## Glencoe Algebra 1 Chapter 2 Vocabulary Noteables

Integers in counting order

Choosing a variable to represent on of the unspecified numbers in a problem and using it to write expressions for the other unspecified numbers in the problem.

The process of carrying units throughout a computation.

Equations that have the same solutions.

In the rations a/b =c/d, a and d are the extremes.

An equation that states a rule in the relationship between certain quantities.

four-step problem solving

1. Explore the problem

2. Plan the solution

3. Solve the problem

4. Check the solution

Equations that are true for all values of the variables.

The middle terms of the proportion.

Problems in which two or more parts are combined into the whole.

Equations with more than one operation.

The study of numbers and the relationships between them.

When an increase or decrease is expressed as a percent.

The ration of an amount of decrease to the previous amount, expressed as a percent.

The ration of an amount of increase to the previous amount, expressed as a percent.

An equation of the form a/b =c/d stating that two ratios are equivalent.

A comparison of two numbers by division.

The ratio of two measurements having different units of measure.

The ratio or rate used when making a model of something that is to large or to small to be conviently shown at actually size.

The process of finding all values of the variable that make the equation a true statement.

Problems in which an object moves at a certain speed, or rate.

The sum of the product of the number of units and the value per unit divided by the sum of the number of units, represented by M.

## Glencoe Algebra, Chapter 2

### New York, New York

Columbus, Ohio

### Woodland Hills, California

Peoria, Illinois

CONSUMABLE WORKBOOKS Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Study Guide Workbook Skills Practice Workbook Practice Workbook Spanish Study Guide and Assessment 0-07-869610-0 0-07-869311-X 0-07-869609-7 0-07-869611-9

ANSWERS FOR WORKBOOKS The answers for Chapter 2 of these workbooks can be found in the back of this Chapter Resource Masters booklet. StudentWorksTM This CD-ROM includes the entire Student Edition along with the English workbooks listed above. TeacherWorksTM All of the materials found in this booklet are included for viewing and printing in the Algebra: Concepts and Applications TeacherWorks CD-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 Place Columbus, OH 43240-4027 ISBN: 0-07-869254-7 1 2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 Algebra: Concepts and Applications Chapter 2 Resource Masters

Contents

Vocabulary Builder . . . . . . . . . . . . . . . . . vii-viii Lesson 2-1 Study Guide and Intervention . . . . . . . . . . . . . . . . 51 Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Reading to Learn Mathematics . . . . . . . . . . . . . . . 54 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Lesson 2-2 Study Guide and Intervention . . . . . . . . . . . . . . . . 56 Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Reading to Learn Mathematics . . . . . . . . . . . . . . . 59 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Lesson 2-3 Study Guide and Intervention . . . . . . . . . . . . . . . . 61 Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Reading to Learn Mathematics . . . . . . . . . . . . . . . 64 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Lesson 2-4 Study Guide and Intervention . . . . . . . . . . . . . . . . 66 Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Reading to Learn Mathematics . . . . . . . . . . . . . . . 69 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 Lesson 2-5 Study Guide and Intervention . . . . . . . . . . . . . . . . 71 Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Reading to Learn Mathematics . . . . . . . . . . . . . . . 74 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Lesson 2-6 Study Guide and Intervention . . . . . . . . . . . . . . . . 76 Skills Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Practice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 Reading to Learn Mathematics . . . . . . . . . . . . . . . 79 Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Chapter 2 Assessment Chapter 2 Test, Form 1A. . . . . . . . . . . . . . . . . . 81-82 Chapter 2 Test, Form 1B . . . . . . . . . . . . . . . . . . 83-84 Chapter 2 Test, Form 2A. . . . . . . . . . . . . . . . . . 85-86 Chapter 2 Test, Form 2B . . . . . . . . . . . . . . . . . . 87-88 Chapter 2 Extended Response Assessment . . . . . . 89 Chapter 2 Mid-Chapter Test . . . . . . . . . . . . . . . . . . 90 Chapter 2 Quizzes A & B. . . . . . . . . . . . . . . . . . . . 91 Chapter 2 Cumulative Review . . . . . . . . . . . . . . . . 92 Chapter 2 Standardized Test Practice . . . . . . . . 93-94 Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . . . . . A1 ANSWERS . . . . . . . . . . . . . . . . . . . . . . . . . . A2-A23

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### A Teachers Guide to Using the Chapter 2 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter 2 Resource Masters include the core materials needed for Chapter 2. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the 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 are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. When to Use Give these pages to students

before beginning Lesson 2-1. Encourage them to add these pages to their Algebra: Concepts and Applications Interactive Study Notebook. Remind them to add definitions and examples as they complete each lesson.

Practice There is one master for each lesson. These problems more closely follow the structure of the Practice section of the Student Edition exercises. These exercises are of average difficulty. 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 One

master is included for each lesson. The first section of each master presents key terms from the lesson. The second section contains questions that ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques.

Study Guide There is one Study Guide master for each lesson. When to Use Use these masters as reteaching

activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for those students who have been absent.

### When to Use This master can be used as a

study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learners) students.

### Skills Practice There is one master for each

lesson. These provide computational practice at a basic level.

### Enrichment There is one master for each

lesson. These activities may extend the concepts in the lesson, offer a historical or multicultural look at the concepts, or widen students perspectives on the mathematics they are learning. These are not written exclusively for honors students, but are accessible for use with all levels of students.

### When to Use These worksheets can be used

with students who have weaker mathematics backgrounds or need additional reinforcement.

### When to Use These may be used as extra

credit, short term projects, or as activities for days when class periods are shortened.

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Assessment Options

The assessment section of the Chapter 2 Resources Masters offers a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use.

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 to offer assessment at appropriate intervals in the chapter.

### Chapter Assessments Chapter 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 freeresponse questions aimed at the averagelevel and basic-level student, respectively. These tests are similar in format to offer comparable testing situations. All of the above tests include a challenging Bonus question. The Extended Response Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment.

Continuing Assessment

The Cumulative Review provides students an opportunity to reinforce and retain skills as they proceed through their study of algebra. It can also be used as a test. The master includes free-response questions. The Standardized Test Practice offers continuing review of algebra concepts in multiple choice format.

Answers

Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on page 89. This improves students familiarity with the answer formats they may encounter in test taking. The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. Full-size answer keys are provided for the assessment options in this booklet.

Glencoe/McGraw-Hill

### Algebra: Concepts and Applications

### Chapter 2 Leveled Worksheets

Glencoes leveled worksheets are helpful for meeting the needs of every student in a variety of ways. These worksheets, many of which are found in the FAST FILE Chapter Resource Masters, are shown in the chart below.

The Prerequisite Skills Workbook provides extra practice on the basic

### skills students need for success in algebra.

Study Guide and Intervention masters provide worked-out examples

### as well as practice problems.

Reading to Learn Mathematics masters help students improve reading

### skills 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 slower

pace to practice concepts using easier problems. Practice masters provide average-level problems for students who are moving at a regular pace.

Each chapters 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 their

learning. Nine Different Options to Meet the Needs of Every Student in a Variety of Ways

### primarily skills primarily concepts primarily applications BASIC AVERAGE ADVANCED

1 2 3 4 5 6 7

Prerequisite Skills Workbook Study Guide and Intervention Reading to Learn Mathematics NoteablesTM: Interactive Study Notebook with FoldablesTM Skills Practice Vocabulary Builder Parent and Student Study Guide (online)

8 9

Practice Enrichment

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NAME

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### Reading to Learn Mathematics

Vocabulary Builder

This is an alphabetical list of the key vocabulary terms you will learn in Chapter 2. As you study the chapter, complete each terms definition or description. Remember to add the page number where you found the term. Vocabulary Term absolute value Found on Page Definition/Description/Example

### additive inverse Aduhtiv

coordinate coORduhnet

coordinate plane

coordinate system

dimensions

element

graph

integers INtahjerz

matrix MAYtriks

natural numbers

negative numbers

### (continued on the next page)

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2

number line

NAME

DATE

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### Reading to Learn Mathematics

Vocabulary Builder (continued)

Found on Page Definition/Description/Example

Vocabulary Term

opposites

ordered array

ordered pair

origin ORajin

quadrants KWAdruntz

### scalar multiplication SKAYler

Venn diagram

x-axis

x-coordinate

y-axis

y-coordinate

zero pair

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Study Guide

### Graphing Integers on a Number Line

The numbers displayed on the number line below belong to the set of integers. The arrows at both ends of the number line indicate that the numbers continue indefinitely in both directions. Notice that the integers are equally spaced.

negative integers positive integers

5 4 3 2 1 0

integers

Use dots to graph numbers on a number line. You can label the dots with capital letters.

A B C D E

1 2 3

F

4 5

5 4 3 2 1 0

### 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. And because 5 is to the left of 1, 5 1. Because 3 and 3 are the same distance from 0, they have the same absolute value, 3. Use two vertical lines to represent absolute value.

3 units 4 3 2 1 0 3 units 1 2 3 4

|3| 3 | 3| 3

### The absolute value of 3 is 3. The absolute value of 3 is 3.

Example:

### Evaluate | 12| |10|. | 12| |10| 12 10 22

| 12|

12 and |10|

10

### Name the coordinate of each point. 1. B

B D

E

1 2

F

3 4

G

5 6

2. D

3. G 5

5 4 3 2 1 0

### Graph each set of numbers on a number line. 4. { 3, 2, 4}

4 3 2 1 0 1 2 3 4

5. { 1, 0, 3}

2 1 0 1 2 3 4

Write 6. 7

or

### in each blank to make a true sentence. 5 7. 3 8 8. | 1| 0

### Evaluate each expression. 9. |9| 9

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11. | 20|

|10| 10

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Skills Practice

### Graphing Integers on a Number Line

Name the coordinate of each point.

R

5 4

S

3

T

2 1

U

0

V

1 2 3

W

4 5

1. S 4. R

3 5

2. U 5. W

0 4

3. T 6. V

2 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 13. 2 16. 19. 5 4

or

in each blank to make a true sentence. 7 2 3 14. 4 17. 20. 0 1 2 2 9 15. 18. 21. 3 5 6 0 8 3

### Evaluate each expression. 22. |4|

23. | 5|

24. | 8| 8

25. |10|

10

26. |3|

| 2|

27. | 7|

| 12|

19

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A E C

NAME

DATE

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Practice

### Graphing Integers on a Number Line

Name the coordinate of each point.

F

1 2

B

3 4

D

5

5 4 3 2 1 0

1. A 4. D 5

2. B 3 5. E

3. C

6. F 1

### Graph each set of numbers on a number line. 7. { 5, 0, 2}

5 4 3 2 1 0 1 2 3 4 5

8. {4,

1,

2}

1 2 3 4 5

5 4 3 2 1 0

9. {3,

4,

3}

1 2 3 4 5

10. { 2, 5, 1}

5 4 3 2 1 0 1 2 3 4 5

5 4 3 2 1 0

11. {2,

5, 0}

1 2 3 4 5

12. { 4, 3,

2, 4}

1 2 3 4 5

5 4 3 2 1 0

5 4 3 2 1 0

### Write 13. 7 16. 6 19. 8

or

in each blank to make a true sentence. 9 3 0 14. 0 17. 20. 4 11 1 5 2 15. 18. 21. 2 7 5 2 3 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

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Key Terms

NAME

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### Reading to Learn Mathematics

Graphing Integers on a Number Line

absolute value the distance a number is from 0 on a number line coordinate (co OR di net) the number that corresponds to a point on a number line graph to plot points named by numbers on a number line number line a line with equal distances marked off to represent numbers

### Reading the Lesson

1. 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 continue infinitely in each direction.

b. What is the absolute value of 3? What is the absolute value of 3? Explain.

5 4 3 2 1 0 1 2 3 4 5

3, 3; line.

### 3 and 3 are both 3 units away from zero on the number

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.

### Whole Numbers Integers

### true false true false

c. All whole numbers are natural numbers. d. All natural numbers are whole numbers. e. All whole numbers are positive numbers. f. All integers are natural numbers.

Natural Numbers

false false

g. Whole numbers are a subset of natural numbers. h. Natural numbers are a subset of integers.

true

### Helping You Remember

3. 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 of absolute value.

Sample answer: On a football field, the distance from each goal line to the 50-yard line is 50 yards.

