Post on 10-Aug-2020
Chapter 2Resource Masters
Consumable WorkbooksMany of the worksheets contained in the Chapter Resource Masters bookletsare available as consumable workbooks in both English and Spanish.
Study Guide and Intervention Workbook 0-07-827753-1Study Guide and Intervention Workbook (Spanish) 0-07-827754-XSkills Practice Workbook 0-07-827747-7Skills Practice Workbook (Spanish) 0-07-827749-3Practice Workbook 0-07-827748-5Practice Workbook (Spanish) 0-07-827750-7
ANSWERS FOR WORKBOOKS The answers for Chapter 2 of these workbookscan be found in the back of this Chapter Resource Masters booklet.
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce the material contained herein on the condition that such material be reproduced only for classroom use; be provided to students, teachers, and families without charge; and be used solely in conjunction with Glencoe’s Algebra 1. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher.
Send all inquiries to:The McGraw-Hill Companies8787 Orion PlaceColumbus, OH 43240-4027
ISBN: 0-07-827726-4 Algebra 1Chapter 2 Resource Masters
2 3 4 5 6 7 8 9 10 024 11 10 09 08 07 06 05 04 03
© Glencoe/McGraw-Hill iii Glencoe Algebra 1
Contents
Vocabulary Builder . . . . . . . . . . . . . . . . vii
Lesson 2-1Study Guide and Intervention . . . . . . . . . 75–76Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 77Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Reading to Learn Mathematics . . . . . . . . . . . 79Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Lesson 2-2Study Guide and Intervention . . . . . . . . . 81–82Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 83Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84Reading to Learn Mathematics . . . . . . . . . . . 85Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Lesson 2-3Study Guide and Intervention . . . . . . . . . 87–88Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 89Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90Reading to Learn Mathematics . . . . . . . . . . . 91Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Lesson 2-4Study Guide and Intervention . . . . . . . . . 93–94Skills Practice . . . . . . . . . . . . . . . . . . . . . . . . 95Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96Reading to Learn Mathematics . . . . . . . . . . . 97Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Lesson 2-5Study Guide and Intervention . . . . . . . . 99–100Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 101Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Reading to Learn Mathematics . . . . . . . . . . 103Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 104
Lesson 2-6Study Guide and Intervention . . . . . . . . 105–106Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 107Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 108Reading to Learn Mathematics . . . . . . . . . . 109Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 110
Lesson 2-7Study Guide and Intervention . . . . . . . . 111–112Skills Practice . . . . . . . . . . . . . . . . . . . . . . . 113Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Reading to Learn Mathematics . . . . . . . . . . 115Enrichment . . . . . . . . . . . . . . . . . . . . . . . . . 116
Chapter 2 AssessmentChapter 2 Test, Form 1 . . . . . . . . . . . . 117–118Chapter 2 Test, Form 2A . . . . . . . . . . . 119–120Chapter 2 Test, Form 2B . . . . . . . . . . . 121–122Chapter 2 Test, Form 2C . . . . . . . . . . . 123–124Chapter 2 Test, Form 2D . . . . . . . . . . . 125–126Chapter 2 Test, Form 3 . . . . . . . . . . . . 127–128Chapter 2 Open-Ended Assessment . . . . . . 129Chapter 2 Vocabulary Test/Review . . . . . . . 130Chapter 2 Quizzes 1 & 2 . . . . . . . . . . . . . . . 131Chapter 2 Quizzes 3 & 4 . . . . . . . . . . . . . . . 132Chapter 2 Mid-Chapter Test . . . . . . . . . . . . 133Chapter 2 Cumulative Review . . . . . . . . . . . 134Chapter 2 Standardized Test Practice . . 135–136
Standardized Test Practice Student Recording Sheet . . . . . . . . . . . . . . A1
ANSWERS . . . . . . . . . . . . . . . . . . . . . . A2–A32
© Glencoe/McGraw-Hill iv Glencoe Algebra 1
Teacher’s Guide to Using theChapter 2 Resource Masters
The Fast File Chapter Resource system allows you to conveniently file the resourcesyou use most often. The Chapter 2 Resource Masters includes the core materials neededfor Chapter 2. These materials include worksheets, extensions, and assessment options.The answers for these pages appear at the back of this booklet.
