Chapter 2 Resource Masters...©Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using...
Transcript of Chapter 2 Resource Masters...©Glencoe/McGraw-Hill iv Glencoe Algebra 1 Teacher’s Guide to Using...
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 2-2Study Guide and Intervention . . . . . . . . . 81–82Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 83Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Reading to Learn Mathematics . . . . . . . . . . . 85Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Lesson 2-3Study Guide and Intervention . . . . . . . . . 87–88Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 89Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Reading to Learn Mathematics . . . . . . . . . . . 91Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Lesson 2-4Study Guide and Intervention . . . . . . . . . 93–94Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 95Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Reading to Learn Mathematics . . . . . . . . . . . 97Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Lesson 2-5Study Guide and Intervention . . . . . . . . 99–100Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 101Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Reading to Learn Mathematics . . . . . . . . . . 103Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 104
Lesson 2-6Study Guide and Intervention . . . . . . . . 105–106Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 107Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Reading to Learn Mathematics . . . . . . . . . . 109Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 110
Lesson 2-7Study Guide and Intervention . . . . . . . . 111–112Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 113Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Reading to Learn Mathematics . . . . . . . . . . 115Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 116
Chapter 2 AssessmentChapter 2 Test, Form 1 . . . . . . . . . . . . 117–118Chapter 2 Test, Form 2A . . . . . . . . . . . 119–120Chapter 2 Test, Form 2B . . . . . . . . . . . 121–122Chapter 2 Test, Form 2C . . . . . . . . . . . 123–124Chapter 2 Test, Form 2D . . . . . . . . . . . 125–126Chapter 2 Test, Form 3 . . . . . . . . . . . . 127–128Chapter 2 Open-Ended Assessment . . . . . . 129Chapter 2 Vocabulary Test/Review . . . . . . . 130Chapter 2 Quizzes 1 & 2 . . . . . . . . . . . . . . . 131Chapter 2 Quizzes 3 & 4 . . . . . . . . . . . . . . . 132Chapter 2 Mid-Chapter Test . . . . . . . . . . . . 133Chapter 2 Cumulative Review . . . . . . . . . . . 134Chapter 2 Standardized Test Practice . . 135–136
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A32
© Glencoe/McGraw-Hill iv Glencoe Algebra 1
Teacher’s Guide to Using theChapter 2 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 2 Resource Masters includes the core materials neededfor Chapter 2. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 2-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 1
Assessment OptionsThe assessment masters in the Chapter 2Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 116–117. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
22
© Glencoe/McGraw-Hill vii Glencoe Algebra 1
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 2.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
absolute value
additive inverses
A·duh·tihv
equally likely
frequency
integers
irrational number
ih·RA·shuh·nuhl
line plot
measures of central tendency
natural number
odds
(continued on the next page)
© Glencoe/McGraw-Hill viii Glencoe Algebra 1
Vocabulary Term Found on Page Definition/Description/Example
opposites
perfect square
principal square root
probability
PRAH·buh·BIH·luh·tee
rational number
RA·shuh·nuhl
real number
sample space
simple event
square root
stem-and-leaf plot
whole number
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
22
Study Guide and InterventionRational Numbers on the Number Line
NAME ______________________________________________ DATE ____________ PERIOD _____
2-12-1
© Glencoe/McGraw-Hill 75 Glencoe Algebra 1
Less
on
2-1
Graph Rational Numbers The figure at the right is part of a number line. A number line can be used to show the sets of natural numbers, whole numbers, and integers. Positive numbers, are located to the right of 0,and negative numbers are located to the left of 0.
Another set of numbers that you can display on a number line is the set of rational numbers. A rational number can
be written as , where a and b are integers and b � 0. Some
examples of rational numbers are , , , and .12��3
�7��8
�3�5
1�4
a�b
10�1�2�3�4 2 3
Natural Numbers
Positive NumbersNegative Numbers
4
Whole Numbers
Integers
Name the coordinates of thepoints graphed on each number line.
a.
The dots indicate each point on the graph.The coordinates are {�3, �1, 1, 3, 5}
b.
The bold arrow to the right means the graphcontinues indefinitely in that direction. Thecoordinates are {2, 2.5, 3, 3.5, 4, 4.5, 5, …}.
32.521.51 3.5 4 4.5 5
10�1�2�3 2 3 4 5
Graph each set ofnumbers.
a. {…, �3, �2, �1, 0, 1, 2}
b. �� , 0, , �12–
31–30�1–
3�2–3
4–3
5–3 2
2�3
1�3
1�3
10�1�2�3�4 2 3 4
Example 1Example 1 Example 2Example 2
ExercisesExercises
Name the coordinates of the points graphed on each number line.
1. 2.
3. 4.
Graph each set of numbers.
5. {�3, �1, 1, 3} 6. {�5, �2, 1, 2} 7. {integers less than 0}
8. {…, �2, �1, 0, 1} 9. ��2 , �1 , � , � 10. {…, �4, �2, 0, 2, …}
�3�4�5�6 �2 �1 0 1 2�21–2�3 �2�11–
2�1 �1–2 0 1–
2 1�3�4 �2 �1 0 1 2 3 4
1�2
1�2
1�2
1�2
�3�4 �2 �1 0 1 2 3 4�3�4�5 �2 �1 0 1 2 3�3�4 �2 �1 0 1 2 3 4
�3�4 �2 �1 0 1 2 3 4�1–4�1–
2 0 1–4
1–2
3–4 1 5–
43–2
0�1 1 2 3 4 5 6 70�1�2 1 2 3 4 5 6
© Glencoe/McGraw-Hill 76 Glencoe Algebra 1
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.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each absolute value.
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
© Glencoe/McGraw-Hill 77 Glencoe Algebra 1
Less
on
2-1
Name the coordinates of the points graphed on each number line.
1. 2.
3. 4.
Graph each set of numbers.
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}
Find each absolute value.
11. �9 12. 15 13. �30
14. � 15. 2.4 16. Evaluate each expression if a � 3, b � �10, c � , x � 9, y � 1.5, and z � 12.
17. 26 � x � 6 18. 11 � 10 � x
19. 12 � a � 5 20. a � 20 � 4
21. 4.5 � y 22. z � 7 � 5
23. 14 � b 24. b � 2
25. c � � 2 26. 9 � 3.5 � y1�2
1�2
9�11
5�7
�3 �2 �1 0 1 2�1 �1–2 0 1–
2 1 3–2 2 5–
2 3 7–2 4
5�2
1�2
1�2
�1 0 1 2 3 4 5 6 7 8 9�10 �9 �8 �7 �6 �5 �4 �3 �2 �1 0
�5�6�7�8�9�10 �4 �3 �2 �1 0�5�6�7�8 �4 �3 �2 �1 0 1 2
1.41.31.21.11.0 1.5 1.6 1.7 1.8 1.9 2.03210�1�2�3 4 5 6 7
10�1�2�3�4�5�6�7 2 310�1�2�3�4�5�6 2 3 4
© Glencoe/McGraw-Hill 78 Glencoe Algebra 1
Name the coordinates of the points graphed on each number line.
1. 2.
Graph each set of numbers.
3. �…, � , � , �1, � , � � 4. {integers less than �4 or greater than 2}
Find each absolute value.
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
© Glencoe/McGraw-Hill 79 Glencoe Algebra 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
© Glencoe/McGraw-Hill 80 Glencoe Algebra 1
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
© Glencoe/McGraw-Hill 81 Glencoe Algebra 1
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
Example 1Example 1 Example 2Example 2
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
© Glencoe/McGraw-Hill 82 Glencoe Algebra 1
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
Study Guide and Intervention (continued)
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
© Glencoe/McGraw-Hill 83 Glencoe Algebra 1
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
Find each difference.
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
© Glencoe/McGraw-Hill 84 Glencoe Algebra 1
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. � �� �
Find each difference.
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
© Glencoe/McGraw-Hill 85 Glencoe Algebra 1
Less
on
2-2
Pre-Activity How can a number line be used to show a football team’s progress?
Read the introduction to Lesson 2-2 at the top of page 73 in your textbook.
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
Helping You Remember
5. Explain why knowing the rules for adding rational numbers can help you to subtractrational numbers.
© Glencoe/McGraw-Hill 86 Glencoe Algebra 1
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
Example 1Example 1 Example 2Example 2
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
© Glencoe/McGraw-Hill 87 Glencoe Algebra 1
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.
Example 1Example 1 Example 2Example 2
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)
© Glencoe/McGraw-Hill 88 Glencoe Algebra 1
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.
Study Guide and Intervention (continued)
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
Example 1Example 1 Example 2Example 2
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
© Glencoe/McGraw-Hill 89 Glencoe Algebra 1
Less
on
2-3
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)
Simplify each expression.
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?
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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
© Glencoe/McGraw-Hill 90 Glencoe Algebra 1
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)
Simplify each expression.
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
© Glencoe/McGraw-Hill 91 Glencoe Algebra 1
Less
on
2-3
Pre-Activity How do consumers use multiplication of rational numbers?
Read the introduction to Lesson 2-3 at the top of page 79 in your textbook.
• 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.
Helping You Remember
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.
© Glencoe/McGraw-Hill 92 Glencoe Algebra 1
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
© Glencoe/McGraw-Hill 93 Glencoe Algebra 1
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)
© Glencoe/McGraw-Hill 94 Glencoe Algebra 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
Study Guide and Intervention (continued)
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
Example 1Example 1 Example 2Example 2
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. � �
Simplify each expression.
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
© Glencoe/McGraw-Hill 95 Glencoe Algebra 1
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. �
Simplify each expression.
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
© Glencoe/McGraw-Hill 96 Glencoe Algebra 1
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. � �� �
Simplify each expression.
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
© Glencoe/McGraw-Hill 97 Glencoe Algebra 1
Less
on
2-4
Pre-Activity How can you use division of rational numbers to describe data?
Read the introduction to Lesson 2-4 at the top of page 84 in your textbook.
• 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.
Helping You Remember
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
© Glencoe/McGraw-Hill 98 Glencoe Algebra 1
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
© Glencoe/McGraw-Hill 99 Glencoe Algebra 1
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 62 � 62
Example 1Example 1 Example 2Example 2
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
© Glencoe/McGraw-Hill 100 Glencoe Algebra 1
Analyze Data Numbers that represent the centralized, or middle, value of a set of dataare called measures of central tendency. Three measures of central tendency are themean, median, and mode.
Definition Example
MeanSum of the data values divided by the
Data: 24, 36, 21, 30, 21, 30; � 27number of values in the data set.
The middle number in a data set when the numbers are arranged in numerical
Median order. If there is an even number of Data: 21, 21, 25, 30, 31, 42; � 27.5values, the median is halfway between the two middle values.
ModeThe number or numbers that occur
Data: 21, 21, 24, 30, 30, 36; 21 and 30 are modesmost often in the set of data.
Which measure of central tendency best represents the data?
Find the mean, median, and mode.
Mean � 105
Median � 102
Modes � 99 and 112
The median best represents the center of the data since the mean is too high.
Find the mean, median, and mode for each data set. Then tell which bestrepresents the data.
1. 2. 3.
4. 5.
3210
4 5 6 7
Month Days above 90�
May 4
June 7
July 14
August 12
September 8
Stem | Leaf
5 | 0 1 96 | 2 2 5 57 | 1 3 58 | 0 3 7 7 5 |0 � 50
Stem | Leaf
9 | 0 0 1 3 910 | 2 2 511 |12 | 0 3 3 8 8 9 9 |0 � 90
Stem | Leaf
2 | 4 7 73 | 1 2 6 6 6 94 | 05 | 8 8 9 2 |4 � 24
Stem | Leaf
9 | 4 6 8 9 910 | 0 1 2 4 8 911 | 2 212 | 0 1 9 |4 �
25 � 30�
2
24 � 36 � 21 � 30 � 21 � 30����
6
Study Guide and Intervention (continued)
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
© Glencoe/McGraw-Hill 101 Glencoe Algebra 1
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?
Use each set of data to make a stem-and-leaf plot.
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
© Glencoe/McGraw-Hill 102 Glencoe Algebra 1
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.
Use each set of data to make a stem-and-leaf plot.
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
© Glencoe/McGraw-Hill 103 Glencoe Algebra 1
Less
on
2-5
Pre-Activity How are line plots and averages used to make decisions?
Read the introduction to Lesson 2-5 at the top of page 88 in your textbook.
• 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.
Helping You Remember
4. Describe how you would explain the process of finding the median and mode from astem-and-leaf plot to a friend who missed Lesson 2-5.
Stem | Leaf
72 | 0 1 1 2 573 | 2 2 2 7 9 974 | 1 3 375 | 6 6 8 976 | 0 1 8 8 8 742 � 742
76543210�1�2�3�4�5�6
© Glencoe/McGraw-Hill 104 Glencoe Algebra 1
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
© Glencoe/McGraw-Hill 105 Glencoe Algebra 1
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
Example 1Example 1 Example 2Example 2
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.
© Glencoe/McGraw-Hill 106 Glencoe Algebra 1
Odds The odds of an event occurring is the ratio of the number of ways an event can occur(successes) to the number of ways the event cannot occur (failures).
Odds
A die is rolled. Find the odds of rolling a number greater than 4.
The sample space is {1, 2, 3, 4, 5, 6}. Therefore, there are six possible outcomes. Since 5 and6 are the only numbers greater than 4, two outcomes are successes and four are failures.
So the odds of rolling a number greater than 4 is , or 1:2.
Find the odds of each outcome if the spinner at the right is spun once.
1. multiple of 4 2. odd number
3. even or a 5 4. less than 4
5. even number greater than 5
Find the odds of each outcome if a computer randomly chooses a number between1 and 20.
6. the number is less than 10 7. the number is a multiple of 4
8. the number is even 9. the number is a one-digit number
A bowl of money at a carnival contains 50 quarters, 75 dimes, 100 nickels, and 125 pennies. One coin is randomly selected.
10. Find the odds that a dime will not be chosen.
11. What are the odds of choosing a quarter if all the dimes are removed?
12. What are the odds of choosing a penny?
Suppose you drop a chip onto the grid at the right. Find the odds of each outcome.
13. land on a shaded square
14. land on a square on the diagonal
15. land on square number 16
16. land on a number greater than 12
17. land on a multiple of 5
1
5
9
13
2
6
10
14
3
7
11
15
4
8
12
16
129
4
38
7
10
56
2�4
number of successes���
number of failures
Study Guide and Intervention (continued)
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
© Glencoe/McGraw-Hill 107 Glencoe Algebra 1
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
© Glencoe/McGraw-Hill 108 Glencoe Algebra 1
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
© Glencoe/McGraw-Hill 109 Glencoe Algebra 1
Less
on
2-6
Pre-Activity Why is probability important in sports?
Read the introduction to Lesson 2-6 at the top of page 96 in your textbook.
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.
Helping You Remember
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?
© Glencoe/McGraw-Hill 110 Glencoe Algebra 1
Geometric ProbabilityIf a dart, thrown at random, hits the triangular board shown at the right, what is the probability that it will hit the shaded region? Thiscan be determined by comparing the area of the shaded region to thearea of the entire board. This ratio indicates what fraction of the tosses should hit in the shaded region.
�
� or
In general, if S is a subregion of some region R, then the probability, P(S), that a point,chosen at random, belongs to subregion S is given by the following:
P(S) �
Find the probability that a point, chosen at random, belongs to the shadedsubregions of the following figures.
1. 2. 3.
4. 5. 6.
7. 8. 9.2
2
4 48
4
4
4
4 4
6
6
66
66
6��3 6��3
5
5
55 55
6
6
4
4
4 4
4
6
44 4
6 63 3
5
5
area of subregion S���area or region R
1�2
12�24
�12
�(4)(6)��12
�(8)(6)
area of shaded region���area of triangular board
6
44
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
2-62-6
Study Guide and InterventionSquare Roots and Real Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
© Glencoe/McGraw-Hill 111 Glencoe Algebra 1
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
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each square root.
1. �64� 2. ��81� 3. �16.81�
4. ��100� 5. � 6. ��121�
7. � 8. � 9. �
10. ��3600� 11. ��6.25� 12. ��0.000�4�
13. 14. � 15. ��1.21�36�49
144�196
121�100
25�16
25�144
4�25
© Glencoe/McGraw-Hill 112 Glencoe Algebra 1
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.
Name the set or sets of numbers to which each real number belongs.
1. 2. � 3. 4. �54�natural, whole, rational rational irrationalinteger, rational
5. 3.145 6. �25� 7. 0.62626262… 8. �22.51�rational natural, whole, rational irrational
integer, rational
Write each set of numbers in order from least to greatest.
9. � , �5, �25�, 10. �0.09�, �0.3131…, 11. �1.2�5�, 0.05, � , �5�
�5, � , , �25� �0.3131…, �0.09�, �1.2�5�, � , 0.05, �5�
12. , �2, �124�, �3.11 13. ��1.44�, �0.35 14. 0.3�5�, 2 , � , �5�
�3.11, �2, , �124� ��1.44�, �0.35, � , 0.3�5�, �5�, 2 1�3
9�5
1�5
5�4
9�5
1�3
1�5
5�4
1�4
3�5
7�4
3�4
1�4
3�5
7�4
3�4
2�3
6�7
84�12
4�11
a�b
a�b
Study Guide and Intervention (continued)
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
© Glencoe/McGraw-Hill 113 Glencoe Algebra 1
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�
Name the set or sets of numbers to which each real number belongs.
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. ●
Write each set of numbers in order from least to greatest.
21. �5�, 2.3�6�, 22. , 0.2�1�, �0.05�
23. ��12�, �3.4�8�, ��11� 24. 0.4�3�, , 3�7
�6��5
2�9
7�3
1��8�
1�8
1�90
4�9
�2 �1�4 �3 0 1 2 3 4�2 �1�4 �3 0 1 2 3 4
�2 �1�4 �3 0 1 2 3 4�2 �1 0 1 2 3 4 5 6
9�13
5�6
28�7
49�100
© Glencoe/McGraw-Hill 114 Glencoe Algebra 1
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�
Name the set or sets of numbers to which each real number belongs.
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. ●
Write each set of numbers in order from least to greatest.
18. �0.03�, , 0.1�7� 19. � , ��8�, � 20. ��8.5�, � , �2
21. SIGHTSEEING The distance you can see to the horizon is given by the formula d � �1.5h�, where d is the distance in miles and h is the height in feet above the horizon line. Mt. Whitney is the highest point in the contiguous 48 states. Its elevation is 14,494 feet. The lowest elevation, at �282 feet, is located near Badwater, California.With a clear enough sky and no obstructions, could you see from the top of Mt. Whitneyto Badwater if the distance between them is 135 miles? Explain.
22. SEISMIC WAVES A tsunami is a seismic wave caused by an earthquake on the oceanfloor. You can use the formula s � 3.1�d�, where s is the speed in meters per second and d is the depth of the ocean in meters, to determine the speed of a tsunami. If anearthquake occurs at a depth of 200 meters, what is the speed of the tsunami generatedby the earthquake?
19�20
�35��2
�7��8
84�30
�2��8
�5��6
5�6
�2 �1�4 �3 0 1 2 3 4�2 �1�4 �3 0 1 2 3 4
144�3
8�7
7�12
4�289
Practice Square Roots and Real Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
Reading to Learn MathematicsSquare Roots and Real Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
© Glencoe/McGraw-Hill 115 Glencoe Algebra 1
Less
on
2-7
Pre-Activity How can using square roots determine the surface area of thehuman body?
Read the introduction to Lesson 2-7 at the top of page 103 in your textbook.
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.
Helping You Remember
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?
© Glencoe/McGraw-Hill 116 Glencoe Algebra 1
Scale DrawingsThe map at the left below shows building lots for sale. The scale ratiois 1:2400. At the right below is the floor plan for a two-bedroomapartment. The length of the living room is 6 m. On the plan theliving room is 6 cm long.
Answer each question.
1. On the map, how many feet are represented by an inch?
2. On the map, measure the frontage of Lot 2 on Sylvan Road in inches. What is the actualfrontage in feet?
3. What is the scale ratio represented on the floor plan?
4. On the floor plan, measure the width of the living room in centimeters. What is theactual width in meters?
5. About how many square meters of carpeting would be needed to carpet the living room?
6. Make a scale drawing of your classroom using an appropriate scale.
7. Use your scale drawing to determine how many square meters of tile would be needed toinstall a new floor in your classroom.
Closet
Closet
Closet
Closet
Kitchen
BedroomBedroom Bath
Dining Area
Living Room
Lot 3
Lot 2
Lot 1
Suns
hine
Lak
e
Sylv
an R
oad
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
Chapter 2 Test, Form 1
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 117 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
1. What set of numbers is graphed below?
A. {2, 4} B. {–4, –2, 2, 4}C. {�4, �3, �2, �1, 0, 1, 2, 3, 4} D. {0} 1.
2. Find � �10 �.A. �10 B. 0 C. 10 D. 10 or �10 2.
3. Evaluate � x � � 2 if x � �3.A. 1 B. �5 C. �1 D. 5 3.
For Questions 4–6, find each sum, difference, or product.