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Enrichment

Venn Diagrams

A type of drawing called a Venn diagram can be useful in explaining conditional statements. A Venn diagram uses circles to represent sets of objects. Consider the statement All rabbits have long ears. To make a Venn diagram for this statement, a large circle is drawn to represent all animals with long ears. Then a smaller circle is drawn inside the first to represent all rabbits. The Venn diagram shows that every rabbit is included in the group of long-eared animals.

animals with long ears

### The set of rabbits is called a subset of the set of long-eared animals.

rabbits

The Venn diagram can also explain how to write the statement, All rabbits have long ears, in if-then form. Every rabbit is in the group of long-eared animals, so if an 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 has long hair.

3. People who live in Iowa like corn.

### If a number is rational, then it is real.

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 in the faculty lounge.

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Study Guide

### 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 four quadrants. 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.

Quadrant II 4 3 2 1 4 3 2 1 O 1 2 3 4 Quadrant III

y Quadrant I S

1 2 3 4 x

Quadrant IV

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.

Quadrant II 4 3 2 1 1 2 3 4 x

y Quadrant I

4 3 2 1 O 1 2 3 M 4 Quadrant III

Quadrant IV

Write the ordered pair that names each point. 1. P (1, 3) 3. R (0, 2) 2. Q ( 4, 4. T ( 4, 0)

y

4 P 3 2 R 1 1 2 3 4 x

3)

T

4 3 2 1 O 1 2 3 Q 4

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 8. D(0, 1) none 10. F( 1, 2) III

O

7. C( 3, 1) II 9. E(3, 3) I

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Skills Practice

### The Coordinate Plane

Write the ordered pair that names each point. 1. L ( 4, 0) 3. N ( 1, 5. Q 2. M

( 3,

1)

3)

### 4. P (0, 0) 6. R (2, 1) 8. T 10. V

L

4 2

R T P S

2 U 2 4 x

( 2, 4) 1) 2)

7. S (2, 9. U (0,

(5, 0) (0, 3)

N

4

Graph each point on the coordinate plane. 11. A( 2, 4) 13. C(5, 3) 12. B(0, 14. D( 2, 16. F(4, 0) 1) 18. H(3, 3)

4

4) 1)

4 2

y

4

### 15. E(1, 4) 17. G( 4, 19. I( 4, 3)

2 2

4 x

20. J( 5, 0)

### Name the quadrant in which each point is located. 21. ( 2, 2)

### III II none IV none

### 22. (3, 4) 24. (4, 26. ( 1, 3)

I IV III II IV

### 23. ( 4, 3) 25. (0, 27. (4, 2) 1)

1)

### 28. ( 3, 5) 30. (8, 4)

29. ( 3, 0)

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Practice

### The Coordinate Plane

Write the ordered pair that names each point. 1. A ( 3, 4) 3. C ( 4, 2. B (5, 2) 4. D (2, 6. F (1, 0) 8. H ( 2, 5) 10. K (5,

A H

y

B

3)

4)

C J

O

G

F D

x

K

5. E ( 1, 1) 7. G (0, 9. J ( 2,

2) 4)

1)

y

Graph each point on the coordinate plane. 11. K(0, 3) 12. L( 2, 3) 14. N( 3, 0)

O

### 13. M(4, 4) 15. P( 4, 1)

### 16. Q(1, 18. S(3, 2) 20. W( 1,

2)

### 17. R( 5, 5) 19. T(2, 1)

4)

Name the quadrant in which each point is located. 21. (1, 9) I 23. (0, 25. (5, 27. ( 1, 1) none 3) IV 1) III 22. ( 2, 7) III

### 24. ( 4, 6) II 26. ( 3, 0) none 28. (6, 30. ( 9, 5) IV 2) III

29. ( 8, 4) II

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Key Terms

NAME

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### Reading to Learn Mathematics

The Coordinate plane

coordinate plane the plane containing the x- and y-axes coordinate system the grid formed by the intersection of two perpendicular number lines that meet at their zero points ordered pair a pair of numbers used to locate any point on a coordinate plane quadrant one of the four regions into which the x- and y-axes separate the coordinate plane x-axis the horizontal number line on a coordinate plane y-axis the vertical number line on a coordinate plane x-coordinate the first number in a coordinate pair y-coordinate the second number in a coordinate pair

### Reading the Lesson

1. Identify each part of the coordinate system.

y

y axis

origin

O

x axis

x

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 the second 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 coordinate plane.

Start at the origin, move two units to the left and then move up three units.

3. What does the term quadrant mean?

Sample answer: It is one of four regions in the coordinate plane. Helping You Remember

4. Describe a method to remember how to write an ordered pair.

Sample answer: Since x comes before y in the alphabet, the xcoordinate is written first in an ordered pair.

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Enrichment

### Points and Lines on a Matrix

A matrix is a rectangular array of rows and columns. Points and lines on a matrix are not defined in the same way as in Euclidean geometry. A point on a matrix is a dot, which can be small 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 other points. Three examples of lines are shown at the upper right. The broad line can be thought of as a single line or as two narrow 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 shows how 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 four points in common. 2. Draw two lines that cross but have no common points.

3. Make the number 0 (zero) so that it extends to the top and bottom sides of the matrix.

4. Make the capital letter O so that it extends to each side of the matrix.

5. Using separate grid paper, make dot designs for several other letters. Which were the easiest and which were the most difficult? See students work.

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Study Guide

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.

2 1 0 1 2 2 1 1 3 3 4 5 4 3 2 1 2 2 1 0 1 ( 1) 3 2

Both integers are positive. First move 2 units right from 0. Then move 1 more unit right.

Both integers are negative. First move 2 units left from 0. 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.

1 2 4 3 2 1 2 1 0 1 1 2 2 1 2 0 1 2 1 2 3 ( 1) 1 4

### 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 To add integers with the same sign, add their absolute values. Give the result the same sign as the integers. To add integers with different signs, subtract their absolute values. Give the result the same sign as the integer with the greater absolute value. Find each sum. 1. 5 5. 5 8 13 ( 8) ( 5) 2. 8 6. ( 9) 8 7 Examples 11 8 ( 2) 5x ( 3x) 4 10 8x

9 1

( 6) 3 ( 5) 4 2x 9x 7x 3y ( 4y) y

17

( 8)

3. 12 20 4

( 8) 4 7. 12 5

4.

16

11

( 1) 16

### Simplify each expression. 8. 3x ( 6x)

3x

9.

5y

( 7y)

12y

10. 2m

( 4m)

( 2m)

4m

Glencoe/McGraw-Hill

61

### Algebra: Concepts and Applications

23

Find each sum. 1. 2 7

NAME

DATE

PERIOD

Skills Practice

Adding Integers

2. 3 ( 2) 3. 4 1

9

4. 3 ( 9) 5.

5

2 12 6.

3

1 ( 6)

6

7. 10 ( 8) 8.

10

9 4 9. 3

7

( 3)

2

10. 5 ( 5) 11. 8

5

( 9) 12.

0

7 4

10

13. 2 2 14.

1

12 10 15.

3

8 ( 5)

0

16. 14 8

2

17. 15 ( 8) 18. 3

13

( 11)

6

19. 9 ( 7)

7

20. 6 ( 9) 21.

8

14 15

16

22. 10 6 ( 4)

3

23. 13 ( 14) 1 24.

1

4 ( 8) 5

8

Simplify each expression. 25. 4c 8c 26.

5a

( 9a)

27.

8d

3d

4c

28. 7x 3x

14a

29. 6y ( 3y) 30.

5d

7t 4t

10x

31. 12s ( 4s)

3y

32. 5t ( 13t)

3t

33. 15h ( 4h)

16s

34. 7b 6b ( 8b) 35.

8t

9w 4w ( 5w)

11h

36. 12t 3t ( 6t)

5b

Glencoe/McGraw-Hill

10w

62

9t

Algebra: Concepts and Applications

23

Find each sum. 1. 8 4

NAME

DATE

PERIOD

Practice

Adding Integers

2. 3 5 3. 9 ( 2)

12

4. 5 11 5.

2

7 ( 4)

7

6. 12 ( 4)

6

7. 9 10 8.

11

4 4

8

9. 2 ( 8)

1

10. 17 ( 4) 11.

0

13 3 12. 6

6

( 7)

13

13. 8 ( 9) 14.

10

2 11 15.

1

9 ( 2)

17

16. 1 3

9

17. 6 ( 5) 18.

11

11 7

2

19. 8 ( 8) 20.

1

6 3 21. 2

4

( 2)

16

22. 7 ( 5) 2 23.

3

4 8 ( 3) 24.

0

5 ( 5) 5

4

Simplify each expression. 25. 5a ( 3a) 26.

7y

2y

27.

9m

( 4m)

2a

28. 2z ( 4z)

5y

29. 8x ( 4x) 30.

13m

10p 5p

6z

31. 5b ( 2b) 32.

4x

4s 7s

5p

33. 2n ( 4n)

3b

34. 5a ( 6a) 4a 35.

3s

6x 3x ( 5x)

2n

36. 7z 2z ( 3z)

3a

Glencoe/McGraw-Hill

8x

63

6z

Algebra: Concepts and Applications

23

Key Terms

NAME

DATE

PERIOD

### Reading to Learn Mathematics

Adding Integers

additive inverses two numbers are additive inverses if their sum is 0 opposite additive inverse zero pair the result of positive algebra tiles paired with negative algebra tiles

### Reading the Lesson

1. Explain how to add integers with the same sign.

Add their absolute values. The result has the same sign as the integers.

2. Explain how to add integers with opposite signs.

Find the difference of their absolute values. The result has the same 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

3

5 4 3 2 1 0 1 2 3 4 5

b. 4

( 6)

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

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

The longer arrow represents the number with the greater absolute 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 the answer.

Write an equation for each situation. 5. a five-yard penalty and a 13-yard pass 6. gained 11 points and lost 18 points

11

### 7. a deposit of $25 and a withdrawal of $15

5 13 8 ( 18) 7 25 ( 15) 10

### Helping You Remember

8. Explain how you can remember the meaning of zero pair.

Sample answer: Since the sum of a number and its opposite is zero, when a positive tile is paired with a negative tile, the sum is zero.

Glencoe/McGraw-Hill

64

### Algebra: Concepts and Applications

23

NAME

DATE

PERIOD

Enrichment

Integer Magic

A magic triangle is a triangular arrangement of numbers in which the sum of the numbers along each side is the same number. For example, in the magic triangle shown at the right, the sum of the numbers along each side is 0. In each triangle, each of the integers from 4 to 4 appears exactly once. Complete the triangle so that the sum of the integers along each side is 3. 1.

3 3 0 1 4 2 2 4 1 3

2.

### Sample answers are given.

1

3.

4.

In these magic stars, the sum of the integers along each line of the star is 2. Complete each magic star using the integers from 6 to 5 exactly once. 5.

4

6.

5

Glencoe/McGraw-Hill

65

### Algebra: Concepts and Applications

24

NAME

DATE

PERIOD

Study Guide

Subtracting Integers

If the sum of two integers is 0, the numbers are opposites or additive inverses. Example 1: a. 3 is the opposite of 3 because 3 3 0 ( 17) 0

### b. 17 is the opposite of Use this rule to subtract integers.

17 because 17

To subtract an integer, add its opposite or additive inverse. Example 2: Find each difference. a. 5 5 b. 7 7 2 2 5 3 ( 1) ( 1) d 1 1 6 9 Find each difference. 1. 5 5. 16 8 3 ( 2) Subtracting 2 is the same as adding its opposite, 2. 1 Subtracting opposite, 1. 1, d ( 3) 3 7, and e 1 is the same as adding its 3. 3.

7 6 e if c 7 7

Example 3: Evaluate c c d e

### Replace c with 1, d with 7, and e with Write 7 ( 3) as 7 3. 1 7 6 6 3 9

2.

( 9) 1 ( 10) 20

3. 7. 0

8 10

10 10

4. 8. 0

( 5) 1 ( 18) 18

8 8

6. 10

### Simplify each expression. 9. 3x 9x

6x

10.

4y 1, y z z

( 6y) 2y 2, and z 5 1 z 7 4.

11. 2m

8m

( 2m)

4m

### Evaluate each expression if x 12. x 15. 9 y

13. y 16. x

14. z 17. 0

y y

( 2)

x 10

Glencoe/McGraw-Hill

66

### Algebra: Concepts and Applications

24

NAME

DATE

PERIOD

Skills Practice

Subtracting Integers

Find each difference. 1. 8 2 2. 12 4 3. 7 ( 2)

6

4. 9 4

8

5. 4 12 6.

5

4 ( 10)

13

7. 6 1 8.

8

5 8 9.

6

5 ( 5)

7

10. 8 8 11.

