.B

"C

8.B

!C

9.(A

!C

) !

B10

.A !

(B "

C)

!2

!1

!4

!3

01

23

4!

2!

1!

4!

30

12

34

!2

!1

!4

!3

01

23

4!

2!

1!

4!

30

12

34

!2

!1

!4

!3

01

23

4!

2!

1!

4!

30

12

34

Inte

rsec

tion

A !

B

AB

Unio

nA

" B

AB

En

rich

men

t

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2-2

2-2



Ans

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s

Rea

din

g t

o L

earn

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csA

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g an

d S

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1

Lesson 2-2

Pre-

Act

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ow c

an a

nu

mbe

r li

ne

be u

sed

to

show

a f

ootb

all

team

’s p

rogr

ess?

Rea

d th

e in

trod

ucti

on t

o L

esso

n 2-

2 at

the

top

of

page

73

in y

our

text

book

.

Use

pos

itiv

eor

neg

ativ

eto

com

plet

e th

e fo

llow

ing

sent

ence

s.

The

fiv

e-ya

rd p

enal

ty is

sho

wn

by t

he

num

ber

!5.

The

13-

yard

pas

s is

sho

wn

by t

he

num

ber

13.

Read

ing

the

Less

on

1.To

add

tw

o ra

tion

al n

umbe

rs,y

ou c

an u

se a

num

ber

line.

Eac

h nu

mbe

r w

ill b

ere

pres

ente

d by

an

arro

w.

a.W

here

on

the

num

ber

line

does

the

arr

ow f

or t

he f

irst

num

ber

begi

n? a

t 0

b.A

rrow

s fo

r ne

gati

ve n

umbe

rs w

ill p

oint

to

the

(lef

t/ri

ght)

.Arr

ows

for

posi

tive

num

bers

will

poi

nt t

o th

e (l

eft/

righ

t).

2.T

wo

stud

ents

add

ed t

he s

ame

pair

of

rati

onal

num

bers

.Bot

h st

uden

ts g

ot t

he c

orre

ctsu

m.O

ne s

tude

nt u

sed

a nu

mbe

r lin

e.T

he o

ther

stu

dent

use

d ab

solu

te v

alue

.The

n th

eyco

mpa

red

thei

r w

ork.

a.H

ow d

o th

e ar

row

s sh

ow w

hich

num

ber

has

the

grea

ter

abso

lute

val

ue?

The

num

ber

with

the

gre

ater

abs

olut

e va

lue

mat

ches

the

long

er a

rrow

.

b.If

the

long

er a

rrow

poi

nts

to t

he le

ft,t

hen

the

sum

is

(pos

itiv

e/ne

gati

ve).

If t

he lo

nger

arr

ow p

oint

s to

the

rig

ht,t

hen

the

sum

is

(pos

itiv

e/ne

gati

ve).

3.If

tw

o nu

mbe

rs a

re a

ddit

ive

inve

rses

,wha

t m

ust

be t

rue

abou

t th

eir

abso

lute

val

ues?

The

abso

lute

val

ues

of t

he t

wo

num

bers

are

equ

al.

4.W

rite

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u to

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ple

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er:S

ince

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trac

tion

is t

he s

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as a

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g th

e op

posi

te,

you

can

chan

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very

sub

trac

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prob

lem

to

an a

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on p

robl

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you

can

use

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rule

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r ad

ding

rat

iona

l num

bers

to

get

the

final

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wer

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posi

tive

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tive

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tle

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posi

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1

Rou

ndin

g Fr

actio

nsR

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ing

frac

tion

s is

mor

e di

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ult

than

rou

ndin

g w

hole

num

bers

or

de

cim

als.

For

exam

ple,

thin

k ab

out

how

you

wou

ld r

ound

in

ches

to

the

near

est

quar

ter-

inch

.Thr

ough

est

imat

ion,

you

mig

ht r

ealiz

e th

at

is le

ss t

han

.But

,is

it c

lose

r to

or

to

?

Her

e ar

e tw

o w

ays

to r

ound

fra

ctio

ns.E

xam

ple

1 us

es o

nly

the

frac

tion

s;E

xam

ple

2 us

es d

ecim

als.

1 " 41 " 2

1 " 24 " 9

4 " 9

En

rich

men

t

NA

ME

____

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2-2

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Subt

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ctio

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to.

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o .

1 " 24 " 9

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4 " 91 " 2

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frac

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the

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2-4

2-4



Ans

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Lesson 2-4

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top

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sum

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ms

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the

exp

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the

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term

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num

ber

758

repr

esen

ted

on t

he p

lot?