4. �4 � (�5)A. 9 B. �9 C. 1 D. �1 4.
5. �2 � (�7)A. 9 B. �5 C. �9 D. 5 5.
6. (6)(�12)A. �6 B. �72 C. �18 D. �62 6.
7. Simplify the expression �3(2n) � 4n.A. �18n B. 10n C. �2n D. �n 7.
8. Evaluate 6x � 3y if x � �23� and y � ��
13�.
A. 5 B. 1 C. 3 D. 4 8.
9. Find �9 � �34�.
A. �247� B. ��
247� C. ��
34� D. �12 9.
Simplify each expression.
10. ��6
��4
14�
A. �2 B. �5 C. 2 D. 5 10.
11. �12x
4� 8�
A. 12x � 2 B. �12x � 2 C. 3x � 2 D. �3x � 2 11.
�1�2�3�4 0 1 2 43
22
Ass
essm
ent
© Glencoe/McGraw-Hill 118 Glencoe Algebra 1
Chapter 2 Test, Form 1 (continued)
For Questions 12–14, use the list that shows the number of gold medals won by 11 countries in the 2000 Summer Olympic Games. Source: World Almanac
40, 32, 28, 16, 14, 13, 13, 11, 11, 11, 812. To create a line plot of this data, how many �’s would be placed above the
number line between 10 and 15?A. 3 B. 6 C. 7 D. 4 12.
13. Which value occurs most frequently?A. 40 B. 13 C. 11 D. 8 13.
14. Which measure of central tendency best describes the data?A. 40 B. mean C. mode D. median 14.
15. A 6-sided die is rolled one time. Find P(5).
A. �56� B. �
12� C. �
16� D. �
15� 15.
16. A bowl contains 2 red chips, 3 blue chips, and 1 green chip. One chip is randomly drawn. Find P(green).
A. �16� B. �
13� C. �
15� D. �
12� 16.
17. The probability that an event will occur is �35�. What are the odds that the
event will occur?A. 5 : 3 B. 3 : 5 C. 2 : 3 D. 3 : 2 17.
18. Find ��36�.A. 6 B. �18 C. �6 D. 18 18.
19. Name the set or sets of numbers to which the real number �23� belongs.
A. rational numbersB. irrational numbersC. natural numbers, rational numbersD. natural numbers, irrational numbers 19.
20. Write 0, ��12�, �
12�, �
13�, �1 in order from least to greatest.
A. 0, ��12�, �
13�, �
12�, �1 B. �1, ��
12�, 0, �
13�, �
12�
C. �12�, �
13�, 0, ��
12�, �1 D. ��
12�, �1, 0, �
12�, �
13� 20.
Bonus Find �25� � � �4 �. B:
NAME DATE PERIOD
22
Chapter 2 Test, Form 2A
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 119 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
1. What set of numbers is graphed below?
A. {0, 1, 2, 3, 4} B. {…, 0, 1, 2, 3, 4}C. {�4, �3, �2, �1, 0, 1, 2, 3, 4} D. {0, 1, 2, 3, 4, …} 1.
2. Evaluate 8 � � 16 � y � if y � 11.A. �19 B. 35 C. 3 D. 13 2.
3. Find ��45� � �
37�.
A. ��1335�
B. ��12� C. 1�3
85�
D. ��112�
3.
For Questions 4 and 5, find each difference.
4. �9 � (�21)A. �30 B. 12 C. �12 D. 30 4.
5. �7.9 � 4.3A. �12.2 B. �3.6 C. 12.2 D. 3.6 5.
6. Find ��56�����2
35��.
A. ��321�
B. ��129�
C. ��381�
D. ��110�
6.
7. Simplify 4m(�2n) � 6mn.A. 0 B. 8mn C. �2mn D. 12mn 7.
8. Evaluate m2 � 2nm if m � 4.2 and n � 1.5.A. 0.7 B. 5.04 C. �10.35 D. 30.24 8.
9. Find �158� � ���
23��.
A. �2�25� B. ��
35� C. ��
1165�
D. �5�25� 9.
Simplify each expression.
10. �2(��
24
�� 1
53)
�
A. 6 B. ��178� C. �
131� D. �
53� 10.
11. ��3x
��6
12�
A. �12�x � 2 B. ��
12�x � 2 C. 3x � 2 D. �3x � 2 11.
�1�2�3�4 0 1 2 43
22
Ass
essm
ent
© Glencoe/McGraw-Hill 120 Glencoe Algebra 1
Chapter 2 Test, Form 2A (continued)
For Questions 12–14, use the list that shows the total number of medals won by 15 countries in the 2000 Summer Olympic Games. Source: World Almanac
57, 17, 18, 97, 28, 59, 88, 26, 38, 58, 34, 25, 23, 28, 2912. To create a stem-and-leaf plot of this data, what values would be used for
the stems?A. 10, 20, 30, 40, 50, 60, 70, 80, 90 B. 17, 23, 34, 57, 88, 97C. 1, 2, 3, 4, 5, 6, 7, 8, 9 D. 3, 4, 5, 6, 7, 8, 9 12.
13. How many countries won more than 42 medals?A. 6 B. 4 C. 5 D. 7 13.
14. Which measure of central tendency best describes the data?A. median B. mean C. mode D. 42 14.
15. A computer randomly selects an integer between 5 and 9. Find P(2).
A. 1 B. �13� C. �
15� D. 0 15.
For Questions 16 and 17, a bowl contains 8 red chips, 7 blue chips, and 10 green chips. One chip is randomly drawn.
16. Find P(red or blue).
A. �185�
B. �35� C. �
32� D. �1
15�
16.
17. Find the odds of drawing a green chip.A. 2 : 3 B. 2 : 5 C. 1 : 10 D. 1 : 15 17.
18. Find ��0.81�.A. 0.9 B. �0.9 C. 0.09 D. �0.09 18.
19. Name the set or sets of numbers to which the real number ��25� belongs.A. natural numbers, irrational numbersB. whole numbers, integers, rational numbersC. integers, rational numbersD. irrational numbers 19.
20. Write �3�, �13�, 0.3, �1
31�, 1 in order from least to greatest.
A. �131�
, 0.3, �13�, 1, �3� B. �3�, 1, 0.3, �1
31�, �
13�
C. �13�, 0.3, �1
31�, 1, �3� D. 0.3, �
13�, �1
31�, �3�, 1 20.
Bonus Evaluate 3a � 8b � �49� if a � 4.1 and b � �34�. B:
NAME DATE PERIOD
22
Chapter 2 Test, Form 2B
NAME DATE PERIOD
SCORE
© Glencoe/McGraw-Hill 121 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
1. What set of numbers is graphed below?
A. {�5, �4, �3, �2, �1, 0, 1, 2, 3} B. {�5, �4, �3, �2, �1, 0}C. {… , �5, �4, �3, �2, �1, 0} D. {�5, �4, �3, �2, �1, 0, …} 1.
2. Evaluate 25 � � 9 � a � if a � 12.A. 4 B. 28 C. 22 D. 46 2.
3. Find 32.5 � (�11.2).A. 41.3 B. 43.7 C. 20.7 D. 21.3 3.
For Questions 4 and 5, find each difference.
4. �12 � (�11)A. �23 B. 1 C. �1 D. 23 4.
5. �45� � �
23�
A. �28� B. �1
25�
C. 1 D. ��185�
5.
6. Find ���13�����
67��.
A. �170�
B. ��170�
C. ��27� D. �
27� 6.
7. Simplify �5x(3y) � 7xy.A. �8xy B. 5xy C. �xy D. �22xy 7.
8. Evaluate 3ab � b2 if a � 3.7 and b � 2.1.A. 4.6 B. 18.9 C. 9.62 D. 19.11 8.
9. Find ��34� � �
65�.
A. ��190�
B. �230�
C. ��110�
D. ��58� 9.
Simplify each expression.
10. ���3(
25
��
63)
�
A. �54� B. �6 C. �3 D. 2 10.
11. �24
�k
4� 8�
A. �6k � 8 B. �6k � 2 C. �24k � 2 D. 24k � 2 11.
�1�2�3�4�5 0 1 2 3
22
Ass
essm
ent
© Glencoe/McGraw-Hill 122 Glencoe Algebra 1
Chapter 2 Test, Form 2B (continued)
For Questions 12–14, use the list which shows the number of 300 games bowled by15 women as sanctioned by the Women’s International Bowling Congress.Source: World Almanac
20, 16, 23, 18, 21, 17, 27, 14, 23, 17, 21, 17, 24, 16, 19
12. To create a stem-and-leaf plot of this data, what values would be used for leaves for the stem value 2?A. 0, 1, 1, 3, 3, 4, 7 B. 20, 21, 22, 23, 24, 25, 26, 27C. 0, 1, 2, 3, 4, 5, 6, 7 D. 20, 21, 21, 23, 23, 24, 27 12.
13. How many of these women bowled more than twenty 300 games?A. 8 B. 7 C. 4 D. 6 13.
14. Which measure of central tendency best describes the data?A. mean B. mode C. median D. mean or
median 14.
15. A computer randomly selects an integer between 1 and 7. Find the probabilityof selecting a number less than 9.
A. 1 B. �17� C. �
19� D. 0 15.
For Questions 16 and 17, a bowl contains 14 red chips, 9 blue chips, and 12 green chips. One chip is randomly drawn.
16. Find P(blue or green).
A. �211�
B. �47� C. �
32� D. �
35� 16.
17. Find the odds of drawing a red chip.A. 2 : 5 B. 2 : 3 C. 1 : 14 D. 1 : 21 17.
18. Find ��28516�.
A. �196�
B. ��196�
C. �34� D. ��
34� 18.
19. Name the set or sets of numbers to which the real number �27� belongs.A. natural numbers, irrational numbersB. rational numbersC. irrational numbersD. natural numbers, rational numbers 19.
20. Write ��5�, �0.5, ��15�, ��1
51�
, �1 in order from least to greatest.
A. �0.5, ��15�, ��1
51�
, �1, ��5� B. ��5�, �1, �0.5, ��151�
, ��15�
C. ��15�, ��1
51�
, �0.5, �1, ��5� D. �1, �0.5, ��15�, ��1
51�
, ��5� 20.
Bonus Evaluate � x � � �xzy� if x � �4, y � 3, and z � 6. B:
NAME DATE PERIOD
22
Chapter 2 Test, Form 2C
© Glencoe/McGraw-Hill 123 Glencoe Algebra 1
1. Name the coordinates of the points graphed on the 1.number line.
2.
Graph each set of numbers.3.
2. ��52�, ��
12�, �
32�, 2� 3. {1, 3, 5, …}
Evaluate each expression if x � �5 and y � 4. 4.
4. � x � � 10 5. 10 � � 3 � y � 5.
Find each sum. 6.
6. �13 � 24 7. �10.5 � (�2.4) 7.
8. �34� � ���1
72�� 8.
Find each difference. 9.
9. 4.32 � (�3.79) 10. ��59� � �
23� 10.
For Questions 11 and 12, find each product. 11.
11. 16(�4) 12. ���47����
25�� 12.
13. Simplify 5(�7a) � 12a. 13.
Evaluate each expression if m � �3.2 and n � 7.1. 14.
14. �3mn 15. m(n � 5) 15.
Find each quotient. 16.
16. �44 � 5 17. ��67� � ���
29�� 17.
For Questions 18 and 19, simplify each expression. 18.
18. �6�(53
��
1112)
� 19. �30w
��6
18� 19.
20. Evaluate �4sts�
if s � 1.3 and t � �5.2. 20.
�2�1�3�4 0 1 2 4 53
NAME DATE PERIOD
SCORE 22
Ass
essm
ent
0 1 32�3 �2 �1
�1�2 0 1 2 4 5 63
© Glencoe/McGraw-Hill 124 Glencoe Algebra 1
Chapter 2 Test, Form 2C (continued)
Use the list that shows the number of touchdowns scored by NFC teams during the first 7 weeks of the 2001 football season. Source: www.nfl.com
2, 3, 1, 5, 2, 0, 4, 3, 4, 3, 3, 4, 6, 3, 2
21. Make a line plot of the data. 21.
22. What is the median of the data? 22.
23. Which values occur least frequently? 23.
24. How many of the teams have made more than 24.3 touchdowns?
25. Does the mean, median, or mode best represent the data? 25.Explain.
For Questions 26–28, a bowl contains 12 red chips,9 blue chips, and 15 green chips. One chip is randomly drawn.
26. Find P(red or green). 26.
27. Find P(blue). 27.
28. Find the odds of drawing a red chip 28.
29. The probability that an event will not occur is �152�
. 29.
What are the odds that the event will occur?
30. Find ��1.21�. 30.
31. Name the set or sets of numbers to which the real number 31.
�231� belongs.
32. Graph the solution set x 2.5. 32.
33. Write ��29�, 0.25, ���
19�, �1
21�
, 0 in order from least to greatest. 33.
Bonus Most historical records do not include a year zero. B:Thus, the year before A.D. 1 is labeled 1 B.C., not 0 B.C.If Rome celebrated its 1000th anniversary in A.D. 248,when was Rome founded?
�1�2�3 0 1 2 3
1 2 3 4 5 60
NAME DATE PERIOD
22
Chapter 2 Test, Form 2D
© Glencoe/McGraw-Hill 125 Glencoe Algebra 1
1. Name the coordinates of the points graphed on the 1.number line.
Graph each set of numbers. 2.
2. ��23�, 0, �
13�, �
43�� 3. {… , �4, �2, 0} 3.
Evaluate each expression if a � �4 and b � 7. 4.
4. 13 � � a � 5. 14 � � b � 2 � 5.
Find each sum. 6.
6. 27 � (�14) 7. �15.3 � (�3.6) 7.
8. ��49� � �
23� 8.
Find each difference. 9.
9. �7.63 � 5.18 10. �38� � ���
34�� 10.
For Questions 11 and 12, find each product. 11.
11. (�15)(7) 12. ��56�����
27�� 12.
13. Simplify �4b � 3(6b). 13.
Evaluate each expression if x � 4.3 and y � �2.7. 14.
14. xy � 6 15. x(y � 3) 15.
Find each quotient. 16.
16. 76 � (�8) 17. ��45� � �
83� 17.
For Questions 18 and 19, simplify each expression. 18.
18. ��8(4�
�13
16� 7)
� 19. ��12�w
2� 10� 19.
20. Evaluate �2nm� if m � �3.6 and n � 4.8. 20.
�1�2�3�4 0 1 2 43
0 1 2�1
�1�2�3�5�4 0 1 2 63 4 5
NAME DATE PERIOD
SCORE 22
Ass
essm
ent
© Glencoe/McGraw-Hill 126 Glencoe Algebra 1
Chapter 2 Test, Form 2D (continued)
Use the list that shows the number of touchdowns scored by AFC teams during the first 7 weeks of the 2001 football season. Source: www.nfl.com
4, 1, 4, 4, 4, 3, 2, 1, 4, 3, 4, 5, 5, 5, 3, 2
21. Make a line plot of the data. 21.
22. What is the median of the data? 22.
23. Which values occur least frequently? 23.
24. How many of the teams made fewer than 3 touchdowns? 24.
25. Does the mean best describe the set of data? Explain. 25.
For Questions 26–28, a bowl contains 8 red chips,16 blue chips, and 10 green chips. One chip is randomly drawn.
26. Find P(red or blue). 26.
27. Find P(green). 27.
28. Find the odds of drawing a blue chip. 28.
29. The probability that an event will not occur is �59�. 29.
What are the odds that the event will not occur?
30. Find ���13669�. 30.
31. Name the set or sets of numbers to which the real number 31.��49� belongs.
32. Graph the solution set x �1. 32.
33. Write ���49�, �
47�, ��
38�, 0.4, 0 in order from least to greatest.
33.
Bonus In a local raffle the odds of winning any prize is 1 : 3, B:and the odds of winning the grand prize is 1 : 999.What is the ratio of grand prizes to the total number of prizes.
�1�2�3�4 0 1 2 43
1 2 3 4 5 60
NAME DATE PERIOD
22
Ass
essm
ent
Chapter 2 Test, Form 3
© Glencoe/McGraw-Hill 127 Glencoe Algebra 1
1. Name the coordinates of the points graphed on the number line. 1.
For Questions 2 and 3, graph each set of numbers.
2. {… , �5, �3, �1, 1, 3, 5, …} 2.
3. {integers less than �2 or greater than 3} 3.
4. Evaluate � 2 � b � � a if a � �23� and b � ��
19�. 4.
5. Find the sum of �3�16� and 1�
23�. 5.
6. The highest point of elevation in the state of California is 6.14,494 feet at Mount Whitney. The lowest point is �282 feet at Death Valley. What is the difference in elevation of these two points?
7. Find �45 � (�91) � 23. 7.
8. Find ���37�� � ���
65��. 8.
9. A bank in Los Angeles, California is a 40-story building. 9.The average height of each story is 12.9 feet. How tall is the bank?
Evaluate each expression if w � 12, x � �7,
y � �34�, and z � ��
56�.
10. 4x2 � 3w 10.
11. xyz � 5yz 11.
For Questions 12 and 13, simplify each expression.
12. �5�(�
6(173
��
1112))� 12.
13. �24x �6
42y� 13.
14. Evaluate �(a �c
b)� if a = �6.3, b = 20.7, and c = 4.5. 14.
0 1 2�1
NAME DATE PERIOD
SCORE 22
© Glencoe/McGraw-Hill 128 Glencoe Algebra 1
Chapter 2 Test, Form 3 (continued)
Use the list that shows the number of silver medals won by 15 countries participating in the 1998 Winter Olympic Games. Source: World Almanac
9, 10, 6, 5, 5, 3, 4, 4, 1, 6, 1, 6, 2, 1, 115. Make a line plot of the data. 15.
16. Which measure of central tendency best describes the data? 16.Explain.
Use the list that shows the height in meters of the winning high jump for women in the Summer Olympic Games from 1936 to 2000. Source: World Almanac 17.
1.60, 1.68, 1.67, 1.76, 1.85, 1.90, 1.82, 1.92,1.93, 1.97, 2.02, 2.03, 2.02, 2.05, 2.01
17. Make a stem-and-leaf plot of the data.
18. Which measure of central tendency best describes the data? 18.Explain.
For Questions 19–21, a state lottery game uses ping pong balls numbered 0–39. Balls with the numbers 20, 8, 7,and 1 have already been selected in the weekly drawing.
19. Find the probability of drawing a ball with a number less 19.than 10 as the fifth ball.
20. Find the odds of drawing a ball with a number between 20.10 and 30 as the fifth ball.
21. Find the probability of drawing a ball with the number 21.42 as the fifth ball.
22. The probability that an event will occur is 30%. What are 22.the odds that the event will not occur?
23. Find ���61265��. 23.
24. Name the set or sets of numbers to which the real number 24.
��346�� belongs.
25. Write ��29�, ��1
21�
, �0.2, ���116��, �1 in order from least to greatest. 25.
Bonus Simplify �2�.25((46..94
��
84))�. B:
NAME DATE PERIOD
22
Chapter 2 Open-Ended Assessment
© Glencoe/McGraw-Hill 129 Glencoe Algebra 1
Demonstrate your knowledge by giving a clear, concise solutionto each problem. Be sure to include all relevant drawings andjustify your answers. You may show your solution in more thanone way or investigate beyond the requirements of the problem.
1. a. Explain what a point on a number line represents, and howthe coordinate of the point is different from the point.
b. Describe how to graph the set {3, 4, 5, …} on a number line.
2. a. Use a number line to determine if �4 � 3 is greater than 4 � (�3). Explain your reasoning.
b. Explain how subtracting a number can be done with addition,and give an example.
3. Let x and y be any real numbers. List the conditions under which
the quotient �xy� is positive. Give examples to support your answer.
4. a. Construct a set of eleven numbers with a median of 10 and amean that is less than 10. What is the mean and mode of yourdata?
b. Make a stem-and-leaf plot of the data created for part a.
5. a. Explain why the probability that an event will occur willnever equal 2.
b. The odds that an event will occur are 1 : 1. Explain why the
probability that the event will occur is �12� and not 1.
6. a. Explain why ��49� � ��49�.b. Give a list of six real numbers ordered from least to greatest
such that the first number is a rational number, the secondnumber is an integer, the third number is an irrationalnumber, the fourth number is negative, the fifth number is anatural number, and the sixth number is a whole number.
NAME DATE PERIOD
SCORE 22
Ass
essm
ent
© Glencoe/McGraw-Hill 130 Glencoe Algebra 1
Chapter 2 Vocabulary Test/Review
Write the letter of the term that best matches each phrase.
1. a number that can be written in the
form �ab�, where a and b are integers
and b � 0
2. a number and its opposite
3. the number of times a data item occurs in a set
4. often used to describe sets of data because they represent a centralized or “middle”value
5. all possible outcomes of an event
6. outcomes for which the probabilities are equal
7. the ratio that compares the number of ways an event can occur to the number of ways it cannot occur
8. one of two equal factors of a number
9. a number that cannot be written in the form �ab�
where a and b are integers and b � 0
10. the set of irrational numbers and rational numbers
In your own words—Define each term.