13

11 7

0

12. 8 ( 7)

16

13. 9 14 14.

18

3 ( 15) 15.

15

14 6

5

16. 3 9 17.

12

7 7

20

18. 13 14

11

14

### Evaluate each expression if a 19. a b

2, b c

3, c

1, and d

1. c

20. b

21. a

5

22. c d 23. a

2

b c

3

24. b d c

2

25. d b a

0

26. c a b 27. a

3

d b

4

Glencoe/McGraw-Hill

0

67

2

Algebra: Concepts and Applications

24

NAME

DATE

PERIOD

Practice

Subtracting Integers

Find each difference. 1. 9 3 2. 1 2 3. 4 ( 5)

6

4. 6 ( 1) 5.

3

7 ( 4)

9

6. 8 10

7

7. 2 5 8.

3

6 ( 7) 9. 2

2

8

7

10. 10 ( 2) 11.

1

4 6 12. 5

6

3

8

13. 8 ( 4) 14. 7

10

9 15.

2

9 ( 11)

4

16. 3 4 17. 6

2

( 5)

2

18. 6 5

11

### Evaluate each expression if a 19. b c 20. a

1, b b

5, c

2, and d 21. c

4. d

7

22. a c d 23. a

6

b c

2

24. a c d

1

25. b c d 26. b

8

c d 27. a

3

b c

3

Glencoe/McGraw-Hill

11

68

4

Algebra: Concepts and Applications

24

Key Terms

NAME

DATE

PERIOD

### Reading to Learn Mathematics

Subtracting Integers

additive inverses two numbers are additive inverses if their sum is 0 opposite additive inverse zero pair the result of positive algebra tiles paired with negative algebra tiles

### Reading the Lesson

1. Write each subtraction problem as an addition problem. a. 12 b. c. 0 d. e. f. 16 15 11 20 15 4 7

12 15 0

34 ( 4)

( 4) ( 7)

( 11) 20 15 16 ( 34) 4 18

( 18)

### 2. Describe how to find each difference. Then find each difference. a. 8 b. 5 c. 17 d. 8 11

### Add the opposite of 11 to 8; Add the opposite of

( 8) 14 19

8 to 5; 13

### Add the opposite of 14 to 17; 3 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 tile is to be subtracted from negative tiles, first add a zero pair. Then you can subtract one positive tile. Helping You Remember

4. Explain why knowing the rules for adding integers can help you to subtract integers.

Sample answer: Since subtraction is really adding the numbers additive inverse, the rules for addition also apply to subtraction.

Glencoe/McGraw-Hill

69

### Algebra: Concepts and Applications

24

Closure

NAME

DATE

PERIOD

Enrichment

A binary operation matches two numbers in a set to just one number. Addition is a binary operation on the set of whole numbers. It matches two numbers such as 4 and 5 to a single number, their sum. If the result of a binary operation is always a member of the original set, the set is said to be closed under the operation. For example, the set of whole numbers is not closed under subtraction because 3 6 is not a whole number.

Is each operation binary? Write yes or no. 1. the operation , where a b means to choose the lesser number from a and b yes 3. the operation sq, where sq(a) means to square the number a no 5. the operation , where a b means to match a and b to any number greater than either number no 2. the operation , where a b means to cube the sum of a and b yes 4. the operation exp, where exp(a, b) means to find the value of a b yes 6. the operation , where a b means to round the product of a and b up to the nearest 10 yes

Is each set closed under addition? Write yes or no. If your answer is no, give an example. 7. even numbers yes 9. multiples of 3 yes 11. prime numbers no; 3 8. odd numbers no; 3 10. multiples of 5 yes

10

### 12. nonprime numbers

no; 22

31

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

b yes

14. division: a

b no; 4

3 is not a

b)2 yes

whole number

15. exponentation: a yes 16. squaring the sum: (a

Glencoe/McGraw-Hill

70

### Algebra: Concepts and Applications

25

NAME

DATE

PERIOD

Study Guide

Multiplying Integers

Use these rules to multiply integers and to simplify expressions. 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. 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. 3 and b 5. Replace a with 3 and b with 3 3 9 Both factors are negative.

### Example 2: Evaluate 3ab if a 3ab 3(3)( 5) 9( 5) 45 Example 3: Simplify 12(4x)

5.

### 12(4x). ( 12 4)(x) 48x

Associative Property 12 4 48

Find each product. 1. 3(8) 24 5. 4( 1)( 5) 20 Evaluate each expression if a 8. 5c 2. ( 7)( 9) 63 3. 12( 1)

12

4.

6(5)

30

6. ( 8)( 8)( 2) 3, b

128

3.

7. 2( 5)(10)

100

2, and c

15

9. 2ab

12

10. abc 18

11. 3b

### Simplify each expression. 12. 3( 6x)

18x

13.

5( 7y) 35y 71

### 14. (2p)( 4q)

8pq

Glencoe/McGraw-Hill

### Algebra: Concepts and Applications

25

NAME

DATE

PERIOD

Skills Practice

Multiplying Integers

Find each product. 1. 3(12) 2. 4(7) 3. 8( 8)

36

4. 5( 9) 5.

28

2( 9) 6.

64

3( 10)

45

7. 0( 5) 8.

18

13( 4)

30

9. 4( 11)

0

10. 5(12)

52

11. 14(0) 12.

44

8(7)

60

13. 15( 4)

0

14. 9( 3) 15.

56

8(11)

60

16. ( 2)(4)( 3)

27

17. ( 4)( 5)( 1)

88

18. (3)(5)( 5)

24

Evaluate each expression if x 19. 3xy 20.

20

2 and y 2xy 4. 21.

75

5x

24

22. 7y

16

23. 8xy 24.

10

6xy

28

Simplify each expression. 25. 3(2a) 26.

64

48

4( 3c)

27.

5( 8b)

6a

28. (5c)( 7d)

12c

29. ( 8m)( 2n)

40b

30. ( 9s)(7t)

35cd

Glencoe/McGraw-Hill

16mn

72

63st

Algebra: Concepts and Applications

25

NAME

DATE

PERIOD

Practice

Multiplying Integers

Find each product. 1. 3( 7) 2. 2(8) 3. 4(5)

21

4. 7( 7) 5.

16

9(3)

20

6. 8( 6)

49

7. 6(2) 8.

27

5( 7)

48

9. 2( 8)

12

10. 10( 2)

35

11. 9( 8)

16

12. 12(0)

20

13. 4( 4)(2)

72

14. 7( 9)( 1) 15.

0

3(5)(2)

32

16. 3( 4)( 2)(2)

63

17. 6( 1)(2)(1) 18.

30

5( 3)( 2)( 1)

48

Evaluate each expression if a 19. 6b

12

3 and b 5.

30

20. 8a

21. 4ab

30

22. 3ab 23.

24

9a 24.

60

2ab

45

Simplify each expression. 25. 5( 5y) 26.

27

30

7( 3b)

27.

3(6n)

25y

28. (6a)( 2b)

21b

29. ( 4m)( 9n)

18n

30. ( 8x)(7y)

12ab

Glencoe/McGraw-Hill

36mn

73

56xy

Algebra: Concepts and Applications

25

Key Terms

NAME

DATE

PERIOD

### Reading to Learn Mathematics

Multiplying Integers

factors the numbers being multiplied product the result when two or more factors are multiplied together

### Reading the Lesson

1. Complete: If two numbers have different signs, the one number is positive and the other number is 2. Complete the table. Multiplication Example a. ( 4)(9) b. ( 2)( 13) c. 5( 8) d. 6(3) Are the signs of the numbers the same or different? Is the product positive or negative?

neg

### different same different same

### neg pos neg pos 2 3

3. Explain what the term additive inverse means. Then give an example.

### The product of any number and 2 ( 1) . 3 Helping You Remember

### 1 is its additive inverse;

4. Describe how you know that the product of 3 and you know that the product of 3 and 5 is negative.

### 5 is positive. Then describe how

Sample answer: The signs are the same; the signs are different.

Glencoe/McGraw-Hill

74

### Algebra: Concepts and Applications

25

NAME

DATE

PERIOD

Enrichment

### 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 16 0 4 2 1 23 1 2 1 1

### 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

Glencoe/McGraw-Hill

75

### Algebra: Concepts and Applications

8 4 2 1 1 1 0 1 1 1

2 2 2 2

16 8 4 2

26

NAME

DATE

PERIOD

Study Guide

Dividing Integers

Example 1: Use the multiplication problems at the right to find each quotient. a. 15 5 Since 3 5 15, 15 5 3. ( 5) 5 ( 5) 3. 3. 3. 3 5 3( 5) 3 5 3( 5) 15 15 15 15

### b. 15 ( 5) Since 3 ( 5) c. d. 15 5 Since 3 5 15 ( 5) Since 3 ( 5)

### 15, 15 15, 15, 15 15

Use these rules to divide integers. 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. Example 2: Evaluate

3r s 3r s 3 8 2 24 2

if r

8 and s

2. 2.

### Replace r with 8 and s with 3 8 24 24 ( 2) 12

### 12 Find each quotient. 1. 36 9 4 2. 63

( 7) 9

3. 25

( 1)

25

4.

60

12

5.

20 5

6.

18 3

7.

1 1

8.

56 8

### Evaluate each expression if k 9. 21 m

1, m

3, and n 11. m k

2.

10.

2n k

12.

m n

Glencoe/McGraw-Hill

76

### Algebra: Concepts and Applications

26

NAME

DATE

PERIOD

Skills Practice

Dividing Integers

Find each quotient. 1. 36 3 2. 15 5 3. 24 ( 8)

12

4. 45 ( 3)

3

5. 81 ( 9) 6.

3

28 4

15

7. 121 11 8.

9

144 ( 12)

7

9. 32 ( 4)

11

10. 64 ( 8) 11.

12

80 10

8

12. 48 ( 6)

8

13. 100 ( 25) 14.

8

20 5

8

15. 36 ( 9)

4

16. 56 ( 7) 17.

4

63 ( 9) 18.

4

32 ( 16)

8

19. 21 3 20.

7

18 2

2

21. 72 ( 8)

7

22.

35 7

9

23.

39 13

9

24.

125 5

5

Evaluate each expression if d 25. f g

3

3, f g 8, and g 4.

25

26. 8d

27. 4g

2

28.

gf 2

6

29.

df 12

2

30.

5f g

16

31.

9g d

2

32.

2f g

10

33.

4f g

12

Glencoe/McGraw-Hill

77

### Algebra: Concepts and Applications

26

NAME

DATE

PERIOD

Practice

Dividing Integers

Find each quotient. 1. 28 7 2. 33 3 3. 42 ( 6)

4

4. 81 ( 9)

11

5. 12 4

7

6. 72 ( 9)

9

7. 15 15 8.

3

30 5 9.

8

40 ( 8)

1

10. 56 ( 7) 11.

6

21 ( 3) 12.

5

64 8

8

13. 8 8 14.

7

22 ( 2)

8

15. 32 ( 8)

1

16. 54 ( 9)

11

17. 60 ( 6)

4

18. 63 9

6

19. 45 ( 9) 20.

10

60 5

7

21. 24 ( 3)

5

22.

12 6

12

23.

40 10

8

24.

45 9

2

Evaluate each expression if a 25. 48 a

4

4, b 3 9, and c 6.

26. b

27. 9c

12

28.

ab c

3

29.

bc 6

6

30.

3c b

6

31.

12a c

9

32.

4b a

2

33.

ac 6

8

Glencoe/McGraw-Hill

9

78

4

Algebra: Concepts and Applications

26

Key Terms

NAME

DATE

PERIOD

### Reading to Learn Mathematics

Dividing Integers

additive inverses two numbers are additive inverses if their sum is 0 opposite additive inverse zero pair the result of positive algebra tiles paired with negative algebra tiles

### Reading the Lesson

1. Write the math sentence 18 divided by 6 two different ways. Then find the quotient.

18

3;

18 6

2. Write negative or positive to describe each quotient. Explain your answer. Expression a. 15 b. 9 c. d. e. f.

35 7 78 13 13x 2 46 6y

### Negative or Positive? pos neg neg pos neg pos

Explanation The signs of two numbers are the same. The signs of the two numbers are different. The signs of the two numbers are different. The signs of two numbers are the same. The signs of the two numbers are different. The signs of two numbers are the same.

12 10

### Helping You Remember

3. 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 the same for multiplication and division. If the signs of the factors are the same, the answer will be positive. If the signs of the factors are different, the answer will be negative.

