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Transcript of Glencoe Algebra, chapter 2
Chapter 2Resource Masters
New York, New York Columbus, Ohio Woodland Hills, California Peoria, Illinois
CONSUMABLE WORKBOOKS Many of the worksheets contained in the ChapterResource Masters booklets are available as consumable workbooks in bothEnglish and Spanish.
Study Guide Workbook 0-07-869610-0Skills Practice Workbook 0-07-869311-XPractice Workbook 0-07-869609-7Spanish Study Guide and Assessment 0-07-869611-9
ANSWERS FOR WORKBOOKS The answers for Chapter 2 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
StudentWorksTM This CD-ROM includes the entire Student Edition along with theEnglish workbooks listed above.
TeacherWorksTM All of the materials found in this booklet are included for viewingand printing in the Algebra: Concepts and Applications TeacherWorksCD-ROM.
Copyright © 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 Algebra: Concepts and Applications. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:Glencoe/McGraw-Hill 8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-869254-7 Algebra: Concepts and Applications Chapter 2 Resource Masters
1 2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04
© Glencoe/McGraw-Hill iii Algebra: Concepts and Applications
Vocabulary Builder . . . . . . . . . . . . . . . . . vii-viii
Lesson 2-1Study Guide and Intervention . . . . . . . . . . . . . . . . 51Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53Reading to Learn Mathematics . . . . . . . . . . . . . . . 54Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Lesson 2-2Study Guide and Intervention . . . . . . . . . . . . . . . . 56Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58Reading to Learn Mathematics . . . . . . . . . . . . . . . 59Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Lesson 2-3Study Guide and Intervention . . . . . . . . . . . . . . . . 61Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63Reading to Learn Mathematics . . . . . . . . . . . . . . . 64Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Lesson 2-4Study Guide and Intervention . . . . . . . . . . . . . . . . 66Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Reading to Learn Mathematics . . . . . . . . . . . . . . . 69Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Lesson 2-5Study Guide and Intervention . . . . . . . . . . . . . . . . 71Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Reading to Learn Mathematics . . . . . . . . . . . . . . . 74Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75Lesson 2-6Study Guide and Intervention . . . . . . . . . . . . . . . . 76Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Reading to Learn Mathematics . . . . . . . . . . . . . . . 79Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Chapter 2 AssessmentChapter 2 Test, Form 1A. . . . . . . . . . . . . . . . . . 81-82Chapter 2 Test, Form 1B . . . . . . . . . . . . . . . . . . 83-84Chapter 2 Test, Form 2A. . . . . . . . . . . . . . . . . . 85-86Chapter 2 Test, Form 2B . . . . . . . . . . . . . . . . . . 87-88Chapter 2 Extended Response Assessment . . . . . . 89Chapter 2 Mid-Chapter Test . . . . . . . . . . . . . . . . . . 90Chapter 2 Quizzes A & B. . . . . . . . . . . . . . . . . . . . 91Chapter 2 Cumulative Review . . . . . . . . . . . . . . . . 92Chapter 2 Standardized Test Practice . . . . . . . . 93-94
Standardized Test PracticeStudent Recording Sheet . . . . . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . . . . . A2-A23
Contents
© Glencoe/McGraw-Hill iv Algebra: Concepts and Applications
A Teacher’s Guide to Using theChapter 2 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file theresources you use most often. The Chapter 2 Resource Masters include the corematerials needed for Chapter 2. These materials include worksheets, extensions,and assessment options. The answers for these pages appear at the back of thisbooklet.
All of the materials found in this booklet are included for viewing and printing inthe Algebra: Concepts and Applications TeacherWorks CD-ROM.
Vocabulary Builder Pages vii-viii include a student study tool that presents the key vocabulary terms from the chapter. Students areto record definitions and/or examples for eachterm. You may suggest that students highlight orstar the terms with which they are not familiar.
When to Use Give these pages to studentsbefore beginning Lesson 2-1. Encourage them toadd these pages to their Algebra: Concepts andApplications Interactive Study Notebook.Remind them to add definitions and examples asthey complete each lesson.
Study Guide There is one Study Guide master for each lesson.
When to Use Use these masters as reteachingactivities for students who need additional reinforcement. These pages can also be used inconjunction with the Student Edition as aninstructional tool for those students who havebeen absent.
Skills Practice There is one master for eachlesson. These provide computational practice at a basic level.
When to Use These worksheets can be usedwith students who have weaker mathematicsbackgrounds or need additional reinforcement.
Practice There is one master for each lesson.These problems more closely follow the structure of the Practice section of the StudentEdition exercises. These exercises are of averagedifficulty.
When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson.
Reading to Learn Mathematics Onemaster is included for each lesson. The first section of each master presents key terms fromthe lesson. The second section contains questions that ask students to interpret the context of and relationships among terms in thelesson. Finally, students are asked to summarizewhat they have learned using various representation techniques.
When to Use This master can be used as astudy tool when presenting the lesson or as aninformal reading assessment after presenting thelesson. It is also a helpful tool for ELL (EnglishLanguage Learners) students.
Enrichment There is one master for each lesson. These activities may extend the conceptsin the lesson, offer a historical or multiculturallook at the concepts, or widen students’perspectives on the mathematics they are learning. These are not written exclusively forhonors students, but are accessible for use withall levels of students.
When to Use These may be used as extracredit, short term projects, or as activities fordays when class periods are shortened.
© Glencoe/McGraw-Hill v Algebra: Concepts and Applications
Assessment OptionsThe assessment section of the Chapter 2Resources Masters offers a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter AssessmentsChapter Tests• Forms 1A and 1B contain multiple-choice
questions and are intended for use with average-level and basic-level students,respectively. These tests are similar in format to offer comparable testing situations.
• Forms 2A and 2B are composed of free-response questions aimed at the average-level and basic-level student, respectively.These tests are similar in format to offercomparable testing situations.
All of the above tests include a challengingBonus question.
• The Extended Response Assessmentincludes performance assessment tasks thatare suitable for all students. A scoring rubricis included for evaluation guidelines. Sample answers are provided for assessment.
Intermediate Assessment• A Mid-Chapter Test provides an option to
assess the first half of the chapter. It is composed of free-response questions.
• Two free-response quizzes are included tooffer assessment at appropriate intervals inthe chapter.
Continuing Assessment• The Cumulative Review provides students
an opportunity to reinforce and retain skillsas they proceed through their study of algebra. It can also be used as a test. Themaster includes free-response questions.
• The Standardized Test Practice offers continuing review of algebra concepts inmultiple choice format.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questions thatappear in the Student Edition on page 89.This improves students’ familiarity with theanswer formats they may encounter in testtaking.
• The answers for the lesson-by-lesson masters are provided as reduced pages withanswers appearing in red.
• Full-size answer keys are provided for theassessment options in this booklet.
© Glencoe/McGraw-Hill vi Algebra: Concepts and Applications
Chapter 2 Leveled Worksheets
Glencoe’s leveled worksheets are helpful for meeting the needs of everystudent in a variety of ways. These worksheets, many of which are foundin the FAST FILE Chapter Resource Masters, are shown in the chartbelow.
• The Prerequisite Skills Workbook provides extra practice on the basicskills students need for success in algebra.
• Study Guide and Intervention masters provide worked-out examplesas well as practice problems.
• Reading to Learn Mathematics masters help students improve readingskills by examining lesson concepts more closely.
• Noteables™: Interactive Study Notebook with Foldables™ helps students improve note-taking and study skills.
• Skills Practice masters allow students who are progressing at a slowerpace to practice concepts using easier problems. Practice masters provide average-level problems for students who are moving at a regular pace.
• Each chapter’s Vocabulary Builder master provides students the opportunity to write out key concepts and definitions in their own words.
• Enrichment masters offer students the opportunity to extend theirlearning.
Nine Different Options to Meet the Needs ofEvery Student in a Variety of Ways
primarily skillsprimarily conceptsprimarily applications
BASIC AVERAGE ADVANCED
1
2
Prerequisite Skills Workbook
Study Guide and Intervention
3 Reading to Learn Mathematics
4 NoteablesTM: Interactive Study Notebook with FoldablesTM
5 Skills Practice
6 Vocabulary Builder
7 Parent and Student Study Guide (online)
8 Practice
9 Enrichment
Reading to Learn MathematicsVocabulary Builder
This 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.
© Glencoe/McGraw-Hill vii Algebra: Concepts and Applications
Vocabulary Term Foundon Page Definition/Description/Example
absolute value
additive inverseA•duh•tiv
coordinateco•OR•duh•net
coordinate plane
coordinate system
dimensions
element
graph
integersIN•tah•jerz
matrixMAY•triks
natural numbers
negative numbers
(continued on the next page)
22NAME DATE PERIOD
© Glencoe/McGraw-Hill viii Algebra: Concepts and Applications
NAME DATE PERIOD
22 Reading to Learn MathematicsVocabulary Builder (continued)
Vocabulary Term Foundon Page Definition/Description/Example
number line
opposites
ordered array
ordered pair
originOR•a•jin
quadrantsKWA•druntz
scalar multiplicationSKAY•ler
Venn diagram
x-axis
x-coordinate
y-axis
y-coordinate
zero pair
© Glencoe/McGraw-Hill 51 Algebra: Concepts and Applications
NAME DATE PERIOD
Study Guide2–12–1
Graphing Integers on a Number Line
The numbers displayed on the number line below belong to the setof integers. The arrows at both ends of the number line indicatethat the numbers continue indefinitely in both directions. Noticethat the integers are equally spaced.
Use dots to graph numbers on a number line. You can label the dotswith capital letters.
The coordinate of B is �3 and the coordinate of D is 0.
Because 3 is to the right of �3 on the number line, 3 � �3. Andbecause �5 is to the left of 1, �5 � 1. Because 3 and �3 are thesame distance from 0, they have the same absolute value, 3. Usetwo vertical lines to represent absolute value.
|3| � 3 The absolute value of 3 is 3.
|�3| � 3 The absolute value of �3 is 3.
Example: Evaluate |�12| � |10|.|�12| � |10| � 12 � 10 |�12| � 12 and |10| � 10
� 22
Name the coordinate of each point.
1. B �4 2. D �3 3. G 5
Graph each set of numbers on a number line.
4. {�3, 2, 4} 5. {�1, 0, 3}
Write � or � in each blank to make a true sentence.
6. �7 5 7. �3 �8 8. |�1| 0
Evaluate each expression.
9. |9| 9 10. |�15| 15 11. |�20| � |10| 10
���
4–2 –1 0 1 2 34–3 –2 –1 0 1 2 3–4
4–3 –2 –1 0 1 2 3 5 6–5 –4
B D FE G
4–3 –2 –1 0
3 units 3 units
1 2 3–4
4–3 –2 –1 0 1 2 3 5–5 –4
A B C D E F
4–3 –2 –1 0
integers
negative integers positive integers
1 2 3 5–5 –4
© Glencoe/McGraw-Hill 52 Algebra: Concepts and Applications
Graphing Integers on a Number LineName the coordinate of each point.
1. S �3 2. U 0 3. T �2
4. R �5 5. W 4 6. V 1
Graph each set of numbers on a number line.
7. {�2, 0, 3} 8. {�5, �3, �1}
9. {2, 4, �4} 10. {�1, 3, 5}
11. {�4, �2, 2} 12. {�3, �1, 1, 3}
Write � or � in each blank to make a true sentence.
13. 2 7 14. 4 �2 15. �3 0
16. �5 �2 17. �1 2 18. �5 �8
19. �4 3 20. 0 �9 21. �6 �3
Evaluate each expression.
22. |4| 4 23. |�5| 5
24. |�8| 8 25. |10| 10
26. |3| � |�2| 5 27. |�7| � |�12| 19
�� �
� ��
�� �
�5 �4 �3 �2 �1 0 1 2 3 4 5
R S T U V W
NAME DATE PERIOD
Skills Practice2–12–1
© Glencoe/McGraw-Hill 53 Algebra: Concepts and Applications
NAME DATE PERIOD
Practice2–12–1
Graphing Integers on a Number LineName the coordinate of each point.
1. A �4 2. B 3 3. C �1
4. D 5 5. E �2 6. F 1
Graph each set of numbers on a number line.
7. {�5, 0, 2} 8. {4, �1, �2}
9. {3, �4, �3} 10. {�2, 5, 1}
11. {2, �5, 0} 12. {�4, 3, �2, 4}
Write � or � in each blank to make a true sentence.
13. 7 9 14. 0 �1 15. �2 2
16. 6 �3 17. �4 �5 18. �7 �3
19. �8 0 20. �11 2 21. �5 �6
Evaluate each expression.
22. |�4| 4 23. |6| 6
24. |�3| � |1| 4 25. |9| � |�8| 1
26. |�7| � |�2| 5 27. |�8| � |11| 19
���
���
���
4–3 –2 –1 0 1 2 3 5–5 –44–3 –2 –1 0 1 2 3 5–5 –4
4–3 –2 –1 0 1 2 3 5–5 –44–3 –2 –1 0 1 2 3 5–5 –4
4–3 –2 –1 0 1 2 3 5–5 –44–3 –2 –1 0 1 2 3 5–5 –4
4–3 –2 –1 0 1 2 3 5–5 –4
A E C F B D
© Glencoe/McGraw-Hill 54 Algebra: Concepts and Applications
NAME DATE PERIOD
Reading to Learn MathematicsGraphing Integers on a Number Line
2–12–1
Key Termsabsolute value the distance a number is from 0 on a
number linecoordinate (co OR di net) the number that corresponds to a
point on a number linegraph to plot points named by numbers on a number linenumber line a line with equal distances marked off to
represent numbers
Reading the Lesson1. Refer to the number line.
a. What do the arrowheads on each end of the number line mean?The line and the set of numbers continueinfinitely in each direction.
b. What is the absolute value of �3? What is the absolute value of 3? Explain.3, 3; �3 and 3 are both 3 units away from zero on the numberline.
2. Refer to the Venn diagram shown at the right. Write true or false for each of the following statements. a. All whole numbers are integers. true
b. All natural numbers are integers. true
c. All whole numbers are natural numbers. false
d. All natural numbers are whole numbers. true
e. All whole numbers are positive numbers. false
f. All integers are natural numbers. false
g. Whole numbers are a subset of natural numbers. false
h. Natural numbers are a subset of integers. true
Natural Numbers
WholeNumbers
Integers
�5 543210�4 �1�2�3
Helping You Remember3. One way to remember a mathematical concept is to connect it to something you have
seen or heard in everyday life. Describe a situation that illustrates the concept ofabsolute value.
Sample answer: On a football field, the distance from each goal lineto the 50-yard line is 50 yards.
© Glencoe/McGraw-Hill 55 Algebra: Concepts and Applications
NAME DATE PERIOD
Enrichment2–12–1
Venn DiagramsA type of drawing called a Venn diagram can be useful in explaining conditionalstatements. A Venn diagram uses circles to represent sets of objects.
Consider the statement “All rabbits have long ears.” To make a Venn diagram forthis statement, a large circle is drawn to represent all animals with long ears. Thena smaller circle is drawn inside the first to represent all rabbits. The Venn diagramshows that every rabbit is included in the group of long-eared animals.
The set of rabbits is called a subset of the set of long-eared animals.
The Venn diagram can also explain how to write the statement, “All rabbits havelong ears,” in if-then form. Every rabbit is in the group of long-eared animals, so ifan animal is a rabbit, then it has long ears.
For each statement, draw a Venn diagram. The write the sentence in if-then form.
1. Every dog has long hair. 2. All rational numbers are real.
If an animal is a dog, then it If a number is rational, thenhas long hair. it is real.
3. People who live in Iowa like corn. 4. Staff members are allowed in the faculty lounge.
If a person lives in Iowa,then the person likes corn. If a person is a staff member,
then the person is allowed inthe faculty lounge.
animals withlong ears
rabbits
© Glencoe/McGraw-Hill 56 Algebra: Concepts and Applications
NAME DATE PERIOD
Study Guide2–22–2
The Coordinate Plane
The two intersecting lines and the grid at the right form a coordinate system. The horizontal number line is called the x-axis, and the vertical number line is called the y-axis. The x- and y-axes divide the coordinate plane into fourquadrants. Point S in Quadrant I is the graph of the ordered pair (3, 2). The x-coordinate of point S is 3, and the y-coordinate of point S is 2.
The point at which the axes meet has coordinates (0, 0) and is called the origin.
Example 1: What is the ordered pair for point J? In what quadrant is point J located?
You move 4 units to the left of the origin and then 1 unit up to get to J. So the ordered pair for J is (�4, 1). Point J is located in Quadrant II.
Example 2: Graph M(�2, � 4) on the coordinate plane. Start at the origin. Move left on the x-axis to �2 and then down 4 units. Draw a dot here and label it M.
Write the ordered pair that names each point.
1. P (1, 3) 2. Q (�4, �3)
3. R (0, 2) 4. T (�4, 0)
Graph each point on the coordinate plane. Name the quadrant, if any, in which each point is located.
5. A(5, �1) IV 6. B(�3, 0) none
7. C(�3, 1) II 8. D(0, 1) none
9. E(3, 3) I 10. F(�1, �2) III
O x
y
O x
y
1 2 3 4
4321
–1–2–3–4
–1–2–3–4T
R
P
Q
O x
y
1
Quadrant I
Quadrant IV
Quadrant II
Quadrant III
2 3 4
4321
–1–2–3–4
–1–2–3–4
J
M
O x
y
1
Quadrant I
Quadrant IV
Quadrant II
Quadrant III
2 3 4
4321
–1–2–3–4
–1–2–3–4
S
The Coordinate PlaneWrite the ordered pair that names each point.