75⏐8

b.E

xpla

in h

ow y

ou k

now

the

re a

re 2

3 nu

mbe

rs in

the

data

.

Ther

e ar

e 23

leav

es.

Hel

ping

You

Rem

embe

r

4.D

escr

ibe

how

you

wou

ld e

xpla

in t

he p

roce

ss o

f fi

ndin

g th

e m

edia

n an

d m

ode

from

ast

em-a

nd-l

eaf

plot

to

a fr

iend

who

mis

sed

Les

son

2-5.

Sam

ple

answ

er:T

o fin

d th

e m

edia

n,co

unt

the

num

ber

of le

aves

,the

nfin

d th

e nu

mbe

r in

the

mid

dle.

To f

ind

the

mod

e,id

entif

y th

e le

af t

hat

occu

rs m

ost

freq

uent

ly a

nd u

se t

he s

tem

and

key

to

iden

tify

the

data

num

ber.

Ste

m|L

eaf

72|0

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25

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s C

reat

ed

In T

he 1

978

Bil

l Ja

mes

Bas

ebal

l Abs

trac

t,th

e au

thor

intr

oduc

ed t

he “

runs

cre

ated

”fo

rmul

a.

R$

whe

re f

or e

ach

play

erh

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mbe

r of

hit

s

w$

num

ber

of w

alks

,

t$

num

ber

of t

otal

bas

es,

b$

num

ber

of a

t-ba

ts,a

nd

R$

appr

oxim

ate

num

ber

of r

uns

a te

am

scor

es d

ue t

o th

is p

laye

r’s a

ctio

ns

1.A

s of

Jun

e 29

,200

1,R

ober

to A

lom

ar o

f th

e C

leve

land

Ind

ians

and

Sea

ttle

Mar

iner

spl

ayer

Ich

iro

Suzu

ki w

ere

tied

wit

h th

e hi

ghes

t A

mer

ican

Lea

gue

batt

ing

aver

age

at.3

51.F

ind

the

num

ber

of r

uns

crea

ted

by e

ach

play

er u

sing

the

dat

a be

low

.

hw

tb

Run

s C

reat

ed

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mar

9737

145

276

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Suz

uki

121

1315

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Bas

ed o

n th

is in

form

atio

n,w

ho d

o yo

u th

ink

is t

he m

ore

valu

able

Am

eric

an L

eagu

epl

ayer

? W

hy?

Sam

ple

answ

er:A

lom

ar,b

ecau

se h

e cr

eate

s m

ore

runs

.

2.C

arlo

s L

ee o

f th

e C

hica

go W

hite

Sox

and

New

Yor

k Ya

nkee

Ber

nie

Will

iam

s w

ere

both

batt

ing

.314

.Fin

d th

e nu

mbe

r of

run

s cr

eate

d by

eac

h pl

ayer

usi

ng t

he d

ata

belo

w.

hw

tb

Run

s C

reat

ed

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8113

141

258

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iam

s74

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hy w

ould

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ebal

l tea

ms

wan

t to

cal

cula

te t

he n

umbe

r of

run

s cr

eate

d by

eac

h of

the

irpl

ayer

s?

Sam

ple

answ

er:T

o he

lp m

ake

deci

sion

s ab

out

star

ting

line-

ups;

To h

elp

mak

e de

cisi

ons

abou

t tr

adin

g pl

ayer

s.

(h+

w)t

# (b+

w)En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-5

2-5



Ans

wer

s

Stu

dy

Gu

ide

and I

nte

rven

tion

Pro

babi

lity:

Sim

ple

Pro

babi

lity

and

Odd

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

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RIO

D__

___

2-6

2-6

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cGra

w-H

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5G

lenc

oe A

lgeb

ra 1

Lesson 2-6

Prob

abili

tyT

he p

roba

bili

tyof

a s

imp

le e

ven

tis

a r

atio

tha

t te

lls h

ow li

kely

it is

tha

tth

e ev

ent

will

tak

e pl

ace.

It is

the

rat

io o

f th

e nu

mbe

r of

fav

orab

le o

utco

mes

of

the

even

t to

the

num

ber

of p

ossi

ble

outc

omes

of

the

even

t.Yo

u ca

n ex

pres

s th

e pr

obab

ility

eit

her

as a

frac

tion

,as

a de

cim

al,o

r as

a p

erce

nt.