Glencoe/McGraw-Hill

79

### Algebra: Concepts and Applications

26

NAME

DATE

PERIOD

Enrichment

### 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 s d m y 2m [(3m 3) 5] y

y 4 y 100 y 400

sum day of the month, using numbers from 131 month, beginning with March is 3, April is 4, and so on, up to December is 12, January is 13, and February is 14 year except for dates in January or February when the previous year is used 1984;

For example, for February 13, 1985, d 13, m 14, and y 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 the quotient. 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 s 3 [ 2(10) ] [ (3 3, m 10 6 3) 10, and y 5] 1854.

1854 4 1854 100 1854 400

1854 1854

2 2

### 3 20 2334 s 7 2334 7 333 R3

463

18

Since the remainder is 3, the day of the week was Tuesday. Solve. 1. See if the formula works for todays 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 13 s 4 4 2(4) 8 2(7) 14 3 [(3 4 [(3 4 3) 501 3) 444 5] 5] 20 2006 4 2

2006 4 2006 100 2006 400

2 Thursday

2006 7 1776

2518; 2518

1776 100

359 R5 2

### 4. On what day of the week was July 4, 1776?

1776 17 4

1776 4 1776 400

2231; 2231

318 R5

Thursday

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

80

NAME

DATE

PERIOD

### Chapter 2 Test, Form 1A

Write the letter for the correct answer in the blank at the right of each problem. 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 number line at the right. A. 4 B. 2 C. 2 D. 3

F C D

1 2

1.

E

3

4 3 2 1 0

2.

### 3. Order 8, 6, 7, 7, and 0 from greatest to least. A. 8, 7, 0, 6, 7 B. 8, 7, 7, 6, 0 C. 7, 6, 0, 7, 8 D. 7, 6, 0, 8, 7 4. Evaluate A. 21 |14| | 7|. B. 7 C. 7 D. 21

y

B C

3. 4.

For Questions 56, 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. I B. II C. No quadrant; it lies on the y-axis. D. No quadrant; it lies on the x-axis.

O

A

5.

6.

7. Which of the following points is located in Quadrant III? A. ( 2, 4) B. ( 6, 0) C. ( 5, 3) D. (1, 8. The graph of P(x, y) satisfies the condition that y quadrant(s) could point P be located? A. III only B. IV only C. II or III

2)

7.

0. In which D. III or IV 8.

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: A. 42 18 ( 24). B. 32 ( 58) C. 6 k? D. 14 D. 7z D. 6

### 9. 10. 11. 12.

### 11. What is the value of k if 40 A. 130 B. 50 12. Simplify 15z A. 27z

32 C. 16 C. 63z

### ( 23z) 25z. B. 17z

Glencoe/McGraw-Hill

81

### Algebra: Concepts and Applications

NAME

DATE

PERIOD

### Chapter 2 Test, Form 1A (continued)

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 many points 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 A. 17 B. 7 15. Evaluate 20 A. 43 16. Simplify A. d 14d a b if a B. 33 8d B. ( 5). C. 7 18 and b C. 5. 3 D. 17

13.

14.

D.

15.

( 21d ). 43d

C.

15d

D. d

16.

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 your rent? A. $87 B. $177 C. $187 D. $737 18. Find the product: 2(3)( 1)(5)( 2). A. 60 B. 30 C. 30 19. Evaluate A. 31 2xy 3z if x B. 1 8, y 1, and z C. 1 2? C. 60 5. D. 31

17.

D. 60

18.

19.

### 20. What is the product of 5, A. 70 B. 60 21. Simplify 2( 3r)(5s). A. 6r 5s B. 11r

6, and

D. 70

20.

C. 25rs

D. 30rs

21.

22. Find the quotient: 125 ( 5). A. 120 B. 24 23. Find the value of s if 84 A. 72 B. 7 24. Evaluate A. 7

mp 3 n

C. 24 s. C. 7 3.

D. 25

22.

12

D.

23.

if m B. 3

5, n

6, and p C. 3

D. 7

24.

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 A.

25.

96 6

### ( 2)( 9). B. 0 C. 2 D. 34 Bonus

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

82

NAME

DATE

PERIOD

### Chapter 2 Test, Form 1B

Write the letter for the correct answer in the blank at the right of each problem. 1. Name the coordinate of Z on the number line at the right. A. 3 B. 2 C. 1 D. 3 2. Order 4, 2, 1, 3, and A. 1, 2, 3, 4, 2 C. 4, 3, 2, 1, 2

Z

4 3 2 1 0

X Y

1 2 3

1.

### 2 from least to greatest. B. 2, 1, 2, 3, D. 2, 1, 2, 3,

4 4

2.

### 3. Which of the following sentences is true? A. |2| | 2| B. 4 C. 6 | 7| D. | 1| 4. Evaluate |5| A. 7 | 2|. B. 3

3 1

3.

C.

D.

4.

5. Which of the following points is located in Quadrant II? A. ( 4, 0) B. ( 2, 7) C. (5, 1) D. ( 3, For Questions 67, 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. II C. III D. IV 8. The graph of P(x, y) satisfies the conditions that x which quadrant is point P located? A. I B. II C. III 0 and y D. IV

P

4)

y

Q

5.

O

R

6.

7. 0. In 8.

9. Which ordered pair names a point that lies on the x-axis and to the left of the y-axis? A. (0, 3) B. (4, 0) C. (0, 0) D. ( 1, 0) 10. What is the value of m if m A. 40 B. 24 11. Simplify A. 2k 4k ( 2k) 8k. B. 2k 50 28. B. 32 13 ( 27)? C. 14

9.

D. 40

10.

C. 14k

D. 6k

11.

### 12. Find the sum: A. 78

C.

22

D. 78

12.

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

83

NAME

DATE

PERIOD

### Chapter 2 Test, Form 1B (continued)

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 golfers overall score for the four days? A. 1 B. 1 C. 2 D. 4 14. Evaluate y A. 20 x if x 12 and y B. 4 8. C. 4

13.

D. 20

14.

15. On January 13, the low temperature was 12F. The next day, the low temperature dropped by 25. What was the low temperature on January 14? A. 37F B. 25F C. 13F D. 37F 16. Find the difference: 9 A. 45 B. 14 17. Simplify A. 3p 18. Evaluate A. 7 19. Simplify A. 20t 6p ( 9p). B. 3p n if B. 4 1, m 5. C. 4 D. 14

15.

16.

C.

15p 3.

D. 15p

17.

2 m

2, and n C. 1

D. 7

18.

### 5( 4t). B. 9t C. t D. 20t 19.

20. Find the product: 8( 6). A. 56 B. 48 21. What is the value of n if n A. 54 B. 36 22. Evaluate A. 4

fg 2

C. 14 ( 6)(3)( 3)? C. 36 2. C. 1

D. 48

20.

D. 54

21.

if f

4 and g B. 3

D.

22.

### 23. Find the quotient: 54 ( 3). A. 18 B. 16 24. Find the value of b if b A. 6 B. 4 72

C. 16 ( 18). C. 4

D. 18

23.

D. 6

24.

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 A.

25.

9 3

( 4)(2). B. 5 C. 5 D. 11 Bonus

Algebra: Concepts and Applications

11

Glencoe/McGraw-Hill

84

NAME

DATE

PERIOD

### Chapter 2 Test, Form 2A

1, 0} on a number line. or to make a true 2. 3. 4. |0|.

y

R P

### 1. Graph the set of numbers {3,

1.

1 0

### For Questions 24, replace each with sentence. 2. | 10| 11 3. 4. 6 3 8 | 2| | 6|

5. Evaluate

5.

For Questions 69, 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 1113, find each sum. 11. 18 12. 36 ( 27) ( 8) ( 36) 46 20 ( 12)

O

T

6.

x

S

7. 8. 9. 10.

### 11. 12. 13.

13. 50

14. During one week the Dow Jones Industrial average, the most commonly 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.

14. 15.

Find each difference. 16. 22 17. 18. 8 30 ( 9) ( 12) ( 8) ( 18) ( 25) 75 16. 17. 18. 19.

19. 45

Glencoe/McGraw-Hill

85

### Algebra: Concepts and Applications

2

20. Simplify

NAME

DATE

PERIOD

### Chapter 2 Test, Form 2A (continued)

28k ( 18k) 14k. 20.

21. What is the difference in elevation between the highest point in California, Mount Whitney, which towers 4421 meters above sea level, and the lowest point in California, Death Valley, which lies 86 meters below sea level? For Questions 2224, find each product. 22. 2( 3)( 3)

21.

### 22. 23. 24.

### 23. 4( 2)( 1)(5)( 2) 24. 12( 2)( 1)

25. A small company buys 8 chairs, each at a price of $40 less than the regular price, and 6 lamps, each at a price of $15 less than the regular price. What number describes the price the company pays in all compared to the regular price? 26. Evaluate 3xz 8y if x 4, y 1, and z 8, 32, 2. 128, .

### 25. 26. 27.

27. Find the next term in the pattern 2, For Questions 2830, find each quotient. 28. 29. 30.

57 3

### 28. ( 15) 29.

120

100 4

30.

s2 s1

31. The acceleration a of an object (in feet per second squared) is given by a

t

### , where t is the time in seconds, s1 is the

speed at the beginning of the time, and s2 is the speed at the end of the time. What is the acceleration of a car that brakes from a speed of 114 feet per second to a speed of 18 feet per second in 6 seconds? 32. Evaluate

z y x

31. 32.

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 value for each of these five years?

33.

Bonus From Sunday to Monday, the minimum daily humidity drops 3%. Over the next three days, it rises 8%, rises 16%, and then drops 21%. What is the average daily change when you compare the minimum humidity on Thursday Bonus to the minimum humidity on Sunday?

Glencoe/McGraw-Hill

86

### Algebra: Concepts and Applications

2

1. 5 7

NAME

DATE

PERIOD

### Chapter 2 Test, Form 2B

or to make a true 1. 2. 3. | 8|. 4. 5.

### For Questions 13, replace each with sentence.

2. 3 | 4| 3. | 2| 1

4. Evaluate | 4|

5. Graph the set of numbers { 2, 1, 0} on a number line. For Questions 69, use the coordinate plane at the right. 6. In what quadrant is point B located?

B D

3 2 1 0

y

A

6.

O

C

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, 11. Evaluate 4 b |c| if b

7. 8. 9.

2) located? 2.

10. 11.

7 and c

For Questions 1214, find each sum. 12. 6 13. 14. 21 12 ( 3) 9 31 12. 13. 14.

( 15) 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 many feet does the reservoir rise or fall overall for the week? For Questions 1619, find each difference. 16. 9 17. 18. 19.

15.

( 5) 15 6 11 ( 32) ( 5) ( 28) 3

### 16. 17. 18. 19.

Glencoe/McGraw-Hill

87

### Algebra: Concepts and Applications

2

20. Simplify 8b

NAME

DATE

PERIOD

### Chapter 2 Test, Form 2B (continued)

5b ( 3b). 20.

21. The temperature dropped 42F overnight from yesterdays high temperature of 25F. What is the temperature this morning? 22. Find the next term in the pattern 3, 23. Evaluate 2x 3y when x 5 and y 15, 75, . 4.

### 21. 22. 23.

For Questions 2426, find each product. 24. 4(6)( 2) 25. 2(3)( 1)(5) 24. 25. 26.

26. 3( 3)( 2)( 1) 27. You and several friends go together to buy detergent from a warehouse store. By buying 12 economy boxes, you get a price that is $2 less per box than the regular price. What number describes the price you pay for the total purchase compared to the regular price? 28. Evaluate

a b c

27. 28.

if a

16, b

4, and c

8.

### For Questions 2931, find each quotient. 29. 30. 31. 42

150 25 64 4

( 3)

### 29. 30. 31.

s2 t s1

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 the end of the time. What is the acceleration of a sled testing child car seats that goes from a speed of 88 feet per second to a speed of 0 feet per second in 2 seconds? 33. Over the past three years, the zoos attendance figures have decreased from 185,000 to 176,000. What is the average change in attendance for each of the last three years?

32.

33.

Bonus From Sunday to Monday, the maximum daily temperature in a small pond rises 1F. Over the next three days, it rises 4F, falls 1F, and then falls 8F. What is the average daily change when you compare the maximum temperature on Thursday to the maximum temperature on Sunday? Bonus

Glencoe/McGraw-Hill

88

### Algebra: Concepts and Applications

NAME

DATE

PERIOD

### Chapter 2 Extended Response Assessment

Instructions: Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and to justify your answers. You may show your solution in more than 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.