1. L (�4, 0) 2. M (�3, �1)
3. N (�1, �3) 4. P (0, 0)
5. Q (�2, 4) 6. R (2, 1)
7. S (2, �1) 8. T (5, 0)
9. U (0, �2) 10. V (0, 3)
Graph each point on the coordinate plane.
11. A(�2, 4) 12. B(0, �4)
13. C(5, �3) 14. D(�2, �1)
15. E(1, 4) 16. F(4, 0)
17. G(�4, �1) 18. H(3, 3)
19. I(�4, 3) 20. J(�5, 0)
Name the quadrant in which each point is located.
21. (�2, �2) III 22. (3, 4) I
23. (�4, 3) II 24. (4, �3) IV
25. (0, �2) none 26. (�1, �1) III
27. (4, �1) IV 28. (�3, 5) II
29. (�3, 0) none 30. (8, �4) IV
y
x�4 �2 2 4
�4
�2
2
4
y
x�4 �2 2 4
�4
�2
2
4
L
M
N
P
Q
R
S
T
U
V
© Glencoe/McGraw-Hill 57 Algebra: Concepts and Applications
NAME DATE PERIOD
Skills Practice2–22–2
© Glencoe/McGraw-Hill 58 Algebra: Concepts and Applications
NAME DATE PERIOD
Practice2–22–2
The Coordinate PlaneWrite the ordered pair that names each point.
1. A (�3, 4) 2. B (5, 2)
3. C (�4, �3) 4. D (2, �4)
5. E (�1, 1) 6. F (1, 0)
7. G (0, �2) 8. H (�2, 5)
9. J (�2, �4) 10. K (5, �1)
Graph each point on the coordinate plane.
11. K(0, �3) 12. L(�2, 3)
13. M(4, 4) 14. N(�3, 0)
15. P(�4, �1) 16. Q(1, �2)
17. R(�5, 5) 18. S(3, 2)
19. T(2, 1) 20. W(�1, �4)
Name the quadrant in which each point is located.
21. (1, 9) I 22. (�2, �7) III
23. (0, �1) none 24. (�4, 6) II
25. (5, �3) IV 26. (�3, 0) none
27. (�1, �1) III 28. (6, �5) IV
29. (�8, 4) II 30. (�9, �2) III
O x
y
O x
yA
H
E
F
B
K
DJ
C G
© Glencoe/McGraw-Hill 59 Algebra: Concepts and Applications
NAME DATE PERIOD
Reading to Learn MathematicsThe Coordinate plane
2–22–2
Key Termscoordinate plane the plane containing the x- and y-axescoordinate system the grid formed by the intersection of two
perpendicular number lines that meet at their zero pointsordered pair a pair of numbers used to locate any point on a
coordinate planequadrant one of the four regions into which the x- and y-axes
separate the coordinate planex-axis the horizontal number line on a coordinate planey-axis the vertical number line on a coordinate planex-coordinate the first number in a coordinate pairy-coordinate the second number in a coordinate pair
Reading the Lesson1. Identify each part of the coordinate system.
2. Use the ordered pair (�2, 3). a. Explain how to identify the x- and y-coordinates.
The x-coordinate is the first number; the y-coordinate is thesecond number.
b. Name the x-and y-coordinates. The x-coordinate is �2 and the y-coordinate 3.
c. Describe the steps you would use to locate the point at (�2, 3) on the coordinateplane.Start at the origin, move two units to the left and then move upthree units.
3. What does the term quadrant mean? Sample answer: It is one of four regions in the coordinate plane.
x
y
O
Helping You Remember4. Describe a method to remember how to write an ordered pair.
Sample answer: Since x comes before y in the alphabet, the x-coordinate is written first in an ordered pair.
y axis
x axisorigin
© Glencoe/McGraw-Hill 60 Algebra: Concepts and Applications
NAME DATE PERIOD
Enrichment2–22–2
Points and Lines on a MatrixA matrix is a rectangular array of rows and columns. Pointsand lines on a matrix are not defined in the same way as inEuclidean geometry. A point on a matrix is a dot, which can besmall or large. A line on a matrix is a path of dots that “line up.”Between two points on a line there may or may not be otherpoints. Three examples of lines are shown at the upper right.The broad line can be thought of as a single line or as two nar-row lines side by side.
A dot-matrix printer for a computer uses dots to form characters.The dots are often called pixels. The matrix at the right showshow a dot-matrix printer might print the letter P.
Sample answers are given.Draw points on each matrix to create the given figures.
1. Draw two intersecting lines that have 2. Draw two lines that cross but have four points in common. no common points.
3. Make the number 0 (zero) so that it 4. Make the capital letter O so that itextends to the top and bottom sides extends to each side of the matrix.of the matrix.
5. Using separate grid paper, make dot designs for severalother letters. Which were the easiest and which were themost difficult? See students’ work.
© Glencoe/McGraw-Hill 61 Algebra: Concepts and Applications
NAME DATE PERIOD
Study Guide2–32–3
Adding Integers
You can use a number line to add integers. Start at 0. Then move to the right for positive integers and move to the left for negative integers.
Both integers are positive. Both integers are negative. First move 2 units right from 0. First move 2 units left from 0. Then move 1 more unit right. Then move 1 more unit left.
When you add one positive integer and one negative integer on the number line, you change directions, which results in one move being subtracted from the other move.
Move 2 units left, then 1 unit right. Move 2 units right, then 1 unit left.
Use the following rules to add two integers and to simplify expressions.
Rule Examples
To add integers with the same sign, add 7 � 4 � 11their absolute values. Give the result the �8 � (�2) � �10same sign as the integers. �5x � (�3x) � �8x
To add integers with different signs, 9 � (�6) � 3subtract their absolute values. Give the 1 � (�5) � �4result the same sign as the integer with �2x � 9x � 7xthe greater absolute value. 3y � (�4y) � �y
Find each sum.
1. 5 � 8 13 2. �8 � (�9) �17 3. 12 � (�8) 4 4. �16 � 5 �11
5. 5 � (�8) � (�5) �8 6. �8 � (�8) � 20 4 7. 12 � 5 � (�1) 16
Simplify each expression.
8. 3x � (�6x) �3x 9. �5y � (�7y) �12y 10. 2m � (�4m) � (�2m) �4m
4�1 0 12 � (�1) � 1
2 3�2
�1
�2
�3 �1 0 1
�2
�2 � 1 � �1
�1
2�4 �2
�3 �1 0 1
�2
�2 � (�1) � �3
�1
2�4 �24�1 0 1
�2
2 � 1 � 3
�1
2 3 5
© Glencoe/McGraw-Hill 62 Algebra: Concepts and Applications
Adding IntegersFind each sum.
1. 2 � 7 2. �3 � (�2) 3. �4 � 1
9 �5 �3
4. 3 � (�9) 5. �2 � 12 6. �1 � (�6)
�6 10 �7
7. 10 � (�8) 8. �9 � 4 9. 3 � (�3)
2 �5 0
10. �5 � (�5) 11. 8 � (�9) 12. �7 � 4
�10 �1 �3
13. �2 � 2 14. �12 � 10 15. �8 � (�5)
0 �2 �13
16. �14 � 8 17. 15 � (�8) 18. 3 � (�11)
�6 7 �8
19. �9 � (�7) 20. 6 � (�9) 21. �14 � 15
�16 �3 1
22. �10 � 6 � (�4) 23. 13 � (�14) � 1 24. �4 � (�8) � 5
�8 0 �7
Simplify each expression.
25. �4c � 8c 26. �5a � (�9a) 27. �8d � 3d
4c �14a �5d
28. 7x � 3x 29. 6y � (�3y) 30. �7t � 4t
10x 3y �3t
31. �12s � (�4s) 32. 5t � (�13t) 33. 15h � (�4h)
�16s �8t 11h
34. 7b � 6b � (�8b) 35. �9w � 4w � (�5w) 36. 12t � 3t � (�6t)
5b �10w 9t
NAME DATE PERIOD
Skills Practice2–32–3
© Glencoe/McGraw-Hill 63 Algebra: Concepts and Applications
NAME DATE PERIOD
Practice2–32–3
Adding IntegersFind each sum.
1. 8 � 4 2. �3 � 5 3. 9 � (�2)
12 2 7
4. �5 � 11 5. �7 � (�4) 6. 12 � (�4)
6 �11 8
7. �9 � 10 8. �4 � 4 9. 2 � (�8)
1 0 �6
10. 17 � (�4) 11. �13 � 3 12. 6 � (�7)
13 �10 �1
13. �8 � (�9) 14. �2 � 11 15. �9 � (�2)
�17 9 �11
16. �1 � 3 17. 6 � (�5) 18. �11 � 7
2 1 �4
19. �8 � (�8) 20. �6 � 3 21. 2 � (�2)
�16 �3 0
22. 7 � (�5) � 2 23. �4 � 8 � (�3) 24. �5 � (�5) � 5
4 1 �5
Simplify each expression.
25. 5a � (�3a) 26. �7y � 2y 27. �9m � (�4m)
2a �5y �13m
28. �2z � (�4z) 29. 8x � (�4x) 30. �10p � 5p
�6z 4x �5p
31. 5b � (�2b) 32. �4s � 7s 33. 2n � (�4n)
3b 3s �2n
34. 5a � (�6a) � 4a 35. �6x � 3x � (�5x) 36. 7z � 2z � (�3z)
3a �8x 6z
© Glencoe/McGraw-Hill 64 Algebra: Concepts and Applications
NAME DATE PERIOD
Reading to Learn MathematicsAdding Integers
2–32–3
Key Termsadditive inverses two numbers are additive inverses if their
sum is 0opposite additive inversezero pair the result of positive algebra tiles paired with negative
algebra tiles
Reading the Lesson1. Explain how to add integers with the same sign.
Add their absolute values. The result has the same sign as theintegers.
2. Explain how to add integers with opposite signs.Find the difference of their absolute values. The result has thesame sign as the integer with the greater absolute value.
3. If two numbers are additive inverses, what must be true about their absolute values?The absolute values must be equal.
4. Use the number line to find each sum.
a. � 3 � 5 2
b. 4 � (�6) �2
c. How do the arrows show which number has the greater absolute value?The longer arrow represents the number with the greaterabsolute value.
d. Explain how the arrows can help you determine the sign of the answer.The direction of the longer arrow determines the sign of theanswer.
Write an equation for each situation.5. a five-yard penalty and a 13-yard pass �5 � 13 � 86. gained 11 points and lost 18 points 11 � (�18) � �77. a deposit of $25 and a withdrawal of $15 25 � (�15) � 10
�5�4�3�2�1 0 1 4 532
�4
�6
�5�4�3�2�1 0 1 4 532
�3
�5
Helping You Remember8. Explain how you can remember the meaning of “zero pair.”
Sample answer: Since the sum of a number and its opposite iszero, when a positive tile is paired with a negative tile, the sum iszero.
© Glencoe/McGraw-Hill 65 Algebra: Concepts and Applications
NAME DATE PERIOD
Enrichment2–32–3
Integer Magic
A magic triangle is a triangular arrangement of numbers in which the sum of the numbers along each side is the samenumber. For example, in the magic triangle shown at theright, the sum of the numbers along each side is 0.
In each triangle, each of the integers from �4 to 4 appearsexactly once. Complete the triangle so that the sum of theintegers along each side is �3.
1. 2.
3. 4.
In these magic stars, the sum of the integers along each line ofthe star is �2. Complete each magic star using the integers from�6 to 5 exactly once.
5. 6.
1
0
–2
2
54–6
4
–4
2
–2
–3
–5
–2
–3
–4
0
4
–1
3
–3 –2
4
–1
–4
–3
–2
4
1
3 –2 2
0
–3
41
–4 –1
Sample answersare given.
© Glencoe/McGraw-Hill 66 Algebra: Concepts and Applications
NAME DATE PERIOD
Study Guide2–42–4
Subtracting Integers
If the sum of two integers is 0, the numbers are opposites oradditive inverses.
Example 1: a. �3 is the opposite of 3 because �3 � 3 � 0
b. 17 is the opposite of �17 because 17 � (�17) � 0
Use this rule to subtract integers.
Example 2: Find each difference.
a. 5 � 25 � 2 � 5 � (�2) Subtracting 2 is the same as adding its
� 3 opposite, �2.
b. �7 � (�1)�7 � (�1) � �7 � 1 Subtracting �1 is the same as adding its
� �6 opposite, 1.
Example 3: Evaluate c � d � e if c � �1, d � 7, and e � �3.
c � d � e � �1 � 7 � (�3) Replace c with �1, d with 7, and e with �3. � �1 � 7 � 3 Write 7 � (�3) as 7 � 3. � 6 � 3 �1 � 7 � 6 � 9 6 � 3 � 9
Find each difference.
1. 5 � 8 �3 2. �8 � (�9) 1 3. �2 � 8 �10 4. �4 � (�5) 1
5. 16 � 8 8 6. 10 � (�10) 20 7. 0 � 10 �10 8. 0 � (�18) 18
Simplify each expression.
9. 3x � 9x �6x 10. �4y � (�6y) 2y 11. 2m � 8m � (�2m) �4m
Evaluate each expression if x � �1, y � 2, and z � �4.
12. x � y �3 13. y � z � 5 1 14. z � y � (�2) �4
15. 9 � x 10 16. x � z � z 7 17. 0 � y �2
To subtract an integer, add its oppositeor additive inverse.
© Glencoe/McGraw-Hill 67 Algebra: Concepts and Applications
NAME DATE PERIOD
Skills Practice2–42–4
Subtracting IntegersFind each difference.
1. 8 � 2 2. 12 � 4 3. �7 � (�2)
6 8 �5
4. �9 � 4 5. 4 � 12 6. �4 � (�10)
�13 �8 6
7. �6 � 1 8. �5 � 8 9. �5 � (�5)
�7 �13 0
10. �8 � 8 11. �11 � 7 12. 8 � (�7)
�16 �18 15
13. 9 � 14 14. �3 � (�15) 15. �14 � 6
�5 12 �20
16. �3 � 9 17. �7 � 7 18. 13 � 14
�11 �14 �1
Evaluate each expression if a � 2, b � �3, c � �1, and d � 1.
19. a � b 20. b � c 21. a � c
5 �2 3
22. c � d 23. a � b � c 24. b � d � c
�2 0 �3
25. d � b � a 26. c � a � b 27. a � d � b
�4 0 �2
© Glencoe/McGraw-Hill 68 Algebra: Concepts and Applications
NAME DATE PERIOD
Practice2–42–4
Subtracting IntegersFind each difference.
1. 9 � 3 2. �1 � 2 3. 4 � (�5)
6 �3 9
4. 6 � (�1) 5. �7 � (�4) 6. 8 � 10
7 �3 �2
7. �2 � 5 8. �6 � (�7) 9. 2 � 8
�7 1 �6
10. �10 � (�2) 11. �4 � 6 12. 5 � 3
�8 �10 2
13. �8 � (�4) 14. 7 � 9 15. �9 � (�11)
�4 �2 2
16. �3 � 4 17. 6 � (�5) 18. 6 � 5
�7 11 1
Evaluate each expression if a � �1, b � 5, c � �2, and d � �4.
19. b � c 20. a � b 21. c � d
7 �6 2
22. a � c � d 23. a � b � c 24. a � c � d
1 �8 �3
25. b � c � d 26. b � c � d 27. a � b � c
3 11 �4
© Glencoe/McGraw-Hill 69 Algebra: Concepts and Applications
NAME DATE PERIOD
Reading to Learn MathematicsSubtracting Integers
2–42–4
Key Termsadditive inverses two numbers are additive inverses if their sum
is 0opposite additive inversezero pair the result of positive algebra tiles paired with negative
algebra tiles
Reading the Lesson1. Write each subtraction problem as an addition problem.
a. 12 � 4 12 � (�4)
b. �15 � 7 �15 � (�7)
c. 0 � 11 0 � (�11)
d. �20 � 34 �20 � (�34)
e. �15 � (�4)�15 � 4
f. 16 � (�18) 16 � 18
2. Describe how to find each difference. Then find each difference.
a. 8 � 11 Add the opposite of 11 to 8; �3
b. 5 � (�8) Add the opposite of �8 to 5; 13
c. 17 � 14 Add the opposite of 14 to 17; 3
d. �8 � 19 Add the opposite of 19 to �8; �27
3. Explain how zero pairs are used to subtract with algebra tiles. Zero pairs are not needed to subtract negative tiles. If a positive tileis to be subtracted from negative tiles, first add a zero pair. Thenyou can subtract one positive tile.
Helping You Remember4. Explain why knowing the rules for adding integers can help you to subtract integers.
Sample answer: Since subtraction is really adding the number’sadditive inverse, the rules for addition also apply to subtraction.
© Glencoe/McGraw-Hill 70 Algebra: Concepts and Applications
NAME DATE PERIOD
Enrichment2–42–4
ClosureA binary operation matches two numbers in a set to just onenumber. Addition is a binary operation on the set of wholenumbers. It matches two numbers such as 4 and 5 to a singlenumber, their sum.
If the result of a binary operation is always a member of theoriginal set, the set is said to be closed under the operation. For example, the set of whole numbers is not closed undersubtraction because 3 � 6 is not a whole number.