All of the materials found in this booklet are included for viewing and printing in theAlgebra 1 TeacherWorks CD-ROM.
Vocabulary Builder Pages vii–viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.
WHEN TO USE Give these pages tostudents before beginning Lesson 2-1.Encourage them to add these pages to theirAlgebra Study Notebook. Remind them toadd definitions and examples as theycomplete each lesson.
Study Guide and InterventionEach lesson in Algebra 1 addresses twoobjectives. There is one Study Guide andIntervention master for each objective.
WHEN TO USE Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.
Skills Practice There is one master foreach lesson. These provide computationalpractice at a basic level.
WHEN TO USE These masters can be used with students who have weakermathematics backgrounds or needadditional reinforcement.
Practice There is one master for eachlesson. These problems more closely followthe structure of the Practice and Applysection of the Student Edition exercises.These exercises are of average difficulty.
WHEN TO USE These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.
Reading to Learn MathematicsOne master is included for each lesson. Thefirst section of each master asks questionsabout the opening paragraph of the lessonin the Student Edition. Additionalquestions ask students to interpret thecontext of and relationships among termsin the lesson. Finally, students are asked tosummarize what they have learned usingvarious representation techniques.
WHEN TO USE This master can be usedas a study tool when presenting the lessonor as an informal reading assessment afterpresenting the lesson. It is also a helpfultool for ELL (English Language Learner)students.
Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.
WHEN TO USE These may be used asextra credit, short-term projects, or asactivities for days when class periods areshortened.
© Glencoe/McGraw-Hill v Glencoe Algebra 1
Assessment OptionsThe assessment masters in the Chapter 2Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.
Chapter Assessment CHAPTER TESTS• Form 1 contains multiple-choice questions
and is intended for use with basic levelstudents.
• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.
• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.
• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.
All of the above tests include a free-response Bonus question.
• The Open-Ended Assessment includesperformance assessment tasks that aresuitable for all students. A scoring rubricis included for evaluation guidelines.Sample answers are provided forassessment.
• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used in conjunc-tion with one of the chapter tests or as areview worksheet.
Intermediate Assessment• Four free-response quizzes are included
to offer assessment at appropriateintervals in the chapter.
• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice andfree-response questions.
Continuing Assessment• The Cumulative Review provides
students an opportunity to reinforce andretain skills as they proceed throughtheir study of Algebra 1. It can also beused as a test. This master includes free-response questions.
• The Standardized Test Practice offerscontinuing review of algebra concepts invarious formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, grid-in, and quantitative-comparison questions. Bubble-in andgrid-in answer sections are provided onthe master.
Answers• Page A1 is an answer sheet for the
Standardized Test Practice questionsthat appear in the Student Edition onpages 116–117. This improves students’familiarity with the answer formats theymay encounter in test taking.
• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.
• Full-size answer keys are provided forthe assessment masters in this booklet.
Reading to Learn MathematicsVocabulary Builder
NAME ______________________________________________ DATE ____________ PERIOD _____
22
© Glencoe/McGraw-Hill vii Glencoe Algebra 1
Voca
bula
ry B
uild
erThis is an alphabetical list of the key vocabulary terms you will learn in Chapter 2.As you study the chapter, complete each term’s definition or description.Remember to add the page number where you found the term. Add these pages toyour Algebra Study Notebook to review vocabulary at the end of the chapter.