A C

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 original triangle. 2. Now we will investigate more generally what happens to points when their x- and/or y-coordinates are multiplied by a negative number. a. Pick a negative integer n. Fill out the table below, in which you will choose one point (a, b) in each quadrant, and then multiply one or both coordinates by n.

Quadrant of (a, b) Coordinates of (a, b) Coord. and quad. of (na, b) Coord. and quad. of (a, nb) Coord. and quad. of (na, nb) I II III

O

B

IV

b. How does multiplying one or both coordinates of a point by a negative number change the quadrant in which a point lies? 3. In an investment club, members pool their money and their knowledge to invest in the stocks of various companies. Members share any profits or losses equally. a. One club charges each member a $250 initial investment and monthly investments of $30. In its first year, the 15-member club loses $1320. In its second year, the club makes a $990 profit. Write and evaluate an expression to find each members net gain or loss after two years. b. Another club charges each member a $150 initial investment and monthly investments of $20. In its first year, the 25-member club loses $1750. In its second year, the club makes a $1200 profit. Write and evaluate an expression to find each members net gain or loss after two years. c. Compare the results of the two investment clubs.

Glencoe/McGraw-Hill

89

### Algebra: Concepts and Applications

2

1. C 2. D

NAME

DATE

PERIOD

### Chapter 2 Mid-Chapter Test

(Lessons 21 through 23)

B C A

1 2 3

For Questions 12, name the coordinate of each point on the number line at the right.

D

4

4 3 2 1 0

### 1. 2. or to make a true sentence. 3. | 2| 4. 5. 6.

### Replace each with 3. 8 2 4. | 3| 5. 4 6. 5

6 | 7|

Order each set of numbers from greatest to least. 7. 8. 12, 10, 4, 6, 5, 8, 0, 3 3, 2, 5 7. 8. 911.

y

Graph each point on the same coordinate plane. 9. P(3, 0) 10. Q( 2, 11. R(4, 1) 3)

For Questions 1215, 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 1618, find each sum. 16. 9 18 ( 35) 4 ( 27) 15 ( 9x) y 6x. 4 and z 8.

C

y

D B

12.

O

A E x

### 13. 14. 15.

### 16. 17. 18. 19. 20.

Algebra: Concepts and Applications

17. 84 18. 8

( 9)

### 19. Simplify 12x 20. Evaluate

11

z if y

Glencoe/McGraw-Hill

90

NAME

DATE

PERIOD

Chapter 2 Quiz A

(Lessons 21 through 22)

2, 0} on a number line. or to make a true 2. 3. | 2|. 4.

y

### 1. Graph the set of numbers {3,

1.

2 1 0

### For Questions 23, replace each with sentence. 2. | 12| 3. 8 10

| 7| | 6|

4. Evaluate

For Questions 57, graph each point on the same coordinate plane. 5. A(2, 3) 57.

O

6. B(3, 4) 7. C( 3, 4) 1) located? 8.

### 8. In what quadrant is the point T(4,

2

1. Find the sum: 2. Evaluate a

NAME

DATE

PERIOD

Chapter 2 Quiz B

(Lessons 23 through 26)

11 8 ( 7). 16 and b 28. 1. 2. 3.

( 12) if a

### 3. Find the difference: 120

( 54).

4. Write and evaluate an expression to find the difference (in the number of floors) between the 21st story of a building and the parking level three stories below the ground floor. 5. Find the product: 2(7)( 3)( 1). 1 and t 90 8. ( 15)?

4. 5. 6. 7.

### 6. Evaluate ( 2s)(5t) if s 7. What is the value of b if b

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 for each of the last four years?

8.

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

91

NAME

DATE

PERIOD

### Chapter 2 Cumulative Review

1. 2.

1. Write an equation for the sentence below. (Lesson 11) Six less than four times a is the same as eleven more than the product of b and c. 2. Find the value of 6 2(7 4) 6. (Lesson 12)

3. 3. Name the property shown by the statement below. (Lesson 13) 8 6 (5 11) 8 (6 5) 11 4. Simplify 6(2x 3) 4x. (Lesson 14) 5. 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 apples does she buy? (Lesson 15) 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 16)

Goals Frequency 0 2 1 3 2 4 3 1 4 1

4.

6.

7. 7. What kind of a graph or plot is best to use to display how a quantity changes over time? (Lesson 17) 8. Order 11, 25, 36, (Lesson 21) 64, 2, and 3 from least to greatest. 8.

For Questions 910, refer to the coordinate plane at the right. (Lesson 22) 9. Write the ordered pair that names point W. 10. Name the quadrant in which point V is located. 11. Find the sum: 12. Evaluate a (Lesson 24) 22 b ( 31). (Lesson 23) c if a 12, b 22, and c

S

y

U T V

9.

x

### 10. 11. 12.

8.

13. At 20F with a 5-mile-per-hour wind, the windchill factor is 16F. At this temperature with a 45-mile-per-hour wind, the windchill factor drops 38F. What is the windchill factor at 20F with a 45-mile-per-hour wind? (Lesson 24) 14. Find the product of 15. Evaluate

3xy 4

### 13. 14. 15. 16.

2, 3,

### 1, and 8. (Lesson 25) 2. (Lesson 26)

if x

6 and y

### 16. Find the quotient: ( 126)

### ( 9). (Lesson 26)

Glencoe/McGraw-Hill

92

### Algebra: Concepts and Applications

NAME

DATE

PERIOD

### Chapter 2 Standardized Test Practice

(Chapters 12)

Write the letter for the correct answer in the blank at the right of the problem. 1. Write an equation for the sentence below. Three less than the quotient of b and 5 equals 4 more than twice b. A. 5 C. 5

b b

3 3

6b 2b 4

B.

b 5

3 b 5

4 4

2b 2b 1.

D. 3

2. Annie buys a pair of pants for $25 and several T-shirts for $8 each. Write an expression for her total cost if she buys n T-shirts. A. n(8 25) B. 25 8n 5 2 C. 25 3. C. 14 10

8 n

D. 25n

2. 3.

### 3. Find the value of 14 2 A. 1 B. 2

D. 21 15.

4. Name the property of equality shown by the statement below. A. B. C. D. If 2b 10 5x and 5x 15, then 2b Reflexive Property of Equality Transitive Property of Equality Symmetric Property of Equality Multiplication Property of Equality 6 (5 3) 6 (3 5) Commutative Property of Addition Commutative Property of Multiplication Associative Property of Addition Associative Property of Multiplication 2a) 8(a B. 2a 6). 60 C. 60 2a D. 50 14a

4.

### 5. Name the property shown by the statement below. A. B. C. D.

5. 6. 7.

### 6. Simplify 3(4 A. 20 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. 12 C. 15 D. 16

Shoe Size Frequency 6 4 7 1 8 7 9 5 10 3

8.

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 fewer than 25 times? A. 4 B. 5 C. 7 D. 8

Stem 1 2 3

Leaf 6 9 0 3 5 6 1 2 2 4 8 3 | 1 31

9.

Glencoe/McGraw-Hill

93

### Algebra: Concepts and Applications

NAME

DATE

PERIOD

### Chapter 2 Standardized Test Practice (Chapters 12) (continued)

10. You want to show how the number of computers per 100 students has changed in your state over the past 20 years. The most appropriate way to display your data would be a A. 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| C. 3 5 D. | 5| 3 12. Evaluate | 8| A. 17 |9|. B. 1

10.

|3| 11.

C. 1

D. 17

y

E A

12.

For Questions 1314, refer to the coordinate plane at 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. II C. III D. IV 15. Find the sum: A. 16 16. Simplify A. 2b 17. Evaluate A. 22 8b 15 ( 11) B. 6 20. C. 4b. C. 6 D.

O

D

x

C

13.

14.

16

15.

### ( 3b) ( 5b) B. 2b x B. y when x 10

10b 4.

D.

20b

16.

12

6 and y C. 2

D. 2

17.

18. Find the value of p if 2(3)( 1)( 5) p. A. 30 B. 11 C. 30 19. What is the value of k if 216 A. 24 B. 22 9 k? C. 22

D. 60

18.

D. 24

19.

20. Over seven years, the number of books in a school library increased from 1160 to 2000. What was the average change in the number of books in the library for each of the seven years? A. 115 B. 120 C. 134 D. 840

20.

Glencoe/McGraw-Hill

94

### Algebra: Concepts and Applications

### Preparing for Standardized Tests Answer Sheet

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

/

A A A A A A A A

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

1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

0 1 2 3 4 5 6 7 8 9

### 10. Show your work.

Glencoe/McGraw-Hill

A1

### Algebra: Concepts and Applications

21 21

Skills Practice

Graphing Integers on a Number Line

Name the coordinate of each point.

R

5 0 1 2 3 4 5 4 3 2 1

### NAME NAME DATE PERIOD

DATE

PERIOD

Study Guide

### Graphing Integers on a Number Line

S T U V W

Glencoe/McGraw-Hill

positive integers

The numbers displayed on the number line below belong to the set of integers. The arrows at both ends of the number line indicate that the numbers continue indefinitely in both directions. Notice that the integers are equally spaced. 1. S 2. U 5. W 3. T 6. V 4. R

1 2 3 4 5

negative integers

3 5 4 1

5 4 3 2 1 0

integers

### Graph each set of numbers on a number line. 7. { 2, 0, 3}

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

Use dots to graph numbers on a number line. You can label the dots with capital letters. The coordinate of B is 3 and the coordinate of D is 0. 9. {2, 4,

5 0 1 2 3 4 4 3 2 1 5

8. { 5,

4

3,

3

1}

2 1 0 1 2 3 4 5

B C

D E

5 4 3 2 1 0

4}

10. { 1, 3, 5}

5 4 3 2 1 0 1 2 3 4 5

Answers

Because 3 is to the right of 3 on the number line, 3 3. And because 5 is to the left of 1, 5 1. Because 3 and 3 are the same distance from 0, they have the same absolute value, 3. Use two vertical lines to represent absolute value. 11. { 4,

5 0 1 4 3 2 1 2 3

2, 2}

4 5

12. { 3,

5

1, 1, 3}

4 3 2 1 0 1 2 3 4 5

A2

The absolute value of 3 is 3. The absolute value of 3 is 3. Write | 12| 16.

B D E

1 2 3 4 5 6

3 units

3 units

|3| 3 | 3| 3 or 7 5 4 3 2

4 3 2 1 0

in each blank to make a true sentence. 14. 4 17. 20. 0 1 2 2 9 15. 18. 21. 3 5 6 0 8 3

### Example: 12 and |10| 10 13. 2

(Lesson 2-1)

### Evaluate | 12| |10|. | 12| |10| 12 10 22

F G

### Name the coordinate of each point. 3. G 5

5 4 3 2 1 0

19.

1. B

2. D

### Evaluate each expression. 22. |4|

### Graph each set of numbers on a number line. 5. { 1, 0, 3}

2 1 0 1 2 3 4

23. | 5|

4. { 3, 2, 4}

24. | 8| 8

25. |10|

10

Write 8 8. | 1| 0

or

in each blank to make a true sentence. 26. |3| 11. | 20| |10| 10

Glencoe/McGraw-Hill

6.

7.

| 2|

27. | 7|

| 12|

19

### Evaluate each expression.

9. |9| 9 51

10. | 15| 15

### Algebra: Concepts and Applications

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

52

### Algebra: Concepts and Applications

21 21

Reading to Learn Mathematics

Graphing Integers on a Number Line Key Terms

### NAME NAME DATE PERIOD

DATE

PERIOD

Practice

### Graphing Integers on a Number Line

### Name the coordinate of each point.

E C

Glencoe/McGraw-Hill

3. C

5 4 3 2 1 0

1. A

### 4 2 Reading the Lesson

1,

1 2 3 4 5

2. B 3 6. F 1

4. D 5

5. E

absolute value the distance a number is from 0 on a number line coordinate (co OR di net) the number that corresponds to a point on a number line graph to plot points named by numbers on a number line number line a line with equal distances marked off to represent numbers

### Graph each set of numbers on a number line. 8. {4,

5 4 3 2 1 0

7. { 5, 0, 2}

a. What do the arrowheads on each end of the number line mean?

2}

### 1. Refer to the number line.

5 4 3 2 1 0

9. {3,

5 4 3 2 1 0 1 2 3 4 5

4,

3}

10. { 2, 5, 1}

The line and the set of numbers continue infinitely in each direction.

b. What is the absolute value of 3? What is the absolute value of 3? Explain.