Is each operation binary? Write yes or no.
Is each set closed under addition? Write yes or no. If youranswer is no, give an example.
Is the set of whole numbers closed under each operation?Write yes or no. If your answer is no, give an example.
13. multiplication: a � b yes
15. exponentation: ab yes
14. division: a � b no; 4 � 3 is not awhole number
16. squaring the sum: (a � b)2 yes
7. even numbers yes
9. multiples of 3 yes
11. prime numbers no; 3 � 5 � 8
8. odd numbers no; 3 � 7 � 10
10. multiples of 5 yes
12. nonprime numbersno; 22 � 9 � 31
1. the operation ←, where a ← b meansto choose the lesser number from aand b yes
3. the operation sq, where sq(a) meansto square the number a no
5. the operation ⇑ , where a ⇑ b meansto match a and b to any numbergreater than either number no
2. the operation ©, where a © b meansto cube the sum of a and b yes
4. the operation exp, where exp(a, b)means to find the value of ab yes
6. the operation ⇒ , where a ⇒ b meansto round the product of a and b up tothe nearest 10 yes
© Glencoe/McGraw-Hill 71 Algebra: Concepts and Applications
NAME DATE PERIOD
Study Guide2–52–5
Multiplying Integers
Use these rules to multiply integers and to simplify expressions.
Example 1: Find each product.a. 7(12)
7(12) � 84 Both factors are positive, so the product is positive.
b. �5(�9)�5(�9) � 45 Both factors are negative, so the
product is positive.
c. �4(8)�4(8) � �32 The factors have different signs,
so the product is negative.
Example 2: Evaluate �3ab if a � 3 and b � �5.�3ab � �3(3)(�5) Replace a with 3 and b with �5.
� �9(�5) �3 � 3 � �9� 45 Both factors are negative.
Example 3: Simplify �12(4x).�12(4x) � (�12 � 4)(x) Associative Property
� �48x �12 � 4 � �48
Find each product.
1. 3(8) 24 2. (�7)(�9) 63 3. 12(�1) �12 4. �6(5) �30
5. 4(�1)(�5) 20 6. (�8)(�8)(�2) �128 7. 2(�5)(10) �100
Evaluate each expression if a � 3, b � �2, and c � �3.
8. 5c �15 9. 2ab �12 10. abc 18 11. 3b � c �3
Simplify each expression.
12. 3(�6x) �18x 13. �5(�7y) 35y 14. (2p)(�4q) �8pq
The product of two positive integers is positive.The product of two negative integers is positive.The product of a positive integer and a negative integer is negative.
© Glencoe/McGraw-Hill 72 Algebra: Concepts and Applications
Multiplying IntegersFind each product.
1. 3(12) 2. �4(7) 3. �8(�8)
36 �28 64
4. 5(�9) 5. �2(�9) 6. �3(�10)
�45 18 30
7. 0(�5) 8. �13(�4) 9. 4(�11)
0 52 �44
10. �5(12) 11. 14(0) 12. �8(7)
�60 0 �56
13. �15(�4) 14. 9(�3) 15. �8(11)
60 �27 �88
16. (�2)(4)(�3) 17. (�4)(�5)(�1) 18. (3)(5)(�5)
24 �20 �75
Evaluate each expression if x � �2 and y � �4.
19. �3xy 20. �2xy 21. �5x
24 �16 10
22. �7y 23. 8xy 24. �6xy
28 64 �48
Simplify each expression.
25. 3(2a) 26. �4(�3c) 27. �5(�8b)
6a 12c 40b
28. (5c)(�7d) 29. (�8m)(�2n) 30. (�9s)(7t)
�35cd 16mn �63st
NAME DATE PERIOD
Skills Practice2–52–5
© Glencoe/McGraw-Hill 73 Algebra: Concepts and Applications
NAME DATE PERIOD
Practice2–52–5
Multiplying IntegersFind each product.
1. 3(�7) 2. �2(8) 3. 4(5)
�21 �16 20
4. �7(�7) 5. �9(3) 6. 8(�6)
49 �27 �48
7. 6(2) 8. �5(�7) 9. 2(�8)
12 35 �16
10. �10(�2) 11. 9(�8) 12. 12(0)
20 �72 0
13. �4(�4)(2) 14. 7(�9)(�1) 15. �3(5)(2)
32 63 �30
16. 3(�4)(�2)(2) 17. 6(�1)(2)(1) 18. �5(�3)(�2)(�1)
48 �12 30
Evaluate each expression if a � �3 and b � �5.
19. �6b 20. 8a 21. 4ab
30 �24 60
22. �3ab 23. �9a 24. �2ab
�45 27 �30
Simplify each expression.
25. 5(�5y) 26. �7(�3b) 27. �3(6n)
�25y 21b �18n
28. (6a)(�2b) 29. (�4m)(�9n) 30. (�8x)(7y)
�12ab 36mn �56xy
© Glencoe/McGraw-Hill 74 Algebra: Concepts and Applications
NAME DATE PERIOD
Reading to Learn MathematicsMultiplying Integers
2–52–5
Key Termsfactors the numbers being multipliedproduct the result when two or more factors are multiplied
together
Reading the Lesson1. Complete: If two numbers have different signs, the one number is positive and the other
number is .
2. Complete the table.
a.
b.
c.
d.
3. Explain what the term “additive inverse” means. Then give an example.
The product of any number and �1 is its additive inverse; � �
(�1) � .2 3
2 3
neg
Helping You Remember4. Describe how you know that the product of �3 and �5 is positive. Then describe how
you know that the product of 3 and �5 is negative.Sample answer: The signs are the same; the signs are different.
Multiplication Are the signs of the numbers Is the product positiveExample the same or different? or negative?
(�4)(9) different neg(�2)(�13) same pos5(�8) different neg6(3) same pos
© Glencoe/McGraw-Hill 75 Algebra: Concepts and Applications
NAME DATE PERIOD
Enrichment2–52–5
The Binary Number System
Our standard number system in base ten has ten digits, 0 through 9. In base ten, the values of the places are powers of 10.
A system of numeration that is used in computer technology is the binary number system. In a binary number, the place value of each digit is two times the place value of the digit to its right. There are only two digits in the binary system: 0 and 1.
The binary number 10111 is written 10111two. You can use a place-value chart like the one at the right to find the standard number that is equivalent to this number.
10111two � 1 � 16 � 0 � 8 � 1 � 4 � 1 � 2 � 1 � 1� 16 � 0 � 4 � 2 � 1� 23
Write each binary number as a standard number.
1. 11two 3 2. 111two 7 3. 100two 4
4. 1001two 9 5. 11001two 25 6. 100101two 37
Write each standard number as a binary number.
7. 8 1000two 8. 10 1010two 9. 15 1111two
10. 17 10001two 11. 28 11100two 12. 34 100010two
Write each answer as a binary number.
13. 1two � 10two 11two 14. 101two � 10two 11two
15. 10two � 11two 110two 16. 10000two � 10two 1000two
17. What standard number is equivalent to 12021three? 142
8 �
2 �
164
�2
�8
2 �
2 �
41
�2
�2
1
1 0 1 1 1
© Glencoe/McGraw-Hill 76 Algebra: Concepts and Applications
NAME DATE PERIOD
Study Guide2–62–6
Dividing Integers
Example 1: Use the multiplication problems at the rightto find each quotient.
a. 15 � 5Since 3 � 5 � 15, 15 � 5 � 3.
b. 15 � (�5)Since �3 � (�5) � 15, 15 � (�5) � �3.
c. �15 � 5Since �3 � 5 � �15, �15 � 5 � �3.
d. �15 � (�5)Since 3 � (�5) � �15, �15 � (�5) � 3.
Use these rules to divide integers.
Example 2: Evaluate if r � 8 and s � �2.
� Replace r with 8 and s with �2.
� �3 � 8 � �24
� 12 �24 � (�2) � 12
Find each quotient.
1. 36 � 9 4 2. �63 � (�7) 9 3. 25 � (�1) �25 4. �60 � 5 �12
5. �4 6. 6 7. 1 8. �7
Evaluate each expression if k � �1, m � 3, and n � �2.
9. �21 � m �7 10. 4 11. m � k �3 12. �4m � 5
n2nk
�56
8�1�1
�18�3
20�5
�24�2
�3 � 8
�2�3r
s
�3r
s
The quotient of two positive integers is positive.The quotient of two negative integers is positive.The quotient of a positive integer and a negative integer is negative.
3 � 5 � 15
�3(�5) � 15
�3 � 5 � �15
3(�5) � �15
© Glencoe/McGraw-Hill 77 Algebra: Concepts and Applications
NAME DATE PERIOD
Skills Practice2–62–6
Dividing IntegersFind each quotient.
1. 36 � 3 2. �15 � 5 3. 24 � (�8)
12 �3 �3
4. �45 � (�3) 5. 81 � (�9) 6. �28 � 4
15 �9 �7
7. �121 � 11 8. �144 � (�12) 9. 32 � (�4)
�11 12 �8
10. �64 � (�8) 11. �80 � 10 12. 48 � (�6)
8 �8 �8
13. 100 � (�25) 14. �20 � 5 15. 36 � (�9)
4 �4 �4
16. 56 � (�7) 17. �63 � (�9) 18. �32 � (�16)
�8 7 2
19. �21 � 3 20. �18 � 2 21. 72 � (�8)
�7 �9 �9
22. 23. 24.
�5 �3 25
Evaluate each expression if d � �3, f � 8, and g � �4.
25. f � g 26. 8d � g 27. 4g � f
�2 6 �2
28. 29. 30.
�16 2 �10
31. 32. 33.
12 4 �8
4fg
�2f
g9g
d
5fg
df�12
gf2
�125
�539�13
�35
7
© Glencoe/McGraw-Hill 78 Algebra: Concepts and Applications
NAME DATE PERIOD
Practice2–62–6
Dividing IntegersFind each quotient.
1. 28 � 7 2. �33 � 3 3. 42 � (�6)
4 �11 �7
4. �81 � (�9) 5. 12 � 4 6. 72 � (�9)
9 3 �8
7. 15 � 15 8. �30 � 5 9. �40 � (�8)
1 �6 5
10. 56 � (�7) 11. �21 � (�3) 12. �64 � 8
�8 7 �8
13. �8 � 8 14. �22 � (�2) 15. 32 � (�8)
�1 11 �4
16. �54 � (� 9) 17. 60 � (�6) 18. 63 � 9
6 �10 7
19. �45 � (�9) 20. �60 � 5 21. 24 � (�3)
5 �12 �8
22. 23. 24.
�2 �4 5
Evaluate each expression if a � 4, b � �9, and c � �6.
25. �48 � a 26. b � 3 27. 9c � b
�12 �3 6
28. 29. 30.
6 �9 2
31. 32. 33.
�8 9 �4
ac6
�4b
a12a
c
3cb
bc�6
abc
�45�9
40�10
�12
6
© Glencoe/McGraw-Hill 79 Algebra: Concepts and Applications
NAME DATE PERIOD
Reading to Learn MathematicsDividing Integers
2–62–6
Key Termsadditive inverses two numbers are additive inverses if their
sum is 0opposite additive inversezero pair the result of positive algebra tiles paired with negative
algebra tiles
Reading the Lesson1. Write the math sentence 18 divided by 6 two different ways. Then find the quotient.
18 � 6 � 3; � 3
2. Write negative or positive to describe each quotient. Explain your answer.
a.
b.
c.
d.
e.
f.
18 6
Helping You Remember3. Explain how knowing the rules for multiplying integers can help you to divide integers.
Sample answer: The rules to find the sign of the answer are thesame for multiplication and division. If the signs of the factors arethe same, the answer will be positive. If the signs of the factors aredifferent, the answer will be negative.
Expression Negative or Positive? Explanation
15 � 12 pos The signs of two numbers are the same.
9 � �10 neg The signs of the two numbers are different.
�35
7 neg The signs of the two numbers are different.
��
7183
pos The signs of two numbers are the same.
�1
23x neg The signs of the two numbers are different.
466y pos The signs of two numbers are the same.
© Glencoe/McGraw-Hill 80 Algebra: Concepts and Applications
NAME DATE PERIOD
Enrichment2–62–6
Day of the Week Formula
The following formula can be used to determine the specific day of the week on which a date occurred.
s � d � 2m � [(3m � 3) � 5] � y � �4y
� � �10y
0� � �
40y
0� � 2
s � sumd � day of the month, using numbers from 1–31m� month, beginning with March is 3, April is 4, and so on,
up to December is 12, January is 13, and February is 14y � year except for dates in January or February when the
previous year is used
For example, for February 13, 1985, d � 13, m � 14, and y � 1984;and for July 4, 1776, d � 4, m � 7, and y � 1776
The brackets, [ ], mean you are to do the division inside them,discard the remainder, and use only the whole number part of thequotient. The next step is to divide s by 7 and note the remainder.The remainder 0 is Saturday, 1 is Sunday, 2 is Monday, and so on,up to 6 is Friday.
Example: What day of the week was October 3, 1854?
For October 3, 1854, d � 3, m � 10, and y � 1854.
s � 3 � [ 2(10) ] � [ (3 � 10 � 3) � 5 ] � 1854 � � � � � � � � � � 2
� 3 � 20 � 6 � 1854 � 463 � 18 � 4 � 2� 2334
s � 7 � 2334 � 7� 333 R3
Since the remainder is 3, the day of the week was Tuesday.
Solve.
1. See if the formula works for today’s date. Answers will vary.
2. On what day of the week were you born? Answers will vary.
3. What will be the day of the week on April 13, 2006?s � 13 � 2(4) � [(3 � 4 � 3) � 5] � 2006 � ��20
406�� � ��2100006�� � ��2400006�� � 2
� 13 � 8 � 3 � 2006 � 501 � 20 � 4 � 2 � 2518; 2518 � 7 � 359 R5 Thursday4. On what day of the week was July 4, 1776?
s � 4 � 2(7) � [(3 � 7 � 3) � 5] � 1776 � ��17476�� � ��1170706�� � ��1470706�� � 2
� 4 � 14 � 4 � 1776 � 444 � 17 � 4 � 2 � 2231; 2231 � 7 � 318 R5 Thursday
1854400
1854100
1854
4��
2NAME DATE PERIOD
Chapter 2 Test, Form 1A2
© Glencoe/McGraw-Hill 81 Algebra: Concepts and Applications
Write the letter for the correct answer in the blank at the right of eachproblem.
1. Which of the following sentences is true?A. |�3| � �|�3| B. 2 � |�2|C. |�5| � |�3| D. �5 � �3
2. Name the coordinate of C on the numberline at the right.A. �4 B. �2C. 2 D. 3
3. Order �8, 6, �7, 7, and 0 from greatest to least.A. �8, �7, 0, 6, 7 B. �8, 7, �7, 6, 0C. 7, 6, 0, �7, �8 D. 7, 6, 0, �8, �7
4. Evaluate �|14| � |�7|.A. �21 B. �7 C. 7 D. 21
For Questions 5–6, refer to the coordinate plane at the right.
5. Which ordered pair names point A?A. (�3, 4) B. (�4, �3)C. (3, �4) D. (4, �3)
6. In which quadrant is point C located?A. IB. IIC. No quadrant; it lies on the y-axis.D. No quadrant; it lies on the x-axis.
7. Which of the following points is located in Quadrant III?A. (�2, �4) B. (�6, 0) C. (�5, 3) D. (1, �2)
8. The graph of P (x, y) satisfies the condition that y � 0. In whichquadrant(s) could point P be located?A. III only B. IV only C. II or III D. III or IV
9. Which ordered pair names a point that lies on the y-axis and below the x-axis?A. (�1, �4) B. (�6, 0) C. (0, �3) D. (0, 2)
10. Find the sum: �18 � (�24).A. �42 B. �32 C. �6 D. 6
11. What is the value of k if 40 � (�58) � 32 � k?A. 130 B. 50 C. 16 D. 14
12. Simplify 15z � (�23z) � 25z.A. 27z B. 17z C. 63z D. �7z
O x
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BC
–3 –2 –1 0 1 2 3–4
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2NAME DATE PERIOD
Chapter 2 Test, Form 1A (continued)2
© Glencoe/McGraw-Hill 82 Algebra: Concepts and Applications
13. A basketball player averages 24 points per game. In her next four games,she scores 5 points above her average, 4 points below her average, 6 points below her average, and 11 points above her average. How manypoints total is she above or below average for the four games?A. 6 below B. 4 below C. 4 above D. 6 above
14. Find the difference: �12 � (�5).A. �17 B. �7 C. 7 D. 17
15. Evaluate 20 � a � b if a � 18 and b � �5.A. 43 B. 33 C. �3 D. �7
16. Simplify �14d � 8d � (�21d ). A. �d B. �43d C. �15d D. d
17. The week that your rent is due your paycheck is $462. If your rent is$275, how much money do you have left for the week after paying yourrent?A. $87 B. $177 C. $187 D. $737
18. Find the product: �2(3)(�1)(5)(�2).A. �60 B. �30 C. 30 D. 60
19. Evaluate �2xy � 3z if x � 8, y � �1, and z � �5.A. 31 B. 1 C. �1 D. �31
20. What is the product of �5, �6, and �2?A. �70 B. �60 C. 60 D. 70
21. Simplify �2(�3r)(5s).A. 6r � 5s B. 11r � s C. 25rs D. 30rs
22. Find the quotient: �125 � (�5).A. �120 B. �24 C. 24 D. 25
23. Find the value of s if �84 � 12 � s.A. 72 B. 7 C. �7 D. �8
24. Evaluate if m � �5, n � 6, and p � �3.
A. �7 B. �3 C. 3 D. 7
25. Over a six-year period, the enrollment of a school decreased from 812 to 482. What was the average change in enrollment for each of those six years?A. �330 B. �55 C. �45 D. �38
Bonus Simplify � (�2)(�9).