Pro

babi

lity

of a

Sim

ple

Eve

ntF

or a

n ev

ent a

, P(a

) $

.nu

mbe

r of

favo

rabl

e ou

tcom

es#

##

#nu

mbe

r of

pos

sibl

e ou

tcom

es

Mr.

Bab

cock

ch

oose

s 5

out

of 2

5 st

ud

ents

in

his

alg

ebra

cla

ssat

ran

dom

for

a s

pec

ial

pro

ject

.Wh

at i

sth

e p

roba

bili

ty o

f be

ing

chos

en?

P(b

eing

cho

sen)

$

The

pro

babi

lity

of b

eing

cho

sen

is

or

.1 # 5

5 # 25

num

ber

of s

tude

nts

chos

en#

##

#to

tal n

umbe

r of

stu

dent

s

A b

owl

con

tain

s 3

pea

rs,

4 ba

nan

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

babi

lity

th

at i

t is

not

a ba

nan

a?

The

re a

re 3

"4

"2

or 9

pie

ces

of f

ruit

.T

here

are

3 "

2 or

5 p

iece

s of

fru

it t

hat

are

not

bana

nas.

P(n

ot b

anan

a)$ $

The

pro

babi

lity

of n

otch

oosi

ng a

ban

ana

is.

5 # 9

5 # 9num

ber

of o

ther

pie

ces

of f

ruit

##

##

tota

l num

ber

of p

iece

s of

fru

it

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

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k o

f 52

car

ds.

Det

erm

ine

each

pro

babi

lity

.

1.P

(10)

2.P

(red

2)

3.P

(kin

g or

que

en)

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

babi

lity

.

7.P

(sum

is 1

)0

8.P

(sum

is 6

)9.

P(s

um is

less

tha

n 4)

10.P

(sum

is g

reat

er t

han

11)

11.P

(sum

is le

ss t

han

15)

12.P

(sum

is g

reat

er t

han

8)

1

A b

owl

con

tain

s 4

red

ch

ips,

3 bl

ue

chip

s,an

d 8

gre

en c

hip

s.Yo

u c

hoo

se o

ne

chip

at r

and

om.F

ind

eac

h p

roba

bili

ty.

13.P

(not

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ed c

hip)

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(red

or

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chi

p)15

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ot a

gre

en c

hip)

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um

ber

is s

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ted

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ran

dom

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m t

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list

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2,3,

…,1

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ind

eac

h p

roba

bili

ty.

16.P

(eve

n nu

mbe

r)17

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ulti

ple

of 3

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ess

than

4)

19.A

com

pute

r ra

ndom

ly c

hoos

es a

lett

er f

rom

the

wor

d C

OM

PU

TE

R.F

ind

the

prob

abili

tyth

at t

he le

tter

is 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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w-H

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6G

lenc

oe A

lgeb

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Odd

sT

he o

dds

of a

n ev

ent

occu

rrin

g is

the

rat

io o

f th

e nu

mbe

r of

way

s an

eve

nt c

an o

ccur

(suc

cess

es)

to t

he n

umbe

r of

way

s th

e ev

ent

cann

ot o

ccur

(fa

ilure

s).

Odd

s

A d

ie i

s ro

lled

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d t

he

odd

s of

rol

lin

g a

nu

mbe

r gr

eate

r th

an 4

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sam

ple

spac

e is

{1,

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4,5,

6}.T

here

fore

,the

re a

re s

ix p

ossi

ble

outc

omes

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ce 5

and

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e th

e on

ly n

umbe

rs g

reat

er t

han

4,tw

o ou

tcom

es a

re s

ucce

sses

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fou

r ar

e fa

ilure

s.

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dds

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ollin

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num

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grea

ter

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,o

r 1:

2.

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d t

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odd

s of

eac

h o

utc

ome

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he

spin

ner

at

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t is

sp

un

on

ce.

1.m

ulti

ple

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2.od

d nu

mbe

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1

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en o

r a

53:

24.

less

tha

n 4

3:7

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en n

umbe

r gr

eate

r th

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Fin

d t

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odd

s of

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h o

utc

ome

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pu

ter

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hoo

ses

a n

um

ber

betw

een

1 an

d 2

0.

6.th

e nu

mbe

r is

less

tha

n 10

9:11

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e nu

mbe

r is

a m

ulti

ple

of 4

1:3

8.th

e nu

mbe

r is

eve

n1:

19.

the

num

ber

is a

one

-dig

it n

umbe

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

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10.F

ind

the

odds

tha

t a

dim

e w

ill n

ot b

e ch

osen

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:3

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hat

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the

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sing

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uart

er if

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dim

es a

re r

emov

ed?