5 4 3 2 1 0 1 2 3 4 5

5 4 3 2 1 0

Answers

11. {2,

5 4 3 2 1 0 1 2 3 4 5

5, 0}

12. { 4, 3,

2, 4}

3, 3; line.

### 3 and 3 are both 3 units away from zero on the number

A3

1 5 2 21. 5 6 18. 7 3 15. 2 2 23. |6| 6 25. |9| | 8| 1 27. | 8| |11| 19 53

Algebra: Concepts and Applications Glencoe/McGraw-Hill

5 4 3 2 1 0

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.

Write

or

### in each blank to make a true sentence.

Whole Numbers

(Lesson 2-1)

13. 7

14. 0

true

c. All whole numbers are natural numbers. d. All natural numbers are whole numbers. e. All whole numbers are positive numbers. f. All integers are natural numbers.

Integers

16. 6

17.

### false true false false

g. Whole numbers are a subset of natural numbers. h. Natural numbers are a subset of integers.

Natural Numbers

19.

20.

11

### Evaluate each expression.

22. | 4| 4

### false true Helping You Remember

3. 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 of absolute value.

24. | 3|

|1| 4

26. | 7|

| 2| 5

Sample answer: On a football field, the distance from each goal line to the 50-yard line is 50 yards.

54

Algebra: Concepts and Applications

### Algebra: Concepts and Applications

Glencoe/McGraw-Hill

21

Study Guide

The Coordinate Plane

Quadrant II 4 3 2 1 4 3 2 1 O 1 2 3 4 Quadrant III

NAME

DATE

PERIOD

Enrichment

22

y Quadrant I S

1 2 3 4 x

NAME

DATE

PERIOD

Venn Diagrams

Glencoe/McGraw-Hill

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 four quadrants. 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.

Quadrant IV

A type of drawing called a Venn diagram can be useful in explaining conditional statements. A Venn diagram uses circles to represent sets of objects.

Consider the statement All rabbits have long ears. To make a Venn diagram for this statement, a large circle is drawn to represent all animals with long ears. Then a smaller circle is drawn inside the first to represent all rabbits. The Venn diagram shows that every rabbit is included in the group of long-eared animals.

### animals with long ears

### The set of rabbits is called a subset of the set of long-eared animals.

The point at which the axes meet has coordinates (0, 0) and is called the origin.

Quadrant II

rabbits

Answers

y Quadrant I

The Venn diagram can also explain how to write the statement, All rabbits have long ears, in if-then form. Every rabbit is in the group of long-eared animals, so if an animal is a rabbit, then it has long ears.

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.

4 3 2 1 1 2 3 4 x 4 3 2 1 O 1 2 3 M 4 Quadrant III

### (Lessons 2-1 and 2-2)

A4

2. All rational numbers are real.

real numbers rational numbers

For each statement, draw a Venn diagram. The write the sentence in if-then form.

### 1. Every dog has long hair.

### animals with long hair

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.

Quadrant IV

dogs

Write the ordered pair that names each point. 1. P (1, 3) 3. R (0, 2) 2. Q ( 4, 4. T ( 4, 0)

3)

T

4 P 3 2 R 1 1 2 3 4 x 4 3 2 1 O 1 2 3 Q 4

### If an animal is a dog, then it has long hair.

4. Staff members are allowed in the faculty lounge.

people in the faculty lounge

### If a number is rational, then it is real.

### 3. People who live in Iowa like corn.

### people who like corn

Graph each point on the coordinate plane. Name the quadrant, if any, in which each point is located. 5. A(5, 1) IV 7. C( 3, 1) II 9. E(3, 3) I 6. B( 3, 0) none 8. D(0, 1) none 10. F( 1, 2) III

C B F O

y D

### people who live in Iowa staff members

x A

### If a person lives in Iowa, then the person likes corn.

If a person is a staff member, then the person is allowed in the faculty lounge.

55

Algebra: Concepts and Applications Glencoe/McGraw-Hill

### Algebra: Concepts and Applications

Glencoe/McGraw-Hill

56

### Algebra: Concepts and Applications

22 22

Practice

The Coordinate Plane

Write the ordered pair that names each point.

A E H

y

### NAME NAME DATE PERIOD

DATE

PERIOD

Skills Practice

### The Coordinate Plane

y

### Write the ordered pair that names each point.

Glencoe/McGraw-Hill

( 3,

Q

4

1. L ( 4, 0) 1. A ( 3, 4) 3. C ( 4,

R L

4 2

2. M

V

2

1)

2. B (5, 2) 4. D (2, 6. F (1, 0) 8. H ( 2, 5) 10. K (5,

3. N ( 1,

3) 3) 4)

T P

2 4 x

4. P (0, 0) 5. E ( 1, 1) 7. G (0,

4

O

C J G

F D

x

K

5. Q

M

2 U

( 2, 4)

S N

6. R (2, 1)

7. S (2,

1) 2) 4) 1)

9. J ( 2,

8. T

(5, 0)

9. U (0,

2)

10. V

(0, 3)

### Graph each point on the coordinate plane. 4)

A E H

2 4

### Graph each point on the coordinate plane.

y

### 11. A( 2, 4) 11. K(0, 3) 13. M(4, 4)

F

4 2 2 2 4 x

12. B(0,

I

12. L( 2, 3) 14. N( 3, 0)

R L T N

O

M S

x

Answers

A5

1)

J

### 13. C(5, 15. P( 4, 17. R( 5, 5) 19. T(2, 1) 1)

3)

14. D( 2,

15. E(1, 4)

G D C

4

16. F(4, 0)

### 16. Q(1, 18. S(3, 2) 20. W( 1,

2)

P W K

17. G( 4,

B

(Lesson 2-2)

1)

18. H(3, 3)

19. I( 4, 3)

20. J( 5, 0)

4)

Name the quadrant in which each point is located. 22. (3, 4) 24. (4, 26. ( 1, 28. ( 3, 5) 30. (8, 4) 1) 3)

### Name the quadrant in which each point is located.

21. ( 2,

2)

III IV III II IV

21. (1, 9) I 23. (0, 25. (5, 27. ( 1, 1) none 3) IV 1) III 29. ( 8, 4) II

22. ( 2,

### 7) III 24. ( 4, 6) II 26. ( 3, 0) none 28. (6, 30. ( 9, 5) IV 2) III

23. ( 4, 3)

II

25. (0,

2)

none

27. (4,

1)

IV

29. ( 3, 0)

none

### Algebra: Concepts and Applications

57

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

Glencoe/McGraw-Hill

58

### Algebra: Concepts and Applications

NAME

DATE

PERIOD

22

Enrichment

Points and Lines on a Matrix

A matrix is a rectangular array of rows and columns. Points and lines on a matrix are not defined in the same way as in Euclidean geometry. A point on a matrix is a dot, which can be small 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 other points. Three examples of lines are shown at the upper right. The broad line can be thought of as a single line or as two narrow 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 shows how a dot-matrix printer might print the letter P.

### Reading to Learn Mathematics

22

NAME

DATE

PERIOD

### The Coordinate plane

Glencoe/McGraw-Hill

Sample answers are given.

Draw points on each matrix to create the given figures. 1. Draw two intersecting lines that have four points in common. 2. Draw two lines that cross but have no common points.

Key Terms

coordinate plane the plane containing the x- and y-axes coordinate system the grid formed by the intersection of two perpendicular number lines that meet at their zero points ordered pair a pair of numbers used to locate any point on a coordinate plane quadrant one of the four regions into which the x- and y-axes separate the coordinate plane x-axis the horizontal number line on a coordinate plane y-axis the vertical number line on a coordinate plane x-coordinate the first number in a coordinate pair y-coordinate the second number in a coordinate pair

### Reading the Lesson

### 1. Identify each part of the coordinate system.

Answers

y axis

A6

4. Make the capital letter O so that it extends to each side of the matrix. 3. Make the number 0 (zero) so that it extends to the top and bottom sides of the matrix. 5. Using separate grid paper, make dot designs for several other letters. Which were the easiest and which were the most difficult? See students work.

Glencoe/McGraw-Hill

origin

x axis

(Lesson 2-2)

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 the second 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 coordinate plane.

Start at the origin, move two units to the left and then move up three units.

### 3. What does the term quadrant mean?

### Sample answer: It is one of four regions in the coordinate plane.

### Helping You Remember

### 4. Describe a method to remember how to write an ordered pair.

Sample answer: Since x comes before y in the alphabet, the xcoordinate is written first in an ordered pair.

59

Algebra: Concepts and Applications

### Algebra: Concepts and Applications

Glencoe/McGraw-Hill

60

### Algebra: Concepts and Applications

NAME

DATE

PERIOD

23

Skills Practice

Adding Integers

Find each sum. 1. 2 7 2. 3 ( 2) 3. 4 1

Study Guide

23

NAME

DATE

PERIOD

Adding Integers

Glencoe/McGraw-Hill

1 4 2 3 2 1 0 1 ( 1) 3 2 2

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.

9

4. 3 ( 9) 5. 2 12

5

6.

3

1 ( 6)

1 2

2 1

3 3

6

7. 10 ( 8) 8. 9 4

10

9. 3

7

( 3)

Both integers are positive. First move 2 units right from 0. Then move 1 more unit right.

Both integers are negative. First move 2 units left from 0. Then move 1 more unit left.

2

10. 5 ( 5) 11. 8 ( 9)

5

12.

0

7 4

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.

10

1

1

2 14. 12 10 15.

3

8 ( 5)

1 2 2 2 1 0 1 2 3 ( 1) 1 4

13.

0

16. 14 8

2

17. 15 ( 8) 18. 3

13

( 11)

Answers

2 1 2 1

A7

6

Move 2 units right, then 1 unit left. 19. 9 ( 7)

7

20. 6 ( 9) 21.

8

14 15

### Move 2 units left, then 1 unit right.

Use the following rules to add two integers and to simplify expressions.

16

22. 10 6 ( 4)

3

23. 13 ( 14) 1 24.

1

4 ( 8) 5

(Lesson 2-3)

Rule 7 10 8x 11 8 ( 2) 5x ( 3x) 4

Examples

To add integers with the same sign, add their absolute values. Give the result the same sign as the integers. 9 1

8

Simplify each expression. 25. 4c 8c 26.

5a

( 9a)

27.

8d

3d

To add integers with different signs, subtract their absolute values. Give the result the same sign as the integer with the greater absolute value.

( 6) 3 ( 5) 4 2x 9x 7x 3y ( 4y) y

4c

28. 7x 3x

14a

29. 6y ( 3y) 30.

5d

7t 4t

### Find each sum.

10x 17

3. 12 20 4 7. 12 5 4. ( 8) ( 8) 4 16 5

3y 11

31. 12s ( 4s) 32. 5t ( 13t)

3t

33. 15h ( 4h)

1. 5

8 13

2.

( 9)

5. 5

( 8)

( 5)

6.

( 1) 16

16s

( 2m)

8t 4m

34. 7b 6b ( 8b) 35. 9w 4w ( 5w)

11h

36. 12t 3t ( 6t)

### Simplify each expression. ( 7y)

8. 3x

( 6x)

3x

9.

5y

12y

10. 2m

( 4m)

5b

Algebra: Concepts and Applications Glencoe/McGraw-Hill

10w

62

9t

Algebra: Concepts and Applications

### Algebra: Concepts and Applications

61

Glencoe/McGraw-Hill

23

Reading to Learn Mathematics

Adding Integers Key Terms

5 3. 9 ( 2)

NAME

DATE

PERIOD

Practice

23

NAME

DATE

PERIOD

Adding Integers

### Find each sum.

Glencoe/McGraw-Hill

7

( 4) 6. 12 ( 4) additive inverses two numbers are additive inverses if their sum is 0 opposite additive inverse zero pair the result of positive algebra tiles paired with negative algebra tiles

1. 8

2.

### 12 Reading the Lesson

( 8)

1. Explain how to add integers with the same sign.

4.

11

5.

6

4 9. 2

11

7.

10

8.

1

2. Explain how to add integers with opposite signs.

0

3 12. 6 ( 7)

Add their absolute values. The result has the same sign as the integers. Find the difference of their absolute values. The result has the same sign as the integer with the greater absolute value.

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

10. 17

( 4)

11.

13

13

11 15. 9 ( 2)

4. Use the number line to find each sum. a. 3

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

### 10 The absolute values must be equal.

5

13.

( 9)

14.

17 2

( 5) 18. 11 7

11

Answers

16.