A. �2 B. 0 C. 2 D. 34
�96��6
mp � n�
�3
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Bonus
2NAME DATE PERIOD
Chapter 2 Test, Form 1B2
© Glencoe/McGraw-Hill 83 Algebra: Concepts and Applications
Write the letter for the correct answer in the blank at the right of eachproblem.
1. Name the coordinate of Z on the number line at the right.A. 3 B. 2C. 1 D. �3
2. Order �4, 2, �1, �3, and �2 from least to greatest.A. �1, �2, �3, �4, 2 B. �2, �1, 2, �3, �4C. �4, �3, �2, �1, 2 D. 2, �1, �2, �3, �4
3. Which of the following sentences is true?A. �|2| � |�2| B. �4 � �3C. 6 � |�7| D. |�1| � 1
4. Evaluate |5| � |�2|.A. 7 B. 3 C. �3 D. �7
5. Which of the following points is located in Quadrant II?A. (�4, 0) B. (�2, 7) C. (5, �1) D. (�3, �4)
For Questions 6–7, refer to the coordinate plane at the right.
6. Which ordered pair names point P?A. (0, 4) B. (4, 0)C. (�4, 0) D. (0, �4)
7. In which quadrant is point Q located?A. I B. IIC. III D. IV
8. The graph of P (x, y) satisfies the conditions that x � 0 and y � 0. Inwhich quadrant is point P located?A. I B. II C. III D. IV
9. Which ordered pair names a point that lies on the x-axis and to the left ofthe y-axis?A. (0, �3) B. (4, 0) C. (0, 0) D. (�1, 0)
10. What is the value of m if m � 13 � (�27)?A. �40 B. �24 C. �14 D. 40
11. Simplify �4k � (�2k) � 8k.A. �2k B. 2k C. 14k D. 6k
12. Find the sum: �50 � 28.A. �78 B. �32 C. �22 D. 78
O x
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2NAME DATE PERIOD
Chapter 2 Test, Form 1B (continued)2
© Glencoe/McGraw-Hill 84 Algebra: Concepts and Applications
13. In four days, a golfer has rounds of four over par (�4), 1 under par (�1), 2 over par (�2) and 3 under par (�3). What is the golfer’s overall score forthe four days?A. �1 B. �1 C. �2 D. �4
14. Evaluate y � x if x � 12 and y � �8.A. �20 B. �4 C. 4 D. 20
15. On January 13, the low temperature was 12°F. The next day, the lowtemperature dropped by 25°. What was the low temperature on January 14?A. �37°F B. �25°F C. �13°F D. 37°F
16. Find the difference: �9 � 5.A. 45 B. 14 C. �4 D. �14
17. Simplify �6p � (�9p).A. �3p B. 3p C. �15p D. 15p
18. Evaluate �2�m � n if � � �1, m � 2, and n � �3.A. �7 B. �4 C. 1 D. 7
19. Simplify �5(�4t).A. 20t B. �9t C. �t D. �20t
20. Find the product: �8(�6).A. �56 B. �48 C. 14 D. 48
21. What is the value of n if n � (�6)(3)(�3)?A. �54 B. �36 C. 36 D. 54
22. Evaluate if f � �4 and g � 2.
A. 4 B. 3 C. 1 D. �4
23. Find the quotient: 54 � (�3).A. �18 B. �16 C. 16 D. 18
24. Find the value of b if b � �72 � (�18).A. �6 B. �4 C. 4 D. 6
25. Over eight years, the population of a town decreased from 1000 to 800.What was the average change in population for each of the eight years?A. �200 B. �25 C. 25 D. 200
Bonus Simplify � (�4)(2).
A. �11 B. �5 C. 5 D. 11
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fg��2
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Bonus
2NAME DATE PERIOD
Chapter 2 Test, Form 2A2
© Glencoe/McGraw-Hill 85 Algebra: Concepts and Applications
1. Graph the set of numbers {3, �1, 0} on a number line.
For Questions 2–4, replace each ● with � or � to make a truesentence.
2. |�10| ● 11
3. �6 ● �8
4. �3 ● �|�2|
5. Evaluate �|�6| � |0|.
For Questions 6–9, use the coordinate plane at the right.
6. What ordered pair names point P?
7. What ordered pair names point R?
8. In what quadrant is point S located?
9. In what quadrant is point T located?
10. In what quadrant is the point D(�4, 8) located?
For Questions 11–13, find each sum.
11. 18 � (�27) � 46
12. �36 � (�8) � 20
13. 50 � (�36) � (�12)
14. During one week the Dow Jones Industrial average, the mostcommonly used measure of the stock market, rises 43 points,falls 11 points, rises 38 points, rises 69 points, and falls 148 points. By how many points is it up or down overall for the week?
15. Evaluate �26 � |z| � y if y � �8 and z � �15.
Find each difference.
16. 22 � (�9)
17. �8 � (�12)
18. �30 � (�8) � (�25)
19. 45 � (�18) � 75
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–1 0 1 2 3
2NAME DATE PERIOD
Chapter 2 Test, Form 2A (continued)2
© Glencoe/McGraw-Hill 86 Algebra: Concepts and Applications
20. Simplify �28k � (�18k) � 14k.
21. What is the difference in elevation between the highest pointin California, Mount Whitney, which towers 4421 metersabove sea level, and the lowest point in California, DeathValley, which lies 86 meters below sea level?
For Questions 22–24, find each product.
22. �2(�3)(�3)
23. 4(�2)(�1)(5)(�2)
24. �12(�2)(�1)
25. A small company buys 8 chairs, each at a price of $40 lessthan the regular price, and 6 lamps, each at a price of $15 lessthan the regular price. What number describes the price thecompany pays in all compared to the regular price?
26. Evaluate 3xz � 8y if x � 4, y � �1, and z � �2.
27. Find the next term in the pattern 2, �8, 32, �128, ….
For Questions 28–30, find each quotient.
28.
29. �120 � (�15)
30.
31. The acceleration a of an object (in feet per second squared) is
given by a � , where t is the time in seconds, s1 is the
speed at the beginning of the time, and s2 is the speed at theend of the time. What is the acceleration of a car that brakesfrom a speed of 114 feet per second to a speed of 18 feet persecond in 6 seconds?
32. Evaluate if x � �6, y � �4, and z � 10.
33. Over a five-year period, the value of a house increased from$135,000 to $150,000. What was the average change in valuefor each of these five years?
Bonus From Sunday to Monday, the minimum daily humiditydrops 3%. Over the next three days, it rises 8%, rises 16%,and then drops 21%. What is the average daily changewhen you compare the minimum humidity on Thursday to the minimum humidity on Sunday?
z � x�
y
s2 � s1�
t
�100�
�4
57��3
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Bonus
2NAME DATE PERIOD
Chapter 2 Test, Form 2B2
© Glencoe/McGraw-Hill 87 Algebra: Concepts and Applications
For Questions 1–3, replace each ● with � or � to make a truesentence.
1. �5 ● �7
2. 3 ● |�4|
3. �|�2| ● 1
4. Evaluate |�4| � |�8|.
5. Graph the set of numbers {�2, 1, 0} on a number line.
For Questions 6–9, use the coordinate plane at the right.
6. In what quadrant is point B located?
7. In what quadrant is point C located?
8. What ordered pair names point A?
9. What ordered pair names point E?
10. In what quadrant is the point R(6, �2) located?
11. Evaluate �4 � b � |c| if b � 7 and c � �2.
For Questions 12–14, find each sum.
12. 6 � (�3) � 9
13. �21 � (�15) � 31
14. �12 � 18 � (�20)
15. During one week a small town reservoir falls 3 feet, drops 2 feet, rises 3 feet, rises 1 foot, and falls 1 foot. By how manyfeet does the reservoir rise or fall overall for the week?
For Questions 16–19, find each difference.
16. 9 � (�5)
17. �15 � (�32)
18. �6 � (�5)
19. �11 � (�28) � 3
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–1 0 1–3 –2
2NAME DATE PERIOD
Chapter 2 Test, Form 2B (continued)2
© Glencoe/McGraw-Hill 88 Algebra: Concepts and Applications
20. Simplify 8b � 5b � (�3b).
21. The temperature dropped 42°F overnight from yesterday’shigh temperature of 25°F. What is the temperature thismorning?
22. Find the next term in the pattern 3, �15, 75, … .
23. Evaluate 2x � 3y when x � �5 and y � �4.
For Questions 24–26, find each product.
24. 4(6)(�2)
25. �2(3)(�1)(5)
26. 3(�3)(�2)(�1)
27. You and several friends go together to buy detergent from awarehouse store. By buying 12 economy boxes, you get a pricethat is $2 less per box than the regular price. What numberdescribes the price you pay for the total purchase compared tothe regular price?
28. Evaluate if a � 16, b � �4, and c � �8.
For Questions 29–31, find each quotient.
29. �42 � (�3)
30.
31.
32. The acceleration a of an object (in feet per second squared) is
given by a � , where t is the time in seconds, s1 is the
speed at the beginning of the time, and s2 is the speed at theend of the time. What is the acceleration of a sled testing childcar seats that goes from a speed of 88 feet per second to aspeed of 0 feet per second in 2 seconds?
33. Over the past three years, the zoo’s attendance figures havedecreased from 185,000 to 176,000. What is the averagechange in attendance for each of the last three years?
Bonus From Sunday to Monday, the maximum daily temperaturein a small pond rises 1°F. Over the next three days, it rises 4°F,falls 1°F, and then falls 8°F. What is the average daily changewhen you compare the maximum temperature on Thursday to the maximum temperature on Sunday?
s2 � s1�
t
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�150�
25
a � c�
b
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Bonus
2NAME DATE PERIOD
Chapter 2 Extended Response Assessment2
© Glencoe/McGraw-Hill 89 Algebra: Concepts and Applications
Instructions: Demonstrate your knowledge by giving a clear, concisesolution to each problem. Be sure to include all relevant drawingsand to justify your answers. You may show your solution in morethan one way or investigate beyond the requirements of the problem.
1. Refer to the coordinate plane at the right.
a. Write the ordered pair that names each point.
b. Multiply the x- and y-coordinates of each point by �2.
c. Graph the new points. Label the point corresponding to A as X, the point corresponding to B as Y, and the point corresponding to C as Z.
d. Describe how the new triangle is related to the originaltriangle.
2. Now we will investigate more generally what happens to pointswhen their x- and/or y-coordinates are multiplied by a negativenumber.
a. Pick a negative integer n. Fill out the table below, in which youwill choose one point (a, b) in each quadrant, and then multiplyone or both coordinates by n.
b. How does multiplying one or both coordinates of a point by anegative number change the quadrant in which a point lies?
3. In an investment club, members pool their money and theirknowledge to invest in the stocks of various companies. Membersshare any profits or losses equally.
a. One club charges each member a $250 initial investment andmonthly investments of $30. In its first year, the 15-memberclub loses $1320. In its second year, the club makes a $990profit. Write and evaluate an expression to find each member’snet gain or loss after two years.
b. Another club charges each member a $150 initial investmentand monthly investments of $20. In its first year, the 25-member club loses $1750. In its second year, the club makesa $1200 profit. Write and evaluate an expression to find eachmember’s net gain or loss after two years.
c. Compare the results of the two investment clubs.
Quadrant of (a, b) I II III IV
Coordinates of (a, b)
Coord. and quad. of (na, b)
Coord. and quad. of (a, nb)
Coord. and quad. of (na, nb)
O x
y
B
AC
2NAME DATE PERIOD
Chapter 2 Mid-Chapter Test(Lessons 2–1 through 2–3)
2
© Glencoe/McGraw-Hill 90 Algebra: Concepts and Applications
For Questions 1–2, name the coordinate of each point on thenumber line at the right.
1. C
2. D
Replace each ● with � or � to make a true sentence.
3. �8 ● �2
4. |�3| ● �|�2|
5. 4 ● �5
6. �6 ● |�7|
Order each set of numbers from greatest to least.
7. �12, 10, �8, 0, 3
8. �4, 6, �5, �3, 2, 5
Graph each point on the same coordinate plane.
9. P(3, 0)
10. Q(�2, �1)
11. R(4, �3)
For Questions 12–15, use the coordinate plane at the right.
12. What ordered pair names point A?
13. What ordered pair names point D?
14. In what quadrant is point C located?
15. In what quadrant is point B located?
For Questions 16–18, find each sum.
16. �9 � 18
17. 84 � (�35) � (�27)
18. �8 � 4 � (�9) � 15
19. Simplify 12x � (�9x) � 6x.
20. Evaluate �11 � y � z if y � �4 and z � 8.
O x
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O x
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1. Graph the set of numbers {3, �2, 0} on a number line.
For Questions 2–3, replace each ● with � or � to make a truesentence.
2. |�12| ● �10
3. �8 ● �|�7|
4. Evaluate �|�6| � |�2|.
For Questions 5–7, graph each point on the same coordinateplane.
5. A(2, �3)
6. B(3, 4)
7. C(�3, �4)
8. In what quadrant is the point T(4, �1) located?
1. Find the sum: �11 � 8 � (�7).
2. Evaluate a � b � (�12) if a � �16 and b � 28.
3. Find the difference: 120 � (�54).
4. Write and evaluate an expression to find the difference (in thenumber of floors) between the 21st story of a building and theparking level three stories below the ground floor.
5. Find the product: �2(7)(�3)(�1).
6. Evaluate (�2s)(5t) if s � �1 and t � 8.
7. What is the value of b if b � �90 � (�15)?
8. Over the past four years, the value of a car has decreased from$22,000 to $12,000. What is the average change in value foreach of the last four years?
2NAME DATE PERIOD
2
© Glencoe/McGraw-Hill 91 Algebra: Concepts and Applications
Chapter 2 Quiz A(Lessons 2–1 through 2–2)
2NAME DATE PERIOD
Chapter 2 Quiz B(Lessons 2–3 through 2–6)
21.
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2NAME DATE PERIOD
2
© Glencoe/McGraw-Hill 92 Algebra: Concepts and Applications
1. Write an equation for the sentence below. (Lesson 1–1)Six less than four times a is the same as eleven more than theproduct of b and c.
2. Find the value of 6 � 2(7 � 4) � 6. (Lesson 1–2)
3. Name the property shown by the statement below. (Lesson 1–3) 8 � 6 � (5 � 11) � 8 � (6 � 5) � 11
4. Simplify 6(2x � 3) � 4x. (Lesson 1–4)
5. Mrs. Esposito buys apples at $2 per pound and walnuts at $5 per pound. If she spends three times as much on walnuts as apples and her total bill is $20, how many pounds of applesdoes she buy? (Lesson 1–5)
6. The frequency table gives the number of goals a soccer team scored in 11 games. In how many games did the team score at least two goals? (Lesson 1–6)
7. What kind of a graph or plot is best to use to display how aquantity changes over time? (Lesson 1–7)
8. Order 11, �25, 36, �64, �2, and 3 from least to greatest.(Lesson 2–1)
For Questions 9–10, refer to the coordinate plane at the right. (Lesson 2–2)
9. Write the ordered pair that names point W.
10. Name the quadrant in which point Vis located.
11. Find the sum: �22 � (�31). (Lesson 2–3)
12. Evaluate �a � b � c if a � �12, b � 22, and c � �8. (Lesson 2–4)
13. At 20°F with a 5-mile-per-hour wind, the windchill factor is16°F. At this temperature with a 45-mile-per-hour wind, thewindchill factor drops 38°F. What is the windchill factor at20°F with a 45-mile-per-hour wind? (Lesson 2–4)
14. Find the product of �2, 3, �1, and 8. (Lesson 2–5)
15. Evaluate if x � �6 and y � 2. (Lesson 2–6)
16. Find the quotient: (�126) � (�9). (Lesson 2–6)
3xy��4
O x
y
SV
WU
T
Goals Frequency0 21 32 43 14 1
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
Chapter 2 Cumulative Review
2NAME DATE PERIOD
2
© Glencoe/McGraw-Hill 93 Algebra: Concepts and Applications
Write the letter for the correct answer in the blank at the right of theproblem.
1. Write an equation for the sentence below.
Three less than the quotient of b and 5 equals 4 more than twice b.
A. � 3 � 6b B. � 4 � 2b
C. � 3 � 2b � 4 D. 3 � � 4 � 2b
2. Annie buys a pair of pants for $25 and several T-shirts for $8 each. Writean expression for her total cost if she buys n T-shirts.