Vocabulary Term Found on Page Definition/Description/Example
absolute value
additive inverses
A·duh·tihv
equally likely
frequency
integers
irrational number
ih·RA·shuh·nuhl
line plot
measures of central tendency
natural number
odds
(continued on the next page)
⎧ ⎪ ⎨ ⎪ ⎩
⎧ ⎪ ⎨ ⎪ ⎩
© Glencoe/McGraw-Hill viii Glencoe Algebra 1
Vocabulary Term Found on Page Definition/Description/Example
opposites
perfect square
principal square root
probability
PRAH·buh·BIH·luh·tee
rational number
RA·shuh·nuhl
real number
sample space
simple event
square root
stem-and-leaf plot
whole number
⎧ ⎪ ⎨ ⎪ ⎩
⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩
Reading to Learn MathematicsVocabulary Builder (continued)
NAME ______________________________________________ DATE ____________ PERIOD _____
22
Study Guide and InterventionRational Numbers on the Number Line
NAME ______________________________________________ DATE ____________ PERIOD _____
2-12-1
© Glencoe/McGraw-Hill 75 Glencoe Algebra 1
Less
on 2
-1
Graph Rational Numbers The figure at the right is part of a number line. A number line can be used to show the sets of natural numbers, whole numbers, and integers. Positive numbers, are located to the right of 0,and negative numbers are located to the left of 0.
Another set of numbers that you can display on a number line is the set of rational numbers. A rational number can
be written as , where a and b are integers and b ! 0. Some
examples of rational numbers are , , , and .12"#3
#7"#8
#3"5
1"4
a"b
10!1!2!3!4 2 3
Natural Numbers
Positive NumbersNegative Numbers
4
Whole Numbers
Integers
Name the coordinates of thepoints graphed on each number line.
a.
The dots indicate each point on the graph.The coordinates are {#3, #1, 1, 3, 5}
b.
The bold arrow to the right means the graphcontinues indefinitely in that direction. Thecoordinates are {2, 2.5, 3, 3.5, 4, 4.5, 5, …}.
32.521.51 3.5 4 4.5 5
10!1!2!3 2 3 4 5
Graph each set ofnumbers.
a. {…, !3, !2, !1, 0, 1, 2}
b. !! , 0, , "12–
31–30!1–
3!2–3
4–3
5–3 2
2"3
1"3
1"3
10!1!2!3!4 2 3 4
Example 1Example 1 Example 2Example 2
ExercisesExercises
Name the coordinates of the points graphed on each number line.
1. 2.
3. 4.
Graph each set of numbers.
5. {#3, #1, 1, 3} 6. {#5, #2, 1, 2} 7. {integers less than 0}
8. {…, #2, #1, 0, 1} 9. !#2 , #1 , # , " 10. {…, #4, #2, 0, 2, …}
!3!4!5!6 !2 !1 0 1 2!21–2!3 !2!11–
2!1 !1–2 0 1–
2 1!3!4 !2 !1 0 1 2 3 4
1"2
1"2
1"2
1"2
!3!4 !2 !1 0 1 2 3 4!3!4!5 !2 !1 0 1 2 3!3!4 !2 !1 0 1 2 3 4
!3!4 !2 !1 0 1 2 3 4!1–4!1–
2 0 1–4
1–2
3–4 1 5–
43–2
0!1 1 2 3 4 5 6 70!1!2 1 2 3 4 5 6
© Glencoe/McGraw-Hill 76 Glencoe Algebra 1
Absolute Value On a number line, #3 is three units from zero in the negative direction, and 3 is three units from zero in the positive direction. The number line at the right illustrates the meaning of absolute value. Theabsolute value of a number n is the distance from zero on a number line and is represented ⏐n⏐. For this example,⏐#3⏐ $ 3 and ⏐3⏐ $ 3.
10!1!2!3!4!5 2 3
3 units 3 units
# direction! direction4 5
Study Guide and Intervention (continued)
Rational Numbers on the Number Line
NAME ______________________________________________ DATE ____________ PERIOD _____
2-12-1
Find each absolute value.
a. ⏐!6⏐#6 is six units from zero in the negativedirection.⏐#6⏐ $ 6
b. ⏐ ⏐is three halves units from zero in the
positive direction.
⏐ ⏐ $3"2
3"2
3"2
3"2
Evaluate 4 # ⏐x ! 2⏐ if x $ 5.
4 % ⏐x # 2⏐ $ 4 % ⏐5 # 2⏐ Replace x with 5.
$ 4 % ⏐3⏐ 5 # 2 $ 3
$ 4 % 3 ⏐3⏐ $ 3
$ 7 Simplify.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each absolute value.