11. absolute value
12. opposites
absolute valueadditive inversesback-to-back stem-and-leaf plot
Completeness Propertycoordinateequally likelyfrequency
graphinfinityintegersirrational numberline plotmeasures of central tendency
natural number
negative numberoddsoppositesperfect squarepositive numberprincipal square rootprobabilityradical sign
rational approximationrational numberreal numbersample spacesimple eventsquare rootstem-and-leaf plotwhole number
NAME DATE PERIOD
SCORE 22
a. frequency
b. measures of centraltendency
c. equally likely
d. odds
e. rational number
f. square root
g. irrational number
h. additive inverses
i. real numbers
j. sample space
Chapter 2 Quiz (Lessons 2–1 and 2–2)
22
© Glencoe/McGraw-Hill 131 Glencoe Algebra 1
1. Name the coordinates of the points graphed on the number 1.line.
2. Graph {�5, 2, 4}.
For Questions 3 and 4, find each absolute value.
3. � �72 � 4. � 4.9 �
5. Evaluate �� 17 � y � if y � 13.
Find each sum.
6. 5 � (�2) 7. �51 � 47
8. �12� � �
13�
Find each difference.
9. �54 � 23 10. 3.1 � 1.7
�1�2�3�4 0 1 2 43
NAME DATE PERIOD
SCORE
Chapter 2 Quiz (Lessons 2–3 and 2–4)
For Questions 1 and 2, find each product.
1. 7(�31) 2. ���23����
67��
3. Simplify 4(7a) � 3a.
4. Evaluate xy � 3 if x � �1.2 and y � �2.3.
Find each quotient.
5. �42 � 6 6. �95� � �
32�
Simplify each expression.
7. ��5(217
��4
13)� 8. ��9x
��3
15y�
Evaluate each expression if n � �2, m � 3.5, and p � �34�.
9. �n4p�
10. �8 �
nm
�
NAME DATE PERIOD
SCORE 22
Ass
essm
ent
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
�2�1�3�4�5 0 1 2 43
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
© Glencoe/McGraw-Hill 132 Glencoe Algebra 1
For Questions 1–3, the heights (in inches) of the students in Mrs. Graham’s class are 60, 75, 58, 73, 59, 74, 59, 61, 59, 63, 62,and 61.
1. Draw a line plot for the data. 1.
2. Which height occurs most frequently? 2.
3. Which measure of central tendency best describes the data? 3.Explain.
4. One shirt is randomly selected from a drawer containing 4.5 red shirts, 6 blue shirts, and 3 yellow shirts. Find P(red).
5. A weather forecast states that the probability of snow the 5.next day is 75%. What are the odds that it will snow?
55 60 65 70 75
Chapter 2 Quiz (Lesson 2–7)
Find each square root.
1. ��49� 2. �0.36� 3. ���12251
��For Questions 4 and 5, name the set or sets of numbers to which each real number belongs.
4. �248� 5. ��13�
6. Graph the solution set x 1.3.
For Questions 7 and 8, replace � with �, �, or � to make each sentence true.
7. 0.6 � �23� 8. �11� � 3.3�1�
9. Write ��13�, �
�110��, 0.3, ��
49� in order from least to greatest.
10. Standardized Test Practice Which of the following is a true statement?
A. ��13��
��12��
B. �5� �7� C. ��12��
� �2� D. �9� � �8�
NAME DATE PERIOD
SCORE
Chapter 2 Quiz (Lessons 2–5 and 2–6)
22
NAME DATE PERIOD
SCORE
22
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
�1�2�3�4 0 1 2 43
Ass
essm
ent
Chapter 2 Mid-Chapter Test (Lessons 2–1 through 2–4)
© Glencoe/McGraw-Hill 133 Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
1. What set of numbers is graphed at the right?
A. {�2, �1, 0, 1, 2, 3, 4} B. {… , �2, �1, 0, 1, 2, 3, 4}C. {�2, �1, 0, 1, 2, 3, 4, …} D. {0, 1, 2, 3, 4} 1.
2. Evaluate 15 � � a � if a � �6.A. 21 B. �21 C. �9 D. 9 2.
3. Find �1.07 � 0.12.A. �1.19 B. �0.95 C. 1.19 D. 0.95 3.
4. Find ��14� � �
38�.
A. ��58� B. ��
18� C. �
18� D. �
58� 4.
5. Simplify the expression �2(�7m) � 3m.A. �11m B. �6m C. 12m D. 17m 5.
6. Evaluate x2 � 3y if x � ��12� and y � ��
56�.
A. �3�12� B. 1�
16� C. �2�
14� D. 2�1
52�
6.
7. Simplify �6r��
618
�.
A. �r � 18 B. �r � 3 C. �18r D. 6r � 3 7.
8. Graph {integers less than or equal to �2}. 8.
9. Find �61 � 18. 9.
10. Find �15� � �
12�. 10.
11. Find �6(�12). 11.
12. Find �92� � ���
43��. 12.
For Questions 13 and 14, evaluate each expression if u � �7, and v � 3.9
13. �2u8� � (�2) 13.
14. uv 14.
15. Evaluate � z � � 0.13 if z � �0.45. 15.
�1�2�3�5�6�7 �4 0 1 2 3 4
Part I
NAME DATE PERIOD
SCORE 22
Part II
© Glencoe/McGraw-Hill 134 Glencoe Algebra 1
Chapter 2 Cumulative Review (Chapters 1–2)
1. Write an algebraic expression for the verbal expression 1.seven more than the square of a number. (Lesson 1–1)
2. Evaluate 3a(a � b) if a � 4 and b � 3. (Lesson 1–2) 2.
For Questions 3 and 4, simplify each expression.
3. 6a � 11a � 3 4. 2(4 � 2x) � 6(Lesson 1–5) (Lesson 1–6)
5. Identify the hypothesis and conclusion of the statement.Then write the statement in if-then form. I’ll go to the store when I finish my homework. (Lesson 1–7) 5.
6. As the weather gets warmer, the beaches become more 6.crowded. Draw a reasonable graph that shows the number of people at the beach as the temperature increases. Let the horizontal axis show the temperature and the vertical axis show the number of people. (Lesson 1–8)
7. Name the coordinates of the points graphed on the number line. (Lesson 2–1) 7.
8. Evaluate 12 � �x � 11�, if x � 13. (Lesson 2–1) 8.
9. Find 32.4 � (�14.6). (Lesson 2–2) 9.
10. Find 31 � 17. (Lesson 2–2) 10.
11. Find ��25�����
37��. (Lesson 2–3) 11.
12. Simplify �12t6� 18�. (Lesson 2–4) 12.
13. Use the data to make a line plot. (Lesson 2–5) 13.46 42 45 41 42 40 44 46 42 40 47
14. A card is selected from a standard deck of cards. 14.Determine P(black ace). (Lesson 2–6)
15. Write ��5�, �5275�
, � �94�, 2.2�4� in order from least to 15.
greatest. (Lesson 2–7)
NAME DATE PERIOD
22
�1�2�3�5�4 0 1 2 63 4 5
3.
4.
Standardized Test Practice (Chapters 1–2)
© Glencoe/McGraw-Hill 135 Glencoe Algebra 1
1. Evaluate x2 � y2 � z, if x � 7, y � 6, and z � 4. (Lesson 1–2)
A. 17 B. 101 C. 89 D. 59 1.
2. Find the solution set for 5(7 � x) � 18 if the replacement set is {0, 1, 2, 3, 4, 5, 6}. (Lesson 1–3)
E. {4, 5, 6} F. {0, 1, 2, 3} G. {2, 3, 4} H. {5, 6} 2.
3. Using the Distributive Property to find 9�5�23�� would give which
expression? (Lesson 1–5)
A. 9(5) � �23� B. 9��
137�� C. 9(5) � 9��
23�� D. 9(5)��
23�� 3.
4. Identify the conclusion of the statement. (Lesson 1–7)
If you are at the Grand Canyon, then you are in Arizona.E. you are at the Grand Canyon F. you are in AmericaG. you are not in Arizona H. you are in Arizona 4.
5. Evaluate �26 � r� � 7 if r � 9. (Lesson 2–1)
A. 45 B. 10 C. 22 D. 24 5.
6. Simplify 6a(�4b). (Lesson 2–3)
E. 2ab F. �24ab G. �2a H. 24b 6.
7. Simplify �17 �8
15�. (Lesson 2–4)
A. �167� � �
185� B. 4 C. 3�
58� D. �
383� 7.
8. Which set of data was used to make the stem-and-leaf plot? (Lesson 2–5)
E. 14, 245, 36 F. 4, 4, 5, 6G. 14, 24, 25, 36 H. 1.4, 2.4, 2.5, 3.6 8.
9. What is the probability that a number chosen at random from the domain {�3, �2, �1, 0, 1, 2, 3} will satisfy the inequality 3 � 2x � 5? (Lesson 2–6)
A. {0, 1, 2, 3} B. �37� C. �
47� D. �
57� 9.
10. Which number is greater than �3� and less than 1.9? (Lesson 2–7)
E. 1.72 F. �1.8�2� G. �95� H. �
3290�
10. HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
NAME DATE PERIOD
22
Ass
essm
ent
Stem Leaf
123
44 56
1 4 � 14
Part I: Multiple Choice
Instructions: Fill in the appropriate oval for the best answer.
© Glencoe/McGraw-Hill 136 Glencoe Algebra 1
Standardized Test Practice (continued)
11. Evaluate 123. (Lesson 1–1) 11. 12.
12. Evaluate 3.7 � 7.4 � 8.6 � 2.3. (Lesson 1–6)
13. Kendrick needs to mix two types of flour for 13. 14.
his secret cookie dough. If he adds �34� cup of
one type of flour to �18� cup of the second type
of flour, how much flour in cups does he have? (Lesson 2–2)
14. Dalila ran 5.3 miles yesterday, but only ran 3.7 miles this morning. How far must she run this afternoon to run the same distance today as she ran yesterday? (Lesson 2–2)
Column A Column B
15. 15.
(Lesson 1–2)
16. 16.
(Lesson 1–4)
17. 17.
(Lesson 2–1)
DCBA� �6 � � � �3 �� �10 �
DCBA8 � �18
� � 2 � 08 � 0 � 2 � �12
�
DCBA4(3) � 2 � 24(3 � 2) � 2
Part 3: Quantitative Comparison
Instructions: Compare the quantities in columns A and B. Shade in if the quantity in column A is greater; if the quantity in column B is greater; if the quantities are equal; or if the relationship cannot be determined from the information given.
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
NAME DATE PERIOD
22
NAME DATE PERIOD
A
D
C
B
Part 2: Grid In
Instructions: Enter your answer by writing each digit of the answer in a column boxand then shading in the appropriate oval that corresponds to that entry.
Standardized Test PracticeStudent Record Sheet (Use with pages 116–117 of the Student Edition.)
© Glencoe/McGraw-Hill A1 Glencoe Algebra 1
Select the best answer from the choices given and fill in the corresponding oval.
1 4 7
2 5 8
3 6 9
Solve the problem and write your answer in the blank.
For Questions 11 and 12, also enter your answer by writing each number orsymbol in a box. Then fill in the corresponding oval for that number or symbol.
10 11 12
11 (grid in)
12 (grid in)
13
14
Select the best answer from the choices given and fill in the corresponding oval.
15
16
17
18
Record your answers for Questions 19–20 on the back of this paper.
DCBA
DCBA
DCBA
DCBA
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
DCBADCBADCBA
DCBADCBADCBA
DCBADCBADCBA
NAME DATE PERIOD
22
An
swer
s
Part 2 Short Response/Grid InPart 2 Short Response/Grid In
Part 3 Quantitative ComparisonPart 3 Quantitative Comparison
Part 4 Open-EndedPart 4 Open-Ended
Part 1 Multiple ChoicePart 1 Multiple Choice
©G
lenc
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cGra
w-H
ill76
Gle
ncoe
Alg
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1
Ab
solu
te V
alu
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n a
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mbe
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is t
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s fr
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e di
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is t
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s fr
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at
the
righ
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s th
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of a
bso
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Th
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alu
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a n
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th
e di
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rom
zer
o on
a
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and
is r
epre
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ted
n.
For
th
is e
xam
ple,
�3
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and
3
�3.
10
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23
3 un
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Stu
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)
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____
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Fin
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a.�
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s fr
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1 � 21 � 4
3 � 41 � 2
1 � 4
35 � 4135 � 41
2 � 32 � 3
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Rat
ion
al N
um
ber
s o
n t
he
Nu
mb
er L
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ME
____
____
____
____
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____
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____
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2-1
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©G
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Alg
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1
Lesson 2-1
Gra
ph
Rat
ion
al N
um
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sT
he
figu
re a
t th
e ri
ght
is
part
of
a n
um
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e.A
nu
mbe
r li
ne
can
be
use
d to
sh
ow
the
sets
of
nat
ura
l n
um
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s,w
hol
e n
um
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s,an
d in
tege
rs.P
osit
ive
nu
mb
ers,
are
loca
ted
to t
he
righ
t of
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and
neg
ativ
e n
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e lo
cate
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ft o
f 0.
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oth
er s
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at y
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atio
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ritt
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e a
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tege
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1 � 4
a � b
10
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23
Natu
ral N
umbe
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Posi
tive
Num
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Nega
tive
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4
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le N
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gers
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e th
e co
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rap
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e gr
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}.
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5
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2
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4
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ple1
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ple1
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45
67
0�
1�
21
23
45
6
Answers (Lesson 2-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Rat
ion
al N
um
ber
s o
n t
he
Nu
mb
er L
ine
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
2-1
©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
ber
s.
5.{�
8,�
5,�
3,0,
2}6.
{�9,
�6,
�4,
�3,
�1}
7.{�
3,�
2,�
1,0,
…}
8.{…
,�1,
0,1,
2,3}
9.��
,0,
,1,
�10
.{…
,�3,
�2.
5,�
2,�
1.5,
�1}
Fin
d e
ach
ab
solu
te v
alu
e.
11.
�9
912
.15
15
13.
�30
30
14. �
15
.2.
42.
416
.
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
�3,
b�
�10
,c�
,x�
9,y
�1.
5,an
d z
�12
.
17.2
6 �
x�
611
18.1
1 �
10
�x
12
19.
12 �
a�
514
20.
a�
20
�4
19
21.4
.5 �
y
322
.z
�7
�5
10
23.1
4 �
b
424
.b
�2
8
25. c
��
23
26.9
�3
.5 �
y11
1 � 2
1 � 2
9 � 119 � 11
5 � 75 � 7
�3
�2
�1
01
2�
1�
1 – 20
1 – 21
3 – 22
5 – 23
7 – 24
5 � 21 � 2
1 � 2
�1
01
23
45
67
89
�10
�9
�8
�7
�6
�5
�4
�3
�2
�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
ber
s.
3.�…
,�,�
,�1,
�,�
�4.
{in
tege
rs l
ess
than
�4
or g
reat
er t
han
2}
Fin
d e
ach
ab
solu
te v
alu
e.
5.�
11
116.
100
10
07.
�0.
35
0.35
8.�
E
valu
ate
each
exp
ress
ion
if
a�
4,b
�,c
�,x
�14
,y�
2.4,
and
z�
�3.
9.41
�16
�z
22
10.
3a�
20
�15
1711
.2x
�4
�6
2612
.2.5
�3
.8 �
y1.
1
13. �b
���
�14
.�
b�
15
.c
�1
�16
.�
c�
AST
RO
NO
MY
For
Exe
rcis
es 1
7–19
,use
th
e fo
llow
ing
info
rmat
ion
.
Th
e ab
solu
te m
agn
itu
de
of a
sta
r is
how
bri
ght
the
star
wou
ld
appe
ar f
rom
a s
tan
dard
dis
tan
ce o
f 10
par
secs
,or
32.6
lig
ht
year
s.T
he
low
er t
he
nu
mbe
r,th
e gr
eate
r th
e m
agn
itu
de,o
r br
igh
tnes
s,of
th
e st
ar.T
he
tabl
e gi
ves
the
mag
nit
ude
s of
sev
eral
sta
rs.
17.U
se a
nu
mbe
r li
ne
to o
rder
th
e m
agn
itu
des
from
lea
st
to g
reat
est.
18.W
hic
h o
f th
e st
ars
are
the
brig
hte
st a
nd
the
leas
t br
igh
t?b
rig
hte
st:
Rig
el;
leas
t b
rig
ht:
Alt
air
19.W
rite
th
e ab
solu
te v
alu
e of
th
e m
agn
itu
de o
f ea
ch s
tar
2.3,
7.2,
0.5,
4.7,
0.7,
0.3,
8.1,
1.4
Sour
ce:w
ww.as
tro.w
isc.ed
u
20.C
LIM
ATE
Th
e ta
ble
show
s th
e m
ean
win
d sp
eeds
in
m
iles
per
hou
r at
Day
ton
aB
each
,Flo
rida
.So
urce
:Nat
iona
l Clim
atic
Data
Cen
ter
Gra
ph t
he
win
d sp
eeds
on
a n
um
ber
lin
e.W
hic
h
mon
th h
as t
he
grea
test
mea
n w
ind
spee
d?M
arch
7.1
7.4
7.9
8.3
8.7
9.1�
2�
2
9.7
10.1
77.
58
8.5
99.
510
10.5
Jan
Feb
Mar
Ap
rM
ayJu
ne
July
Au
gS
epO
ctN
ovD
ec
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
agn
itu
de
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 (
Ave
rag
e)
Rat
ion
al N
um
ber
s o
n t
he
Nu
mb
er L
ine
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
2-1
Answers (Lesson 2-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csR
atio
nal
Nu
mb
ers
on
th
e N
um
ber
Lin
e
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
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
mb
er l
ine
to s
how
dat
a?
Rea
d th
e in
trod
uct
ion
to
Les
son
2-1
at
the
top
of p
age
68 i
n y
our
text
book
.
In t
he
tabl
e,w
hat
doe
s th
e n
um
ber
�0.
2 te
ll y
ou?
Th
e le
vel o
f th
e B
razo
s R
iver
incr
ease
d b
y 0.
2 fo
ot
in
24 h
ou
rs.
Rea
din
g t
he
Less
on
1.R
efer
to
the
nu
mbe
r li
ne
on p
age
68 i
n y
our
text
book
.Wri
te t
rue
or f
alse
for
each
of
the
foll
owin
g st
atem
ents
.
a.A
ll w
hol
e n
um
bers
are
in
tege
rs.
tru
e
b.
All
nat
ura
l n
um
bers
are
in
tege
rs.
tru
e
c.A
ll w
hol
e n
um
bers
are
nat
ura
l n
um
bers
.fa
lse
d.
All
nat
ura
l n
um
bers
are
wh
ole
nu
mbe
rs.
tru
e
e.A
ll w
hol
e n
um
bers
are
pos
itiv
e n
um
bers
.fa
lse
2.U
se t
he
wor
ds d
enom
inat
or,f
ract
ion
,an
d n
um
erat
orto
com
plet
e th
e fo
llow
ing
sen
ten
ce.
You
kn
ow t
hat
a n
um
ber
is a
rat
ion
al n
um
ber
if i
t ca
n b
e w
ritt
en a
s a
that
has
a
and
that
are
in
tege
rs,w
her
e th
e de
nom
inat
or i
s n
ot e
qual
to
zero
.
3.E
xpla
in w
hy
,0.6 �
,an
d 15
are
rat
ion
al n
um
bers
.
Eac
h n
um
ber
is in
or
can
be
wri
tten
in t
he
form
,w
her
e a
and
bar
e
inte
ger
s an
d b
�0.
0.6�
can
be
wri
tten
as
,an
d 1
5 ca
n b
e w
ritt
en a
s .
Hel
pin
g Y
ou
Rem
emb
er
4.C
onn
ecti
ng
a m
ath
emat
ical
con
cept
to
som
eth
ing
in y
our
ever
yday
lif
e is
on
e w
ay o
fre
mem
beri
ng.
Des
crib
e a
situ
atio
n o
r se
ttin
g in
you
r li
fe t
hat
rem
inds
you
of
abso
lute
valu
e.
Sam
ple
an
swer
:Th
e d
ista
nce
fro
m e
ach
go
al li
ne
to t
he
50-y
ard
lin
e is
50
yard
s.
15 � 12 � 3
a � b
�3
�7
den
om
inat
or
nu
mer
ato
rfr
acti
on
©G
lenc
oe/M
cGra
w-H
ill80
Gle
ncoe
Alg
ebra
1
Inte
rsec
tio
n a
nd
Un
ion
The
inte
rsec
tion
of
two
sets
is t
he s
et o
f el
emen
ts t
hat
are
in b
oth
sets
.T
he in
ters
ecti
on o
f se
ts A
and
B is
wri
tten
A �
B.T
he u
nion
of
two
sets
is t
he s
et o
f el
emen
ts in
eit
her
A,B
,or
both
.The
uni
on is
wri
tten
A �
B.