2:9

12.W

hat

are

the

odds

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choo

sing

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enny

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9

Su

pp

ose

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dro

p a

ch

ip o

nto

th

e gr

id a

t th

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ght.

Fin

d t

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odd

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h o

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ome.

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and

on a

sha

ded

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re1:

1

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and

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are

on t

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iago

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and

on s

quar

e nu

mbe

r 16

1:15

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and

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num

ber

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ter

than

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and

on a

mul

tipl

e of

53:

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

##

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mbe

r of

failu

res

Stu

dy

Gu

ide

and I

nte

rven

tion

(c

onti

nued

)

Pro

babi

lity:

Sim

ple

Pro

babi

lity

and

Odd

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-6

2-6

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Skil

ls P

ract

ice

Pro

babi

lity:

Sim

ple

Pro

babi

lity

and

Odd

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-6

2-6

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lenc

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w-H

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7G

lenc

oe A

lgeb

ra 1

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

roba

bili

ty.

1.P

(blu

e)&

33%

2.P

(gre

en)

&23

%

3.P

(yel

low

or

gree

n)"

50%

4.P

(blu

e or

yel

low

)"

60%

5.P

(not

red

)&

83%

6.P

(not

blu

e)&

67%

Fin

d t

he

pro

babi

lity

of

each

ou

tcom

e if

th

e sp

inn

er i

s sp

un

on

ce.

7.P

(mul

tipl

e of

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 bo

rn i

n t

he

mon

th o

f Ju

ne.

Fin

d e

ach

pro

babi

lity

.

11.P

(dat

e is

a m

ulti

ple

of 6

)12

.P(d

ate

is b

efor

e Ju

ne 1

5)

&17

%&

47%

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June

7 o

r af

ter

June

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er J

une

5)

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%&

17%

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d t

he

odd

s of

eac

h o

utc

ome

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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.

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he le

tter

f2

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:816

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tter

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1

CL

AS

S S

CH

ED

UL

ES

For

Exe

rcis

es 1

9–22

,use

th

e fo

llow

ing

info

rmat

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.

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tude

nt c

an s

elec

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the

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hysi

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in jo

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ma.

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tude

nt f

orge

ts t

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tive

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sch

ool a

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t ra

ndom

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he c

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ompu

ter

prog

ram

min

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:20

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he c

lass

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ram

a.6

:22

or 3

:11

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he c

lass

is n

ot p

hysi

cal e

duca

tion

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:5

22.T

he c

lass

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ot a

rt.

24:4

or

6:1

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7 # 151 # 6

7 # 85 # 8

3 # 41 # 4

18

45

63

72

2 # 35 # 6

3 # 51 # 2

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w-H

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8G

lenc

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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

roba

bili

ty.

1.P

(bro

wn)

&36

%2.

P(g

reen

)&

14%

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(blu

e or

yel

low

)"

50%

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(not

yel

low

)&

81%

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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

babi

lity

.

5.P

(hea

rt)

"25

%6.

P(b

lack

car

d)"

50%

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(jack

)&

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

babi

lity

.

9.P

(sum

less

tha

n 6)

&28

%10

.P(s

um le

ss t

han

2)0

"0%

11.P

(sum

gre

ater

tha

n 10

)&

8%12

.P(s

um 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

ako

ta.

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he le

tter

d3

:21

or 1

:714

.the

lett

er a

4:2

0 or

1:5

15.t

he le

tter

h2

:22

or 1

:11

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con

sona

nt16

:8 o

r 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.

Stud

ents

in a

bio

logy

cla

ss c

an c

hoos

e a

sem

este

r pr

ojec

t fr

om t

he f

ollo

win

g lis

t:an

imal

beha

vior

(4)

,cel

lula

r pr

oces

ses

(2),

ecol

ogy

(6),

heal

th (

7),a

nd p

hysi

olog

y (3

).F

ind

each

of

the

odds

if a

stu

dent

sel

ects

a t

opic

at

rand

om.

17.t

he t

opic

is e

colo

gy6

:16

or 3

:8

18.t

he t

opic

is a

nim

al b

ehav

ior

4:1

8 or

2:9

19.t

he t

opic

is n

ot c

ellu

lar

proc

esse

s20

:2 o

r 10

:1

20.t

he t

opic

is n

ot h

ealt

h15

: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

sur

veye

d st

uden

ts in

gra

des

9–12

on

whe

ther

to

ch

ange

the

tim

e sc

hool

beg

ins.