A. n(8 � 25) B. 25 � 8n C. 25 � D. 25n � 8
3. Find the value of 14 � 2 � 5 � 2 � 3.A. 1 B. 2 C. 14 D. 21
4. Name the property of equality shown by the statement below.
If 2b � 10 � 5x and 5x � 15, then 2b � 10 � 15. A. Reflexive Property of EqualityB. Transitive Property of EqualityC. Symmetric Property of EqualityD. Multiplication Property of Equality
5. Name the property shown by the statement below.
6 � (5 � 3) � 6 � (3 � 5)A. Commutative Property of AdditionB. Commutative Property of MultiplicationC. Associative Property of AdditionD. Associative Property of Multiplication
6. Simplify 3(4 � 2a) � 8(a � 6).A. 20 � 14a B. 2a � 60 C. 60 � 2a D. 50 � 14a
7. How many ways are there to make $1.20 using quarters and/or dimes?A. 2 B. 3 C. 4 D. 5
8. Use the frequency table to determine how many out of 20 students wear shoes larger than size 7.A. 7 B. 12C. 15 D. 16
9. The stem-and-leaf plot shows the number of times students ran the length of a football field in 15 minutes. How many students ran this length fewerthan 25 times?A. 4 B. 5 C. 7 D. 8
Stem Leaf1 6 92 0 3 5 63 1 2 2 4 8
3 |1 � 31
Shoe Size Frequency6 47 18 79 5
10 3
8�n
b�5
b�5
b � 3�
5b�5
Chapter 2 Standardized Test Practice(Chapters 1–2)
1.
2.
3.
4.
5.
6.
7.
8.
9.
2NAME DATE PERIOD
2
© Glencoe/McGraw-Hill 94 Algebra: Concepts and Applications
10. You want to show how the number of computers per 100 students haschanged in your state over the past 20 years. The most appropriate wayto display your data would be aA. histogram.B. stem-and-leaf plot.C. cumulative frequency table.D. line graph.
11. Which of the following statements is true?A. |�5| � |�3| B. �|�5| � �|3|C. �3 � �5 D. |�5| � 3
12. Evaluate |�8| � |9|.A. �17 B. �1 C. 1 D. 17
For Questions 13–14, refer to the coordinate planeat the right.
13. What ordered pair names point D?A. (�3, 0) B. (0, 3)C. (3, 0) D. (0, �3)
14. In which quadrant is point E located?A. I B. IIC. III D. IV
15. Find the sum: �15 � (�11) � 20.A. 16 B. 6 C. �6 D. �16
16. Simplify �8b � (�3b) � (�5b) � 4b.A. 2b B. �2b C. �10b D. �20b
17. Evaluate �12 � x � y when x � �6 and y � �4.A. �22 B. �10 C. �2 D. 2
18. Find the value of p if �2(3)(�1)(�5) � p.A. �30 B. �11 C. 30 D. 60
19. What is the value of k if �216 � 9 � k?A. �24 B. �22 C. 22 D. 24
20. Over seven years, the number of books in a school library increased from1160 to 2000. What was the average change in the number of books in thelibrary for each of the seven years?A. 115 B. 120 C. 134 D. 840
O x
y
B
D
EA
C
Chapter 2 Standardized Test Practice(Chapters 1–2) (continued)
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
© Glencoe/McGraw-Hill A1 Algebra: Concepts and Applications
Preparing for Standardized TestsAnswer Sheet
1.
2.
3.
4.
5.
6.
7.
8.
9.
10. Show your work.
A
A
A
A
A
A
A
A
•
123456789
/•
0123456789
/•
0123456789
•
0123456789
B
B
B
B
B
B
B
B
C
C
C
C
C
C
C
C
D
D
D
D
D
D
D
D
E
E
E
E
E
E
E
E
Answers (Lesson 2-1)
© Glencoe/McGraw-Hill A2 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill52
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
Gra
ph
ing
Inte
ger
s on
a N
um
ber
Lin
eN
ame
the
coor
din
ate
of e
ach
poi
nt.
1.S
�3
2.U
03.
T�
2
4.R
�5
5.W
46.
V1
Gra
ph
eac
h s
et o
f n
um
ber
s on
a n
um
ber
lin
e.
7.{�
2, 0
, 3}
8.{�
5, �
3, �
1}
9.{2
, 4, �
4}10
.{�
1, 3
, 5}
11.{
�4,
�2,
2}
12.
{�3,
�1,
1, 3
}
Wri
te �
or �
in e
ach
bla
nk
to m
ake
a tr
ue
sen
ten
ce.
13.2
7
14.
4 �
215
.�
3 0
16.�
5 �
217
.�
1 2
18.
�5
�8
19.�
4 3
20.
0 �
921
.�
6 �
3
Eva
luat
e ea
ch e
xpre
ssio
n.
22.|
4|4
23.
|�
5|5
24.|
�8|
8
25.
|10
|10
26.|
3| �
|�
2|5
27.
|�
7| �
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12|
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�5
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01
23
45
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01
23
45
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�4
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01
23
45
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�4
�3
�2
�1
01
23
45
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�4
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�2
�1
01
23
45
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01
23
45
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01
23
45
RS
TU
VW
NA
ME
DAT
EP
ER
IOD
Skil
ls P
ract
ice
2–1
2–1
© G
lenc
oe/M
cGra
w-H
ill51
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Stud
y G
uide
2–1
2–1
Gra
ph
ing
Inte
ger
s on
a N
um
ber
Lin
e
Th
e n
um
bers
dis
play
ed o
n t
he
nu
mbe
r li
ne
belo
w b
elon
g to
th
e se
tof
in
tege
rs. T
he
arro
ws
at b
oth
en
ds o
f th
e n
um
ber
lin
e in
dica
teth
at t
he
nu
mbe
rs c
onti
nu
e in
defi
nit
ely
in b
oth
dir
ecti
ons.
Not
ice
that
th
e in
tege
rs a
re e
qual
ly s
pace
d.
Use
dot
s to
gra
ph n
um
bers
on
a n
um
ber
lin
e. Y
ou c
an l
abel
th
e do
tsw
ith
cap
ital
let
ters
.
Th
e co
ordi
nat
e of
Bis
�3
and
the
coor
din
ate
of D
is 0
.
Bec
ause
3 i
s to
th
e ri
ght
of �
3 on
th
e n
um
ber
lin
e, 3
��
3. A
nd
beca
use
�5
is t
o th
e le
ft o
f 1,
�5
�1.
Bec
ause
3 a
nd
�3
are
the
sam
e di
stan
ce f
rom
0, t
hey
hav
e th
e sa
me
abso
lute
val
ue,
3. U
setw
o ve
rtic
al l
ines
to
repr
esen
t ab
solu
te v
alu
e.
|3|
�3
Th
e ab
solu
te v
alu
e of
3 i
s 3.
|�
3| �
3T
he
abso
lute
val
ue
of �
3 is
3.
Exa
mp
le:
Eva
luat
e |
�12
| �
|10
|.
|�
12|
�|
10|
�12
�10
|�
12|
�12
an
d |
10|
�10
�22
Nam
e th
e co
ord
inat
e of
eac
h p
oin
t.
1.B
�4
2.D
�3
3.G
5
Gra
ph
eac
h s
et o
f n
um
ber
s on
a n
um
ber
lin
e.
4.{�
3, 2
, 4}
5.{�
1, 0
, 3}
Wri
te �
or �
in e
ach
bla
nk
to m
ake
a tr
ue
sen
ten
ce.
6.�
7
57.
�3
�
88.
|�
1|
0
Eva
luat
e ea
ch e
xpre
ssio
n.
9.|
9|9
10.
|�
15|
1511
.|
�20
| �
|10
|10
��
�
4–2
–10
12
34
–3–2
–10
12
3–4
4–3
–2–1
01
23
56
–5–4B
DF
EG
4–3
–2–1
0
3 un
its3
units
12
3–4
4–3
–2–1
01
23
5–5
–4
AB
CD
EF
4–3
–2–1
0
inte
gers
nega
tive
inte
gers
pos
itive
inte
gers
12
35
–5–4
Answers (Lesson 2-1)
© Glencoe/McGraw-Hill A3 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill54
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Rea
ding
to
Lear
n M
athe
mat
ics
Gra
phi
ng In
tege
rs o
n a
Num
ber
Lin
e2
–12
–1
Key
Ter
ms
abso
lute
val
ue
the
dis
tanc
e a
num
ber
is fr
om 0
on
a nu
mb
er li
neco
ord
inat
e (c
o O
Rd
i net
)th
e nu
mb
er t
hat
corr
esp
ond
s to
a
poi
nt o
n a
num
ber
line
gra
ph
to p
lot
poi
nts
nam
ed b
y nu
mb
ers
on a
num
ber
line
nu
mb
er li
ne
a lin
e w
ith e
qua
l dis
tanc
es m
arke
d o
ff to
re
pre
sent
num
ber
s
Rea
din
g t
he
Les
son
1.R
efer
to
the
nu
mbe
r li
ne.
a.W
hat
do
the
arro
wh
eads
on
eac
h e
nd
of t
he
nu
mbe
r li
ne
mea
n?
The
line
and
the
set
of
num
ber
s co
ntin
uein
finit
ely
in e
ach
dir
ecti
on.
b.
Wh
at i
s th
e ab
solu
te v
alu
e of
�3?
Wh
at
is t
he
abso
lute
val
ue
of 3
? E
xpla
in.
3, 3
; �3
and
3 a
re b
oth
3 u
nits
aw
ay f
rom
zer
o o
n th
e nu
mb
erlin
e.
2.R
efer
to
the
Ven
n d
iagr
am s
how
n a
t th
e ri
ght.
Wri
te
tru
eor
fal
sefo
r ea
ch o
f th
e fo
llow
ing
stat
emen
ts.
a.A
ll w
hol
e n
um
bers
are
in
tege
rs.
true
b.
All
nat
ura
l n
um
bers
are
in
tege
rs.
true
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.
true
e.A
ll w
hol
e n
um
bers
are
pos
itiv
e n
um
bers
.fa
lse
f.A
ll i
nte
gers
are
nat
ura
l n
um
bers
.fa
lse
g.W
hol
e n
um
bers
are
a s
ubs
et o
f n
atu
ral
nu
mbe
rs.
fals
e
h.N
atu
ral
nu
mbe
rs a
re a
su
bset
of
inte
gers
.tr
ue
Nat
ural
Num
bers
Who
leN
umbe
rsIn
tege
rs
�5
54
32
10
�4
�1
�2
�3
Hel
pin
g Y
ou
Rem
emb
er3.
On
e w
ay t
o re
mem
ber
a m
ath
emat
ical
con
cept
is
to c
onn
ect
it t
o so
met
hin
g yo
u h
ave
seen
or
hea
rd i
n e
very
day
life
. Des
crib
e a
situ
atio
n t
hat
ill
ust
rate
s th
e co
nce
pt o
fab
solu
te v
alu
e.
Sam
ple
ans
wer
: On
a fo
otb
all f
ield
, the
dis
tanc
e fr
om
eac
h g
oal
line
to t
he 5
0-ya
rd li
ne is
50
yard
s.
© G
lenc
oe/M
cGra
w-H
ill53
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Pra
ctic
e2
–12
–1
Gra
ph
ing
Inte
ger
s on
a N
um
ber
Lin
eN
ame
the
coor
din
ate
of e
ach
poi
nt.
1.A
�4
2.B
33.
C�
1
4.D
55.
E�
26.
F1
Gra
ph
eac
h s
et o
f n
um
ber
s on
a n
um
ber
lin
e.
7.{�
5, 0
, 2}
8.{4
, �1,
�2}
9.{3
, �4,
�3}
10.
{�2,
5, 1
}
11.{
2, �
5, 0
}12
.{�
4, 3
, �2,
4}
Wri
te �
or �
in e
ach
bla
nk
to m
ake
a tr
ue
sen
ten
ce.
13.7
9
14.
0 �
115
.�
2 2
16.6
�
317
.�
4 �
518
.�
7 �
3
19.�
8 0
20.
�11
2
21.
�5
�6
Eva
luat
e ea
ch e
xpre
ssio
n.
22.|
�4|
423
.|
6|6
24.|
�3|
�|
1|4
25.
|9|
�|
�8|
1
26.|
�7|
�|
�2|
527
.|
�8|
�|
11|
19
��
�
��
�
��
�
4–3
–2–1
01
23
5–5
–44
–3–2
–10
12
35
–5–4
4–3
–2–1
01
23
5–5
–44
–3–2
–10
12
35
–5–4
4–3
–2–1
01
23
5–5
–44
–3–2
–10
12
35
–5–4
4–3
–2–1
01
23
5–5
–4AE
CF
BD
Answers (Lessons 2-1 and 2-2)
© Glencoe/McGraw-Hill A4 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill56
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Stud
y G
uide
2–2
2–2
Th
e C
oord
inat
e P
lan
e
Th
e tw
o in
ters
ecti
ng
lin
es a
nd
the
grid
at
the
righ
t fo
rm
a co
ord
inat
e sy
stem
. Th
e h
oriz
onta
l n
um
ber
lin
e is
cal
led
the
x-ax
is,a
nd
the
vert
ical
nu
mbe
r li
ne
is c
alle
d th
e y-
axis
. T
he
x- a
nd
y-ax
es d
ivid
e th
e co
ordi
nat
e pl
ane
into
fou
rq
uad
ran
ts. P
oin
t S
in Q
uad
ran
t I
is t
he
grap
h o
f th
e or
der
ed p
air
(3, 2
). T
he
x-co
ord
inat
eof
poi
nt
Sis
3, a
nd
the
y-co
ord
inat
eof
poi
nt
Sis
2.
Th
e po
int
at w
hic
h t
he
axes
mee
t h
as c
oord
inat
es (
0, 0
) an
d is
cal
led
the
orig
in.
Exa
mp
le 1
:W
hat
is
the
orde
red
pair
for
poi
nt
J?
In
wh
at q
uad
ran
t is
poi
nt
Jlo
cate
d?Yo
u m
ove
4 u
nit
s to
th
e le
ft o
f th
e or
igin
an
d th
en 1
un
it u
p to
get
to
J. S
o th
e or
dere
d pa
ir f
or J
is (
�4,
1).
Poi
nt
Jis
lo
cate
d in
Qu
adra
nt
II.
Exa
mp
le 2
:G
raph
M(�
2, �
4) o
n t
he
coor
din
ate
plan
e.
Sta
rt a
t th
e or
igin
. Mov
e le
ft o
n t
he
x-ax
is t
o �
2 an
d th
en d
own
4 u
nit
s. D
raw
a d
ot h
ere
and
labe
l it
M.
Wri
te t
he
ord
ered
pai
r th
at n
ames
eac
h p
oin
t.
1.P
(1, 3
)2.
Q(�
4, �
3)
3.R
(0, 2
)4.
T(�
4, 0
)
Gra
ph
eac
h p
oin
t on
th
e co
ord
inat
e p
lan
e. N
ame
the
qu
adra
nt,
if a
ny,
in w
hic
h e
ach
poi
nt
is lo
cate
d.
5.A
(5, �
1)IV
6.B
(�3,
0)
none
7.C
(�3,
1)
II8.
D(0
, 1)
none
9.E
(3, 3
)I
10.
F(�
1, �
2)III
Ox
y
BC
A
E
F
DOx
y
12
34
4 3 2 1 –1 –2 –3 –4
–1–2
–3–4
TR
P
Q
Ox
y
1Quad
rant
I
Quad
rant
IV
Quad
rant
II
Quad
rant
III
23
4
4 3 2 1 –1 –2 –3 –4
–1–2
–3–4
J
M
Ox
y
1Quad
rant
I
Quad
rant
IV
Quad
rant
II
Quad
rant
III
23
4
4 3 2 1 –1 –2 –3 –4
–1–2
–3–4
S
© G
lenc
oe/M
cGra
w-H
ill55
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Enri
chm
ent
2–1
2–1
Ven
n D
iag
ram
sA
type
of
draw
ing
call
ed a
Ven
n d
iagr
amca
n b
e u
sefu
l in
exp
lain
ing
con
diti
onal
stat
emen
ts. A
Ven
n d
iagr
am u
ses
circ
les
to r
epre
sen
t se
ts o
f ob
ject
s.
Con
side
r th
e st
atem
ent
“All
rab
bits
hav
e lo
ng
ears
.” T
o m
ake
a V
enn
dia
gram
for
this
sta
tem
ent,
a la
rge
circ
le is
dra
wn
to
repr
esen
t al
l an
imal
s w
ith
lon
g ea
rs. T
hen
a sm
alle
r ci
rcle
is d
raw
n in
side
th
e fi
rst
to r
epre
sen
t al
l rab
bits
. Th
e V
enn
dia
gram
show
s th
at e
very
rab
bit
is in
clu
ded
in t
he
grou
p of
lon
g-ea
red
anim
als.
Th
e se
t of
rab
bits
is c
alle
d a
sub
set
of t
he
set
of lo
ng-
eare
d an
imal
s.
Th
e V
enn
dia
gram
can
als
o ex
plai
n h
ow t
o w
rite
th
e st
atem
ent,
“A
ll r
abbi
ts h
ave
lon
g ea
rs,”
in if
-th
en f
orm
. Eve
ry r
abbi
t is
in t
he
grou
p of
lon
g-ea
red
anim
als,
so
ifan
an
imal
is a
rab
bit,
th
en it
has
lon
g ea
rs.
For
each
sta
tem
ent,
dra
w a
Ven
n d
iag
ram
. Th
e w
rite
th
e se
nte
nce
in if
-th
en f
orm
.
1.E
very
dog
has
lon
g h
air.
2.A
ll r
atio
nal
nu
mbe
rs a
re r
eal.
If a
n an
imal
is a
do
g, t
hen
itIf
a n
umb
er is
rat
iona
l, th
enha
s lo
ng h
air.
it is
rea
l.