In t
he
draw
ings
bel
ow,s
upp
ose
A i
s th
e se
t of
poi
nts
in
side
th
e ci
rcle
and
B i
s th
e se
t of
poi
nts
in
side
th
e sq
uar
e.T
hen
,th
e sh
aded
are
assh
ow t
he
inte
rsec
tion
in
th
e fi
rst
draw
ing
and
the
un
ion
in
th
e se
con
ddr
awin
g.
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
inte
gers
bet
wee
n 2
an
d 7}
A �
B �
{3}
B �
{0,3
,8}
A �
B �
{0,3
,4,5
,6,8
}
3.A
�{t
he
stat
es w
hos
e n
ames
sta
rt w
ith
K}
A �
B �
{Kan
sas}
B �
{th
e st
ates
wh
ose
capi
tals
are
Hon
olu
lu o
r T
opek
a}A
�B
�{H
awai
i,K
ansa
s,K
entu
cky}
4.A
�{t
he
posi
tive
in
tege
r fa
ctor
s of
24}
A �
B �
{1,2
,3,4
,6,8
}B
�{t
he
cou
nti
ng
nu
mbe
rs l
ess
than
10}
A �
B �
{1,2
,3,4
,5,6
,7,8
,9,1
2,24
}
Su
pp
ose
A �
{nu
mb
ers
xsu
ch t
hat
x�
3},B
�{n
um
ber
s x
such
as
x
�1}
,an
d
C �
{nu
mb
ers
xsu
ch t
hat
x
1.5}
.Gra
ph
eac
h o
f th
e fo
llow
ing.
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
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-1
2-1
Answers (Lesson 2-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Add
ing
an
d S
ub
trac
tin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
2-2
©G
lenc
oe/M
cGra
w-H
ill81
Gle
ncoe
Alg
ebra
1
Lesson 2-2
Ad
d R
atio
nal
Nu
mb
ers
Ad
din
g R
atio
nal
Nu
mb
ers,
Add
the
num
bers
. If
both
are
pos
itive
, th
e su
m is
pos
itive
; if
both
are
neg
ativ
e,
Sam
e S
ign
the
sum
is n
egat
ive.
Ad
din
g R
atio
nal
Nu
mb
ers,
Sub
trac
t th
e nu
mbe
r w
ith t
he le
sser
abs
olut
e va
lue
from
the
num
ber
with
the
Dif
fere
nt
Sig
ns
grea
ter
abso
lute
val
ue. T
he s
ign
of t
he s
um is
the
sam
e as
the
sig
n of
the
num
ber
with
the
gre
ater
abs
olut
e va
lue.
Use
a n
um
ber
lin
e to
fin
d t
he
sum
�2
�(�
3).
Ste
p 1
Dra
w a
n a
rrow
fro
m 0
to
�2.
Ste
p 2
Fro
m t
he
tip
of t
he
firs
t ar
row
,dra
wa
seco
nd
arro
w 3
un
its
to t
he
left
to
repr
esen
t ad
din
g �
3.S
tep
3T
he
seco
nd
arro
w e
nds
at
the
sum
�5.
So
�2
�(�
3) �
�5.
10
�1
�2
�3
�4
�5
�6
�7
�8
�9
23
�3
�2
Fin
d e
ach
su
m.
a.�
8 �
5�
8 �
5�
�(
�8
�5
)�
�(8
�5)
��
3
b.
���
��
����
���
��
��
��
��
��
��
�1 � 4
2 � 43 � 4
2 � 43 � 4
2 � 43 � 4
1 � 23 � 4
1 � 23 � 4
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
su
m.
1.12
�24
362.
�6
�14
83.
�12
�(�
15)
�27
4.�
21.5
�34
.212
.75.
8.2
�(�
3.5)
4.7
6.23
.5 �
(�15
.2)
8.3
7.90
�(�
105)
�15
8.10
8 �
(�62
)46
9.�
84 �
(�90
)�
174
10.
�o
r 1
11.
�12
.��
13.�
���
��
14.�
�15
.��
����
16.�
���
�17
.�1.
6 �
(�1.
8)18
.�0.
008
�(�
0.25
)
�o
r �
1�
3.4
�0.
258
13 � 3043 � 30
5 � 63 � 5
19 � 2010 � 20
18 � 4024 � 55
7 � 111 � 5
11 � 121 � 4
2 � 3
7 � 453 � 5
4 � 913
5� 23
86 � 17
3 � 141 � 21
22 � 211 � 3
5 � 7
©G
lenc
oe/M
cGra
w-H
ill82
Gle
ncoe
Alg
ebra
1
Sub
trac
t R
atio
nal
Nu
mb
ers
Eve
ry p
osit
ive
rati
onal
nu
mbe
r ca
n b
e pa
ired
wit
h a
neg
ativ
e ra
tion
al n
um
ber
so t
hat
th
eir
sum
is
0.T
he
nu
mbe
rs,c
alle
d op
pos
ites
,are
add
itiv
e in
vers
esof
eac
h o
ther
.
Ad
dit
ive
Inve
rse
Pro
per
tyF
or e
very
num
ber
a, a
�(�
a) �
0.
To s
ubtr
act
a ra
tion
al n
umbe
r,ad
d it
s in
vers
e an
d us
e th
e ru
les
for
addi
tion
giv
en o
n pa
ge 8
1.
Su
btr
acti
on
of
Rat
ion
al N
um
ber
sF
or a
ny n
umbe
rs a
and
b, a
�
b�
a�
(�b)
.
Fin
d 8
.5 �
10.2
.
8.5
�10
.2 �
8.5
�( �
10.2
)To
sub
trac
t 10
.2,
add
its in
vers
e.
��
(�
10.2
�
8.5
)�
10.2
is
gre
ater
, so
the
res
ult
is n
egat
ive.
��
1.7
Sim
plify
.
Fin
d e
ach
dif
fere
nce
.
1.11
�41
2.15
�(�
21)
3.�
33 �
(�17
)
�30
36�
16
4.18
�(�
12)
5.15
.5 �
(�2.
5)6.
65.8
�(�
23.5
)
3018
89.3
7.90
�(�
15)
8.�
10.8
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.8)
9.�
84 �
(�72
)
105
�17
.6�
12
10.5
8.8
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11.2
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.2 �
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12.�
9 �
(�5.
6)
70�
21.4
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4
13.�
� ��
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15.
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or
1
16.
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�17
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18.
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or
1�
or
1
19.S
anel
le w
as p
layi
ng
a vi
deo
gam
e.H
er s
core
s w
ere
�50
,�75
,�18
,an
d �
22.W
hat
was
her
fin
al s
core
?�
85
20.T
he
foot
ball
tea
m o
ffen
se b
egan
a d
rive
fro
m t
hei
r 20
-yar
d li
ne.
Th
ey g
ain
ed 8
yar
ds,l
ost
12 y
ards
an
d lo
st 2
yar
ds b
efor
e h
avin
g to
kic
k th
e ba
ll.W
hat
yar
d li
ne
wer
e th
ey o
nw
hen
th
ey h
ad t
o ki
ck t
he
ball
?14
-yar
d li
ne
1 � 23 � 2
13 � 241 � 46
47 � 46
18 � 2024 � 10
3 � 97 � 8
1 � 212 � 23
25 � 3661 � 36
13 � 355 � 12
5 � 99 � 4
4 � 71 � 5
3 � 41 � 3
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Add
ing
an
d S
ub
trac
tin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
2-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 2-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
Add
ing
an
d S
ub
trac
tin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
2-2
©G
lenc
oe/M
cGra
w-H
ill83
Gle
ncoe
Alg
ebra
1
Lesson 2-2
Fin
d e
ach
su
m.
1.28
�13
2.18
�54
3.�
6 �
15
4172
9
4.�
12 �
255.
�14
�11
6.�
42 �
18
13�
3�
24
7.�
19 �
(�3)
8.�
9 �
(�17
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25 �
(�30
)
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10.1
6 �
(�20
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.�
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12.�
2.5
�3.
2
�4
�0.
7
Fin
d e
ach
dif
fere
nce
.
13.3
1 �
1214
.53
�47
15.1
7 �
20
196
�3
16.2
8 �
3917
.�15
�65
18.�
27 �
13
�11
�80
�40
19.�
11 �
(�12
)20
.�25
�(�
36)
21.�
9 �
(�7)
111
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22.�
14 �
(�8)
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1.5
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24.3
.6 �
4.8
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1.2
25.�
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27.�
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0�
28.W
EATH
ERA
t 6:
00 P
.M.,
the
tem
pera
ture
in
Nor
th F
ork
was
28
degr
ees
Fah
ren
hei
t.S
hor
tly
afte
rwar
d,a
stro
ng
cold
fro
nt
pass
ed t
hro
ugh
,an
d th
e te
mpe
ratu
re d
ropp
ed
36 d
egre
es b
y 8:
00 A
.M.t
he
nex
t m
orn
ing.
Wh
at w
as t
he
tem
pera
ture
at
8:00
A.M
.?�
8�F
3 � 41 � 2
3 � 23 � 4
1 � 61 � 3
1 � 21 � 2
1 � 2
3 � 41 � 4
©G
lenc
oe/M
cGra
w-H
ill84
Gle
ncoe
Alg
ebra
1
Fin
d e
ach
su
m.
1.�
82 �
14�
682.
�33
�47
143.
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�(�
39)
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4.8
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11)
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21.
56.
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06)
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r 1
10.�
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12.
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or
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Fin
d e
ach
dif
fere
nce
.
13.6
5 �
93�
2814
.�42
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17)
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15.1
3 �
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16.�
8 �
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5117
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8 �
(�12
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95.2
18.1
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18.1
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4.7)
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22.
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24.
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��
or
�2
FIN
AN
CE
For
Exe
rcis
es 2
5–27
,use
th
e fo
llow
ing
info
rmat
ion
.
Th
e ta
ble
show
s ac
tivi
ty i
n B
en’s
ch
ecki
ng
acco
un
t.T
he
bala
nce
bef
ore
the
acti
vity
was
$200
.00.
Dep
osit
s ar
e ad
ded
to a
n a
ccou
nt
and
chec
ks a
re s
ubt
ract
ed.
Nu
mb
erD
ate
Tran
sact
ion
Am
ou
nt
Bal
ance
5/2
depo
sit
52.5
025
2.50
101
5/10
chec
k to
Cas
tle M
usic
25.5
0?
102
6/1
chec
k to
Com
p U
Sav
e23
5.40
?
25.W
hat
is
the
acco
un
t ba
lan
ce a
fter
wri
tin
g ch
eck
nu
mbe
r 10
1?$2
27.0
0
26.W
hat
is
the
acco
un
t ba
lan
ce a
fter
wri
tin
g ch
eck
nu
mbe
r 10
2?�
$8.4
0
27.R
eali
zin
g th
at h
e h
as ju
st w
ritt
en a
ch
eck
for
mor
e th
an i
s in
th
e ac
cou
nt,
Ben
imm
edia
tely
dep
osit
s $4
25.W
hat
wil
l th
is m
ake
his
new
acc
oun
t ba
lan
ce?
$416
.60
28.C
HEM
ISTR
YT
he
mel
tin
g po
ints
of
kryp
ton
,rad
on,a
nd
sulf
ur
in d
egre
es C
elsi
us
are
�15
6.6,
�61
.8,a
nd
112.
8,re
spec
tive
ly.W
hat
is
the
diff
eren
ce i
n m
elti
ng
poin
ts b
etw
een
rado
n a
nd
kryp
ton
an
d be
twee
n s
ulf
ur
and
kryp
ton
?94
.8�C
an
d 2
69.4
�C
23 � 241 � 14
29 � 141 � 2
5 � 61 � 8
3 � 75 � 2
5 � 64 � 3
13 � 152 � 3
1 � 57 � 247 � 20
27 � 201 � 15
2 � 33 � 8
3 � 53 � 4
2 � 33 � 5
7 � 1825 � 18
5 � 65 � 9
Pra
ctic
e (
Ave
rag
e)
Add
ing
an
d S
ub
trac
tin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
2-2
Answers (Lesson 2-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csA
dd
ing
an
d S
ub
trac
tin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
2-2
©G
lenc
oe/M
cGra
w-H
ill85
Gle
ncoe
Alg
ebra
1
Lesson 2-2
Pre-
Act
ivit
yH
ow c
an a
nu
mb
er l
ine
be
use
d t
o sh
ow a
foo
tbal
l te
am’s
pro
gres
s?
Rea
d th
e in
trod
uct
ion
to
Les
son
2-2
at
the
top
of p
age
73 i
n y
our
text
book
.
Use
pos
itiv
eor
neg
ativ
eto
com
plet
e th
e fo
llow
ing
sen
ten
ces.
Th
e fi
ve-y
ard
pen
alty
is
show
n b
y th
e n
um
ber
�5.
Th
e 13
-yar
d pa
ss i
s sh
own
by
the
nu
mbe
r 13
.
Rea
din
g t
he
Less
on
1.T
o ad
d tw
o ra
tion
al n
um
bers
,you
can
use
a n
um
ber
lin
e.E
ach
nu
mbe
r w
ill
bere
pres
ente
d by
an
arr
ow.
a.W
her
e on
th
e n
um
ber
lin
e do
es t
he
arro
w f
or t
he
firs
t n
um
ber
begi
n?
at 0
b.
Arr
ows
for
neg
ativ
e n
um
bers
wil
l po
int
to t
he
(lef
t/ri
ght)
.Arr
ows
for
posi
tive
nu
mbe
rs w
ill
poin
t to
th
e (l
eft/
righ
t).
2.T
wo
stu
den
ts a
dded
th
e sa
me
pair
of
rati
onal
nu
mbe
rs.B
oth
stu
den
ts g
ot t
he
corr
ect
sum
.On
e st
ude
nt
use
d a
nu
mbe
r li
ne.
Th
e ot
her
stu
den
t u
sed
abso
lute
val
ue.
Th
en t
hey
com
pare
d th
eir
wor
k.
a.H
ow d
o th
e ar
row
s sh
ow w
hic
h n
um
ber
has
th
e gr
eate
r ab
solu
te v
alu
e?
Th
e n
um
ber
wit
h t
he
gre
ater
ab
solu
te v
alu
e m
atch
es t
he
lon
ger
arr
ow
.
b.
If t
he
lon
ger
arro
w p
oin
ts t
o th
e le
ft,t
hen
th
e su
m i
s (p
osit
ive/
neg
ativ
e).I
f th
e lo
nge
r ar
row
poi
nts
to
the
righ
t,th
en t
he
sum
is
(pos
itiv
e/n
egat
ive)
.
3.If
tw
o n
um
bers
are
add
itiv
e in
vers
es,w
hat
mu
st b
e tr
ue
abou
t th
eir
abso
lute
val
ues
?
Th
e ab
solu
te v
alu
es o
f th
e tw
o n
um
ber
s ar
e eq
ual
.
4.W
rite
eac
h s
ubt
ract
ion
pro
blem
as
an a
ddit
ion
pro
blem
.
a.12
�4
12 �
(�4)
b.
�15
�7
�15
�(�
7)
c.0
�9
0 �
(�9)
d.
�20
�34
�20
�(�
34)
Hel
pin
g Y
ou
Rem
emb
er
5.E
xpla
in w
hy
know
ing
the
rule
s fo
r ad
din
g ra
tion
al n
um
bers
can
hel
p yo
u t
o su
btra
ctra
tion
al n
um
bers
.
Sam
ple
an
swer
:S
ince
su
btr
acti
on
is t
he
sam
e as
ad
din
g t
he
op
po
site
,yo
u c
an c
han
ge
ever
y su
btr
acti
on
pro
ble
m t
o a
n a
dd
itio
n p
rob
lem
.Th
enyo
u c
an u
se t
he
rule
s fo
r ad
din
g r
atio
nal
nu
mb
ers
to g
et t
he
fin
al a
nsw
er.
po
siti
ve
neg
ativ
e
rig
ht
left
po
siti
ven
egat
ive
©G
lenc
oe/M
cGra
w-H
ill86
Gle
ncoe
Alg
ebra
1
Ro
un
din
g F
ract
ion
sR
oun
din
g fr
acti
ons
is m
ore
diff
icu
lt t
han
rou
ndi
ng
wh
ole
nu
mbe
rs o
r
deci
mal
s.F
or e
xam
ple,
thin
k ab
out
how
you
wou
ld r
oun
d in
ches
to
the
nea
rest
qu
arte
r-in
ch.T
hro
ugh
est
imat
ion
,you
mig
ht
real
ize
that
is l
ess
than
.B
ut,
is i
t cl
oser
to
or t
o ?
Her
e ar
e tw
o w
ays
to r
oun
d fr
acti
ons.
Exa
mpl
e 1
use
s on
ly t
he
frac
tion
s;E
xam
ple
2 u
ses
deci
mal
s.
1 � 41 � 2
1 � 24 � 9
4 � 9
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-2
2-2
Su
btra
ct t
he
frac
tion
tw
ice.
Use
th
e tw
on
eare
st q
uar
ters
.
��
��
Com
pare
th
e di
ffer
ence
s.
�
Th
e sm
alle
r di
ffer
ence
sh
ows
you
wh
ich
frac
tion
to
rou
nd
to.
rou
nds
to
.1 � 2
4 � 9
7 � 361 � 18
7 � 361 � 4
4 � 91 � 18
4 � 91 � 2
Ch
ange
th
e fr
acti
on a
nd
the
two
nea
rest
quar
ters
to
deci
mal
s.
�0.
44�,
�0.
5,�
0.25
Fin
d th
e de
cim
al h
alfw
ay b
etw
een
th
e tw
on
eare
st q
uar
ters
.
(0.5
�0.
25)
�0.
375
If t
he
frac
tion
is
grea
ter
than
th
e h
alfw
ayde
cim
al,r
oun
d u
p.If
not
,rou
nd
dow
n.
0.44�
�0.
3675
.So,
is m
ore
than
hal
f w
ay
betw
een
an
d .
rou
nds
to
.1 � 2
4 � 9
1 � 21 � 4
4 � 9
1 � 2
1 � 41 � 2
4 � 9
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Rou
nd
eac
h f
ract
ion
to
the
nea
rest
on
e-q
uar
ter.
Use
eit
her
met
hod
.
1.2.
3.4.
5.6.
7.8.
Rou
nd
eac
h d
ecim
al o
r fr
acti
on t
o th
e n
eare
st o
ne-
eigh
th.
9.0.
610
.0.1
11.0
.45
12.0
.85
13.
14.
15.
16.
1 � 25 � 9
7 � 823 � 25
1 � 83 � 20
3 � 45 � 7
7 � 81 � 2
1 � 85 � 8
3 � 423 � 30
1 � 49 � 25
1 � 231 � 50
1 � 47 � 20
1 � 44 � 15
3 � 47 � 11
1 � 23 � 7
1 � 41 � 3
Answers (Lesson 2-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Mu
ltip
lyin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
2-3
©G
lenc
oe/M
cGra
w-H
ill87
Gle
ncoe
Alg
ebra
1
Lesson 2-3
Mu
ltip
ly In
teg
ers
You
can
use
th
e ru
les
belo
w w
hen
mu
ltip
lyin
g in
tege
rs a
nd
rati
onal
nu
mbe
rs.
Mu
ltip
lyin
g N
um
ber
s w
ith
th
e S
ame
Sig
nT
he p
rodu
ct o
f tw
o nu
mbe
rs h
avin
g th
e sa
me
sign
is p
ositi
ve.
Mu
ltip
lyin
g N
um
ber
s w
ith
Dif
fere
nt
Sig
ns
The
pro
duct
of
two
num
bers
hav
ing
diffe
rent
sig
ns is
neg
ativ
e.
Fin
d e
ach
pro
du
ct.
a.�
7(6)
Th
e si
gns
are
diff
eren
t,so
th
e pr
odu
ct i
sn
egat
ive.
�7(
6) �
�42
b.
�18
(�10
)T
he
sign
s ar
e th
e sa
me,
so t
he
prod
uct
is
posi
tive
.�
18(�
10)
�18
0
Sim
pli
fy t
he
exp
ress
ion
(�2x
)5y.
(�2x
)5y
�(�
2)(5
)x
yC
omm
utat
ive
Pro
pert
y (
)
�(�
2
5)xy
Ass
ocia
tive
Pro
pert
y
��
10xy
Sim
plify
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
pro
du
ct.
1.11
(4)
2.�
5(�
3)3.
(�24
)(�
2)
4415
48
4.(6
0)(�
3)5.
(�2)
(�3)
(�4)
6.8(
�15
)
�18
0�
24�
120
7.�
15(3
)8.
(12)
(�10
)9.
(�22
)(�
3)(2
)
�45
�12
013
2
10.(
5)(�
5)(0
)(4)
11.(
�15
)(45
)12
.(�
12)(
�23
)
0�
675
276
Sim
pli
fy e
ach
exp
ress
ion
.