17. 6

A8

4

3 21. 2 ( 2)

b. 4 ( 6)

2 2

19.

( 8)

20.

16

8 ( 3) 24. 5 ( 5) 5

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

(Lesson 2-3)

22. 7

( 5)

23.

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

### Simplify each expression. 2y 27. 9m ( 4m)

The longer arrow represents the number with the greater absolute value.

d. Explain how the arrows can help you determine the sign of the answer.

25. 5a

( 3a)

26.

7y

2a

( 4x) 30. 10p 5p

5y

13m

The direction of the longer arrow determines the sign of the answer.

Write an equation for each situation. 5. a five-yard penalty and a 13-yard pass 6. gained 11 points and lost 18 points

28.

2z

( 4z)

29. 8x

6z

7s 33. 2n ( 4n)

4x

5p

11

7. a deposit of $25 and a withdrawal of $15

31. 5b

( 2b)

32.

4s

### 5 13 8 ( 18) 7 25 ( 15) 10 Helping You Remember

8. Explain how you can remember the meaning of zero pair.

3b

3x ( 5x) 36. 7z 2z ( 3z)

3s

2n

34. 5a

( 6a)

4a

35.

6x

3a

63

8x

6z

Algebra: Concepts and Applications

Sample answer: Since the sum of a number and its opposite is zero, when a positive tile is paired with a negative tile, the sum is zero.

Glencoe/McGraw-Hill

### Algebra: Concepts and Applications

Glencoe/McGraw-Hill

64

### Algebra: Concepts and Applications

23

Study Guide

Subtracting Integers

0 1 4 3 2 2 3 1 4

NAME

DATE

PERIOD

Enrichment

24

If the sum of two integers is 0, the numbers are opposites or additive inverses. Example 1: a. 3 is the opposite of 3 because 17 because 17 3 3 0 ( 17) 0 b. 17 is the opposite of Use this rule to subtract integers. To subtract an integer, add its opposite or additive inverse. Example 2: Find each difference.

NAME

DATE

PERIOD

Glencoe/McGraw-Hill

2. 4 1

1

Integer Magic

A magic triangle is a triangular arrangement of numbers in which the sum of the numbers along each side is the same number. For example, in the magic triangle shown at the right, the sum of the numbers along each side is 0.

In each triangle, each of the integers from 4 to 4 appears exactly once. Complete the triangle so that the sum of the integers along each side is 3.

1.

### Sample answers are given.

0 3

4

3 a. 5 5 5 3 ( 1) ( 1) d c 1

2 2

Answers

1

3

2 2

( 2)

Subtracting 2 is the same as adding its opposite, 2. 1 e if c 1 is the same as adding its 7 6

2 b. 4.

3

0 7 7

3.

### (Lessons 2-3 and 2-4)

A9

3 4 1

4

3 0

### Subtracting opposite, 1. 1, d 7, and e

### Example 3: Evaluate c d e 6 9 Find each difference. 1. 5 5. 16 8

3. 1 1 3 7 7 ( 3) 3 3.

### Replace c with 1, d with 7, and e with Write 7 ( 3) as 7 3. 1 7 6 6 3 9

In these magic stars, the sum of the integers along each line of the star is 2. Complete each magic star using the integers from 6 to 5 exactly once. 6. 3

3

8 8

2.

### 8 6. 10 Simplify each expression.

( 9) 1 ( 10) 20

3. 7. 0

8 10

10 10

4. 8. 0

( 5) 1 ( 18) 18

5.

1 3

0 2 1 2

9. 3x

9x

6x

### 10. Evaluate each expression if x 12. x y

4y 1, y

( 6y) 2y 2, and z 4.

11. 2m

8m

( 2m)

4m

1 6

4 5

3

5 15. 9 x 10

13. y 16. x

z z

5 1 z 7

14. z 17. 0

y y

( 2)

4 2

5 4 65

### Algebra: Concepts and Applications

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

Glencoe/McGraw-Hill

66

### Algebra: Concepts and Applications

24

Practice

Subtracting Integers

Find each difference. 4 3. 7 ( 2) 1. 9 3 2. 1 2 3. 4 ( 5)

NAME

DATE

PERIOD

Skills Practice

24

NAME

DATE

PERIOD

Subtracting Integers

### Find each difference.

Glencoe/McGraw-Hill

5

12 6. 4 ( 10) 4. 6 ( 1) 5. 7 ( 4) 6. 8 10

1. 8

2. 12

4.

5. 4

13

8 9. 5 ( 5) 7. 2 5 8. 6 ( 7)

3

9. 2

2

8

7.

8.

7

7 12. 8 ( 7) 10. 10 ( 2) 11. 4 6

13

1

12. 5

6

3

10.

11.

11

Answers

16

( 15) 15. 14 6 13. 8 ( 4) 14. 7 9

18

15

10

15.

2

9 ( 11)

A10

20

7 18. 13 14 16. 3 4

13. 9

14

14.

12

4

17. 6

2

( 5)

2

18. 6 5

16.

17.

(Lesson 2-4)

11

14

11

### Evaluate each expression if a c 21. a c 19. b

2, b

3, c

1, and d

1.

### Evaluate each expression if a c 20. a

1, b b

5, c

2, and d 21. c

4. d

19. a

20. b

5

b c 24. b d c

7

22. a c d 23. a

6

b c

2

24. a c d

22. c

23. a

2

a b 27. a d b

1

25. b c d 26. b

8

c d 27. a

3

b c

25. d

26. c

4

67

2

Algebra: Concepts and Applications

3

Glencoe/McGraw-Hill

11

68

4

Algebra: Concepts and Applications

### Algebra: Concepts and Applications

Glencoe/McGraw-Hill

NAME

DATE

PERIOD

24

Enrichment

Closure

A binary operation matches two numbers in a set to just one number. Addition is a binary operation on the set of whole numbers. It matches two numbers such as 4 and 5 to a single number, their sum.

### Reading to Learn Mathematics

24

NAME

DATE

PERIOD

Subtracting Integers

Glencoe/McGraw-Hill

If the result of a binary operation is always a member of the original set, the set is said to be closed under the operation. For example, the set of whole numbers is not closed under subtraction because 3 6 is not a whole number. Is each operation binary? Write yes or no. 1. the operation , where a b means to choose the lesser number from a and b yes 3. the operation sq, where sq(a) means to square the number a no 4. the operation exp, where exp(a, b) means to find the value of a b yes 5. the operation , where a b means to match a and b to any number greater than either number no

Key Terms

### Reading the Lesson

### 1. Write each subtraction problem as an addition problem.

a. 12

12

( 4)

b.

15

15

( 7)

c. 0

11

( 11)

### 2. the operation , where a b means to cube the sum of a and b yes

d.

20

34

20

( 34)

Answers

e.

15

( 4)

15

A11

3 8 to 5; 13 8; 27

69

Algebra: Concepts and Applications Glencoe/McGraw-Hill

f. 16

( 18)

16

18

### 2. Describe how to find each difference. Then find each difference.

6. the operation , where a b means to round the product of a and b up to the nearest 10 yes

a. 8

11

### Add the opposite of 11 to 8;

(Lesson 2-4)

b. 5

( 8)

### Add the opposite of

c. 17

14

### Add the opposite of 14 to 17; 3

Is each set closed under addition? Write yes or no. If your answer is no, give an example. 7. even numbers yes 9. multiples of 3 yes 11. prime numbers no; 3 8. odd numbers no; 3 10. multiples of 5 yes

d.

19

### Add the opposite of 19 to

7 5 8

12. nonprime numbers

10

3. Explain how zero pairs are used to subtract with algebra tiles.

Zero pairs are not needed to subtract negative tiles. If a positive tile is to be subtracted from negative tiles, first add a zero pair. Then you can subtract one positive tile.

no; 22

31

### Helping You Remember

4. Explain why knowing the rules for adding integers can help you to subtract integers.

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: a b yes 14. division: a b no; 4 whole number 16. squaring the sum: (a

Sample answer: Since subtraction is really adding the numbers additive inverse, the rules for addition also apply to subtraction.

3 is not a

b)2 yes

### Algebra: Concepts and Applications

Glencoe/McGraw-Hill

70

### Algebra: Concepts and Applications

25 25

Skills Practice

Multiplying Integers

Find each product. 1. 3(12) 2. 4(7) 3. 8( 8)

### NAME NAME DATE PERIOD

DATE

PERIOD

Study Guide

Multiplying Integers

Glencoe/McGraw-Hill

36

4. 5( 9) 5. 2( 9) 6. 3( 10)

### Use these rules to multiply integers and to simplify expressions.

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.

28

64

45

Both factors are positive, so the product is positive. 7. 0( 5) 8. 13( 4)

18

30

9. 4( 11)

### Example 1: Find each product. a. 7(12) 7(12) 84

0

10. 5(12) 11. 14(0)

52

12.

44

8(7)

### b. Both factors are negative, so the product is positive.

5( 9) 5( 9)

45

60

13. 15( 4) 14. 9( 3)

0

15.

56

8(11)

### c. The factors have different signs, so the product is negative.

Answers

4(8) 4(8)

32

A12

60

16. ( 2)(4)( 3) 5.

27

17. ( 4)( 5)( 1)

88

18. (3)(5)( 5)

### Example 2: Evaluate 3ab if a 3ab 3(3)( 5) 9( 5) 45

### 3 and b 5. Replace a with 3 and b with 3 3 9 Both factors are negative.

24

Evaluate each expression if x 19. 3xy 20.

20

2 and y 2xy 4. 21.

(Lesson 2-5)

75

### Example 3: Simplify 12(4x) Associative Property 12 4 48

5x

### 12(4x). ( 12 4)(x) 48x

24

22. 7y

16

23. 8xy 24.

10

6xy

### Find each product. 3. 12( 1)

1. 3(8) 24 4. 6(5)

2. ( 7)( 9) 63

12

7. 2( 5)(10)

30

28

Simplify each expression. 25. 3(2a) 26.

64

48

### 5. 4( 1)( 5) 20 2, and c 10. abc 18 11. 3b c 3.

6. ( 8)( 8)( 2)

128

100

### Evaluate each expression if a

3, b

4( 3c)

27.

5( 8b)

8. 5c

15

9. 2ab

12

6a

28. (5c)( 7d)

12c

29. ( 8m)( 2n)

40b

30. ( 9s)(7t)

### Simplify each expression. 14. (2p)( 4q)

12. 3( 6x) 71

18x

13.

5( 7y) 35y

8pq

35cd

Glencoe/McGraw-Hill

16mn

72

63st

Algebra: Concepts and Applications

### Algebra: Concepts and Applications

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

25

Reading to Learn Mathematics

Multiplying Integers Key Terms

3. 4(5) factors the numbers being multiplied product the result when two or more factors are multiplied together

NAME

DATE

PERIOD

Practice

25

NAME

DATE

PERIOD

Multiplying Integers

### Find each product.

Glencoe/McGraw-Hill

20 Reading the Lesson

6. 8( 6)

1. Complete: If two numbers have different signs, the one number is positive and the other number is 2. Complete the table.

1. 3( 7)

2.

2(8)

21

16

4.

7( 7)

5.

9(3)

49

9. 2( 8)

27

48

neg

.

7. 6(2)

8.

5( 7)

12

a. ( 4)(9)

35

12. 12(0)

b. ( 2)( 13) c. 5( 8) d. 6(3)

16

Multiplication Example

### Are the signs of the numbers the same or different?

### Is the product positive or negative?

10.

10( 2)

11. 9( 8)

20

15. 3(5)(2)

72

### different same different same

### neg pos neg pos

Answers

13.

4( 4)(2)

14. 7( 9)( 1)

A13

30

18. 5( 3)( 2)( 1)

32

63

3. Explain what the term additive inverse means. Then give an example.

### 1 is its additive inverse;

### 16. 3( 4)( 2)(2)

17. 6( 1)(2)(1)

48

5. 21. 4ab

12

30

### The product of any number and 2 ( 1) . 3 Helping You Remember

2 3

(Lesson 2-5)

### Evaluate each expression if a

3 and b

19.

6b

20. 8a

4. Describe how you know that the product of 3 and you know that the product of 3 and 5 is negative.

### 5 is positive. Then describe how

30

24. 2ab

24

60

Sample answer: The signs are the same; the signs are different.

22.

3ab

23.

9a

45

27

30

### Simplify each expression. 27. 3(6n)

25. 5( 5y)

26.