3.P
eopl
e w
ho
live
in I
owa
like
cor
n.
4.S
taff
mem
bers
are
all
owed
in t
he
facu
lty
lou
nge
.
If a
per
son
lives
in Io
wa,
then
the
per
son
likes
co
rn.
If a
per
son
is a
sta
ff m
emb
er,
then
the
per
son
is a
llow
ed in
the
facu
lty
loun
ge.
anim
als
with
long
ear
s
rabb
its
anim
als
with
long
hai
r
dogs
real
num
bers
ratio
nal
num
bers
peop
le w
holik
e co
rn
peop
le w
holiv
e in
Iow
a
peop
le in
the
facu
lty lo
unge
staf
fm
embe
rs
Answers (Lesson 2-2)
© Glencoe/McGraw-Hill A5 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill58
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Pra
ctic
e2
–22
–2
Th
e C
oord
inat
e P
lan
eW
rite
th
e or
der
ed p
air
that
nam
es e
ach
poi
nt.
1.A
(�3,
4)
2.B
(5, 2
)
3.C
(�4,
�3)
4.D
(2, �
4)
5.E
(�1,
1)
6.F
(1, 0
)
7.G
(0, �
2)8.
H(�
2, 5
)
9.J
(�2,
�4)
10.
K(5
, �1)
Gra
ph
eac
h p
oin
t on
th
e co
ord
inat
e p
lan
e.
11.K
(0, �
3)12
.L
(�2,
3)
13.M
(4, 4
)14
.N
(�3,
0)
15.P
(�4,
�1)
16.
Q(1
, �2)
17.R
(�5,
5)
18.
S(3
, 2)
19.T
(2, 1
)20
.W
(�1,
�4)
Nam
e th
e q
uad
ran
t in
wh
ich
eac
h p
oin
t is
loca
ted
.
21.(
1, 9
)I
22.
(�2,
�7)
III
23.(
0, �
1)no
ne24
.(�
4, 6
)II
25.(
5, �
3)IV
26.
(�3,
0)
none
27.(
�1,
�1)
III28
.(6
, �5)
IV
29.(
�8,
4)
II30
.(�
9, �
2)III
Ox
y KW
QPN
LR
M ST
Ox
yA
H
E
F
B K
DJ
CG
Th
e C
oord
inat
e P
lan
eW
rite
th
e or
der
ed p
air
that
nam
es e
ach
poi
nt.
1.L
(�4,
0)
2.M
(�3,
�1)
3.N
(�1,
�3)
4.P
(0, 0
)
5.Q
(�2,
4)
6.R
(2, 1
)
7.S
(2, �
1)8.
T(5
, 0)
9.U
(0, �
2)10
.V
(0, 3
)
Gra
ph
eac
h p
oin
t on
th
e co
ord
inat
e p
lan
e.
11.A
(�2,
4)
12.
B(0
, �4)
13.C
(5, �
3)14
.D
(�2,
�1)
15.E
(1, 4
)16
.F
(4, 0
)
17.G
(�4,
�1)
18.
H(3
, 3)
19.I
(�4,
3)
20.
J(�
5, 0
)
Nam
e th
e q
uad
ran
t in
wh
ich
eac
h p
oin
t is
loca
ted
.
21.(
�2,
�2)
III22
.(3
, 4)
I
23.(
�4,
3)
II24
.(4
, �3)
IV
25.(
0, �
2)no
ne26
.(�
1, �
1)III
27.(
4, �
1)IV
28.
(�3,
5)
II
29.(
�3,
0)
none
30.
(8, �
4)IV
y
x�
4�
22
4
�4
�224
E
DA
C
H
F
G
B
J
I
y
x�
4�
22
4
�4
�224
L
M
N
P
Q
R S
T
UV
© G
lenc
oe/M
cGra
w-H
ill57
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Skil
ls P
ract
ice
2–2
2–2
Answers (Lesson 2-2)
© Glencoe/McGraw-Hill A6 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill60
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Enri
chm
ent
2–2
2–2
Poi
nts
an
d L
ines
on
a M
atri
xA
mat
rix
is a
rec
tan
gula
r ar
ray
of r
ows
and
colu
mn
s. P
oin
tsan
d li
nes
on
a m
atri
x ar
e n
ot d
efin
ed in
th
e sa
me
way
as
inE
ucl
idea
n g
eom
etry
. Ap
oin
t on
a m
atri
x is
a d
ot, w
hic
h c
an b
esm
all o
r la
rge.
Ali
ne
on a
mat
rix
is a
pat
h o
f do
ts t
hat
“li
ne
up.
”B
etw
een
tw
o po
ints
on
a li
ne
ther
e m
ay o
r m
ay n
ot b
e ot
her
poin
ts. T
hre
e ex
ampl
es o
f li
nes
are
sh
own
at
the
upp
er r
igh
t.T
he
broa
d li
ne
can
be
thou
ght
of a
s a
sin
gle
lin
e or
as
two
nar
-ro
w li
nes
sid
e by
sid
e.
Ado
t-m
atri
x pr
inte
r fo
r a
com
pute
r u
ses
dots
to
form
ch
arac
ters
.T
he
dots
are
oft
en c
alle
d p
ixel
s.T
he
mat
rix
at t
he
righ
t sh
ows
how
a d
ot-m
atri
x pr
inte
r m
igh
t pr
int
the
lett
er P
.
Sam
ple
ans
wer
s ar
e g
iven
.D
raw
poi
nts
on
eac
h m
atri
x to
cre
ate
the
giv
en f
igu
res.
1.D
raw
tw
o in
ters
ecti
ng
lin
es t
hat
hav
e2.
Dra
w t
wo
lin
es t
hat
cro
ss b
ut
hav
e fo
ur
poin
ts in
com
mon
.n
o co
mm
on p
oin
ts.
3.M
ake
the
nu
mbe
r 0
(zer
o) s
o th
at it
4.M
ake
the
capi
tal l
ette
r O
so
that
itex
ten
ds t
o th
e to
p an
d bo
ttom
sid
esex
ten
ds t
o ea
ch s
ide
of t
he
mat
rix.
of t
he
mat
rix.
5.U
sin
g se
para
te g
rid
pape
r, m
ake
dot
desi
gns
for
seve
ral
oth
er le
tter
s. W
hic
h w
ere
the
easi
est
and
wh
ich
wer
e th
em
ost
diff
icu
lt?
See
stu
den
ts’ w
ork
.
© G
lenc
oe/M
cGra
w-H
ill59
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Rea
ding
to
Lear
n M
athe
mat
ics
The
Coo
rdin
ate
pla
ne2
–22
–2
Key
Ter
ms
coo
rdin
ate
pla
ne
the
pla
ne c
onta
inin
g th
e x-
and
y-a
xes
coo
rdin
ate
syst
emth
e gr
id fo
rmed
by
the
inte
rsec
tion
of t
wo
per
pen
dic
ular
num
ber
line
s th
at m
eet
at t
heir
zero
poi
nts
ord
ered
pai
ra
pai
r of
num
ber
s us
ed t
o lo
cate
any
poi
nt o
n a
coor
din
ate
pla
neq
uad
ran
ton
e of
the
four
reg
ions
into
whi
ch t
he x
- an
d y
-axe
sse
par
ate
the
coor
din
ate
pla
nex-
axis
the
horiz
onta
l num
ber
line
on
a co
ord
inat
e p
lane
y-ax
isth
e ve
rtic
al n
umb
er li
ne o
n a
coor
din
ate
pla
nex-
coo
rdin
ate
the
first
num
ber
in a
coo
rdin
ate
pai
ry-
coo
rdin
ate
the
seco
nd n
umb
er in
a c
oord
inat
e p
air
Rea
din
g t
he
Les
son
1.Id
enti
fy e
ach
par
t of
th
e co
ordi
nat
e sy
stem
.
2.U
se t
he
orde
red
pair
(�
2, 3
).
a.
Exp
lain
how
to
iden
tify
th
e x-
an
d y-
coor
din
ates
. T
he x
-co
ord
inat
e is
the
fir
st n
umb
er; t
he y
-co
ord
inat
e is
the
seco
nd n
umb
er.
b.
Nam
e th
e x-
and
y-co
ordi
nat
es.
The
x-c
oo
rdin
ate
is �
2 an
d t
he y
-co
ord
inat
e 3.
c.D
escr
ibe
the
step
s yo
u w
ould
use
to
loca
te t
he
poin
t at
(�
2, 3
) on
th
e co
ordi
nat
epl
ane.
Sta
rt a
t th
e o
rig
in, m
ove
tw
o u
nits
to
the
left
and
the
n m
ove
up
thre
e un
its.
3.
Wh
at d
oes
the
term
qu
adra
nt
mea
n?
S
amp
le a
nsw
er: I
t is
one
of
four
reg
ions
in t
he c
oo
rdin
ate
pla
ne.
x
y
O
Hel
pin
g Y
ou
Rem
emb
er4.
Des
crib
e a
met
hod
to
rem
embe
r h
ow t
o w
rite
an
ord
ered
pai
r.
Sam
ple
ans
wer
: Sin
ce x
com
es b
efo
re y
in t
he a
lpha
bet
, the
x-
coo
rdin
ate
is w
ritt
en f
irst
in a
n o
rder
ed p
air.
yax
is
xax
iso
rig
in
Answers (Lesson 2-3)
© Glencoe/McGraw-Hill A7 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill62
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
Ad
din
g In
teg
ers
Fin
d e
ach
su
m.
1.2
�7
2.�
3 �
(�2)
3.�
4 �
1
9�
5�
3
4.3
�(�
9)5.
�2
�12
6.�
1 �
(�6)
�6
10�
7
7.10
�(�
8)8.
�9
�4
9.3
�(�
3)
2�
50
10.�
5 �
(�5)
11.
8 �
(�9)
12.
�7
�4
�10
�1
�3
13.�
2 �
214
.�
12 �
1015
.�
8 �
(�5)
0�
2�
13
16.�
14 �
817
.15
�(�
8)18
.3
�(�
11)
�6
7�
8
19.�
9 �
(�7)
20.
6 �
(�9)
21.
�14
�15
�16
�3
1
22.�
10 �
6 �
(�4)
23.
13 �
(�14
) �
124
.�
4 �
(�8)
�5
�8
0�
7
Sim
plif
y ea
ch e
xpre
ssio
n.
25.�
4c�
8c26
.�
5a�
(�9a
)27
.�
8d�
3d
4c�
14a
�5d
28.7
x�
3x29
.6y
�(�
3y)
30.
�7t
�4t
10x
3y�
3t
31.�
12s
�(�
4s)
32.
5t�
(�13
t)33
.15
h�
(�4h
)
�16
s�
8t11
h
34.7
b�
6b�
(�8b
)35
.�
9w�
4w�
(�5w
)36
.12
t�
3t�
(�6t
)
5b�
10w
9t
NA
ME
DAT
EP
ER
IOD
Skil
ls P
ract
ice
2–3
2–3
© G
lenc
oe/M
cGra
w-H
ill61
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Stud
y G
uide
2–3
2–3
Ad
din
g In
teg
ers
You
can
use
a n
um
ber
lin
e to
add
in
tege
rs. S
tart
at
0. T
hen
mov
e to
th
e ri
ght
for
posi
tive
in
tege
rs a
nd
mov
e to
th
e le
ft f
or n
egat
ive
inte
gers
.
Bot
h i
nte
gers
are
pos
itiv
e.
Bot
h i
nte
gers
are
neg
ativ
e.
Fir
st m
ove
2 u
nit
s ri
ght
from
0.
Fir
st m
ove
2 u
nit
s le
ft f
rom
0.
Th
en m
ove
1 m
ore
un
it r
igh
t.T
hen
mov
e 1
mor
e u
nit
lef
t.
Wh
en y
ou a
dd o
ne
posi
tive
in
tege
r an
d on
e n
egat
ive
inte
ger
on t
he
nu
mbe
r li
ne,
you
ch
ange
dir
ecti
ons,
wh
ich
res
ult
s in
on
e m
ove
bein
g su
btra
cted
fro
m t
he
oth
er m
ove.
Mov
e 2
un
its
left
, th
en 1
un
it r
igh
t.M
ove
2 u
nit
s ri
ght,
th
en 1
un
it l
eft.
Use
th
e fo
llow
ing
rule
s to
add
tw
o in
tege
rs a
nd
to s
impl
ify
expr
essi
ons.
Rul
eE
xam
ple
s
To a
dd i
nte
gers
wit
h t
he
sam
e si
gn, a
dd
7 �
4 �
11th
eir
abso
lute
val
ues
. Giv
e th
e re
sult
th
e �
8 �
(�2)
��
10sa
me
sign
as
the
inte
gers
.�
5x�
(�3x
) �
�8x
To a
dd i
nte
gers
wit
h d
iffe
ren
t si
gns,
9 �
(�6)
�3
subt
ract
th
eir
abso
lute
val
ues
. Giv
e th
e1
�(�
5) �
�4
resu
lt t
he
sam
e si
gn a
s th
e in
tege
r w
ith
�2x
�9x
�7x
the
grea
ter
abso
lute
val
ue.
3y�
(�4y
) �
�y
Fin
d e
ach
su
m.
1.5
�8
132.
�8
�(�
9)�
173.
12 �
(�8)
44.
�16
�5
�11
5.5
�(�
8) �
(�5)
�8
6.�
8 �
(�8)
�20
47.
12 �
5 �
(�1)
16
Sim
plif
y ea
ch e
xpre
ssio
n.
8.3x
�(�
6x)
�3x
9.�
5y�
(�7y
)�
12y
10.
2m�
(�4m
) �
(�2m
)�
4m
4�
10
12
� (�
1) �
123
�2
�1
�2
�3
�1
01
�2
�2
� 1
� �
1
�1
2�
4�
2
�3
�1
01
�2
�2
� (�
1) �
�3
�1
2�
4�
24
�1
01�2 2 �
1 �
3
�1
23
5
Answers (Lesson 2-3)
© Glencoe/McGraw-Hill A8 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill64
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Rea
ding
to
Lear
n M
athe
mat
ics
Ad
din
g In
tege
rs2
–32
–3
Key
Ter
ms
add
itiv
e in
vers
estw
o nu
mb
ers
are
add
itive
inve
rses
if t
heir
sum
is 0
op
po
site
add
itive
inve
rse
zero
pai
rth
e re
sult
of p
ositi
ve a
lgeb
ra t
iles
pai
red
with
neg
ativ
eal
geb
ra t
iles
Rea
din
g t
he
Les
son
1.E
xpla
in h
ow t
o ad
d in
tege
rs w
ith
th
e sa
me
sign
.A
dd
the
ir a
bso
lute
val
ues.
The
res
ult
has
the
sam
e si
gn
as t
hein
teg
ers.
2.
Exp
lain
how
to
add
inte
gers
wit
h o
ppos
ite
sign
s.Fi
nd t
he d
iffer
ence
of
thei
r ab
solu
te v
alue
s. T
he r
esul
t ha
s th
esa
me
sig
n as
the
inte
ger
wit
h th
e g
reat
er a
bso
lute
val
ue.
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
?T
he a
bso
lute
val
ues
mus
t b
e eq
ual.
4.U
se t
he
nu
mbe
r li
ne
to f
ind
each
su
m.
a.�
3�
5
2
b.
4�
(�6)
�2
c.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?T
he lo
nger
arr
ow
rep
rese
nts
the
num
ber
wit
h th
e g
reat
erab
solu
te v
alue
.d
.E
xpla
in h
ow t
he
arro
ws
can
hel
p yo
u d
eter
min
e th
e si
gn o
f th
e an
swer
.T
he d
irec
tio
n o
f th
e lo
nger
arr
ow
det
erm
ines
the
sig
n o
f th
ean
swer
. W
rite
an
eq
uat
ion
for
eac
h s
itu
atio
n.
5.a
five
-yar
d pe
nal
ty a
nd
a 13
-yar
d pa
ss
�5
�13
�8
6.ga
ined
11
poin
ts a
nd
lost
18
poin
ts
11
�(�
18)
��
77.
a de
posi
t of
$25
an
d a
wit
hdr
awal
of
$15
25
�(�
15)
�10
�5�
4�3�
2�1
01
45
32�4
�6
�5�
4�3�
2�1
01
45
32
�3�
5
Hel
pin
g Y
ou
Rem
emb
er8.
Exp
lain
how
you
can
rem
embe
r th
e m
ean
ing
of “
zero
pai
r.”
Sam
ple
ans
wer
: Sin
ce t
he s
um o
f a
num
ber
and
its
op
po
site
isze
ro, w
hen
a p
osi
tive
tile
is p
aire
d w
ith
a ne
gat
ive
tile
, the
sum
isze
ro.
© G
lenc
oe/M
cGra
w-H
ill63
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Pra
ctic
e2
–32
–3
Ad
din
g In
teg
ers
Fin
d e
ach
su
m.
1.8
�4
2.�
3 �
53.
9 �
(�2)
122
7
4.�
5 �
115.
�7
�(�
4)6.
12 �
(�4)
6�
118
7.�
9 �
108.
�4
�4
9.2
�(�
8)
10
�6
10.1
7 �
(�4)
11.
�13
�3
12.
6 �
(�7)
13�
10�
1
13.�
8 �
(�9)
14.
�2
�11
15.