13.4
(�2x
) �
8x14
.6(�
2n)
�10
n15
.6(3
y�
y)
�16
x�
22n
12y
16.�
3(3d
�2d
)17
.�2x
(2)
�2x
(3y)
18.4
m(�
2n)
�2d
(�4e
)
�15
d�
4x�
6xy
�8m
n�
8de
19.�
5(2x
�x)
�3(
�xy
)20
.(2)
(�4x
�2x
)21
.(�
3)(�
8n�
6m)
�15
x�
3xy
�4x
24n
�18
m
©G
lenc
oe/M
cGra
w-H
ill88
Gle
ncoe
Alg
ebra
1
Mu
ltip
ly R
atio
nal
Nu
mb
ers
Mu
ltip
lyin
g a
rati
onal
nu
mbe
r by
�1
give
s yo
u t
he
addi
tive
in
vers
e of
th
e n
um
ber.
Mu
ltip
licat
ive
Pro
per
ty o
f �
1T
he p
rodu
ct o
f an
y nu
mbe
r an
d �
1 is
(�1)
(5)
�5(
�1)
��
5 its
add
itive
inve
rse.
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Mu
ltip
lyin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
2-3
Eva
luat
e a
3 b2
if a
��
2an
d b
��
5.
a3b2
�(�
2)3 (
�5)
2S
ubst
itutio
n
�(�
8)(2
5)(�
2)3
��
8 an
d (�
5)2
�25
��
200
diffe
rent
sig
ns →
nega
tive
prod
uct
Eva
luat
e n
2 ���if
n�
�.
n2 ��
����
�2 ���S
ubst
itutio
n
��
����
���2
���
����o
r
��
diffe
rent
sig
ns →
nega
tive
prod
uct
3 � 20
1 � 41 � 2
1 � 21 � 2
3 � 51 � 4
3 � 51 � 2
3 � 5
1 � 23 � 5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
pro
du
ct.
1.(�
12)
2.��
����
3.��
���
�3
�
4.(6
.0)(
�0.
3)5.
�����
����
6.8(
�15
)
�1.
8�
�12
0
7.�
15(�
4)8.
��(�
10)
9.��
�(�3)�
�60
�5
10. �
�(�2)
(0) �
�11
. ����
�12
. ��1
���2
�0
�3
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
��
2.5,
b�
4.2,
c�
5.5,
and
d�
�0.
2.
13.�
2a2
14.5
(�2b
)15
.�6(
cd)
�12
.5�
426.
6
16.�
2(3d
�2c
)17
.�ad
�3c
18.b
2 (c
�2d
)
�20
.8�
1710
4.07
6
19.�
5bcd
20.�
3d2
�4
21.(
�3)
(�8a
�2b
)
23.1
3.88
�34
.8
1 � 24 � 15
1 � 31 � 2
4 � 51 � 3
1 � 44 � 5
4 � 5
2 � 32 � 5
1 � 2
1 � 8
3 � 41 � 3
1 � 2
4 � 352 � 15
2 � 52 � 7
2 � 31 � 5
1 � 4
Answers (Lesson 2-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Mu
ltip
lyin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
2-3
©G
lenc
oe/M
cGra
w-H
ill89
Gle
ncoe
Alg
ebra
1
Lesson 2-3
Fin
d e
ach
pro
du
ct.
1.9(
17)
153
2.�
8(�
7)56
3.5(
�7)
�35
4.�
4(11
)�
44
5.�
6(�
12)
726.
7(�
25)
�17
5
7.�
���
8.��
����
9.��
����
10. �
�����
11. ��
����
12.(
1.5)
(2.2
)3.
3
13.(
�2.
8)(0
.5)
�1.
414
.(2.
4)(�
0.6)
�1.
44
15.(
�4.
7)(�
1.3)
6.11
16.(
1.1)
(�1.
2)�
1.32
Sim
pli
fy e
ach
exp
ress
ion
.
17.5
(�2a
) �
8a�
18a
18.�
6(3x
) �
12x
�6x
19.3
(4n
�n
)9n
20.�
4(2d
�d
)�
4d
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
��
1.2,
b�
0.5,
c�
,an
d d
��
.
21.�
4ab
2.4
22.�
3b2
�0.
75
23.�
2a2
�2.
8824
.c2 ��
��
25.
d2
26.�
3cd
1
27.S
TAIR
CA
SES
A s
tair
case
in
an
off
ice
buil
din
g st
arts
at
grou
nd
leve
l.E
ach
ste
p do
wn
low
ers
you
by
7.5
inch
es.W
hat
is
you
r h
eigh
t in
rel
atio
n t
o gr
oun
d le
vel
afte
r de
scen
din
g20
ste
ps?
�15
0 in
.or
�12
ft
6 in
.
1 � 181 � 8
1 � 121 � 3
2 � 31 � 2
5 � 92 � 3
5 � 6
15 � 325 � 8
3 � 43 � 16
1 � 23 � 8
1 � 101 � 6
3 � 51 � 3
2 � 31 � 2
©G
lenc
oe/M
cGra
w-H
ill90
Gle
ncoe
Alg
ebra
1
Fin
d e
ach
pro
du
ct.
1.42
(7)
294
2.�
28(�
17)
476
3.15
(�34
)�
510
4.��
����
5.��
����
6.�
���
7.��
3��2
��o
r �
88.
��2
���1
�o
r 3
9.�1
���1
��o
r �
1
10.(
1.5)
(8.8
)13
.211
.(6.
8)(�
1.3)
�8.
8412
.(�
0.2)
(2.8
)�
0.56
13.(
�3.
6)(�
0.55
)1.
9814
.6.3
(�0.
7)�
4.41
15.
(�4)
(9)
�24
Sim
pli
fy e
ach
exp
ress
ion
.
16.5
(�3a
) �
18a
3a17
.�8(
4c)
�12
c�
20c
18.�
9(2g
�g)
�9g
19.7
(2b
�4b
)20
.�4x
(2y)
�(�
3b)(
�2d
)21
.�5p
(�3q
) �
(4m
)(�
6n)
�14
b�
8xy
�6b
d15
pq
�(�
24m
n)
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
��
,b�
,c�
�3.
4,an
d d
�0.
7.
22.b
2 ����
23.4
ab�
or
�2
24.5
a2(�
b)�
or
�2
25.�
6d2
�2.
9426
.cd
�3
�5.
3827
.c2 (
�5d
)�
40.4
6
28.R
ECIP
ESA
rec
ipe
for
butt
erm
ilk
bisc
uit
s ca
lls
for
3cu
ps o
f fl
our.
How
man
y cu
ps o
f
flou
r do
you
nee
d fo
r th
e re
cipe
?1
c
CO
MPU
TER
SF
or E
xerc
ises
29
and
30,
use
th
e fo
llow
ing
info
rmat
ion
.
Lee
za i
s do
wn
load
ing
a fi
le f
rom
a W
eb s
ite
at 4
7.3
kilo
byte
s pe
r se
con
d.
29.H
ow m
any
kilo
byte
s of
th
e fi
le w
ill
be d
own
load
ed a
fter
on
e m
inu
te?
2838
kilo
byte
s
30.H
ow m
any
kilo
byte
s w
ill
be d
own
load
ed a
fter
4.5
min
ute
s?12
,771
kilo
byte
s
CO
NSE
RV
ATI
ON
For
Exe
rcis
es 3
1 an
d 3
2,u
se t
he
foll
owin
g in
form
atio
n.
A c
oun
ty c
omm
issi
on h
as s
et a
side
640
acr
es o
f la
nd
for
a w
ildl
ife
pres
erve
.
31.S
upp
ose
of t
he
pres
erve
is
mar
shla
nd.
How
man
y ac
res
of t
he
pres
erve
are
mar
shla
nd?
256
acre
s
32.I
f th
e fo
rest
ed a
rea
of t
he
pres
erve
is
1.5
tim
es l
arge
r th
an t
he
mar
shla
nd,
how
man
yac
res
of t
he
pres
erve
are
for
este
d?38
4 ac
res
2 � 5
2 � 31 � 2
1 � 3
2 � 512 � 5
2 � 512 � 5
3 � 82 � 3
3 � 44 � 5
2 � 3
1 � 23 � 2
1 � 51 � 4
1 � 928 � 9
1 � 62 � 3
1 � 865 � 8
1 � 21 � 4
9 � 145 � 7
9 � 102 � 3
5 � 64 � 5
21 � 327 � 8
3 � 4
Pra
ctic
e (
Ave
rag
e)
Mu
ltip
lyin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
2-3
Answers (Lesson 2-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csM
ult
iply
ing
Rat
ion
al N
um
ber
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
2-3
©G
lenc
oe/M
cGra
w-H
ill91
Gle
ncoe
Alg
ebra
1
Lesson 2-3
Pre-
Act
ivit
yH
ow d
o co
nsu
mer
s u
se m
ult
ipli
cati
on o
f ra
tion
al n
um
ber
s?
Rea
d th
e in
trod
uct
ion
to
Les
son
2-3
at
the
top
of p
age
79 i
n y
our
text
book
.
•H
ow i
s th
e am
oun
t of
th
e co
upo
n s
how
n o
n t
he
sale
s sl
ip?
�1.
00•
Bes
ides
th
e am
oun
t,h
ow i
s th
e n
um
ber
repr
esen
tin
g th
e co
upo
n d
iffe
ren
tfr
om t
he
oth
er n
um
bers
on
th
e sa
les
slip
?
It is
neg
ativ
e.
Rea
din
g t
he
Less
on
1.C
ompl
ete:
If t
wo
nu
mbe
rs h
ave
diff
eren
t si
gns,
the
one
nu
mbe
r is
pos
itiv
e an
d th
e ot
her
nu
mbe
r is
.
2.C
ompl
ete
the
tabl
e.
Mu
ltip
licat
ion
Are
th
e si
gn
s o
f th
e n
um
ber
s th
e sa
me
Is
th
e p
rod
uct
po
siti
ve o
r n
egat
ive?
Exa
mp
leo
r d
iffe
ren
t?
a.(�
4)(9
)d
iffe
ren
tn
egat
ive
b.
(�2)
(�13
)th
e sa
me
po
siti
ve
c.5(
�8)
dif
fere
nt
neg
ativ
e
d.
6(3)
the
sam
ep
osi
tive
3.E
xpla
in w
hat
th
e te
rm “
addi
tive
in
vers
e”m
ean
s to
you
.Th
en g
ive
an e
xam
ple.
Th
e p
rod
uct
of
any
nu
mb
er a
nd
�1
is it
s ad
dit
ive
inve
rse;
��
(�1)
�.
Hel
pin
g Y
ou
Rem
emb
er
4.D
escr
ibe
how
you
kn
ow t
hat
th
e pr
odu
ct o
f �
3 an
d �
5 is
pos
itiv
e.T
hen
des
crib
e h
owyo
u k
now
th
at t
he
prod
uct
of
3 an
d �
5 is
neg
ativ
e.
Sam
ple
an
swer
:Th
e si
gn
s ar
e th
e sa
me;
the
sig
ns
are
dif
fere
nt.
2 � 32 � 3
neg
ativ
e
©G
lenc
oe/M
cGra
w-H
ill92
Gle
ncoe
Alg
ebra
1
Co
mp
ou
nd
Inte
rest
In m
ost
ban
ks,i
nte
rest
on
sav
ings
acc
oun
ts i
s co
mpo
un
ded
at s
et t
ime
peri
ods
such
as
thre
e or
six
mon
ths.
At
the
end
of e
ach
per
iod,
the
ban
k ad
ds t
he
inte
rest
ear
ned
to
the
acco
un
t.D
uri
ng
the
nex
t pe
riod
,th
e ba
nk
pays
in
tere
st o
n a
ll t
he
mon
ey i
n t
he
ban
k,in
clu
din
g in
tere
st.
In t
his
way
,th
e ac
cou
nt
earn
s in
tere
st o
n i
nte
rest
.
Su
ppos
e M
s.T
ann
er h
as $
1000
in
an
acc
oun
t th
at i
s co
mpo
un
ded
quar
terl
y at
5%
.Fin
d th
e ba
lan
ce a
fter
th
e fi
rst
two
quar
ters
.
Use
I�
prt
to f
ind
the
inte
rest
ear
ned
in
th
e fi
rst
quar
ter
if p
�10
00
and
r�
5%.W
hy
is t
equ
al t
o ?
Fir
st q
uar
ter:
I�
1000
0.
05
I�
12.5
0
Th
e in
tere
st,$
12.5
0,ea
rned
in
th
e fi
rst
quar
ter
is a
dded
to
$100
0.T
he
prin
cipa
l be
com
es $
1012
.50.
Sec
ond
quar
ter:
I�
1012
.50
0.
05
I�
12.6
5625
Th
e in
tere
st i
n t
he
seco
nd
quar
ter
is $
12.6
6.
Th
e ba
lan
ce a
fter
tw
o qu
arte
rs i
s $1
012.
50 �
12.6
6 or
$10
25.1
6.
An
swer
eac
h o
f th
e fo
llow
ing
qu
esti
ons.
1.H
ow m
uch
in
tere
st i
s ea
rned
in
th
e th
ird
quar
ter
of M
s.T
ann
er’s
acco
un
t?I�
$12.
81
2.W
hat
is
the
bala
nce
in
her
acc
oun
t af
ter
thre
e qu
arte
rs?
$103
7.97
3.H
ow m
uch
in
tere
st i
s ea
rned
at
the
end
of o
ne
year
?I�
$12.
97
4.W
hat
is
the
bala
nce
in
her
acc
oun
t af
ter
one
year
?$1
050.
94
5.S
upp
ose
Ms.
Tan
ner
’s a
ccou
nt
is c
ompo
un
ded
sem
ian
nu
ally
.Wh
atis
th
e ba
lan
ce a
t th
e en
d of
six
mon
ths?
$102
5.00
6.W
hat
is
the
bala
nce
aft
er o
ne
year
if
her
acc
oun
t is
com
pou
nde
dse
mia
nn
ual
ly?
$105
0.63
1 � 4
1 � 4
1 � 4
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-3
2-3
Answers (Lesson 2-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Div
idin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
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AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
©G
lenc
oe/M
cGra
w-H
ill93
Gle
ncoe
Alg
ebra
1
Lesson 2-4
Div
ide
Inte
ger
sT
he
rule
s fo
r fi
ndi
ng
the
sign
of
a qu
otie
nt
are
sim
ilar
to
the
rule
s fo
rfi
ndi
ng
the
sign
of
a pr
odu
ct.
Div
idin
g T
wo
Nu
mb
ers
wit
h t
he
Sam
e S
ign
The
quo
tient
of
two
num
bers
hav
ing
the
sam
e si
gn is
pos
itive
.
Div
idin
g T
wo
Nu
mb
ers
wit
h D
iffe
ren
t S
ign
sT
he q
uotie
nt o
f tw
o nu
mbe
rs h
avin
g di
ffere
nt s
igns
is n
egat
ive.
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otie
nt.
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©G
lenc
oe/M
cGra
w-H
ill94
Gle
ncoe
Alg
ebra
1
Div
ide
Rat
ion
al N
um
ber
sT
he
rule
s fo
r di
visi
on w
ith
in
tege
rs a
lso
appl
y to
div
isio
n
wit
h r
atio
nal
nu
mbe
rs.T
o di
vide
by
any
non
zero
nu
mbe
r,,m
ult
iply
by
the
reci
proc
al o
f
that
nu
mbe
r,.
Div
isio
n o
f R
atio
nal
Nu
mb
ers
��
d � c
a � bc � d
a � b
d � c
c � d
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Div
idin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
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AT
E__
____
____
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ER
IOD
____
_
2-4
2-4
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1 � 8
Answers (Lesson 2-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
Div
idin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
©G
lenc
oe/M
cGra
w-H
ill95
Gle
ncoe
Alg
ebra
1
Lesson 2-4
Fin
d e
ach
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otie
nt.
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©G
lenc
oe/M
cGra
w-H
ill96
Gle
ncoe
Alg
ebra
1
Fin
d e
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nt.
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22.E
XER
CIS
EA
shle
y w
alks
2m
iles
aro
un
d a
lake
th
ree
tim
es a
wee
k.If
Ash
ley
wal
ks
arou
nd
the
lake
in
h
our,
wh
at i
s h
er r
ate
of s
peed
? (H
int:
Use
th
e fo
rmu
la r
�,
wh
ere
ris
rat
e,d
is d
ista
nce
,an
d t
is t
ime.
)3
mi/h
23.P
UB
LIC
ATI
ON
A p
rodu
ctio
n a
ssis
tan
t m
ust
div
ide
a pa
ge o
f te
xt i
nto
tw
o co
lum
ns.
If
the
page
is
6in
ches
wid
e,h
ow w
ide
wil
l ea
ch c
olu
mn
be?
3in
.
RO
LLER
CO
AST
ERS
For
Exe
rcis
es 2
4 an
d 2
5,u
se t
he
foll
owin
g in
form
atio
n.
Th
e fo
rmu
la f
or a
ccel
erat
ion
is
a�
,wh
ere
ais
acc
eler
atio
n,f
is f
inal
spe
ed,s
is
star
tin
g sp
eed,
and
tis
tim
e.
24.T
he
Hyp
erso
nic
XL
C r
olle
r co
aste
r in
Vir
gin
ia g
oes
from
zer
o to
80
mil
es p
er h
our
in
1.8
seco
nds
.Wh
at i
s it
s ac
cele
rati
on i
n m
iles
per
hou
r pe
r se
con
d to
th
e n
eare
st t
enth
?So
urce
: www
.thril
lride
.com
abo
ut
44.4
mi/
h p
er s
eco
nd
25.W
hat
is
the
acce
lera
tion
in
fee
t pe
r se
con
d pe
r se
con
d? (
Hin
t:C
onve
rt m
iles
to
feet
an
dh
ours
to
seco
nds
,th
en a
pply
th
e fo
rmu
la f
or a
ccel
erat
ion
.1 m
ile
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eet)
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ut
3911
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per
sec
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3 � 5Pra
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e (
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e)
Div
idin
g R
atio
nal
Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
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AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
Answers (Lesson 2-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csD
ivid
ing
Rat
ion
al N
um
ber
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
©G
lenc
oe/M
cGra
w-H
ill97
Gle
ncoe
Alg
ebra
1
Lesson 2-4
Pre-
Act
ivit
yH
ow c
an y
ou u
se d
ivis
ion
of
rati
onal
nu
mb
ers
to d
escr
ibe
dat
a?
Rea
d th
e in
trod
uct
ion
to
Les
son
2-4
at
the
top
of p
age
84 i
n y
our
text
book
.
•W
hat
is
mea
nt
by t
he
term
mea
n?
the
sum
of
a se
t o
f d
ata
item
s d
ivid
ed b
y th
e n
um
ber
of
dat
a it
ems.
•In
th
e ex
pres
sion
,w
ill
the
nu
mer
ator
be
posi
tive
or
neg
ativ
e?n
egat
ive
Rea
din
g t
he
Less
on
1.E
xpla
in w
hat
th
e te
rmin
vers
e op
erat
ion
sm
ean
s to
you
.
Sam
ple
an
swer
:In
vers
e o
per
atio
ns
are
op
erat
ion
s th
at u
nd
o
on
e an
oth
er.
2.W
rite
neg
ativ
eor
pos
itiv
eto
des
crib
e th
e qu
otie
nt.
Exp
lain
you
r an
swer
.
Exp
ress
ion
Neg
ativ
e o
r P
osi
tive
?E
xpla
nat
ion
a.n
egat
ive
Th
e si
gn
s o
f th
e tw
o n
um
ber
s ar
e d
iffe
ren
t.
b.
po
siti
veT
he
sig
ns
of
the
two
nu
mb
ers
are
the
sam
e.
c.p
osi
tive
Aft
er m
ult
iply
ing
,th
e si
gn
s o
f th
e n
um
ber
sb
ein
g d
ivid
ed a
re t
he
sam
e.
Hel
pin
g Y
ou
Rem
emb
er
3.E
xpla
in h
ow k
now
ing
the
rule
s fo
r m
ult
iply
ing
rati
onal
nu
mbe
rs c
an h
elp
you
rem
embe
rth
e ru
les
for
divi
din
g ra
tion
al n
um
bers
.
Sam
ple
an
swer
:B
oth
ru
les
stat
e th
at t
he
answ
er(p
rod
uct
fo
rm
ult
iplic
atio
n,q
uo
tien
t fo
r d
ivis
ion
) is
po
siti
ve if
th
e si
gn
s ar
e th
e sa
me
and
neg
ativ
e if
th
e si
gn
s ar
e d
iffe
ren
t.