1. ⏐2⏐ 2. ⏐#5⏐ 3. ⏐#24⏐
4. ⏐#1.3⏐ 5. ⏐# ⏐ 6. ⏐ ⏐Evaluate each expression if a $ 5, b $ , x $ 8, and y $ 2.5.
7. 18 % ⏐4 # y⏐ 8. ⏐x % 8⏐ % 12 9. ⏐x # 2⏐ % 8.2
10. 2 % ⏐x # 5⏐ 11. ⏐2.5 % y⏐ % 12 12. ⏐23 # x⏐ # 9
13. ⏐x # 6⏐ % 4.5 14. 10 # ⏐a # 2⏐ 15. ⏐6 % b ⏐ %
16. ⏐ % b⏐ # ⏐# ⏐ 17. ⏐3 % b⏐ % a 18. ⏐#b⏐ % 1 1"2
1"2
1"4
1"2
1"4
35"41
2"3
Skills PracticeRational Numbers on the Number Line
NAME ______________________________________________ DATE ____________ PERIOD _____
2-12-1
© Glencoe/McGraw-Hill 77 Glencoe Algebra 1
Less
on 2
-1
Name the coordinates of the points graphed on each number line.
1. 2.
3. 4.
Graph each set of numbers.
5. {#8, #5, #3, 0, 2} 6. {#9, #6, #4, #3, #1}
7. {#3, #2, #1, 0, …} 8. {…, #1, 0, 1, 2, 3}
9. !# , 0, , 1, " 10. {…, #3, #2.5, #2, #1.5, #1}
Find each absolute value.
11. ⏐#9⏐ 12. ⏐15⏐ 13. ⏐#30⏐
14. ⏐# ⏐ 15. ⏐2.4⏐ 16. ⏐ ⏐Evaluate each expression if a $ 3, b $ !10, c $ , x $ 9, y $ 1.5, and z $ 12.
17. 26 # ⏐x % 6⏐ 18. 11 % ⏐10 # x⏐
19. ⏐12 # a⏐ % 5 20. ⏐a % 20⏐ # 4
21. 4.5 # ⏐y⏐ 22. ⏐z # 7⏐ % 5
23. 14 # ⏐b⏐ 24. ⏐b⏐ # 2
25. ⏐c % ⏐ % 2 26. 9 % ⏐3.5 # y⏐1"2
1"2
9"11
5"7
!3 !2 !1 0 1 2!1 !1–2 0 1–
2 1 3–2 2 5–
2 3 7–2 4
5"2
1"2
1"2
!1 0 1 2 3 4 5 6 7 8 9!10 !9 !8 !7 !6 !5 !4 !3 !2 !1 0
!5!6!7!8!9!10 !4 !3 !2 !1 0!5!6!7!8 !4 !3 !2 !1 0 1 2
1.41.31.21.11.0 1.5 1.6 1.7 1.8 1.9 2.03210!1!2!3 4 5 6 7
10!1!2!3!4!5!6!7 2 310!1!2!3!4!5!6 2 3 4
© Glencoe/McGraw-Hill 78 Glencoe Algebra 1
Name the coordinates of the points graphed on each number line.
1. 2.
Graph each set of numbers.
3. !…, # , # , #1, # , # " 4. {integers less than #4 or greater than 2}
Find each absolute value.
5. ⏐#11⏐ 6. ⏐100⏐ 7. ⏐#0.35⏐ 8. ⏐# ⏐Evaluate each expression if a $ 4, b $ , c $ , x $ 14, y $ 2.4, and z $ !3.
9. 41 # 16 # ⏐z⏐ 10. ⏐3a % 20⏐ # 15 11. ⏐2x % 4⏐ # 6 12. 2.5 # ⏐3.8 # y⏐
13. #b # $ % ⏐# ⏐ 14. % ⏐b # ⏐ 15. ⏐c # 1⏐ # 16. ⏐#c⏐ #
ASTRONOMY For Exercises 17–19, use the following information.