�9
�(�
2)
�17
9�
11
16.�
1 �
317
.6
�(�
5)18
.�
11 �
7
21
�4
19.�
8 �
(�8)
20.
�6
�3
21.
2 �
(�2)
�16
�3
0
22.7
�(�
5) �
223
.�
4 �
8 �
(�3)
24.
�5
�(�
5) �
5
41
�5
Sim
plif
y ea
ch e
xpre
ssio
n.
25.5
a�
(�3a
)26
.�
7y�
2y27
.�
9m�
(�4m
)
2a�
5y�
13m
28.�
2z�
(�4z
)29
.8x
�(�
4x)
30.
�10
p�
5p
�6z
4x�
5p
31.5
b�
(�2b
)32
.�
4s�
7s33
.2n
�(�
4n)
3b3s
�2n
34.5
a�
(�6a
) �
4a35
.�
6x�
3x�
(�5x
)36
.7z
�2z
�(�
3z)
3a�
8x6z
Answers (Lessons 2-3 and 2-4)
© Glencoe/McGraw-Hill A9 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill66
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Stud
y G
uide
2–4
2–4
Su
btr
acti
ng
Inte
ger
s
If t
he
sum
of
two
inte
gers
is
0, t
he
nu
mbe
rs a
re o
pp
osit
esor
add
itiv
e in
vers
es.
Exa
mp
le 1
:a.
�3
is t
he
oppo
site
of
3 be
cau
se �
3 �
3 �
0
b.
17 i
s th
e op
posi
te o
f �
17 b
ecau
se 1
7 �
(�17
) �
0
Use
th
is r
ule
to
subt
ract
in
tege
rs.
Exa
mp
le 2
:F
ind
each
dif
fere
nce
.
a.5
�2
5 �
2 �
5 �
(�2)
Su
btra
ctin
g 2
is t
he
sam
e as
ad
din
g it
s
�3
oppo
site
, �2.
b.
�7
�(�
1)�
7 �
(�1)
��
7 �
1S
ubt
ract
ing
�1
is t
he
sam
e as
ad
din
g it
s
��
6op
posi
te, 1
.
Exa
mp
le 3
:E
valu
ate
c�
d�
eif
c�
�1,
d�
7, a
nd
e�
�3.
c�
d�
e�
�1
�7
�(�
3)R
epla
ce c
wit
h �
1, d
wit
h 7
, an
d e
wit
h �
3.
��
1 �
7 �
3W
rite
7 �
(�
3) a
s 7
�3.
�
6 �
3�
1 �
7 �
6 �
96
�3
�9
Fin
d e
ach
dif
fere
nce
.
1.5
�8
�3
2.�
8 �
(�9)
13.
�2
�8
�10
4.�
4 �
(�5)
1
5.16
�8
86.
10 �
(�10
)20
7.0
� 1
0�
108.
0 �
(�18
)18
Sim
plif
y ea
ch e
xpre
ssio
n.
9.3x
�9x
�6x
10.
�4y
�(�
6y)
2y11
.2m
�8m
�(�
2m)
�4m
Eva
luat
e ea
ch e
xpre
ssio
n if
x �
�1,
y �
2, a
nd
z �
�4.
12.x
�y
�3
13.
y�
z�
51
14.
z�
y�
(�2)
�4
15.9
�x
1016
.x
�z
�z
717
.0
�y
�2
To s
ubt
ract
an
in
tege
r, a
dd i
ts o
ppos
ite
or a
ddit
ive
inve
rse.
© G
lenc
oe/M
cGra
w-H
ill65
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Enri
chm
ent
2–3
2–3
Inte
ger
Mag
ic
Am
agic
tri
angl
e is
a t
rian
gula
r ar
ran
gem
ent
of n
um
bers
in
wh
ich
th
e su
m o
f th
e n
um
bers
alo
ng
each
sid
e is
th
e sa
me
nu
mbe
r. F
or e
xam
ple,
in t
he
mag
ic t
rian
gle
show
n a
t th
eri
ght,
th
e su
m o
f th
e n
um
bers
alo
ng
each
sid
e is
0.
In e
ach
tri
ang
le, e
ach
of
the
inte
ger
s fr
om �
4 to
4 a
pp
ears
exac
tly
once
. Com
ple
te t
he
tria
ng
le s
o th
at t
he
sum
of
the
inte
ger
s al
ong
eac
h s
ide
is �
3.
1.2.
3.4.
In t
hes
e m
agic
sta
rs, t
he
sum
of
the
inte
ger
s al
ong
eac
h li
ne
ofth
e st
ar is
�2.
Com
plet
e ea
ch m
agic
sta
r us
ing
the
inte
gers
fro
m�
6 to
5 e
xact
ly o
nce
.
5.6.
–6
3
–5
1
0–1
–2
2 54
–3
–4
–6
4
–4
1
–12
–2
0 35
–3
–5
–2
–3
–4
–1
3
4
0 21
–4
–3
–2
0
4
–1
3 21
–3
–4
–2
3
1
4
–1 20
–4
–3
–2
4
0
–1
3 21
3–2
2
0
–3
41
–4–1
Sam
ple
ans
wer
sar
e g
iven
.
Answers (Lesson 2-4)
© Glencoe/McGraw-Hill A10 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill68
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Pra
ctic
e2
–42
–4
Su
btr
acti
ng
Inte
ger
sFi
nd
eac
h d
iffe
ren
ce.
1.9
�3
2.�
1 �
23.
4 �
(�5)
6�
39
4.6
�(�
1)5.
�7
�(�
4)6.
8 �
10
7�
3�
2
7.�
2 �
58.
�6
�(�
7)9.
2 �
8
�7
1�
6
10.�
10 �
(�2)
11.
�4
�6
12.
5 �
3
�8
�10
2
13.�
8 �
(�4)
14.
7 �
915
.�
9 �
(�11
)
�4
�2
2
16.�
3 �
417
.6
�(�
5)18
.6
�5
�7
111
Eva
luat
e ea
ch e
xpre
ssio
n if
a �
�1,
b �
5, c
��
2, a
nd
d �
�4.
19.b
�c
20.
a�
b21
.c
�d
7�
62
22.a
�c
�d
23.
a�
b�
c24
.a
�c
�d
1�
8�
3
25.b
�c
�d
26.
b�
c�
d27
.a
�b
�c
311
�4
© G
lenc
oe/M
cGra
w-H
ill67
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Skil
ls P
ract
ice
2–4
2–4
Su
btr
acti
ng
Inte
ger
sFi
nd
eac
h d
iffe
ren
ce.
1.8
�2
2.12
�4
3.�
7 �
(�2)
68
�5
4.�
9 �
45.
4 �
126.
�4
�(�
10)
�13
�8
6
7.�
6 �
18.
�5
�8
9.�
5 �
(�5)
�7
�13
0
10.�
8 �
811
.�
11 �
712
.8
�(�
7)
�16
�18
15
13.9
�14
14.
�3
�(�
15)
15.
�14
�6
�5
12�
20
16.�
3 �
917
.�
7 �
718
.13
�14
�11
�14
�1
Eva
luat
e ea
ch e
xpre
ssio
n if
a �
2, b
��
3, c
��
1, a
nd
d �
1.
19.a
�b
20.
b�
c21
.a
�c
5�
23
22.c
�d
23.
a�
b�
c24
.b
�d
�c
�2
0�
3
25.d
�b
�a
26.
c�
a�
b27
.a
�d
�b
�4
0�
2
Answers (Lesson 2-4)
© Glencoe/McGraw-Hill A11 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill70
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Enri
chm
ent
2–4
2–4
Clo
sure
Ab
inar
y op
erat
ion
mat
ches
tw
o n
um
bers
in
a s
et t
o ju
st o
ne
nu
mbe
r. A
ddit
ion
is
a bi
nar
y op
erat
ion
on
th
e se
t of
wh
ole
nu
mbe
rs. I
t m
atch
es t
wo
nu
mbe
rs s
uch
as
4 an
d 5
to a
sin
gle
nu
mbe
r, t
hei
r su
m.
If t
he
resu
lt o
f a
bin
ary
oper
atio
n i
s al
way
s a
mem
ber
of t
he
orig
inal
set
, th
e se
t is
sai
d to
be
clos
edu
nde
r th
e op
erat
ion
. F
or e
xam
ple,
th
e se
t of
wh
ole
nu
mbe
rs i
s n
ot c
lose
d u
nde
rsu
btra
ctio
n b
ecau
se 3
�6
is n
ot a
wh
ole
nu
mbe
r.
Is e
ach
op
erat
ion
bin
ary?
Wri
te y
esor
no
.
Is e
ach
set
clo
sed
un
der
ad
dit
ion
? W
rite
yes
or n
o. I
f yo
ur
answ
er is
no,
giv
e an
exa
mp
le.
Is t
he
set
of w
hol
e n
um
ber
s cl
osed
un
der
eac
h o
per
atio
n?
Wri
te y
esor
no
. If
you
r an
swer
is n
o, g
ive
an e
xam
ple
.
13.
mu
ltip
lica
tion
: a�
bye
s
15.
expo
nen
tati
on: a
bye
s
14.
divi
sion
: a�
bno
; 4 �
3 is
no
t a
who
le n
umb
er16
.sq
uar
ing
the
sum
: (a
�b)
2ye
s
7.ev
en n
um
bers
yes
9.m
ult
iple
s of
3ye
s
11.
prim
e n
um
bers
no; 3
�5
�8
8.od
d n
um
bers
no; 3
�7
�10
10.
mu
ltip
les
of 5
yes
12.
non
prim
e n
um
bers
no; 2
2 �
9 �
31
1.th
e op
erat
ion
←, w
her
e a
←b
mea
ns
to c
hoo
se t
he
less
er n
um
ber
from
aan
d b
yes
3.th
e op
erat
ion
sq,
wh
ere
sq(a
) m
ean
sto
squ
are
the
nu
mbe
r a
no
5.th
e op
erat
ion
⇑, w
her
e a
⇑b
mea
ns
to m
atch
aan
d b
to a
ny
nu
mbe
rgr
eate
r th
an e
ith
er n
um
ber
no
2.th
e op
erat
ion
©, w
her
e a
©b
mea
ns
to c
ube
th
e su
m o
f a
and
bye
s
4.th
e op
erat
ion
exp
, wh
ere
exp(
a, b
)m
ean
s to
fin
d th
e va
lue
of a
bye
s
6.th
e op
erat
ion
⇒, w
her
e a
⇒b
mea
ns
to r
oun
d th
e pr
odu
ct o
f a
and
bu
p to
the
nea
rest
10
yes
© G
lenc
oe/M
cGra
w-H
ill69
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Rea
ding
to
Lear
n M
athe
mat
ics
Sub
trac
ting
Inte
gers
2–4
2–4
Key
Ter
ms
add
itiv
e in
vers
estw
o nu
mb
ers
are
add
itive
inve
rses
if t
heir
sum
is 0
op
po
site
add
itive
inve
rse
zero
pai
rth
e re
sult
of p
ositi
ve a
lgeb
ra t
iles
pai
red
with
neg
ativ
eal
geb
ra t
iles
Rea
din
g t
he
Les
son
1.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
�11
0 �
(�11
)
d.
�20
�34
�
20 �
(�34
)
e.�
15�
(�4)
�15
�4
f.16
�(�
18)
16
�18
2.D
escr
ibe
how
to
fin
d ea
ch d
iffe
ren
ce. T
hen
fin
d ea
ch d
iffe
ren
ce.
a.8
�11
A
dd
the
op
po
site
of
11 t
o 8
; �3
b.
5�
(�8)
A
dd
the
op
po
site
of
�8
to 5
; 13
c.17
�14
A
dd
the
op
po
site
of
14 t
o 1
7; 3
d.
�8
�19
A
dd
the
op
po
site
of
19 t
o �
8; �
27
3.E
xpla
in h
ow z
ero
pair
s ar
e u
sed
to s
ubt
ract
wit
h a
lgeb
ra t
iles
.
Zer
o p
airs
are
no
t ne
eded
to
sub
trac
t ne
gat
ive
tile
s. I
f a
po
siti
ve t
ileis
to
be
sub
trac
ted
fro
m n
egat
ive
tile
s, f
irst
ad
d a
zer
o p
air.
The
nyo
u ca
n su
btr
act
one
po
siti
ve t
ile.
Hel
pin
g Y
ou
Rem
emb
er4.
Exp
lain
wh
y kn
owin
g th
e ru
les
for
addi
ng
inte
gers
can
hel
p yo
u t
o su
btra
ct i
nte
gers
.S
amp
le a
nsw
er: S
ince
sub
trac
tio
n is
rea
lly a
dd
ing
the
num
ber
’sad
dit
ive
inve
rse,
the
rul
es f
or
add
itio
n al
so a
pp
ly t
o s
ubtr
acti
on.
Answers (Lesson 2-5)
© Glencoe/McGraw-Hill A12 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill72
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
Mu
ltip
lyin
g In
teg
ers
Fin
d e
ach
pro
du
ct.
1.3(
12)
2.�
4(7)
3.�
8(�
8)
36�
2864
4.5(
�9)
5.�
2(�
9)6.
�3(
�10
)
�45
1830
7.0(
�5)
8.�
13(�
4)9.
4(�
11)
052
�44
10.�
5(12
)11
.14
(0)
12.
�8(
7)
�60
0�
56
13.�
15(�
4)14
.9(
�3)
15.
�8(
11)
60�
27�
88
16.(
�2)
(4)(
�3)
17.
(�4)
(�5)
(�1)
18.
(3)(
5)(�
5)
24�
20�
75
Eva
luat
e ea
ch e
xpre
ssio
n if
x �
�2
and
y �
�4.
19.�
3xy
20.
�2x
y21
.�
5x
24�
1610
22.�
7y23
.8x
y24
.�
6xy
2864
�48
Sim
plif
y ea
ch e
xpre
ssio
n.
25.3
(2a)
26.
�4(
�3c
)27
.�
5(�
8b)
6a12
c40
b
28.(
5c)(
�7d
)29
.(�
8m)(
�2n
)30
.(�
9s)(
7t)
�35
cd16
mn
�63
st
NA
ME
DAT
EP
ER
IOD
Skil
ls P
ract
ice
2–5
2–5
© G
lenc
oe/M
cGra
w-H
ill71
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Stud
y G
uide
2–5
2–5
Mu
ltip
lyin
g In
teg
ers
Use
th
ese
rule
s to
mu
ltip
ly i
nte
gers
an
d to
sim
plif
y ex
pres
sion
s.
Exa
mp
le 1
:F
ind
each
pro
duct
.a.
7(12
)7(
12)
�84
Bot
h f
acto
rs a
re p
osit
ive,
so
the
prod
uct
is
posi
tive
.
b.�
5(�
9)�
5(�
9) �
45B
oth
fac
tors
are
neg
ativ
e, s
o th
e pr
odu
ct i
s po
siti
ve.
c.�
4(8)
�4(
8) �
�32
Th
e fa
ctor
s h
ave
dif
fere
nt
sign
s,
so t
he
prod
uct
is
neg
ativ
e.
Exa
mp
le 2
:E
valu
ate
�3a
bif
a�
3 an
d b
��
5.�
3ab
��
3(3)
(�5)
Rep
lace
a w
ith
3 a
nd
b w
ith
�5.
�
�9(
�5)
�3
�3
��
9�
45B
oth
fac
tors
are
neg
ativ
e.
Exa
mp
le 3
:S
impl
ify
�12
(4x)
.�
12(4
x) �
(�12
�4)
(x)
Ass
ocia
tive
Pro
pert
y�
�48
x�
12 �
4 �
�48
Fin
d e
ach
pro
du
ct.
1.3(
8)24
2.(�
7)(�
9)63
3.12
(�1)
�12
4.�
6(5)
�30
5.4(
�1)
(�5)
206.
(�8)
(�8)
(�2)
�12
87.
2(�
5)(1
0)�
100
Eva
luat
e ea
ch e
xpre
ssio
n if
a �
3, b
��
2, a
nd
c �
�3.
8.5c
�15
9.2a
b�
1210
.abc
1811
.3b
�c
�3
Sim
plif
y ea
ch e
xpre
ssio
n.
12.3
(�6x
)�
18x
13.
�5(
�7y
)35
y14
.(2
p)(�
4q)
�8p
q
Th
e pr
odu
ct o
f tw
o po
siti
ve i
nte
gers
is
posi
tive
.T
he
prod
uct
of
two
neg
ativ
e in
tege
rs i
s po
siti
ve.
Th
e pr
odu
ct o
f a
posi
tive
in
tege
r an
d a
neg
ativ
e in
tege
r is
neg
ativ
e.
Answers (Lesson 2-5)
© Glencoe/McGraw-Hill A13 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill74
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Rea
ding
to
Lear
n M
athe
mat
ics
Mul
tiply
ing
Inte
gers
2–5
2–5
Key
Ter
ms
fact
ors
the
num
ber
s b
eing
mul
tiplie
dp
rod
uct
the
resu
lt w
hen
two
or m
ore
fact
ors
are
mul
tiplie
dto
geth
er
Rea
din
g t
he
Les
son
1.C
ompl
ete:
If
two
nu
mbe
rs h
ave
diff
eren
t si
gns,
th
e on
e n
um
ber
is p
osit
ive
and
the
oth
er
nu
mbe
r is
.
2.C
ompl
ete
the
tabl
e.
a. b.
c. d.