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6)(�
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lenc
oe/M
cGra
w-H
ill98
Gle
ncoe
Alg
ebra
1
Oth
er K
ind
s o
f M
ean
sT
her
e ar
e m
any
diff
eren
t ty
pes
of m
ean
s be
side
s th
e ar
ith
met
icm
ean
.A m
ean
for
a s
et o
f n
um
bers
has
th
ese
two
prop
erti
es:
a.It
typ
ifie
s or
rep
rese
nts
th
e se
t.b
.It
is
not
les
s th
an t
he
leas
t n
um
ber
and
it i
s n
ot g
reat
er t
han
th
egr
eate
st n
um
ber.
Her
e ar
e th
e fo
rmul
as f
or t
he a
rith
met
ic m
ean
and
thre
e ot
her
mea
ns.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-4
2-4
Ari
thm
etic
Mea
n
Add
th
e n
um
bers
in
th
e se
t.T
hen
div
ide
the
sum
by
n,t
he
nu
mbe
r of
ele
men
ts i
nth
e se
t.
Har
mon
ic M
ean
Div
ide
the
nu
mbe
r of
ele
men
ts i
n t
he
set
byth
e su
m o
f th
e re
cipr
ocal
s of
th
e n
um
bers
.
Geo
met
ric
Mea
n
Mu
ltip
ly a
ll t
he
nu
mbe
rs i
n t
he
set.
Th
enfi
nd
the
nth
roo
t of
th
eir
prod
uct
.n �
x 1�
x 2�
�x 3
��
…�
x n�
Qu
adra
tic
Mea
n
Add
th
e sq
uar
es o
f th
e n
um
bers
.Div
ide
thei
r su
m b
y th
e n
um
ber
in t
he
set.
Th
en,t
ake
the
squ
are
root
.
���
�x 12
�x 22
�x 32
�…
�x n
2
��
��
n
n�
��
� x1 1��
� x1 2��
� x1 3��
…�
� x1 n�
x 1�
x 2�
x 3�
…�
x n�
��
n
Fin
d t
he
fou
r d
iffe
ren
t m
ean
s to
th
e n
eare
st h
un
dre
dth
for
eac
h s
et o
f n
um
ber
s.
1.10
,100
2.50
,60
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55G
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2.83
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2.19
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3.32
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3.16
5.U
se t
he
resu
lts
from
Exe
rcis
es 1
to
4 to
com
pare
th
e re
lati
ve s
izes
of t
he
fou
r ty
pes
of m
ean
s.F
rom
leas
t to
gre
ates
t,th
e m
ean
s ar
e th
e h
arm
on
ic,g
eom
etri
c,ar
ith
met
ic,a
nd
qu
adra
tic
mea
ns.
Answers (Lesson 2-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Sta
tist
ics:
Dis
pla
yin
g a
nd
An
alyz
ing
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
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AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
©G
lenc
oe/M
cGra
w-H
ill99
Gle
ncoe
Alg
ebra
1
Lesson 2-5
Cre
ate
Lin
e Pl
ots
an
d S
tem
-an
d-L
eaf
Plo
tsO
ne
way
to
disp
lay
data
gra
phic
ally
is w
ith
a l
ine
plo
t.A
lin
e pl
ot i
s a
nu
mbe
r li
ne
labe
led
wit
h a
sca
le t
hat
in
clu
des
all
the
data
an
d
s pl
aced
abo
ve a
dat
a po
int
each
tim
e it
occ
urs
in
th
e da
ta l
ist.
Th
e
s re
pres
ent
the
freq
uen
cyof
th
e da
ta.A
ste
m-a
nd
-lea
f p
lot
can
als
o be
use
d to
org
aniz
e da
ta.T
he
grea
test
com
mon
plac
e va
lue
is c
alle
d th
e st
em,a
nd
the
nu
mbe
rs i
n t
he
nex
t gr
eate
st p
lace
valu
e fo
rm t
he
leav
es.
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w a
lin
e p
lot
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ct a
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r li
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ing
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e po
ints
.
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p 2
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en p
lace
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ab
ove
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ime
it o
ccu
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us
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4w
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.Th
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Exam
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Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Use
th
e ta
ble
at
the
righ
t fo
r E
xerc
ises
1–3
.
1.M
ake
a li
ne
plot
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rese
nti
ng
the
wei
ghts
of
the
wre
stle
rs s
how
n i
n t
he
tabl
e at
th
e ri
ght.
2.H
ow m
any
wre
stle
rs w
eigh
ove
r 14
0 lb
?7
3.W
hat
is
the
grea
test
wei
ght?
190
lb
Use
eac
h s
et o
f d
ata
to m
ake
a st
em-a
nd
-lea
f p
lot.
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arsi
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170
160
135
135
160
122
188
154
108
135
140
122
103
190
154
©G
lenc
oe/M
cGra
w-H
ill10
0G
lenc
oe A
lgeb
ra 1
An
alyz
e D
ata
Nu
mbe
rs t
hat
rep
rese
nt
the
cen
tral
ized
,or
mid
dle,
valu
e of
a s
et o
f da
taar
e ca
lled
mea
sure
s of
cen
tral
ten
den
cy.T
hre
e m
easu
res
of c
entr
al t
ende
ncy
are
th
em
ean
,med
ian
,an
d m
ode.
Def
init
ion
Exa
mp
le
Mea
nS
um o
f th
e da
ta v
alue
s di
vide
d by
the
D
ata:
24,
36,
21,
30,
21,
30;
�
27nu
mbe
r of
val
ues
in t
he d
ata
set.
The
mid
dle
num
ber
in a
dat
a se
t w
hen
the
num
bers
are
arr
ange
d in
num
eric
al
Med
ian
orde
r. If
ther
e is
an
even
num
ber
of
Dat
a: 2
1, 2
1, 2
5, 3
0, 3
1, 4
2;
�27
.5va
lues
, th
e m
edia
n is
hal
fway
bet
wee
n th
e tw
o m
iddl
e va
lues
.
Mo
de
The
num
ber
or n
umbe
rs t
hat
occu
rD
ata:
21,
21,
24,
30,
30,
36;
21
and
30 a
re m
odes
mos
t of
ten
in t
he s
et o
f da
ta.
Wh
ich
mea
sure
of
cen
tral
ten
den
cy b
est
rep
rese
nts
th
e d
ata?
Fin
d th
e m
ean,
med
ian,
and
mod
e.
Mea
n �
105
Med
ian
�10
2
Mod
es �
99 a
nd 1
12
The
med
ian
best
rep
rese
nts
the
cent
er o
f th
e da
ta s
ince
the
mea
n is
too
hig
h.
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d t
he
mea
n,m
edia
n,a
nd
mod
e fo
r ea
ch d
ata
set.
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en t
ell
wh
ich
bes
tre
pre
sen
ts t
he
dat
a.
1.2.
3.
mea
n �
38.7
;m
ean
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8.8
mea
n �
69.3
;m
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3.5
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des
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r m
od
e12
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ean
or
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ian
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n o
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edia
n
4.5.
mea
n �
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ean
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7;m
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8;m
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no
ne;
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de
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5;
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Stu
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nte
rven
tion
(c
onti
nued
)
Sta
tist
ics:
Dis
pla
yin
g a
nd
An
alyz
ing
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 2-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Sta
tist
ics:
Dis
pla
yin
g a
nd
An
alyz
ing
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
©G
lenc
oe/M
cGra
w-H
ill10
1G
lenc
oe A
lgeb
ra 1
Lesson 2-5
Use
eac
h s
et o
f d
ata
to m
ake
a li
ne
plo
t.
1.59
3950
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OM
EF
or E
xerc
ises
3–5
,use
th
e li
st t
hat
sh
ows
the
inco
me
from
eac
h a
ssig
nm
ent
for
a p
riva
te i
nve
stig
ator
for
a y
ear.
3.M
ake
a li
ne
plot
of
the
data
.
4.W
hat
was
th
e m
edia
n i
nco
me
per
assi
gnm
ent
for
the
inve
stig
ator
?$6
200
5.D
oes
the
med
ian
bes
t re
pres
ent
the
data
?Ye
s;th
e in
com
es o
f $7
800
(th
e m
od
e) a
re f
ar t
o t
he
rig
ht
on
th
e p
lot,
and
also
mak
e th
e m
ean
to
o h
igh
.
Use
eac
h s
et o
f d
ata
to m
ake
a st
em-a
nd
-lea
f p
lot.
6.52
6840
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2.3
1.7
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5563
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2.8
4.3
5.2
4.1
2.2
EMPL
OY
MEN
TF
or E
xerc
ises
8–1
0,u
se t
he
list
th
at s
how
s th
e ag
es o
f em
plo
yees
at
Wat
son
&S
terl
ing
Pu
bli
cati
ons.
8.M
ake
a st
em-a
nd-
leaf
plo
t of
th
e da
ta.
9.W
hic
h a
ge o
ccu
rs m
ost
freq
uen
tly?
20
10.D
oes
the
mod
e be
st r
epre
sen
t th
e da
ta?
Exp
lain
.N
o;
the
mo
de
is t
he
low
est
valu
e o
f th
e d
ata.
Ste
m|L
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ata
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ake
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ne
plo
t.
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For
Exe
rcis
es 3
an
d 4
,use
th
e li
st t
hat
sh
ows
the
gram
s of
sat
ura
ted
fat
in
a s
ervi
ng
of a
var
iety
of
grai
ns
such
as
bre
ad,c
erea
l,cr
ack
ers,
and
pas
ta.
3.M
ake
a li
ne
plot
of
the
data
.
4.W
hic
h m
easu
re o
f ce
ntr
al t
ende
ncy
bes
t de
scri
bes
the
data
? E
xpla
in.
Th
e m
od
e an
dm
edia
n,b
oth
0.4
.Th
e m
ean
is t
oo
hig
h b
ecau
se o
f th
e va
lue
2.8.
Use
eac
h s
et o
f d
ata
to m
ake
a st
em-a
nd
-lea
f p
lot.
5.41
5322
5041
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5720
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7.3
6.9
5.7
4.8
7.3
5.6
2852
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4.4
7.5
4.6
7.9
5.1
7.7
EMPL
0YM
ENT
For
Exe
rcis
es 7
–10,
use
th
e li
sts
that
sh
ow s
urv
ey r
esu
lts
ofst
ud
ents
’ tim
e sp
ent
on t
he
Inte
rnet
an
d o
n t
he
tele
ph
one
for
a m
onth
.
7.M
ake
a st
em-a
nd-
leaf
plo
t to
com
pare
th
e da
ta.
8.W
hic
h v
alu
e ap
pear
s m
ost
freq
uen
tly
in e
ach
set
of
dat
a?In
tern
et:
42;
tele
ph
on
e:8
9.Is
th
e m
ode
the
best
mea
sure
to
com
pare
th
e da
ta?
Exp
lain
.N
o;
it is
to
o h
igh
fo
r th
e In
tern
etan
d t
oo
low
fo
r th
e te
lep
ho
ne.
10.O
vera
ll,d
id s
tude
nts
spe
nd
mor
e ti
me
on t
he
Inte
rnet
or
the
tele
phon
e?te
lep
ho
ne
Inte
rnet
|Ste
m|T
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87
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rnet
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pla
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g a
nd
An
alyz
ing
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
Answers (Lesson 2-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
tati
stic
s:D
isp
layi
ng
an
d A
nal
yzin
g D
ata
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
©G
lenc
oe/M
cGra
w-H
ill10
3G
lenc
oe A
lgeb
ra 1
Lesson 2-5
Pre-
Act
ivit
yH
ow a
re l
ine
plo
ts a
nd
ave
rage
s u
sed
to
mak
e d
ecis
ion
s?
Rea
d th
e in
trod
uct
ion
to
Les
son
2-5
at
the
top
of p
age
88 i
n y
our
text
book
.
•W
hat
was
th
e n
um
ber
one
nam
e fo
r bo
ys i
n a
ll f
ive
deca
des?
Mic
hae
l•
Loo
k at
th
e de
cade
in
wh
ich
you
wer
e bo
rn.I
s yo
ur
nam
e or
th
e n
ames
of
any
of t
he
oth
er s
tude
nts
in
you
r cl
ass
in t
he
top
five
for
th
at d
ecad
e?
See
stu
den
ts’w
ork
.
Rea
din
g t
he
Less
on
1.U
se t
he
lin
e pl
ot s
how
n b
elow
to
answ
er t
he
ques
tion
s.
a.W
hat
are
th
e da
ta p
oin
ts f
or t
he
lin
e pl
ot?
�6,
�5,
�4,
�3,
�2,
�1,
0,1,
2,3,
4,5,
6,7
b.
Wh
at d
o th
e th
ree
’s
abo
ve t
he
6 re
pres
ent?
6 o
ccu
rs in
th
e d
ata
set
3 ti
mes
.
2.E
xpla
in w
hat
is
mea
nt
by t
he
freq
uen
cy o
f a
data
nu
mbe
r.h
ow
man
y ti
mes
th
e d
ata
nu
mb
er o
ccu
rs
3.U
se t
he
stem
-an
d-le
af p
lot
show
n a
t th
e ri
ght.
a.H
ow i
s th
e n
um
ber
758
repr
esen
ted
on t
he
plot
?75
8
b.
Exp
lain
how
you
kn
ow t
her
e ar
e 23
nu
mbe
rs i
n t
he
data
.
Th
ere
are
23 le
aves
.
Hel
pin
g Y
ou
Rem
emb
er
4.D
escr
ibe
how
you
wou
ld e
xpla
in t
he
proc
ess
of f
indi
ng
the
med
ian
an
d m
ode
from
ast
em-a
nd-
leaf
plo
t to
a f
rien
d w
ho
mis
sed
Les
son
2-5
.
Sam
ple
an
swer
:To
fin
d t
he
med
ian
,co
un
t th
e n
um
ber
of
leav
es,t
hen
fin
d t
he
nu
mb
er in
th
e m
idd
le.T
o f
ind
th
e m
od
e,id
enti
fy t
he
leaf
th
ato
ccu
rs m
ost
fre
qu
entl
y an
d u
se t
he
stem
an
d k
ey t
o id
enti
fy t
he
dat
an
um
ber
.
Ste
m|L
eaf
72|0
11
25
73|2
22
79
974
|13
375
|66
89
76|0
18
88
742
�74
2
76
54
32
10
�1
�2
�3
�4
�5
�6�
��
��
��
��
��
��
��
��
��
��
��
����
��
©G
lenc
oe/M
cGra
w-H
ill10
4G
lenc
oe A
lgeb
ra 1
Ru
ns
Cre
ated
In
Th
e 19
78 B
ill
Jam
es B
aseb
all A
bstr
act,
the
auth
or i
ntr
odu
ced
the
“ru
ns
crea
ted”
form
ula
.
R�
wh
ere
for
each
pla
yer
h�
nu
mbe
r of
hit
s
w�
nu
mbe
r of
wal
ks,
t�
nu
mbe
r of
tot
al b
ases
,
b�
nu
mbe
r of
at-
bats
,an
d
R�
appr
oxim
ate
nu
mbe
r of
ru
ns
a te
am
scor
es d
ue
to t
his
pla
yer’
s ac
tion
s
1.A
s of
Ju
ne
29,2
001,
Rob
erto
Alo
mar
of
the
Cle
vela
nd
Indi
ans
and
Sea
ttle
Mar
iner
spl
ayer
Ich
iro
Su
zuki
wer
e ti
ed w
ith
th
e h
igh
est
Am
eric
an L
eagu
e ba
ttin
g av
erag
e at
.351
.Fin
d th
e n
um
ber
of r
un
s cr
eate
d by
eac
h p
laye
r u
sin
g th
e da
ta b
elow
.
hw
tb
Ru
ns
Cre
ated
Alo
mar
9737
145
276
62
Su
zuki
121
1315
934
560
Bas
ed o
n t
his
in
form
atio
n,w
ho
do y
ou t
hin
k is
th
e m
ore
valu
able
Am
eric
an L
eagu
epl
ayer
? W
hy?
Sam
ple
an
swer
:A
lom
ar,b
ecau
se h
e cr
eate
s m
ore
ru
ns.
2.C
arlo
s L
ee o
f th
e C
hic
ago
Wh
ite
Sox
an
d N
ew Y
ork
Yan
kee
Ber
nie
Wil
liam
s w
ere
both
batt
ing
.314
.Fin
d th
e n
um
ber
of r
un
s cr
eate
d by
eac
h p
laye
r u
sin
g th
e da
ta b
elow
.
hw
tb
Ru
ns
Cre
ated
Lee
8113
141
258
49
Will
iam
s74
3112
323
648
3.W
hy
wou
ld b
aseb
all
team
s w
ant
to c
alcu
late
th
e n
um
ber
of r
un
s cr
eate
d by
eac
h o
f th
eir
play
ers?
Sam
ple
an
swer
:To
hel
p m
ake
dec
isio
ns
abo
ut
star
tin
g li
ne-
up
s;To
hel
p m
ake
dec
isio
ns
abo
ut
trad
ing
pla
yers
.
(h+
w)t
� (b+
w)En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-5
2-5
Answers (Lesson 2-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
An
swer
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
Pro
bab
ility
:Sim
ple
Pro
bab
ility
an
d O
dds
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
2-6
©G
lenc
oe/M
cGra
w-H
ill10
5G
lenc
oe A
lgeb
ra 1
Lesson 2-6
Pro
bab
ility
Th
e p
rob
abil
ity
of a
sim
ple
eve
nt
is a
rat
io t
hat
tel
ls h
ow l
ikel
y it
is
that
the
even
t w
ill
take
pla
ce.I
t is
th
e ra
tio
of t
he
nu
mbe
r of
fav
orab
le o
utc
omes
of
the
even
t to
the
nu
mbe
r of
pos
sibl
e ou
tcom
es o
f th
e ev
ent.
You
can
exp
ress
th
e pr
obab
ilit
y ei
ther
as
afr
acti
on,a
s a
deci
mal
,or
as a
per
cen
t.
Pro
bab
ility
of
a S
imp
le E
ven
tF
or a
n ev
ent
a, P
(a)
�.
num
ber
of f
avor
able
out
com
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
rob
abil
ity
of b
ein
g ch
osen
?
P(b
ein
g ch
osen
) �
Th
e pr
obab
ilit
y of
bei
ng
chos
en i
s or
.
1 � 55 � 25
nu
mbe
r of
stu
den
ts c
hos
en�
��
�to
tal
nu
mbe
r of
stu
den
ts
A b
owl
con
tain
s 3
pea
rs,
4 b
anan
as,a
nd
2 a
pp
les.
If y
ou t
ake
ap
iece
of
fru
it a
t ra
nd
om,w
hat
is
the
pro
bab
ilit
y th
at i
t is
not
a b
anan
a?
Th
ere
are
3 �
4 �
2 or
9 p
iece
s of
fru
it.
Th
ere
are
3 �
2 or
5 p
iece
s of
fru
it t
hat
are
not
ban
anas
.
P(n
ot b
anan
a)� �
The
pro
babi
lity
of
not
choo
sing
a b
anan
a is
.5 � 9
5 � 9nu
mbe
r of
oth
er p
iece
s of
fru
it�
��
�to
tal
nu
mbe
r of
pie
ces
of f
ruit
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
A c
ard
is
sele
cted
at
ran
dom
fro
m a
sta
nd
ard
dec
k o
f 52
car
ds.
Det
erm
ine
each
pro
bab
ilit
y.
1.P
(10)
2.P
(red
2)
3.P
(kin
g or
qu
een
)
4.P
(bla
ck c
ard)
5.P
(ace
of
spad
es)
6.P
(spa
de)
Tw
o d
ice
are
roll
ed a
nd
th
eir
sum
is
reco
rded
.Fin
d e
ach
pro
bab
ilit
y.
7.P
(su
m i
s 1)
08.
P(s
um
is
6)9.
P(s
um
is
less
th
an 4
)
10.P
(su
m i
s gr
eate
r th
an 1
1)11
.P(s
um
is
less
th
an 1
5)12
.P(s
um
is
grea
ter
than
8)
1
A b
owl
con
tain
s 4
red
ch
ips,
3 b
lue
chip
s,an
d 8
gre
en c
hip
s.Y
ou c
hoo
se o
ne
chip
at r
and
om.F
ind
eac
h p
rob
abil
ity.
13.P
(not
a r
ed c
hip
)14
.P(r
ed o
r bl
ue
chip
)15
.P(n
ot a
gre
en c
hip
)
A n
um
ber
is
sele
cted
at
ran
dom
fro
m t
he
list
{1,
2,3,
…,1
0}.F
ind
eac
h p
rob
abil
ity.
16.P
(eve
n n
um
ber)
17.P
(mu
ltip
le o
f 3)
18.P
(les
s th
an 4
)
19.A
com
pute
r ra
ndo
mly
ch
oose
s a
lett
er f
rom
th
e w
ord
CO
MP
UT
ER
.Fin
d th
e pr
obab
ilit
yth
at t
he
lett
er i
s a
vow
el.