One

stu

dent

will

be

sele

cted

at

rand

om t

o be

inte

rvie

wed

on

the

even

ing

new

s.T

he t

able

giv

es

the

resu

lts.

21.W

hat

is t

he p

roba

bilit

y th

e st

uden

t se

lect

ed w

ill b

e in

the

9th

grad

e?"

32%

22.W

hat

are

the

odds

the

stu

dent

sel

ecte

d w

ants

no

chan

ge?

16:3

4 or

8:1

7

8 # 25

Gra

de9

1011

12

No

chan

ge6

25

3

Hou

r la

ter

107

98

1 # 61 # 12

5 # 18

1 # 261 # 13

1 # 21 # 4

17 # 211 # 2

1 # 75 # 14

Pra

ctic

e (A

vera

ge)

Pro

babi

lity:

Sim

ple

Pro

babi

lity

and

Odd

s

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-6

2-6



Ans

wer

s

Rea

din

g t

o L

earn

Math

emati

csP

roba

bilit

y:S

impl

e P

roba

bilit

y an

d O

dds

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-6

2-6

©G

lenc

oe/M

cGra

w-H

ill10

9G

lenc

oe A

lgeb

ra 1

Lesson 2-6

Pre-

Act

ivit

yW

hy

is p

roba

bili

ty i

mp

orta

nt

in s

por

ts?

Rea

d th

e in

trod

ucti

on t

o L

esso

n 2-

6 at

the

top

of

page

96

in y

our

text

book

.

Loo

k up

the

def

init

ion

of t

he w

ord

prob

abil

ity

in a

dic

tion

ary.

Rew

rite

the

defi

niti

on in

you

r ow

n w

ords

.

Sam

ple

answ

er:t

he li

kelih

ood

of s

omet

hing

hap

peni

ng

Read

ing

the

Less

on

1.W

rite

whe

ther

eac

h st

atem

ent

is t

rue

or fa

lse.

If fa

lse,

repl

ace

the

unde

rlin

ed w

ord

ornu

mbe

r to

mak

e a

true

sta

tem

ent.

a.P

roba

bilit

y ca

n be

wri

tten

as

a fr

acti

on,a

dec

imal

,or

a pe

rcen

t.tr

ue

b.T

he s

ampl

e sp

ace

of f

lippi

ng o

ne c

oin

is h

eads

or

tails

.tr

ue

c.T

he p

roba

bilit

y of

an

impo

ssib

le e

vent

is 1

.fa

lse;

0

d.T

he o

dds

agai

nst

an e

vent

occ

urri

ng a

re t

he o

dds

that

the

eve

nt w

ill o

ccur

.fa

lse;

will

not

2.E

xpla

in w

hy t

he p

roba

bilit

y of

an

even

t ca

nnot

be

grea

ter

than

1 w

hile

the

odd

s of

an

even

t ca

n be

gre

ater

tha

n 1.

Sam

ple

answ

er:T

o fin

d th

e pr

obab

ility

of

an e

vent

,you

com

pare

a p

art

ofth

e sa

mpl

e sp

ace

to t

he w

hole

sam

ple

spac

e.W

hen

you

find

the

odds

of

an e

vent

,you

com

pare

the

num

ber

of f

avor

able

out

com

es t

o th

e nu

mbe

rof

unf

avor

able

out

com

es.I

n so

me

situ

atio

ns,t

here

may

be

mor

efa

vora

ble

than

unf

avor

able

out

com

es.

Hel

ping

You

Rem

embe

r

3.P

roba

bilit

ies

are

usua

lly w

ritt

en a

s fr

acti

ons,

deci

mal

s,or

per

cent

s.O

dds

are

usua

llyw

ritt

en w

ith

a co

lon

(for

exa

mpl

e,1:

3).H

ow c

an t

he s

pelli

ng o

f th

e w

ord

colo

nhe

lpre

mem

ber

this

?

Sam

ple

answ

er:T

he w

ord

colo

nha

s th

e le

tter

“o”

as it

s on

ly v

owel

,and

the

wor

d od

dsal

so h

as t

he le

tter

“o”

as it

s on

ly v

owel

.