3.E
xpla
in w
hat
th
e te
rm “
addi
tive
in
vers
e” m
ean
s. T
hen
giv
e an
exa
mpl
e.
The
pro
duc
t o
f an
y nu
mb
er a
nd �
1 is
its
add
itiv
e in
vers
e; �
�
(�1)
�.
2 3
2 3
neg
Hel
pin
g Y
ou
Rem
emb
er4.
Des
crib
e h
ow y
ou k
now
th
at t
he
prod
uct
of
�3
and
�5
is p
osit
ive.
Th
en d
escr
ibe
how
you
kn
ow t
hat
th
e pr
odu
ct o
f 3
and
�5
is n
egat
ive.
Sam
ple
ans
wer
: The
sig
ns a
re t
he s
ame;
the
sig
ns a
re d
iffer
ent.
Mu
ltip
licat
ion
Are
th
e si
gn
s o
f th
e n
um
ber
sIs
th
e p
rod
uct
po
siti
veE
xam
ple
the
sam
eo
r d
iffer
ent?
or
neg
ativ
e?
(�4)
(9)
diff
eren
tne
g(�
2)(�
13)
sam
ep
os
5(�
8)d
iffer
ent
neg
6(3)
sam
ep
os
© G
lenc
oe/M
cGra
w-H
ill73
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Pra
ctic
e2
–52
–5
Mu
ltip
lyin
g In
teg
ers
Fin
d e
ach
pro
du
ct.
1.3(
�7)
2.�
2(8)
3.4(
5)
�21
�16
20
4.�
7(�
7)5.
�9(
3)6.
8(�
6)
49�
27�
48
7.6(
2)8.
�5(
�7)
9.2(
�8)
1235
�16
10.�
10(�
2)11
.9(
�8)
12.
12(0
)
20�
720
13.�
4(�
4)(2
)14
.7(
�9)
(�1)
15.
�3(
5)(2
)
3263
�30
16.3
(�4)
(�2)
(2)
17.
6(�
1)(2
)(1)
18.
�5(
�3)
(�2)
(�1)
48�
1230
Eva
luat
e ea
ch e
xpre
ssio
n if
a �
�3
and
b �
�5.
19.�
6b20
.8a
21.
4ab
30�
2460
22.�
3ab
23.
�9a
24.
�2a
b
�45
27�
30
Sim
plif
y ea
ch e
xpre
ssio
n.
25.5
(�5y
)26
.�
7(�
3b)
27.
�3(
6n)
�25
y21
b�
18n
28.(
6a)(
�2b
)29
.(�
4m)(
�9n
)30
.(�
8x)(
7y)
�12
ab36
mn
�56
xy
Answers (Lessons 2-5 and 2-6)
© Glencoe/McGraw-Hill A14 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill76
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Stud
y G
uide
2–6
2–6
Div
idin
g In
teg
ers
Exa
mp
le 1
:U
se t
he
mu
ltip
lica
tion
pro
blem
s at
th
e ri
ght
to f
ind
each
qu
otie
nt.
a.15
�5
Sin
ce 3
�5
�15
, 15
�5
�3.
b.
15 �
(�5)
Sin
ce �
3 �
(�5)
�15
, 15
�(�
5) �
�3.
c.�
15 �
5S
ince
�3
�5
��
15, �
15 �
5 �
�3.
d.
�15
�(�
5)S
ince
3 �
(�5)
��
15, �
15 �
(�5)
�3.
Use
th
ese
rule
s to
div
ide
inte
gers
.
Exa
mp
le 2
:E
valu
ate
if r
�8
and
s�
�2.
�R
epla
ce r
wit
h 8
an
d s
wit
h �
2.
��
3�
8 �
�24
�12
�24
�(�
2) �
12
Fin
d e
ach
qu
otie
nt.
1.36
�9
42.
�63
�(�
7)9
3.25
� (
�1)
�25
4.�
60 �
5�
12
5.�
46.
67.
18.
�7
Eva
luat
e ea
ch e
xpre
ssio
n if
k �
�1,
m �
3, a
nd
n �
�2.
9.�
21 �
m�
710
.4
11.m
�k
�3
12.
�4
m�
5
n2n k
�56
8
�1
�1
�18
�3
20 �5
�24
�2
�3
�8
�
2�
3r
s
�3r
s
Th
e qu
otie
nt
of t
wo
posi
tive
in
tege
rs i
s po
siti
ve.
Th
e qu
otie
nt
of t
wo
neg
ativ
e in
tege
rs i
s po
siti
ve.
Th
e qu
otie
nt
of a
pos
itiv
e in
tege
r an
d a
neg
ativ
e in
tege
r is
neg
ativ
e.
3 �
5 �
15
�3(
�5)
�15
�3
�5
��
15
3(�
5) �
�15
© G
lenc
oe/M
cGra
w-H
ill75
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Enri
chm
ent
2–5
2–5
Th
e B
inar
y N
um
ber
Sys
tem
Ou
r st
anda
rd n
um
ber
syst
em in
bas
e te
n h
as t
en d
igit
s,
0 th
rou
gh 9
. In
bas
e te
n, t
he
valu
es o
f th
e pl
aces
are
po
wer
s of
10.
Asy
stem
of
nu
mer
atio
n t
hat
is u
sed
in c
ompu
ter
tech
nol
ogy
is t
he
bin
ary
nu
mb
er s
yste
m. I
n a
bin
ary
nu
mb
er, t
he
plac
e va
lue
of e
ach
dig
it is
tw
o ti
mes
th
e pl
ace
valu
e of
th
e di
git
to it
s ri
ght.
Th
ere
are
only
tw
o di
gits
in t
he
bin
ary
syst
em: 0
an
d 1.
Th
e bi
nar
y n
um
ber
1011
1 is
wri
tten
101
11tw
o. Y
ou c
an u
se
a pl
ace-
valu
e ch
art
like
th
e on
e at
th
e ri
ght
to f
ind
the
stan
dard
nu
mbe
r th
at is
equ
ival
ent
to t
his
nu
mbe
r.
1011
1 two
�1
�16
�0
�8
�1
�4
�1
�2
�1
�1
�16
�0
�4
�2
�1
�23
Wri
te e
ach
bin
ary
nu
mb
er a
s a
stan
dar
d n
um
ber
.
1.11
two
32.
111 tw
o7
3.10
0 two
4
4.10
01tw
o9
5.11
001 tw
o25
6.10
0101
two
37
Wri
te e
ach
sta
nd
ard
nu
mb
er a
s a
bin
ary
nu
mb
er.
7.8
1000
two
8.10
1010
two
9.15
1111
two
10.1
710
001 tw
o11
.28
1110
0 two
12.
3410
0010
two
Wri
te e
ach
an
swer
as
a b
inar
y n
um
ber
.
13.1
two
�10
two
11tw
o14
.101
two
�10
two
11tw
o
15.1
0 two
�11
two
110 tw
o16
.100
00tw
o�
10tw
o10
00tw
o
17.W
hat
sta
nda
rd n
um
ber
is e
quiv
alen
t to
120
21th
ree?
142
8 �2 �164 �2 �82 �2 �41 �2 �21
10
11
1
Answers (Lesson 2-6)
© Glencoe/McGraw-Hill A15 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill78
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Pra
ctic
e2
–62
–6
Div
idin
g In
teg
ers
Fin
d e
ach
qu
otie
nt.
1.28
�7
2.�
33 �
33.
42 �
(�6)
4�
11�
7
4.�
81 �
(�9)
5.12
�4
6.72
�(�
9)
93
�8
7.15
�15
8.�
30 �
59.
�40
�(�
8)
1�
65
10.5
6 �
(�7)
11.
�21
�(�
3)12
.�
64 �
8
�8
7�
8
13.�
8 �
814
.�
22 �
(�2)
15.
32 �
(�8)
�1
11�
4
16.�
54 �
(�9)
17.
60 �
(�6)
18.
63 �
9
6�
107
19.�
45 �
(�9)
20.
�60
�5
21.
24 �
(�3)
5�
12�
8
22.
23.
24.
�2
�4
5
Eva
luat
e ea
ch e
xpre
ssio
n if
a �
4, b
��
9, a
nd
c �
�6.
25.�
48 �
a26
.b
�3
27.
9c�
b
�12
�3
6
28.
29.
30.
6�
92
31.
32.
33.
�8
9�
4
ac 6�
4b
a12
a
c
3c bbc �
6ab c
�45
�9
40 �
10�
12
6
© G
lenc
oe/M
cGra
w-H
ill77
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Skil
ls P
ract
ice
2–6
2–6
Div
idin
g In
teg
ers
Fin
d e
ach
qu
otie
nt.
1.36
�3
2.�
15 �
53.
24 �
(�8)
12�
3�
3
4.�
45 �
(�3)
5.81
�(�
9)6.
�28
�4
15�
9�
7
7.�
121
�11
8.�
144
�(�
12)
9.32
�(�
4)
�11
12�
8
10.�
64 �
(�8)
11.
�80
�10
12.
48 �
(�6)
8�
8�
8
13.1
00 �
(�25
)14
.�
20 �
515
.36
�(�
9)
4�
4�
4
16.5
6 �
(�7)
17.
�63
�(�
9)18
.�
32 �
(�16
)
�8
72
19.�
21 �
320
.�
18 �
221
.72
�(�
8)
�7
�9
�9
22.
23.
24.
�5
�3
25
Eva
luat
e ea
ch e
xpre
ssio
n if
d �
�3,
f �
8, a
nd
g �
�4.
25.f
�g
26.
8d�
g27
.4g
�f
�2
6�
2
28.
29.
30.
�16
2�
10
31.
32.
33.
124
�8
4f g�
2f
g9g d
5f gd
f �
12gf 2
�12
5
�5
39 �
13�
35
7
Answers (Lesson 2-6)
© Glencoe/McGraw-Hill A16 Algebra: Concepts and Applications
© G
lenc
oe/M
cGra
w-H
ill80
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Enri
chm
ent
2–6
2–6
Day
of
the
Wee
k Fo
rmu
la
Th
e fo
llow
ing
form
ula
can
be
use
d to
det
erm
ine
the
spec
ific
day
of
th
e w
eek
on w
hic
h a
dat
e oc
curr
ed.
s�
d�
2m�
[(3m
�3)
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ith
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en t
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Th
e br
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], m
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sion
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ly t
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ole
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e n
ext
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nd
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e th
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he
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ay, 1
is S
un
day,
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day,
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on
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p to
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Fri
day.
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mp
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Wh
at d
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ve.
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ee if
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e fo
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orks
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e.A
nsw
ers
will
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y.
2.O
n w
hat
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the
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k w
ere
you
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n?
Ans
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s w
ill v
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l be
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© G
lenc
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cGra
w-H
ill79
Alg
ebra
: Con
cep
ts a
nd A
pp
licat
ions
NA
ME
DAT
EP
ER
IOD
Rea
ding
to
Lear
n M
athe
mat
ics
Div
idin
g In
tege
rs2
–62
–6
Key
Ter
ms
add
itiv
e in
vers
estw
o nu
mb
ers
are
add
itive
inve
rses
if t
heir
sum
is 0
op
po
site
add
itive
inve
rse
zero
pai
rth
e re
sult
of p
ositi
ve a
lgeb
ra t
iles
pai
red
with
neg
ativ
eal
geb
ra t
iles
Rea
din
g t
he
Les
son
1.W
rite
th
e m
ath
sen
ten
ce 1
8 di
vide
d by
6tw
o di
ffer
ent
way
s. T
hen
fin
d th
e qu
otie
nt.
18 �
6 �
3;
�3
2.W
rite
neg
ativ
eor
pos
itiv
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e ea
ch q
uot
ien
t. E
xpla
in y
our
answ
er.
a. b.
c. d.
e. f.
18
6
Hel
pin
g Y
ou
Rem
emb
er3.
Exp
lain
how
kn
owin
g th
e ru
les
for
mu
ltip
lyin
g in
tege
rs c
an h
elp
you
to
divi
de i
nte
gers
.S
amp
le a
nsw
er: T
he r
ules
to
fin
d t
he s
ign
of
the
answ
er a
re t
hesa
me
for
mul
tip
licat
ion
and
div
isio
n. I
f th
e si
gns
of
the
fact
ors
are
the
sam
e, t
he a
nsw
er w
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e p
osi
tive
. If
the
sig
ns o
f th
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cto
rs a
red
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ent,
the
ans
wer
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be
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ress
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Neg
ativ
e o
r P
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15�
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umb
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© Glencoe/McGraw-Hill A17 Algebra: Concepts and Applications
Form 1APage 81 Page 82
Form 1BPage 83 Page 84
Chapter 2 Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
A
B
C
B
D
C
A
D
C
A
D
B
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Bonus
D
B
C
A
C
A
B
B
D
D
C
B
B
A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
D
C
A
B
B
C
A
B
D
C
B
C
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
Bonus
C
A
C
D
B
D
A
D
D
A
A
C
B
C
© Glencoe/McGraw-Hill A18 Algebra: Concepts and Applications
Form 2APage 85 Page 86
Chapter 2 Answer Key
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
Bonus
�24k
4507 m
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512
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8
25
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1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
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(�4, 2)
(2, 4)
IV
III
II
37
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2
down 9
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31
4
3
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© Glencoe/McGraw-Hill A19 Algebra: Concepts and Applications
Form 2BPage 87 Page 88
Chapter 2 Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
�
�
�
12
Point B lies on the x-axis. It is not located
in a quadrant.
IV
(4, 3)
(�4, �2)
IV
5
12
�5
�14
falls 2 ft
14
17
�1
14
–1 0 1–3 –2
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
Bonus
6b
�17�F
�375
2
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30
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14
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�44 ft persecond squared
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© Glencoe/McGraw-Hill A20 Algebra: Concepts and Applications
Score General Description Specific Criteria
4 SuperiorA correct solution thatis supported by well-developed, accurateexplanations
3 SatisfactoryA generally correct solution,but may contain minor flawsin reasoning or computation
2 Nearly SatisfactoryA partially correctinterpretation and/orsolution to the problem
1 Nearly UnsatisfactoryA correct solution with nosupporting evidence orexplanation
0 UnsatisfactoryAn incorrect solutionindicating no mathematicalunderstanding of theconcept or task, or nosolution is given
Page 89, Extended Response AssessmentScoring Rubric
Chapter 2 Assessment Answer Key
• Shows thorough understanding of the concepts of points on the coordinate plane, translating between verbal sentences and equations, and solving equations.
• 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 thorough understanding of the concepts of points on the coordinate plane, translating between verbal sentences and equations, and solving equations.
• 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 thorough understanding of the concepts of points on the coordinate plane, translating between verbal sentences and equations, and solving equations.
• 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 thorough understanding of the concepts of points on the coordinate plane, translating between verbal sentences and equations, and solving equations.
• 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.
© Glencoe/McGraw-Hill A21 Algebra: Concepts and Applications
Extended Response AssessmentSample Answers
Page 89
Chapter 2 Answer Key
1. a. A(2, 1), B(3, �2), C(�3, 0)
b. (�4, �2), (�6, 4), (6, 0)
c.
d. The new triangle has the same shape, but its sides seem to be twiceas long. It also seems to be rotated halfway around the origin.
2. a. A sample table is shown below for n � �3.
b. Multiplying the x-coordinate by a negative number moves the pointhorizontally to the quadrant next to it. Multiplying the y-coordinateby a negative number moves the point vertically to the quadrantabove or below it. Multiplying both coordinates by a negativenumber moves the point to the quadrant diagonally across from it.
3. a. � �$22
b. � �$22
c. Both clubs lost the same amount per person, $22, but members ofthe first club invested $970 each, while those in the second clubinvested $630 each.
$1200 � $1750
25
$990 � $1320
15
Quadrant of (a, b) I II III IV
Coordinates of (a, b) (2, 3) (�1, 3) (–3, –3) (1, �2)
Coord. and quad. of (na, b) (�6, 3); II (3, 3); I (9, –3); IV (�3, �2); III
Coord. and quad. of (a, nb) (2, �9); IV (�1, �9); III (–3, 9); II (1, 6); I
Coord. and quad. of (na, nb) (�6, �9); III (3, �9); IV (9, 9); I (�3, 6); II
O x
y
Z
X
Y
© Glencoe/McGraw-Hill A22 Algebra: Concepts and Applications
Mid-Chapter TestPage 90
Quiz APage 91
Chapter 2 Answer Key
Quiz BPage 91
1.
2.
3.
4.
5.
6.
7.
8.
�10
0
174
21 � (�3) � 24
�42
80
6
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1.
2.
3.
4.
5–7.
8.
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O x
y
C A
B
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1.
2.
3.
4.
5.
6.
7.
8.
9–11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
�1
4
�
�
�
�
10, 3, 0, �8, �12
6, 5, 2, �3, �4, �5
(0, �4)
(�2, 3)
III
I
9
22
2
9x
�7
O x
y
Q
R
P
© Glencoe/McGraw-Hill A23 Algebra: Concepts and Applications
Cumulative Review Standardized Test PracticePage 92 Page 93 Page 94
Chapter 2 Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
4a � 6 � bc � 117
AssociativeProperty (�)
8x � 18
2 lb
6
line graph�64, �25, �2, 3,
11, 36
(�1, 4)
IV
�53
42
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914
1�2
1.
2.
3.
4.
5.
6.
7.
8.
9.
C
B
C
B
A
B
B
C
A
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
D
C
B
D
B
C
C
B
A
A
B