3 � 8
3 � 103 � 10
1 � 2
7 � 157 � 15
11 � 15
5 � 181 � 36
1 � 125 � 36
1 � 41 � 52
1 � 2
2 � 131 � 26
1 � 13
©G
lenc
oe/M
cGra
w-H
ill10
6G
lenc
oe A
lgeb
ra 1
Od
ds
Th
e od
ds o
f an
eve
nt
occu
rrin
g is
th
e ra
tio
of t
he
nu
mbe
r of
way
s an
eve
nt
can
occ
ur
(su
cces
ses)
to
the
nu
mbe
r of
way
s th
e ev
ent
can
not
occ
ur
(fai
lure
s).
Od
ds
A d
ie i
s ro
lled
.Fin
d t
he
odd
s of
rol
lin
g a
nu
mb
er
grea
ter
than
4.
Th
e sa
mpl
e sp
ace
is {
1,2,
3,4,
5,6}
.Th
eref
ore,
ther
e ar
e si
x po
ssib
le o
utc
omes
.Sin
ce 5
an
d6
are
the
only
nu
mbe
rs g
reat
er t
han
4,t
wo
outc
omes
are
su
cces
ses
and
fou
r ar
e fa
ilu
res.
So
the
odds
of
roll
ing
a n
um
ber
grea
ter
than
4 i
s ,o
r 1:
2.
Fin
d t
he
odd
s of
eac
h o
utc
ome
if t
he
spin
ner
at
the
righ
t is
sp
un
on
ce.
1.m
ult
iple
of
41:
42.
odd
nu
mbe
r1:
1
3.ev
en o
r a
53:
24.
less
th
an 4
3:7
5.ev
en n
um
ber
grea
ter
than
53:
7
Fin
d t
he
odd
s of
eac
h o
utc
ome
if a
com
pu
ter
ran
dom
ly c
hoo
ses
a n
um
ber
bet
wee
n1
and
20.
6.th
e n
um
ber
is l
ess
than
10
9:11
7.th
e n
um
ber
is a
mu
ltip
le o
f 4
1:3
8.th
e n
um
ber
is e
ven
1:1
9.th
e n
um
ber
is a
on
e-di
git
nu
mbe
r9:
11
A b
owl
of m
oney
at
a ca
rniv
al c
onta
ins
50 q
uar
ters
,75
dim
es,1
00 n
ick
els,
and
12
5 p
enn
ies.
On
e co
in i
s ra
nd
omly
sel
ecte
d.
10.F
ind
the
odds
th
at a
dim
e w
ill
not
be
chos
en.
11:3
11.W
hat
are
th
e od
ds o
f ch
oosi
ng
a qu
arte
r if
all
th
e di
mes
are
rem
oved
?2:
9
12.W
hat
are
th
e od
ds o
f ch
oosi
ng
a pe
nn
y?5:
9
Su
pp
ose
you
dro
p a
ch
ip o
nto
th
e gr
id a
t th
e ri
ght.
Fin
d t
he
odd
s of
eac
h o
utc
ome.
13.l
and
on a
sh
aded
squ
are
1:1
14.l
and
on a
squ
are
on t
he
diag
onal
1:1
15.l
and
on s
quar
e n
um
ber
161:
15
16.l
and
on a
nu
mbe
r gr
eate
r th
an 1
21:
3
17.l
and
on a
mu
ltip
le o
f 5
3:13
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
12
9
4
38 7
10
56
2 � 4
num
ber
of s
ucce
sses
��
�nu
mbe
r of
fai
lure
s
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Pro
bab
ility
:Sim
ple
Pro
bab
ility
an
d O
dds
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
2-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 2-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Pro
bab
ility
:Sim
ple
Pro
bab
ility
an
d O
dds
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
2-6
©G
lenc
oe/M
cGra
w-H
ill10
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
rob
abil
ity.
1.P
(blu
e)�
33%
2.P
(gre
en)
�23
%
3.P
(yel
low
or
gree
n)
�50
%4.
P(b
lue
or y
ello
w)
�60
%
5.P
(not
red
)�
83%
6.P
(not
blu
e)�
67%
Fin
d t
he
pro
bab
ilit
y of
eac
h o
utc
ome
if t
he
spin
ner
is
spu
n o
nce
.
7.P
(mu
ltip
le o
f 3)
�25
%8.
P(l
ess
than
7)
�75
%
9.P
(odd
or
2)�
62.5
%10
.P(n
ot 1
)�
87.5
%
A p
erso
n i
s b
orn
in
th
e m
onth
of
Ju
ne.
Fin
d e
ach
pro
bab
ilit
y.
11.P
(dat
e is
a m
ult
iple
of
6)12
.P(d
ate
is b
efor
e Ju
ne
15)
�17
%�
47%
13.P
(bef
ore
Jun
e 7
or a
fter
Ju
ne
24)
14.P
(not
aft
er J
un
e 5)
�40
%�
17%
Fin
d t
he
odd
s of
eac
h o
utc
ome
if a
com
pu
ter
ran
dom
ly p
ick
s a
lett
er i
n t
he
nam
eT
he
Pet
rifi
ed F
ores
t.
15.t
he
lett
er f
2:1
6 o
r 1
:816
.th
e le
tter
e4
:14
or
2:7
17.t
he
lett
er t
3:1
5 o
r 1
:518
.a v
owel
7:1
1
CL
AS
S S
CH
ED
UL
ES
For
Exe
rcis
es 1
9–22
,use
th
e fo
llow
ing
info
rmat
ion
.
A s
tude
nt
can
sel
ect
an e
lect
ive
clas
s fr
om t
he
foll
owin
g:3
in m
usi
c,5
in p
hys
ical
edu
cati
on,
2 in
jou
rnal
ism
,8 i
n c
ompu
ter
prog
ram
min
g,4
in a
rt,a
nd
6 in
dra
ma.
Fin
d ea
ch o
f th
e od
dsif
a s
tude
nt
forg
ets
to c
hoo
se a
n e
lect
ive
and
the
sch
ool
assi
gns
one
at r
ando
m.
19.T
he
clas
s is
com
pute
r pr
ogra
mm
ing.
8:2
0 o
r 2
:5
20.T
he
clas
s is
dra
ma.
6:2
2 o
r 3
:11
21.T
he
clas
s is
not
ph
ysic
al e
duca
tion
.23
:5
22.T
he
clas
s is
not
art
.24
:4 o
r 6
:1
1 � 62 � 5
7 � 151 � 6
7 � 85 � 8
3 � 41 � 4
18
45
63
72
2 � 35 � 6
3 � 51 � 2
7 � 301 � 3
©G
lenc
oe/M
cGra
w-H
ill10
8G
lenc
oe A
lgeb
ra 1
On
e ch
ip i
s ra
nd
omly
sel
ecte
d f
rom
a j
ar c
onta
inin
g 13
blu
e ch
ips,
8 ye
llow
ch
ips,
15 b
row
n c
hip
s,an
d 6
gre
en c
hip
s.F
ind
eac
h p
rob
abil
ity.
1.P
(bro
wn
)�
36%
2.P
(gre
en)
�14
%
3.P
(blu
e or
yel
low
)�
50%
4.P
(not
yel
low
)�
81%
A c
ard
is
sele
cted
at
ran
dom
fro
m a
sta
nd
ard
dec
k o
f 52
car
ds.
Fin
d e
ach
pro
bab
ilit
y.
5.P
(hea
rt)
�25
%6.
P(b
lack
car
d)�
50%
7.P
(jac
k)�
8%8.
P(r
ed ja
ck)
�4%
Tw
o d
ice
are
roll
ed a
nd
th
eir
sum
is
reco
rded
.Fin
d e
ach
pro
bab
ilit
y.
9.P
(su
m l
ess
than
6)
�28
%10
.P(s
um
les
s th
an 2
)0
�0%
11.P
(su
m g
reat
er t
han
10)
�8%
12.P
(su
m g
reat
er t
han
9)
�17
%
Fin
d t
he
odd
s of
eac
h o
utc
ome
if a
com
pu
ter
ran
dom
ly p
ick
s a
lett
er i
n t
he
nam
eT
he
Ba
dla
nd
s of
Nor
th D
ak
ota
.
13.t
he
lett
er d
3:2
1 o
r 1
:714
.th
e le
tter
a4
:20
or
1:5
15.t
he
lett
er h
2:2
2 o
r 1
:11
16.a
con
son
ant
16:8
or
2:1
CLA
SS P
RO
JEC
TSF
or E
xerc
ises
17–
20,u
se t
he
foll
owin
g in
form
atio
n.
Stu
den
ts i
n a
bio
logy
cla
ss c
an c
hoo
se a
sem
este
r pr
ojec
t fr
om t
he
foll
owin
g li
st:a
nim
albe
hav
ior
(4),
cell
ula
r pr
oces
ses
(2),
ecol
ogy
(6),
hea
lth
(7)
,an
d ph
ysio
logy
(3)
.Fin
d ea
ch o
fth
e od
ds i
f a
stu
den
t se
lect
s a
topi
c at
ran
dom
.
17.t
he
topi
c is
eco
logy
6:1
6 o
r 3
:8
18.t
he
topi
c is
an
imal
beh
avio
r4
:18
or
2:9
19.t
he
topi
c is
not
cel
lula
r pr
oces
ses
20:2
or
10:1
20.t
he
topi
c is
not
hea
lth
15:7
SC
HO
OL
IS
SU
ES
For
Exe
rcis
es 2
1 an
d 2
2,u
se t
he
foll
owin
g in
form
atio
n.
A n
ews
team
su
rvey
ed s
tude
nts
in
gra
des
9–12
on
wh
eth
er t
o
chan
ge t
he
tim
e sc
hoo
l be
gin
s.O
ne
stu
den
t w
ill
be s
elec
ted
atra
ndo
m t
o be
in
terv
iew
ed o
n t
he
even
ing
new
s.T
he
tabl
e gi
ves
the
resu
lts.
21.W
hat
is
the
prob
abil
ity
the
stu
den
t se
lect
ed w
ill
be i
n t
he
9th
gra
de?
�32
%
22.W
hat
are
th
e od
ds t
he
stu
den
t se
lect
ed w
ants
no
chan
ge?
16:3
4 o
r 8
:17
8 � 25
Gra
de
910
1112
No
ch
ang
e6
25
3
Ho
ur
late
r10
79
8
1 � 61 � 12
5 � 18
1 � 261 � 13
1 � 21 � 4
17 � 211 � 2
1 � 75 � 14
Pra
ctic
e (
Ave
rag
e)
Pro
bab
ility
:Sim
ple
Pro
bab
ility
an
d O
dds
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
2-6
Answers (Lesson 2-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
An
swer
s
Readin
g t
o L
earn
Math
em
ati
csP
rob
abili
ty:
Sim
ple
Pro
bab
ility
an
d O
dd
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
2-6
©G
lenc
oe/M
cGra
w-H
ill10
9G
lenc
oe A
lgeb
ra 1
Lesson 2-6
Pre-
Act
ivit
yW
hy
is p
rob
abil
ity
imp
orta
nt
in s
por
ts?
Rea
d th
e in
trod
uct
ion
to
Les
son
2-6
at
the
top
of p
age
96 i
n y
our
text
book
.
Loo
k u
p th
e de
fin
itio
n o
f th
e w
ord
prob
abil
ity
in a
dic
tion
ary.
Rew
rite
th
ede
fin
itio
n i
n y
our
own
wor
ds.
Sam
ple
an
swer
:th
e lik
elih
oo
d o
f so
met
hin
g h
app
enin
g
Rea
din
g t
he
Less
on
1.W
rite
wh
eth
er e
ach
sta
tem
ent
is t
rue
or f
alse
.If
fals
e,re
plac
e th
e u
nde
rlin
ed w
ord
orn
um
ber
to m
ake
a tr
ue
stat
emen
t.
a.P
roba
bili
ty c
an b
e w
ritt
en a
s a
frac
tion
,a d
ecim
al,o
r a
perc
ent.
tru
e
b.
Th
e sa
mpl
e sp
ace
of f
lipp
ing
one
coin
is
hea
ds o
r ta
ils.
tru
e
c.T
he
prob
abil
ity
of a
n i
mpo
ssib
le e
ven
t is
1.
fals
e;0
d.
Th
e od
ds a
gain
st a
n e
ven
t oc
curr
ing
are
the
odds
th
at t
he
even
t w
ill
occu
r.fa
lse;
will
no
t
2.E
xpla
in w
hy
the
prob
abil
ity
of a
n e
ven
t ca
nn
ot b
e gr
eate
r th
an 1
wh
ile
the
odds
of
anev
ent
can
be
grea
ter
than
1.
Sam
ple
an
swer
:To
fin
d t
he
pro
bab
ility
of
an e
ven
t,yo
u c
om
par
e a
par
t o
fth
e sa
mp
le s
pac
e to
th
e w
ho
le s
amp
le s
pac
e.W
hen
yo
u f
ind
th
e o
dd
s o
fan
eve
nt,
you
co
mp
are
the
nu
mb
er o
f fa
vora
ble
ou
tco
mes
to
th
e n
um
ber
of
un
favo
rab
le o
utc
om
es.I
n s
om
e si
tuat
ion
s,th
ere
may
be
mo
refa
vora
ble
th
an u
nfa
vora
ble
ou
tco
mes
.
Hel
pin
g Y
ou
Rem
emb
er
3.P
roba
bili
ties
are
usu
ally
wri
tten
as
frac
tion
s,de
cim
als,
or p
erce
nts
.Odd
s ar
e u
sual
lyw
ritt
en w
ith
a c
olon
(fo
r ex
ampl
e,1:
3).H
ow c
an t
he
spel
lin
g of
th
e w
ord
colo
nh
elp
rem
embe
r th
is?
Sam
ple
an
swer
:Th
e w
ord
co
lon
has
th
e le
tter
“o
”as
its
on
ly v
ow
el,a
nd
the
wo
rd o
dd
sal
so h
as t
he
lett
er “
o”
as it
s o
nly
vo
wel
.
©G
lenc
oe/M
cGra
w-H
ill11
0G
lenc
oe A
lgeb
ra 1
Geo
met
ric
Pro
bab
ility
If a
dar
t,th
row
n a
t ra
ndo
m,h
its
the
tria
ngu
lar
boar
d sh
own
at
the
righ
t,w
hat
is
the
prob
abil
ity
that
it
wil
l h
it t
he
shad
ed r
egio
n?
Th
isca
n b
e de
term
ined
by
com
pari
ng
the
area
of
the
shad
ed r
egio
n t
o th
ear
ea o
f th
e en
tire
boa
rd.T
his
rat
io i
ndi
cate
s w
hat
fra
ctio
n o
f th
e to
sses
sh
ould
hit
in
th
e sh
aded
reg
ion
. � �or
In g
ener
al,i
f S
is a
su
breg
ion
of
som
e re
gion
R,t
hen
th
e pr
obab
ilit
y,P
(S),
that
a p
oin
t,ch
osen
at
ran
dom
,bel
ongs
to
subr
egio
n S
is g
iven
by
the
foll
owin
g:
P(S
) �
Fin
d t
he
pro
bab
ilit
y th
at a
poi
nt,
chos
en a
t ra
nd
om,b
elon
gs t
o th
e sh
aded
sub
regi
ons
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
�3 �
�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
ngu
lar
boar
d
6
44
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-6
2-6
Answers (Lesson 2-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy G
uid
e a
nd I
nte
rven
tion
Sq
uar
e R
oo
ts a
nd
Rea
l Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
2-7
©G
lenc
oe/M
cGra
w-H
ill11
1G
lenc
oe A
lgeb
ra 1
Lesson 2-7
Squ
are
Ro
ots
A s
qu
are
root
is o
ne
of t
wo
equ
al f
acto
rs o
f a
nu
mbe
r.F
or e
xam
ple,
the
squ
are
root
s of
36
are
6 an
d �
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
nu
mbe
r li
ke 3
6,w
hos
e sq
uar
e ro
ot i
s a
rati
onal
nu
mbe
r,is
cal
led
a p
erfe
ctsq
uar
e.T
he
sym
bol
��
is a
rad
ical
sig
n.I
t in
dica
tes
the
non
neg
ativ
e,or
pri
nci
pal
,squ
are
root
of
the
nu
mbe
r u
nde
r th
e ra
dica
l si
gn.S
o �
36��
6 an
d �
�36�
��
6.T
he
sym
bol
��
36�re
pres
ents
bot
h s
quar
e ro
ots.
Fin
d ���
.
�
repr
esen
ts t
he
neg
ativ
e sq
uar
e ro
ot o
f .
��
�2→
�
��
5 � 725 � 49
5 � 725 � 49
25 � 4925 � 49
25 � 49F
ind
�
0.16
�.
��
0.16
�re
pres
ents
th
e po
siti
ve a
nd
neg
ativ
e sq
uar
e ro
ots
of 0
.16.
0.16
�0.
42an
d 0.
16 �
(�0.
4)2
��
0.16
��
�0.
4
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
sq
uar
e ro
ot.
1.�
64�8
2.�
�81�
�9
3.�
16.8
1�
4.1
4.�
�10
0�
�10
5.�
�6.
��
121
��
11
7.�
�8.
�
�9.
�
�
10.�
�36
00�
�60
11.�
�6.
25�
�2.
512
.��
0.00
0�
4��
0.02
13.
14.�
�
15.�
�1.
21�
�1.
16 � 7
36 � 496 � 7
144
� 196
11 � 1012
1� 10
05 � 4
25 � 165 � 12
25 � 144
2 � 54 � 25
©G
lenc
oe/M
cGra
w-H
ill11
2G
lenc
oe A
lgeb
ra 1
Cla
ssif
y an
d O
rder
Nu
mb
ers
Nu
mbe
r su
ch a
s �
2�an
d �
3�ar
e n
ot p
erfe
ct s
quar
es.
Not
ice
wh
at h
appe
ns
wh
en y
ou f
ind
thes
e sq
uar
e ro
ots
wit
h y
our
calc
ula
tor.
Th
e n
um
bers
con
tin
ue
inde
fin
itel
y w
ith
out
any
patt
ern
of
repe
atin
g di
gits
.Nu
mbe
rs t
hat
can
not
be
wri
tten
as
a te
rmin
atin
g or
rep
eati
ng
deci
mal
are
cal
led
irra
tion
al n
um
ber
s.T
he
set
ofre
al n
um
ber
sco
nsi
sts
of t
he
set
of i
rrat
ion
al n
um
bers
an
d th
e se
t of
rat
ion
al n
um
bers
toge
ther
.Th
e ch
art
belo
w i
llu
stra
tes
the
vari
ous
kin
ds o
f re
al n
um
bers
.
Nat
ura
l Nu
mb
ers
{1,
2, 3
, 4,
…}
Wh
ole
Nu
mb
ers
{0,
1, 2
, 3,
4,
…}
Inte
ger
s{…
, �
3, �
2, �
1, 0
, 1,
2,
3, …
}
Rat
ion
al N
um
ber
s{a
ll nu
mbe
rs t
hat
can
be e
xpre
ssed
in t
he f
orm
,
whe
re a
and
bar
e in
tege
rs a
nd b
�0}
Irra
tio
nal
Nu
mb
ers
{all
num
bers
tha
t ca
nnot
be
expr
esse
d in
the
for
m
, w
here
aan
d b
are
inte
gers
and
b�
0}
Nam
e th
e se
t or
set
s of
nu
mb
ers
to w
hic
h e
ach
rea
l n
um
ber
bel
ongs
.
a.B
ecau
se 4
an
d 11
are
in
tege
rs,t
his
nu
mbe
r is
a r
atio
nal
nu
mbe
r.
b.
81�
Bec
ause
�81�
�9,
this
nu
mbe
r is
a n
atu
ral
nu
mbe
r,a
wh
ole
nu
mbe
r,an
in
tege
r,an
d a
rati
onal
nu
mbe
r.
c.
32�B
ecau
se �
32��
5.65
6854
249…
,wh
ich
is
not
a r
epea
tin
g or
ter
min
atin
g de
cim
al,
this
nu
mbe
r is
irr
atio
nal
.
Nam
e th
e se
t or
set
s of
nu
mb
ers
to w
hic
h e
ach
rea
l n
um
ber
bel
ongs
.
1.2.
�3.
4.�
54�n
atu
ral,
wh
ole
,ra
tio
nal
rati
on
alir
rati
on
alin
teg
er,r
atio
nal
5.3.
145
6.�
25�7.
0.62
6262
62…
8.�
22.5
1�
rati
on
aln
atu
ral,
wh
ole
,ra
tio
nal
irra
tio
nal
in
teg
er,r
atio
nal
Wri
te e
ach
set
of
nu
mb
ers
in o
rder
fro
m l
east
to
grea
test
.
9.�
,�5,
�25�
,10
.�0.
09�
,�0.
3131
…,
11.�
1.2�5�
,0.0
5,�
,�5�
�5,
�,
,25�
�0.
3131
…,
0.09
�,
�1.
2�5�,�
,0.0
5,
5�
12.
,�2,
�12
4�
,�3.
1113
.��
1.44
�,�
0.35
14
.0.3�
5�,2
,�,�
5�
�3.
11,�
2,,
124
��
1.
44�
,�0.