The absolute magnitude of a star is how bright the star would appear from a standard distance of 10 parsecs, or 32.6 light years.The lower the number, the greater the magnitude, or brightness,of the star. The table gives the magnitudes of several stars.
17. Use a number line to order the magnitudes from least to greatest.
18. Which of the stars are the brightest and the least bright?
19. Write the absolute value of the magnitude of each star Source: www.astro.wisc.edu
20. CLIMATE The table shows the mean wind speeds in miles per hour at DaytonaBeach, Florida. Source: National Climatic Data Center
Graph the wind speeds on a number line. Which month has the greatest mean wind speed?
7 7.5 8 8.5 9 9.5 10 10.5
Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec
9.0 9.7 10.1 9.7 9.0 7.9 7.4 7.1 8.3 9.1 8.7 8.5
!6!7!8
! ! ! !
!9 !5 !4 !3 !2 !1 0 1 2 3
Star Magnitude
Altair 2.3
Betelgeuse #7.2
Castor 0.5
Deneb #4.7
Pollux 0.7
Regulus #0.3
Rigel #8.1
Sirius 1.4
3"4
1"3
2"5
2"15
3"10
1"5
3"2
3"5
28"53
! ! ! ! ! !!7–5 !6–
5 !1 !3–5!4–
5 !2–5 !1–
51–5
2–5
3–50
3"5
4"5
6"5
7"5
0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4!7–4 !3–
2 !5–4 !1 !3–
4 !1–2 !1–
41–4
1–2
3–40
Practice Rational Numbers on the Number Line
NAME ______________________________________________ DATE ____________ PERIOD _____
2-12-1
Reading to Learn MathematicsRational Numbers on the Number Line
NAME ______________________________________________ DATE ____________ PERIOD _____
2-12-1
© Glencoe/McGraw-Hill 79 Glencoe Algebra 1
Less
on 2
-1
Pre-Activity How can you use a number line to show data?
Read the introduction to Lesson 2-1 at the top of page 68 in your textbook.
In the table, what does the number %0.2 tell you?
Reading the Lesson
1. Refer to the number line on page 68 in your textbook. Write true or false for each of thefollowing statements.
a. All whole numbers are integers.
b. All natural numbers are integers.
c. All whole numbers are natural numbers.
d. All natural numbers are whole numbers.
e. All whole numbers are positive numbers.
2. Use the words denominator, fraction, and numerator to complete the following sentence.
You know that a number is a rational number if it can be written as a
that has a and that are integers, where the denominator is not equal to zero.
3. Explain why , 0.6%, and 15 are rational numbers.
Helping You Remember
4. Connecting a mathematical concept to something in your everyday life is one way ofremembering. Describe a situation or setting in your life that reminds you of absolutevalue.
#3"7
© Glencoe/McGraw-Hill 80 Glencoe Algebra 1
Intersection and UnionThe intersection of two sets is the set of elements that are in both sets.The intersection of sets A and B is written A ! B. The union of two setsis the set of elements in either A, B, or both. The union is written A " B.
In the drawings below, suppose A is the set of points inside the circleand B is the set of points inside the square. Then, the shaded areasshow the intersection in the first drawing and the union in the seconddrawing.
Write A # B and A $ B for each of the following.
1. A $ {p, q, r, s, t}B $ {q, r, s}
2. A $ {the integers between 2 and 7}B $ {0, 3, 8}
3. A $ {the states whose names start with K}B $ {the states whose capitals are Honolulu or Topeka}
4. A $ {the positive integer factors of 24}B $ {the counting numbers less than 10}
Suppose A $ {numbers x such that x % 3}, B $ {numbers x such as x & !1}, and C $ {numbers x such that x ' 1.5}. Graph each of the following.