7( 3b)

25y

21b

18n

30. ( 8x)(7y)

### 28. (6a)( 2b)

### 29. ( 4m)( 9n)

12ab

73

36mn

56xy

Algebra: Concepts and Applications Glencoe/McGraw-Hill

### Algebra: Concepts and Applications

Glencoe/McGraw-Hill

74

### Algebra: Concepts and Applications

25 26

Study Guide

Dividing Integers

Example 1: Use the multiplication problems at the right to find each quotient. 3 5 3( 5) 15, 15 3 5 3. 3. ( 5) 3. 3( 5) 15, 15 15, 15, 15 15 5 ( 5) 5 3. 15 15 15 15 a. 15 5 Since 3 5 16 8 4 2 b. 15 ( 5) Since 3 ( 5) c. 2 2 2 2 8 4 2 1 1 d. 15 5 Since 3 5 15 ( 5) Since 3 ( 5)

### NAME NAME DATE PERIOD

DATE

PERIOD

Enrichment

### The Binary Number System

Glencoe/McGraw-Hill

1 0 1 1 1 Use these rules to divide integers.

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. 1 2 1 1

Answers

10111two

16 0 8 1 4 16 0 4 2 1 23

### Write each binary number as a standard number. 3. 100two 4 Example 2: Evaluate

3r s 24 2 3 8 2 3r s

1. 11two 3 if r

2. 111two 7

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. 8 and s 2. Replace r with 8 and s with 3 8 12 Find each quotient. 24 24 ( 2) 12 2.

### (Lessons 2-5 and 2-6)

A14

6. 100101two 37 9. 15 1111two 12. 34 100010two 1. 36 9 4 2. 63 5. 14. 101two 10two 11two

20 5

4. 1001two 9

5. 11001two 25

### Write each standard number as a binary number.

7. 8 1000two

8. 10 1010two

10. 17 10001two

11. 28 11100two

( 7) 9

3. 25

( 1)

25 4 6

6.

4.

60

12 1

7.

### Write each answer as a binary number.

13. 1two

10two 11two

18 3

1 1

8.

56 8

15. 10two

### 11two 110two 16. 10000two

10two 1000two

### Evaluate each expression if k 9. 21 m

1, m

3, and n

2.

10.

2n k

11. m

12.

m n

### 17. What standard number is equivalent to 12021three? 142

### Algebra: Concepts and Applications

75

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

Glencoe/McGraw-Hill

76

### Algebra: Concepts and Applications

26 26

Practice

Dividing Integers

Find each quotient. 5 1. 28 7 2. 33 3 3. 24 ( 8) 3. 42 ( 6)

### NAME NAME DATE PERIOD

DATE

PERIOD

Skills Practice

Dividing Integers

### Find each quotient.

Glencoe/McGraw-Hill

3 4

4 4. 81 ( 9) 5. 12 4

1. 36

2.

15

12 11

( 9) 6. 28

7

6. 72 ( 9)

4.

45

( 3)

5. 81

15 9

( 4) 7. 15 15 8. 30 5

9 3

( 12) 9. 32

8

9. 40 ( 8)

7.

121

11

8.

144

11 1

( 6) 10. 56 ( 7) 11. 21

12 6

10 12. 48

5

( 3) 12. 64 8

10.

64

( 8)

11.

80

8 8

( 9) 13. 8 8 14. 5 15. 36

7

22 ( 2)

8

15. 32 ( 8)

13. 100

( 25)

14.

20

Answers

4 1

( 16) 16. 54 ( 9) ( 9) 18. 32

11

17. 60 ( 6)

4

18. 63 9

A15

2 6

( 8) 19. 45 ( 9) 2 21. 72

16. 56

( 7)

17.

63

10

20. 60 5

7

21. 24 ( 3)

19.

21

20.

18

(Lesson 2-6)

7 5

22. 24.

125 5

12

12 6

8

23.

40 10

22.

35 7

23.

39 13

24.

45 9

5

8, and g 27. 4g f 4.

25

2

Evaluate each expression if a 25. 48 a

4

4, b 26. b 3 9, and c 6.

### Evaluate each expression if d g

3, f

25. f

26. 8d

27. 9c

2

30. g

5f

6 10

33.

4f g

2

28. c

28. gf

12

ab

3

29.

bc 6

6

30. b

3c

29.

df 12

16

31. d

9g

32.

2f g

6

31.

12a c

9

32.

4b a

2

33. 6

ac

12

8

77

Algebra: Concepts and Applications Glencoe/McGraw-Hill

9

78

4

Algebra: Concepts and Applications

### Algebra: Concepts and Applications

Glencoe/McGraw-Hill

NAME

DATE

PERIOD

26

Enrichment

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 2m [(3m 3) 5] 2 s d m y sum day of the month, using numbers from 131 month, beginning with March is 3, April is 4, and so on, up to December is 12, January is 13, and February is 14 year except for dates in January or February when the previous year is used 1984; d y

y 4 y 100 y 400

### Reading to Learn Mathematics

26

NAME

DATE

PERIOD

Dividing Integers

Glencoe/McGraw-Hill

For example, for February 13, 1985, d 13, m 14, and y and for July 4, 1776, d 4, m 7, and y 1776

Key Terms

### Reading the Lesson

1. Write the math sentence 18 divided by 6 two different ways. Then find the quotient.

18

3;

18 6

2. Write negative or positive to describe each quotient. Explain your answer. Explanation The signs of two numbers are the same.

Answers

Expression

Negative or Positive?

The brackets, [ ], mean you are to do the division inside them, discard the remainder, and use only the whole number part of the quotient. 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?

A16

The signs of the two numbers are different. The signs of the two numbers are different.

a. 15

12

pos

b. 9

10

neg

### For October 3, 1854, d s 3 [ 2(10) ] [ (3

3, m 10 6 3)

10, and y 5]

### 1854. 1854 1854

1854 4 1854 100 1854 400

c. The signs of two numbers are the same. The signs of the two numbers are different.

35 7

neg

2 463 18 4 2

(Lesson 2-6)

d.

78 13

pos

e.

13x 2

neg

### 3 20 2334 s 7 2334 7 333 R3

### f. The signs of two numbers are the same.

46 6y

pos

Since the remainder is 3, the day of the week was Tuesday. Solve. 1. See if the formula works for todays 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 13 s 4 4 2(4) 8 2(7) 14 3 [(3 4

Glencoe/McGraw-Hill

### Helping You Remember

3. 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 the same for multiplication and division. If the signs of the factors are the same, the answer will be positive. If the signs of the factors are different, the answer will be negative.

[(3

4 2006 7 1776

3) 501 3) 444

5] 20 5]

2006 4 1776 17 4 2

2006 4

2006 100

2006 400

### 2 2518; 2518 7 359 R5 Thursday

### 4. On what day of the week was July 4, 1776?

1776 4 1776 100 1776 400

### 2 2 2231; 2231 7 318 R5 Thursday

### Algebra: Concepts and Applications

79

Algebra: Concepts and Applications

Glencoe/McGraw-Hill

80

### Algebra: Concepts and Applications

### Chapter 2 Answer Key

Form 1A Page 81 Page 82 Page 83 Form 1B Page 84

1.

13.

D

1.

13.

C A

D

14.

14. 2.

B C A

2.

B

15.

C

15.

C D B D A D D A A C

3. 4.

C B

16.

3.

A

16.

4. 17.

B

17.

C

5.

B

18.

18. 5.

A B B D

7. 6.

D

19. 19.

20. 6.

C

20.

C

21.

21.

7.

A

22.

D

22.

8.

23.

C B

8.

B

23.

### 9. 10. 11. 12.

C A D B

24.

9.

D

24.

10. 25.

C B C

25.

B

11.

Bonus

A

A17

12.

Bonus

Glencoe/McGraw-Hill

### Algebra: Concepts and Applications

### Chapter 2 Answer Key

Form 2A Page 85

1.

1 0 1 2 3

Page 86

20.

24k

2. 3. 4. 5.

21.

4507 m 18 80 24

22.

23. 24.

6. 7. 8. 9. 10.

( 4, 2) (2, 4) IV III II 37 24 2

28. 29. 25. 26. 27.

$410 16 512

19 8 25

### 11. 12. 13.

30.

14. 15.

down 9 19 31 4 3 12

31. 32.

### 16 ft per second squared 4 $3000

### 16. 17. 18. 19.

Glencoe/McGraw-Hill

33.

Bonus

0%

Algebra: Concepts and Applications

A18

### Chapter 2 Answer Key

Form 2B Page 87

20. 1. 2. 3. 21. 22.

Page 88

6b

12

4. 5.

23.

17 F 375 2

24.

3 2 1 0 1

25. 26.

### Point B lies on the xaxis. It is not located in a quadrant. 6. 7. 8. 9. 10. 11.

48 30 18

IV (4, 3) ( 4, IV 5

29. 30. 27. 28.

$24 6 14 6 16

2)

### 12. 13. 14.

12 5 14

31.

15.

falls 2 ft

32.

### 44 ft per second squared

### 16. 17. 18. 19.

Glencoe/McGraw-Hill

14 17 1 14

A19

33.

3000

Bonus

1F

Algebra: Concepts and Applications

### Chapter 2 Assessment Answer Key

Page 89, Extended Response Assessment Scoring Rubric

Score 4 General Description Superior A correct solution that is supported by welldeveloped, accurate explanations Specific Criteria 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.

Satisfactory A generally correct solution, but may contain minor flaws in reasoning or computation

### Nearly Satisfactory A partially correct interpretation and/or solution to the problem

Nearly Unsatisfactory A correct solution with no supporting evidence or explanation Unsatisfactory An incorrect solution indicating no mathematical understanding of the concept or task, or no solution is given

Glencoe/McGraw-Hill

A20

### Algebra: Concepts and Applications

### Chapter 2 Answer Key

Extended Response Assessment Sample Answers Page 89

1. a. A(2, 1), B(3, b. ( 4, c.

Y

2), C( 3, 0)

y

### 2), ( 6, 4), (6, 0)

O

X

Z x

d. The new triangle has the same shape, but its sides seem to be twice as long. It also seems to be rotated halfway around the origin. 2. a. A sample table is shown below for n

Quadrant of (a, b) Coordinates of (a, b) Coord. and quad. of (na, b) Coord. and quad. of (a, nb) Coord. and quad. of (na, nb) I (2, 3) ( 6, 3); II (2, ( 6, 9); IV 9); III

3.

II ( 1, 3) (3, 3); I ( 1, (3, 9); III 9); IV III (3, 3) (9, 3); IV (3, 9); II (9, 9); I IV (1, ( 3, 2) 2); III

### (1, 6); I ( 3, 6); II

b. Multiplying the x-coordinate by a negative number moves the point horizontally to the quadrant next to it. Multiplying the y-coordinate by a negative number moves the point vertically to the quadrant above or below it. Multiplying both coordinates by a negative number moves the point to the quadrant diagonally across from it. 3. a. b.

$990 $1320 15 $1750 25

$22 $22

$1200

c. Both clubs lost the same amount per person, $22, but members of the first club invested $970 each, while those in the second club invested $630 each.

Glencoe/McGraw-Hill

A21

### Algebra: Concepts and Applications

### Chapter 2 Answer Key

Mid-Chapter Test Page 90

1.

Quiz A Page 91

2 1 0 1 2 3

1. 2.

1 4

2. 3.

3. 4. 5. 6.

4.

8

y

B

57.

O x

A

7. 8. 911.

10, 3, 0, 6, 5, 2, 3,

y

8, 4,

12

C

5

8.

IV

P x R

Quiz B Page 91

1. 2.

10 0 174

### 12. 13. 14. 15.

(0, 4) ( 2, 3) III I

3.

4. 5.

21

( 3) 42 80 6

24

### 16. 17. 18. 19. 20.

Glencoe/McGraw-Hill

9 22 2 9x 7

A22

6. 7.

8.

$2500

Algebra: Concepts and Applications

### Chapter 2 Answer Key

Cumulative Review Page 92

1. 4a 2.

### Standardized Test Practice Page 93 Page 94

bc

11

7

Associative Property ( )

10. 1.

3. 4.

8x

18

C

11.

C B

5.

1 22

lb

2. 3.

B C

12.

6.

6

4.

13.

7. 8.

line graph

64, 25, 2, 3, 11, 36

14.

### 5. 9. 10. 11. 12.

A B

15.

C C B A A

( 1, 4) IV 53 42

6. 7.

16.

B

17.

8.

18.

### 13. 14. 15. 16.

Glencoe/McGraw-Hill

22 F 48 9 14

A23

19.

9.

20.

### Algebra: Concepts and Applications

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