35,
�,0
.3�5�,
5�,
21 � 3
9 � 51 � 5
5 � 4
9 � 51 � 3
1 � 55 � 4
1 � 43 � 5
7 � 43 � 4
1 � 43 � 5
7 � 43 � 4
2 � 36 � 7
84 � 124 � 11
a � b
a � b
Stu
dy G
uid
e a
nd I
nte
rven
tion
(c
onti
nued
)
Sq
uar
e R
oo
ts a
nd
Rea
l Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
2-7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 2-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
An
swer
s
Skil
ls P
ract
ice
Sq
uar
e R
oo
ts a
nd
Rea
l Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
2-7
©G
lenc
oe/M
cGra
w-H
ill11
3G
lenc
oe A
lgeb
ra 1
Lesson 2-7
Fin
d e
ach
sq
uar
e ro
ot.I
f n
eces
sary
,rou
nd
to
the
nea
rest
hu
nd
red
th.
1.�
144
�12
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�6
3.�
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25�
�0.
54.
�
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5.�
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126.
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25�
1.5
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e th
e se
t or
set
s of
nu
mb
ers
to w
hic
h e
ach
rea
l n
um
ber
bel
ongs
.
7.�
8.�
inte
ger
,rat
ion
alra
tio
nal
9.�
29�10
.�19
6�
irra
tio
nal
nat
ura
l,w
ho
le,i
nte
ger
,rat
ion
al
11.
12.�
1.8
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rati
on
alir
rati
on
al
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ph
eac
h s
olu
tion
set
.
13.x
��
114
.x
1
15.x
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516
.x�
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5
Rep
lace
eac
h ●
wit
h �
,�,o
r �
to m
ake
each
sen
ten
ce t
rue.
17.
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4 ��
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●�
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.2�3�
●�
39��
20.
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te e
ach
set
of
nu
mb
ers
in o
rder
fro
m l
east
to
grea
test
.
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5�,2.
3�6�,
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.,0
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4 �8�,�
12�
,�
11�
6�
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3 � 73 � 7
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2 � 92 � 9
7 � 37 � 3
1� �
8�1 � 8
1 � 904 � 9
�2
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01
23
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30
12
34
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10
12
34
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9 � 13
5 � 628 � 7
7 � 1049 � 10
0
©G
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w-H
ill11
4G
lenc
oe A
lgeb
ra 1
Fin
d e
ach
sq
uar
e ro
ot.I
f n
eces
sary
,rou
nd
to
the
nea
rest
hu
nd
red
th.
1.�
324
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��
62�3.
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25�4.
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84�
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17
5.�
6.�
7.�
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3.06
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0.76
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28�
1.75
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e th
e se
t or
set
s of
nu
mb
ers
to w
hic
h e
ach
rea
l n
um
ber
bel
ongs
.
9.�
93�10
.��
0.06
2�
5�11
.12
.�
irra
tio
nal
rati
on
alra
tio
nal
inte
ger
,rat
ion
al
Gra
ph
eac
h s
olu
tion
set
.
13.x
��
0.5
14.x
��
3.5
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lace
eac
h ●
wit
h �
,�,o
r �
to m
ake
each
sen
ten
ce t
rue.
15.0
.9 �3�
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��
16.8
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●�
66��
17.
●�
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te e
ach
set
of
nu
mb
ers
in o
rder
fro
m l
east
to
grea
test
.
18. �
0.03
�,
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7�19
.�,�
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8.5
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,
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8.5
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21.S
IGH
TSEE
ING
Th
e di
stan
ce y
ou c
an s
ee t
o th
e h
oriz
on i
s gi
ven
by
the
form
ula
d
��
1.5h
�,w
her
e d
is t
he
dist
ance
in
mil
es a
nd
his
th
e h
eigh
t in
fee
t ab
ove
the
hor
izon
lin
e.M
t.W
hit
ney
is
the
hig
hes
t po
int
in t
he
con
tigu
ous
48 s
tate
s.It
s el
evat
ion
is
14,
494
feet
.Th
e lo
wes
t el
evat
ion
,at
�28
2 fe
et,i
s lo
cate
d n
ear
Bad
wat
er,C
alif
orn
ia.
Wit
h a
cle
ar e
nou
gh s
ky a
nd
no
obst
ruct
ion
s,co
uld
you
see
fro
m t
he
top
of M
t.W
hit
ney
to B
adw
ater
if
the
dist
ance
bet
wee
n t
hem
is
135
mil
es?
Exp
lain
.Ye
s;yo
u c
an s
eeab
ou
t 14
9 m
iles
fro
m t
he
top
of
Mt.
Wh
itn
ey t
o a
n e
leva
tio
n o
f �
282
feet
.
22.S
EISM
IC W
AV
ESA
tsu
nam
iis
a s
eism
ic w
ave
cau
sed
by a
n e
arth
quak
e on
th
e oc
ean
floo
r.Yo
u c
an u
se t
he
form
ula
s�
3.1 �
d�,w
her
e s
is t
he
spee
d in
met
ers
per
seco
nd
and
d i
s th
e de
pth
of
the
ocea
n i
n m
eter
s,to
det
erm
ine
the
spee
d of
a t
sun
ami.
If a
nea
rth
quak
e oc
curs
at
a de
pth
of
200
met
ers,
wh
at i
s th
e sp
eed
of t
he
tsu
nam
i ge
ner
ated
by t
he
eart
hqu
ake?
abo
ut
43.8
m/s
19 � 20
35��
2
7��
884 � 30
2�
�8
19 � 20�
35��
2�
7��
884 � 30
�2�
�8
�5�
�6
5 � 6
�2
�1
�4
�3
01
23
4�
2�
1�
4�
30
12
34
144
�3
8 � 7
2 � 17
7 � 124
� 289P
ract
ice (
Ave
rag
e)
Sq
uar
e R
oo
ts a
nd
Rea
l Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
2-7
2-7
Answers (Lesson 2-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Readin
g t
o L
earn
Math
em
ati
csS
qu
are
Ro
ots
an
d R
eal N
um
ber
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
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
uct
ion
to
Les
son
2-7
at
the
top
of p
age
103
in y
our
text
book
.
Th
e ex
pres
sion
�36
00�
is r
ead,
“th
e sq
uar
e ro
ot o
f 36
00.”
How
wou
ld y
oure
ad t
he
expr
essi
on �
64�?
the
squ
are
roo
t o
f 64
Rea
din
g t
he
Less
on
Com
ple
te e
ach
sta
tem
ent
bel
ow.
1.T
he
sym
bol
��
is c
alle
d a
and
is u
sed
to i
ndi
cate
an
onn
egat
ive
or p
rin
cipa
l sq
uar
e ro
ot o
f th
e ex
pres
sion
un
der
the
sym
bol.
2.A
of
an
irr
atio
nal
nu
mbe
r is
a r
atio
nal
nu
mbe
r th
at i
s cl
ose
to,b
ut
not
equ
al t
o,th
e va
lue
of t
he
irra
tion
al n
um
ber.
3.T
he
posi
tive
squ
are
root
of
a n
um
ber
is c
alle
d th
e sq
uar
ero
ot o
f th
e n
um
ber.
4.A
nu
mbe
r w
hos
e po
siti
ve s
quar
e ro
ot i
s a
rati
onal
nu
mbe
r is
a
.
5.W
rite
eac
h o
f th
e fo
llow
ing
as a
mat
hem
atic
al e
xpre
ssio
n t
hat
use
s th
e �
�sy
mbo
l.
a.th
e po
siti
ve s
quar
e ro
ot o
f 16
00
1600
�b
.th
e n
egat
ive
squ
are
root
of
729
�
729
�c.
the
prin
cipa
l sq
uar
e ro
ot o
f 30
25
3025
�
6.T
he
irra
tion
al n
um
bers
an
d ra
tion
al n
um
bers
tog
eth
er f
orm
th
e se
t of
n
um
bers
.
Hel
pin
g Y
ou
Rem
emb
er
7.U
se a
dic
tion
ary
to l
ook
up
seve
ral
wor
ds t
hat
beg
in w
ith
“ir
-”.W
hat
doe
s th
e pr
efix
“ir
-”m
ean
? H
ow c
an t
his
hel
p yo
u r
emem
ber
the
mea
nin
g of
th
e w
ord
irra
tion
al?
Sam
ple
an
swer
:Th
e p
refi
x “i
r-”
mea
ns
no
t.S
o a
n ir
rati
on
al n
um
ber
is a
nu
mb
er t
hat
is n
ot
a ra
tio
nal
nu
mb
er.
real
per
fect
sq
uar
e
pri
nci
pal
rati
on
al a
pp
roxi
mat
ion
rad
ical
sig
n
©G
lenc
oe/M
cGra
w-H
ill11
6G
lenc
oe A
lgeb
ra 1
Sca
le D
raw
ing
sT
he
map
at
the
left
bel
ow s
how
s bu
ildi
ng
lots
for
sal
e.T
he
scal
e ra
tio
is 1
:240
0.A
t th
e ri
ght
belo
w i
s th
e fl
oor
plan
for
a t
wo-
bedr
oom
apar
tmen
t.T
he
len
gth
of
the
livi
ng
room
is
6 m
.On
th
e pl
an t
he
livi
ng
room
is
6 cm
lon
g.
An
swer
eac
h q
ues
tion
.
1.O
n t
he
map
,how
man
y fe
et a
re r
epre
sen
ted
by a
n i
nch
?20
0 ft
2.O
n t
he
map
,mea
sure
th
e fr
onta
ge o
f L
ot 2
on
Syl
van
Roa
d in
in
ches
.Wh
at i
s th
e ac
tual
fron
tage
in
fee
t?20
0 ft
3.W
hat
is
the
scal
e ra
tio
repr
esen
ted
on t
he
floo
r pl
an?
1:1
00
4.O
n t
he
floo
r pl
an,m
easu
re t
he
wid
th o
f th
e li
vin
g ro
om i
n c
enti
met
ers.
Wh
at i
s th
eac
tual
wid
th i
n m
eter
s?4
m
5.A
bou
t h
ow m
any
squ
are
met
ers
of c
arpe
tin
g w
ould
be
nee
ded
to c
arpe
t th
e li
vin
g ro
om?
24 m
2
6.M
ake
a sc
ale
draw
ing
of y
our
clas
sroo
m u
sin
g an
app
ropr
iate
sca
le.
An
swer
s w
ill v
ary.
7.U
se y
our
scal
e dr
awin
g to
det
erm
ine
how
man
y sq
uar
e m
eter
s of
til
e w
ould
be
nee
ded
toin
stal
l a
new
flo
or i
n y
our
clas
sroo
m.
An
swer
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
AT
E__
____
____
__P
ER
IOD
____
_
2-7
2-7
Answers (Lesson 2-7)
© Glencoe/McGraw-Hill A23 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. A
A
D
B
C
D
A
B
A
C
D
1
B
A
C
D
A
C
D
C
B
C
A
D
C
C
B
D
B
D
C
B
Chapter 2 Assessment Answer KeyForm 1 Form 2APage 117 Page 118 Page 119
(continued on the next page)
An
swer
s
© Glencoe/McGraw-Hill A24 Glencoe Algebra 1
12.
13.
14.
15.
16.
17.
18.
19.
20.
B:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
B: 2
B
C
A
B
D
A
D
D
A
B
B
D
B
A
D
B
C
D
A
C
13.3
A
C
B
A
B
D
A
C
C
Chapter 2 Assessment Answer KeyForm 2A (continued) Form 2BPage 120 Page 121 Page 122
An
swer
s
© Glencoe/McGraw-Hill A25 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
B: 752 B.c.
���19
��, ��29
�, 0, �121�, 0.25
�1�2�3 0 1 2 3
natural numbers, wholenumbers, integers, and
rational numbers
�1.1
7 : 5
1 : 2
�14
� or 25%
�34
� or 75%
They are all the same, soall of them represent the
data well.
5
0, 1, 5, 6
3
1 2 3 4 5 60
�����
�����
���
��
�1.3
�5w � 3
�4
�277� or 3�
67
�
�8.8
�6.72
68.16
�23a
��385�
�64
� �191� or �1�
29
�
8.11
�16
�
�12.9
11
3
�5
�1�2 0 1 2 4 5 63
0 1 32�3 �2 �1
{�4, �1, 0, 2, 3, 5}
Chapter 2 Assessment Answer KeyForm 2CPage 123 Page 124
© Glencoe/McGraw-Hill A26 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
B:�2150�
���49
��, ��38
�, 0, 0.4, �47
�
�1�2�3�4 0 1 2 43
integers and rationalnumbers
��163�
5 : 4
8 : 9
�157� or about 29%
�1127� or about 71%
No; the mean is lowerthan the cluster of most
of the values.
4
1, 2
4
1 2 3 4 5 60
���
������
���
��
��
�1.5
6w � 5
�4
��130�
�9.5
�24.51
�5.61
�22b
��251�
�105
�98
� or 1�18
�
�12.81
�29
�
�18.9
13
19
9
�1�2�3�4 0 1 2 43
0 1 2�1
{�5, �1, 0, 1, 3, 4}
Chapter 2 Assessment Answer KeyForm 2DPage 125 Page 126
An
swer
s
© Glencoe/McGraw-Hill A27 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
B: �4.3
�1, ���116��, ��
29
�, �0.2, ��121�
natural numbers,whole numbers,
integers, andrational numbers
��245�
7 : 3
0
1 : 1
�376� or about 19%
Sample answer:Median; the mode
is too high.
Sample answer:Median or mean; the
mode is too low.
2 3 4 5 6 7 8 9 101
��
��
� � ��
��
�
��
� �
3.2
4x � 7y
�4.8
�125� or 7�
12
�
160
516 ft
�2375�
�113
14,776 ft
��32
� or �1�12
�
1�29
�
�1�2�3�5�4 0 1 2 63 4 5
�1�2�3�5�4 0 1 2 63 4 5
��1, ��13
�, �23
�, �43
��
Chapter 2 Assessment Answer KeyForm 3Page 127 Page 128
16 � 7 � 1.67
Stem Leaf1617181920
0 7 862 50 2 3 71 2 2 3 5
© Glencoe/McGraw-Hill A28 Glencoe Algebra 1
Chapter 2 Assessment Answer KeyPage 129, Open-Ended Assessment
Scoring Rubric
Score General Description Specific Criteria
• Shows thorough understanding of the concepts ofgraphing rational numbers, adding, subtracting, anddividing rational numbers, displaying and analyzing data,simple probability and odds, square roots, and classifyingand ordering real numbers.
• Uses appropriate strategies to solve problems.• Computations are correct.• Written explanations are exemplary.• Graphs are accurate and appropriate.• Goes beyond requirements of some or all problems.
• Shows an understanding of the concepts of graphingrational numbers, adding, subtracting, and dividing rationalnumbers, displaying and analyzing data, simple probabilityand odds, square roots, and classifying and ordering realnumbers.
• Uses appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are effective.• Graphs are mostly accurate and appropriate.• Satisfies all requirements of problems.
• Shows an understanding of most of the concepts ofgraphing rational numbers, adding, subtracting, anddividing rational numbers, displaying and analyzing data,simple probability and odds, square roots, and classifyingand ordering real numbers.
• May not use appropriate strategies to solve problems.• Computations are mostly correct.• Written explanations are satisfactory.• Graphs are mostly accurate.• Satisfies the requirements of most of the problems.
• Final computation is correct.• No written explanations or work is shown to substantiate
the final computation.• Graphs may be accurate but lack detail or explanation.• Satisfies minimal requirements of some of the problems.
• Shows little or no understanding of the concepts ofgraphing rational numbers, adding, subtracting, anddividing rational numbers, displaying and analyzing data,simple probability and odds, square roots, and classifyingand ordering real numbers.
• Does not use appropriate strategies to solve problems.• Computations are incorrect.• Written explanations are unsatisfactory.• Graphs are inaccurate or inappropriate.• Does not satisfy requirements of problems.• No answer may be given.
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
1 Nearly Unsatisfactory A correct solution with nosupporting evidence orexplanation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
4 SuperiorA correct solution that is supported by well-developed, accurateexplanations
Chapter 2 Assessment Answer KeyPage 129, Open-Ended Assessment
Sample Answers
© Glencoe/McGraw-Hill A29 Glencoe Algebra 1
1a. The student should explain that thepoint on a number line representsthe location of a number relative tothe rest of the real numbers. Thecoordinate of a point is the numberthat the point represents.
1b. Sample answer: Draw a number linewith tick marks labeled from –5 to 5.Plot points at 3, 4, and 5. Make theright arrow bold to represent thatthe graph continues indefinitely inthat direction.
2a.
Since �4 � 3 lies to the left of 4 � (�3) on a number line, thenumber �4 � 3 is not greater than 4 � (�3).
2b. The student should explain thatsubtracting a number is the same asadding the opposite of the number,thus making it possible to subtractby adding. Sample answer:2 � 1 � 2 � (�1) � 1
3. If x and y are both positive, then �xy� is
positive: x � 4, y � 2, �xy� � �
42� � 2.
If x and y are both negative, then �xy� is
positive: x � �6, y � �3, ���
63�
� 2.
4a. Sample answer:{1, 1, 2, 4, 5, 10, 11, 12, 13, 14, 15};mean is 8; mode is 1.
4b. The student should use the set ofdata created for part a.Sample answer:
0 � 1 � 01
5a. The probability that an event willoccur is defined to be the number offavorable outcomes divided by thetotal number of possible outcomes.The number of favorable outcomes isalways less than or equal to the totalnumber of possible outcomes. Thus,this quotient is always less than orequal to 1, which means it can neverequal 2.
5b. The odds that an event will occur isthe ratio of the number of ways anevent can occur to the number ofways the event cannot occur. Thetotal number of possible outcomes isthe sum of the number of ways anevent can occur and the number ofways the event cannot occur. Thus,if the odds that an event will occur is 1 : 1, then the probability that the
event will occur is �1 �1
1� � �12�.
6a. The student should recognize that,since there is no real number thatcan be multiplied by itself to producea negative number, ��49� is not areal number. However, ��49� is thenegative square root of 49, or �7.
6b. Sample answer:�2.1, �2, ��2�, �1, 1, 2
�1�2�3
�3
�4
�4
0 1 2 43
�1�2�3
�3
�4
�4
0 1 2 43
In addition to the scoring rubric found on page A28, the following sample answers may be used as guidance in evaluating open-ended assessment items.
An
swer
s
Stem Leaf
01
1 1 2 4 50 1 2 3 4 5
© Glencoe/McGraw-Hill A30 Glencoe Algebra 1
Chapter 2 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 2–1 and 2–2) Quiz (Lessons 2–5 and 2–6)
Page 130 Page 131 Page 132
1. e
2. h
3. a
4. b
5. j
6. c
7. d
8. f
9. g
10. i
11. The absolute valueof any number n isits distance fromzero on the numberline.
12. A pair of numbersconsisting of apositive rationalnumber and anegative rationalnumber with a sumof zero.
1.
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7.
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10.
Quiz (Lessons 2–3 and 2–4)
Page 131
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5.
Quiz (Lesson 2–7)
Page 132
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2.
3.
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5.
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7.
8.
9.
10. C
��49
�, ��13
�, 0.3, ��
110��
�
�
�1�2�3�4 0 1 2 43
irrational numbers
natural numbers,whole numbers, integers,and rational numbers
��151�
0.6�7
3 : 1
�154�
Sample answer:Median; the mode istoo low and the meanis too high.
59
55 60 65 70 75
�� � ��� ��
� ���
�5.75
��83
� or �2�23
�
3x � 5y
10
�65
� or 1�15
�
�7
�0.24
31a
��47
�
�217
1.4�77
�56
�
�43
�4
4.972
�2�1�3�4�5 0 1 2 43
{…, �4, �3, �2,�1, 0, 1}
© Glencoe/McGraw-Hill A31 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
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13.
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15.
1.
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6.
7.
8.
9.
10.
11.
12.
13.
14.
15.��
94
�, ��5�, 2.2�4�, �5275�
�216�
40 41 42 43 44 45 46 47
� � ���
���
� ��
2t � 3
��365�
14
17.8
36
�3, �1, 2, 5, 6
Temperature
Peo
ple
Sample answer:
hypothesis: I finish myhomework; conclusion:I’ll go to the store; If Ifinish my homework,
then I’ll go to the store.
4x � 14
17a � 3
84
x2 � 7
0.58
�27.3
�2
��287� or �3�
38
�
72
�170�
�79
�1�2�3�5�4 0 1 2 3
B
C
D
A
B
D
C
Chapter 2 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 133 Page 134
An
swer
s
© Glencoe/McGraw-Hill A32 Glencoe Algebra 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11. 12.
13. 14.
15.
16.
17. DCBA
DCBA
DCBA
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
1 . 6
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
87 1
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
2 2
0 0 0
.. ./ /
.
99 9 987654321
87654321
87654321
87654321
1 7 2 8
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
HGFE
DCBA
Chapter 2 Assessment Answer KeyStandardized Test Practice
Page 135 Page 136