©G

lenc

oe/M

cGra

w-H

ill11

0G

lenc

oe A

lgeb

ra 1

Geo

met

ric

Pro

babi

lity

If a

dar

t,th

row

n at

ran

dom

,hit

s th

e tr

iang

ular

boa

rd s

how

n at

the

ri

ght,

wha

t is

the

pro

babi

lity

that

it w

ill h

it t

he s

hade

d re

gion

? T

his

can

be d

eter

min

ed b

y co

mpa

ring

the

are

a of

the

sha

ded

regi

on t

o th

ear

ea o

f th

e en

tire

boa

rd.T

his

rati

o in

dica

tes

wha

t fr

acti

on o

f th

e to

sses

sho

uld

hit

in t

he s

hade

d re

gion

. ! !or

In g

ener

al,i

f Sis

a s

ubre

gion

of

som

e re

gion

R,t

hen

the

prob

abili

ty,P

(S),

that

a p

oint

,ch

osen

at

rand

om,b

elon

gs t

o su

breg

ion

Sis

giv

en b

y th

e fo

llow

ing:

P(S

) !

Fin

d t

he

pro

babi

lity

th

at a

poi

nt,

chos

en a

t ra

nd

om,b

elon

gs t

o th

e sh

aded

subr

egio

ns

of t

he

foll

owin

g fi

gure

s.

1.2.

3.

4.5.

6.

7.8.

9.3 ! 4

2 2

44

" ! 4

8

4

" ! 44 4

44

2 ! 36 6

66

66

6!"3

6!"3

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"4

5 5

55

55

1 ! 2

6

6

4

" ! 4

4

44

45 ! 9

644

46

6

1 ! 23

3

5 5

area

of

subr

egio

n S

""

"ar

ea o

r re

gion

R

1 " 212 " 24"1 2" (

4)(6

)" "1 2" (

8)(6

)

area

of

shad

ed r

egio

n"

""

area

of

tria

ngul

ar b

oard

6

44

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-6

2-6



Stu

dy

Gu

ide

and I

nte

rven

tion

Squ

are

Roo

ts a

nd R

eal N

umbe

rs

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-7

2-7

©G

lenc

oe/M

cGra

w-H

ill11

1G

lenc

oe A

lgeb

ra 1

Lesson 2-7

Squa

re R

oots

A s

quar

e ro

otis

one

of

two

equa

l fac

tors

of

a nu

mbe

r.Fo

r ex

ampl

e,th

esq

uare

roo

ts o

f 36

are

6 a

nd !

6,si

nce

6 %

6 or

62

is 3

6 an

d (!

6)(!

6) o

r (!

6)2

is a

lso

36.A

rati

onal

num

ber

like

36,w

hose

squ

are

root

is a

rat

iona

l num

ber,

is c

alle

d a

per

fect

squ

are.

The

sym

bol &

'is

a r

adic

al s

ign

.It

indi

cate

s th

e no

nneg

ativ

e,or

pri

nci

pal

,squ

are

root

of

the

num

ber

unde

r th

e ra

dica

l sig

n.So

&36%

$6

and

!&

36%$

!6.

The

sym

bol (

&36%

repr

esen

ts b

oth

squa

re r

oots

.

Fin

d !'(

.

!()

repr

esen

ts t

he n

egat

ive

squa

re r

oot

of

.

$#

$2→

!()

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5 # 725 # 49

5 # 725 # 49

25 # 4925 # 49

25 # 49F

ind

-)

0.16

#.

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0.16

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pres

ents

the

pos

itiv

e an

dne

gati

ve s

quar

e ro

ots

of 0

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0.16

$0.

42an

d 0.

16 $

(!0.

4)2

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0.16

%$

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4

Exam

ple1

Exam

ple1

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ple2

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ple2

Exer

cises

Exer

cises

Fin

d e

ach

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root

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64%8

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16 # 7

36 # 496 # 7

144

# 196

11 # 1012

1# 10

05 # 4

25 # 165 # 12

25 # 144

2 # 54 # 25

©G

lenc

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w-H

ill11

2G

lenc

oe A

lgeb

ra 1

Clas

sify

and

Ord

er N

umbe

rsN

umbe

r su

ch a

s &

2%an

d &

3%ar

e no

t pe

rfec

t sq

uare

s.N

otic

e w

hat

happ

ens

whe

n yo

u fi

nd t

hese

squ

are

root

s w

ith

your

cal

cula

tor.