5. A ! B 6. A " B
7. B " C 8. B ! C
9. (A ! C) ! B 10. A ! (B " C)
!2 !1!4 !3 0 1 2 3 4!2 !1!4 !3 0 1 2 3 4
!2 !1!4 !3 0 1 2 3 4!2 !1!4 !3 0 1 2 3 4
!2 !1!4 !3 0 1 2 3 4!2 !1!4 !3 0 1 2 3 4
Intersection A ! B
A B
Union A " B
A B
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
2-12-1
Study Guide and InterventionAdding and Subtracting Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-22-2
© Glencoe/McGraw-Hill 81 Glencoe Algebra 1
Less
on 2
-2
Add Rational Numbers
Adding Rational Numbers, Add the numbers. If both are positive, the sum is positive; if both are negative, Same Sign the sum is negative.
Adding Rational Numbers,Subtract the number with the lesser absolute value from the number with the
Different Signsgreater absolute value. The sign of the sum is the same as the sign of the numberwith the greater absolute value.
Use a number line tofind the sum !2 # (!3).
Step 1 Draw an arrow from 0 to #2.Step 2 From the tip of the first arrow, draw
a second arrow 3 units to the left torepresent adding #3.
Step 3 The second arrow ends at the sum#5. So #2 % (#3) $ #5.
10!1!2!3!4!5!6!7!8!9 2 3
!3 !2
Find each sum.
a. !8 # 5#8 % 5 $ #(⏐#8⏐ # ⏐5⏐)
$ #(8 # 5)$ #3
b. # #! $% ## $ $ % ## $
$ %#⏐ ⏐ # ⏐# ⏐$$ %# # $$
1"4
2"4
3"4
2"4
3"4
2"4
3"4
1"2
3"4
1"2
3"4
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each sum.
1. 12 % 24 2. #6 % 14 3. #12 % (#15)
4. #21.5 % 34.2 5. 8.2 % (#3.5) 6. 23.5 % (#15.2)
7. 90 % (#105) 8. 108 % (#62) 9. #84 % (#90)
10. % 11. % 12. # %
13. # % ## $ 14. # % 15. # % ## $
16. # % ## $ 17. #1.6 % (#1.8) 18. #0.008 % (#0.25)5"6
3"5
10"20
18"40
7"11
1"5
1"4
2"3
3"5
4"9
6"17
3"14
1"3
5"7
© Glencoe/McGraw-Hill 82 Glencoe Algebra 1
Subtract Rational Numbers Every positive rational number can be paired with anegative rational number so that their sum is 0. The numbers, called opposites, areadditive inverses of each other.
Additive Inverse Property For every number a, a % (#a) $ 0.
To subtract a rational number, add its inverse and use the rules for addition given on page 81.
Subtraction of Rational Numbers For any numbers a and b, a # b $ a % (#b).
Find 8.5 ! 10.2.
8.5 # 10.2 $ 8.5 % (#10.2) To subtract 10.2, add its inverse.
$ #(⏐#10.2⏐ # ⏐8.5⏐) ⏐#10.2⏐ is greater, so the result is negative.
$ #1.7 Simplify.
Find each difference.
1. 11 # 41 2. 15 # (#21) 3. #33 # (#17)
4. 18 # (#12) 5. 15.5 # (#2.5) 6. 65.8 # (#23.5)
7. 90 # (#15) 8. #10.8 # (6.8) 9. #84 # (#72)
10. 58.8 # (#11.2) 11. #18.2 # 3.2 12. #9 # (#5.6)
13. # # ## $ 14. # # ## $ 15. #
16. # ## $ 17. # # ## $ 18. #
19. Sanelle was playing a video game. Her scores were %50, %75, #18, and #22. What washer final score?
20. The football team offense began a drive from their 20-yard line. They gained 8 yards, lost12 yards and lost 2 yards before having to kick the ball. What yard line were they onwhen they had to kick the ball?
18"20
24"10
3"9
7"8
1"2
12"23
5"9
9"4
4"7
1"5
3"4
1"3
Study Guide and Intervention (continued)
Adding and Subtracting Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-22-2
ExampleExample
ExercisesExercises
Skills PracticeAdding and Subtracting Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-22-2
© Glencoe/McGraw-Hill 83 Glencoe Algebra 1
Less
on 2
-2
Find each sum.