The

num

bers

cont

inue

inde

fini

tely

wit

hout

any

pat

tern

of

repe

atin

g di

gits

.Num

bers

tha

t ca

nnot

be

wri

tten

as

a te

rmin

atin

g or

rep

eati

ng d

ecim

al a

re c

alle

d ir

rati

onal

nu

mbe

rs.T

he s

et o

fre

al n

um

bers

cons

ists

of

the

set

of ir

rati

onal

num

bers

and

the

set

of

rati

onal

num

bers

toge

ther

.The

cha

rt b

elow

illu

stra

tes

the

vari

ous

kind

s of

rea

l num

bers

.

Nat

ural

Num

bers

{1, 2

, 3, 4

, …}

Who

le N

umbe

rs{0

, 1, 2

, 3, 4

, …}

Inte

gers

{…, !

3, !

2, !

1, 0

, 1, 2

, 3, …

}

Rat

iona

l Num

bers

{all

num

bers

that

can

be

expr

esse

d in

the

form

, w

here

aan

d b

are

inte

gers

and

b)

0}

Irra

tiona

l Num

bers

{all

num

bers

that

can

not b

e ex

pres

sed

in th

e fo

rm

, whe

re a

and

bar

e in

tege

rs a

nd b

)0}

Nam

e th

e se

t or

set

s of

nu

mbe

rs t

o w

hic

h e

ach

rea

l n

um

ber

belo

ngs

.

a.B

ecau

se 4

and

11

are

inte

gers

,thi

s nu

mbe

r is

a r

atio

nal n

umbe

r.

b.)

81#B

ecau

se &

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r is

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atur

al n

umbe

r,a

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le n

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ger,

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a ra

tion

al n

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c.)

32#B

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se &

32%$

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249…

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ch is

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ting

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term

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ing

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mal

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umbe

r is

irra

tion

al.

Nam

e th

e se

t or

set

s of

nu

mbe

rs t

o w

hic

h e

ach

rea

l n

um

ber

belo

ngs

.

1.2.

!3.

4.&

54%na

tura

l,w

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ratio

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145

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25%7.

0.62

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natu

ral,

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le,

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Wri

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ach

set

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7 # 43 # 4

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2 # 36 # 7

84 # 124 # 11

a # b

a # b

Stu

dy

Gu

ide

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nte

rven

tion

(c

onti

nued

)

Squ

are

Roo

ts a

nd R

eal N

umbe

rs

NA

ME

____

____

____

____

____

____

____

____

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____

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ATE

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____

PE

RIO

D__

___

2-7

2-7

Exam

ple

Exam

ple

Exer

cises

Exer

cises



Ans

wer

s

Skil

ls P

ract

ice

Squ

are

Roo

ts a

nd R

eal N

umbe

rs

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-7

2-7

©G

lenc

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cGra

w-H

ill11

3G

lenc

oe A

lgeb

ra 1

Lesson 2-7

Fin

d e

ach

squ

are

root

.If

nec

essa

ry,r

oun

d t

o th

e n

eare

st h

un

dre

dth

.

1.&

144

%12

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25%

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54.

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126.

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1.5

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e th

e se

t or

set

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rs t

o w

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l n

um

ber

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ngs

.

7.!

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ger,

ratio

nal

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nal

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29%10

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4G

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Fin

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ach

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nec

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d t

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e th

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o w

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l n

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xpla

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you

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abou

t 14

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iles

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tney

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feet

.

22.S

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eter

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eed

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tsu

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i.If

an

eart

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ccur

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a d

epth

of

200

met

ers,

wha

t is

the

spe

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f th

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i gen

erat

edby

the

ear

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ake?

abou

t 43

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ract

ice

(Ave

rage

)

Squ

are

Roo

ts a

nd R

eal N

umbe

rs

NA

ME

____

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ATE

____

____

____

PE

RIO

D__

___

2-7

2-7



Rea

din

g t

o L

earn

Math

emati

csS

quar

e R

oots

and

Rea

l Num

bers

NA

ME

____

____

____

____

____

____

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__D

ATE

____

____

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RIO

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2-7

2-7

©G

lenc

oe/M

cGra

w-H

ill11

5G

lenc

oe A

lgeb

ra 1

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

ucti

on t

o L

esso

n 2-

7 at

the

top

of

page

103

in y

our

text

book

.

The

exp

ress

ion

&36

00%

is r

ead,

“the

squ

are

root

of

3600

.”H

ow w

ould

you

read

the

exp

ress

ion

&64%

?

the

squa

re r

oot

of 6

4

Read

ing

the

Less

on

Com

ple

te e

ach

sta

tem

ent

belo

w.