1. 28 % 13 2. 18 % 54 3. #6 % 15
4. #12 % 25 5. #14 % 11 6. #42 % 18
7. #19 % (#3) 8. #9 % (#17) 9. 25 % (#30)
10. 16 % (#20) 11. % ## $ 12. #2.5 % 3.2
Find each difference.
13. 31 # 12 14. 53 # 47 15. 17 # 20
16. 28 # 39 17. #15 # 65 18. #27 # 13
19. #11 # (#12) 20. #25 # (#36) 21. #9 # (#7)
22. #14 # (#8) 23. #1.5 # 1 24. 3.6 # 4.8
25. # # ## $ 26. # # 27. # %
28. WEATHER At 6:00 P.M., the temperature in North Fork was 28 degrees Fahrenheit.Shortly afterward, a strong cold front passed through, and the temperature dropped 36 degrees by 8:00 A.M. the next morning. What was the temperature at 8:00 A.M.?
3"2
3"4
1"6
1"3
1"2
1"2
3"4
1"4
© Glencoe/McGraw-Hill 84 Glencoe Algebra 1
Find each sum.
1. #82 % 14 2. #33 % 47 3. #17 % (#39)
4. 8 % (#11) 5. #1.7 % 3.2 6. #13.3 % (#0.9)
7. #51.8 % 29.7 8. 7.34 % (#9.06) 9. %
10. # % 11. # % ## $ 12. % ## $
Find each difference.
13. 65 # 93 14. #42 # (#17) 15. 13 # (#19)
16. #8 # 43 17. 82.8 # (#12.4) 18. 1.27 # 2.34
19. #9.26 # 12.05 20. #18.1 # (#4.7) 21. # #
22. # 23. # # ## $ 24. # ## $
FINANCE For Exercises 25–27, use the following information.
The table shows activity in Ben’s checking account. The balance before the activity was$200.00. Deposits are added to an account and checks are subtracted.
Number Date Transaction Amount Balance
5/2 deposit 52.50 252.50
101 5/10 check to Castle Music 25.50 ?
102 6/1 check to Comp U Save 235.40 ?
25. What is the account balance after writing check number 101?
26. What is the account balance after writing check number 102?
27. Realizing that he has just written a check for more than is in the account, Benimmediately deposits $425. What will this make his new account balance?
28. CHEMISTRY The melting points of krypton, radon, and sulfur in degrees Celsius are#156.6, #61.8, and 112.8, respectively. What is the difference in melting points betweenradon and krypton and between sulfur and krypton?
5"6
1"8
3"7
5"2
5"6
4"3
2"3
1"5
2"3
3"8
3"5
3"4
2"3
3"5
5"6
5"9
Practice Adding and Subtracting Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-22-2
Reading to Learn MathematicsAdding and Subtracting Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-22-2
© Glencoe/McGraw-Hill 85 Glencoe Algebra 1
Less
on 2
-2
Pre-Activity How can a number line be used to show a football team’s progress?
Read the introduction to Lesson 2-2 at the top of page 73 in your textbook.
Use positive or negative to complete the following sentences.
The five-yard penalty is shown by the number #5.
The 13-yard pass is shown by the number 13.
Reading the Lesson
1. To add two rational numbers, you can use a number line. Each number will berepresented by an arrow.
a. Where on the number line does the arrow for the first number begin?
b. Arrows for negative numbers will point to the (left/right). Arrows for
positive numbers will point to the (left/right).
2. Two students added the same pair of rational numbers. Both students got the correctsum. One student used a number line. The other student used absolute value. Then theycompared their work.
a. How do the arrows show which number has the greater absolute value?
b. If the longer arrow points to the left, then the sum is (positive/negative). If the longer arrow points to the right, then the sum is
(positive/negative).
3. If two numbers are additive inverses, what must be true about their absolute values?
4. Write each subtraction problem as an addition problem.
a. 12 # 4 b. #15 # 7
c. 0 # 9 d. #20 # 34
Helping You Remember
5. Explain why knowing the rules for adding rational numbers can help you to subtractrational numbers.
© Glencoe/McGraw-Hill 86 Glencoe Algebra 1
Rounding FractionsRounding fractions is more difficult than rounding whole numbers or decimals. For example, think about how you would round inches to
the nearest quarter-inch. Through estimation, you might realize that
is less than . But, is it closer to or to ?