1.T

he s

ymbo

l &'

is c

alle

d a

and

is u

sed

to in

dica

te a

nonn

egat

ive

or p

rinc

ipal

squ

are

root

of

the

expr

essi

on u

nder

the

sym

bol.

2.A

of

an

irra

tion

al n

umbe

r is

a r

atio

nal n

umbe

r th

at is

clo

seto

,but

not

equ

al t

o,th

e va

lue

of t

he ir

rati

onal

num

ber.

3.T

he p

osit

ive

squa

re r

oot

of a

num

ber

is c

alle

d th

e sq

uare

root

of

the

num

ber.

4.A

num

ber

who

se p

osit

ive

squa

re r

oot

is a

rat

iona

l num

ber

is a

.

5.W

rite

eac

h of

the

fol

low

ing

as a

mat

hem

atic

al e

xpre

ssio

n th

at u

ses

the

&'

sym

bol.

a.th

e po

siti

ve s

quar

e ro

ot o

f 16

00)

1600

#b.

the

nega

tive

squ

are

root

of

729

!)

729

#c.

the

prin

cipa

l squ

are

root

of

3025

)30

25#

6.T

he ir

rati

onal

num

bers

and

rat

iona

l num

bers

tog

ethe

r fo

rm t

he s

et o

f nu

mbe

rs.

Hel

ping

You

Rem

embe

r

7.U

se a

dic

tion

ary

to lo

ok u

p se

vera

l wor

ds t

hat

begi

n w

ith

“ir-

”.W

hat

does

the

pre

fix

“ir-

”m

ean?

How

can

thi

s he

lp y

ou r

emem

ber

the

mea

ning

of

the

wor

d ir

rati

onal

?

Sam

ple

answ

er:T

he p

refix

“ir

-”m

eans

not

.So

an ir

ratio

nal n

umbe

r is

anu

mbe

r th

at is

not

a r

atio

nal n

umbe

r.

real

perf

ect

squa

re

prin

cipa

l

ratio

nal a

ppro

xim

atio

n

radi

cal s

ign

©G

lenc

oe/M

cGra

w-H

ill11

6G

lenc

oe A

lgeb

ra 1

Sca

le D

raw

ings

The

map

at

the

left

bel

ow s

how

s bu

ildin

g lo

ts f

or s

ale.

The

sca

le r

atio

is 1

:240

0.A

t th

e ri

ght

belo

w is

the

flo

or p

lan

for

a tw

o-be

droo

map

artm

ent.

The

leng

th o

f th

e liv

ing

room

is 6

m.O

n th

e pl

an t

heliv

ing

room

is 6

cm

long

.

An

swer

eac

h q

ues

tion

.

1.O

n th

e m

ap,h

ow m

any

feet

are

rep

rese

nted

by

an in

ch?

200

ft

2.O

n th

e m

ap,m

easu

re t

he f

ront

age

of L

ot 2

on

Sylv

an R

oad

in in

ches

.Wha

t is

the

act

ual

fron

tage

in f

eet?

200

ft

3.W

hat

is t

he s

cale

rat

io r

epre

sent

ed o

n th

e fl

oor

plan

?1

:100

4.O

n th

e fl

oor

plan

,mea

sure

the

wid

th o

f th

e liv

ing

room

in c

enti

met

ers.

Wha

t is

the

actu

al w

idth

in m

eter

s?4

m

5.A

bout

how

man

y sq

uare

met

ers

of c

arpe

ting

wou

ld b

e ne

eded

to

carp

et t

he li

ving

roo

m?

24 m

2

6.M

ake

a sc

ale

draw

ing

of y

our

clas

sroo

m u

sing

an

appr

opri

ate

scal

e.A

nsw

ers

will

var

y.

7.U

se y

our

scal

e dr

awin

g to

det

erm

ine

how

man

y sq

uare

met

ers

of t

ile w

ould

be

need

ed t

oin

stal

l a n

ew f

loor

in y

our

clas

sroo

m.

Ans

wer

s w

ill v

ary.

Clos

et

Clos

et

Clos

et

Clos

et

Kitc

hen

Bedr

oom

Bedr

oom

Bath

Dini

ng A

rea

Livi

ng R

oom

Lot 3

Lot 2

Lot 1

Sunshine Lake

Sylvan Road

En

rich

men

t

NA

ME

____

____

____

____

____

____

____

____

____

____

____

__D

ATE

____

____

____

PE

RIO

D__

___

2-7

2-7


Documents

Chapter 2 Resource Masters - Math Class · ©Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using the Chapter 2 Resource Masters The Fast File Chapter Resource system