Here are two ways to round fractions. Example 1 uses only thefractions; Example 2 uses decimals.
1"4
1"2
1"2
4"9
4"9
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
2-22-2
Subtract the fraction twice. Use the twonearest quarters.
# $ # $
Compare the differences.
&
The smaller difference shows you whichfraction to round to.
rounds to .1"2
4"9
7"36
1"18
7"36
1"4
4"9
1"18
4"9
1"2
Change the fraction and the two nearestquarters to decimals.
$ 0.44%, $ 0.5, $ 0.25
Find the decimal halfway between the twonearest quarters.
(0.5 % 0.25) $ 0.375
If the fraction is greater than the halfwaydecimal, round up. If not, round down.
0.44% ' 0.3675. So, is more than half way
between and .
rounds to .1"2
4"9
1"2
1"4
4"9
1"2
1"4
1"2
4"9
Example 1Example 1 Example 2Example 2
Round each fraction to the nearest one-quarter. Use either method.
1. 2. 3. 4.
5. 6. 7. 8.
Round each decimal or fraction to the nearest one-eighth.
9. 0.6 10. 0.1 11. 0.45 12. 0.85
13. 14. 15. 16. 5"9
23"25
3"20
5"7
23"30
9"25
31"50
7"20
4"15
7"11
3"7
1"3
Study Guide and InterventionMultiplying Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-32-3
© Glencoe/McGraw-Hill 87 Glencoe Algebra 1
Less
on 2
-3
Multiply Integers You can use the rules below when multiplying integers and rationalnumbers.
Multiplying Numbers with the Same Sign The product of two numbers having the same sign is positive.
Multiplying Numbers with Different Signs The product of two numbers having different signs is negative.
Find each product.
a. !7(6)The signs are different, so the product isnegative.#7(6) $ #42
b. !18(!10)The signs are the same, so the product ispositive.#18(#10) $ 180
Simplify the expression(!2x)5y.
(#2x)5y $ (#2)(5)x ( y Commutative Property ())
$ (#2 ( 5)xy Associative Property
$ #10xy Simplify.
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each product.
1. 11(4) 2. #5(#3) 3. (#24)(#2)
4. (60)(#3) 5. (#2)(#3)(#4) 6. 8(#15)
7. #15(3) 8. (12)(#10) 9. (#22)(#3)(2)
10. (5)(#5)(0)(4) 11. (#15)(45) 12. (#12)(#23)
Simplify each expression.
13. 4(#2x) # 8x 14. 6(#2n ) # 10n 15. 6(3y # y)
16. #3(3d % 2d) 17. #2x(2) % 2x(3y) 18. 4m(#2n) % 2d(#4e)
19. #5(2x % x) # 3(#xy) 20. (2)(#4x % 2x) 21. (#3)(#8n # 6m)
© Glencoe/McGraw-Hill 88 Glencoe Algebra 1
Multiply Rational Numbers Multiplying a rational number by #1 gives you theadditive inverse of the number.
Multiplicative Property of !1The product of any number and #1 is
(#1)(5) $ 5(#1) $ #5 its additive inverse.
Study Guide and Intervention (continued)
Multiplying Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-32-3
Evaluate a3b2 if a $ !2and b $ !5.
a3b2 $ (#2)3(#5)2 Substitution
$ (#8)(25) (#2)3 $ #8 and (#5)2 $ 25
$ #200 different signs → negative product
Evaluate n2#! $ if n $ ! .
n2## $ $ ## $2## $ Substitution
$ # $## $ ## $2
$ ## $## $ or
$ # different signs → negative product3
"20
1"4
1"2
1"2
1"2
3"5
1"4
3"5
1"2
3"5
1"2
3"5
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each product.
1. (#12) 2. ## $## $ 3. ## $# $
4. (6.0)(#0.3) 5. ## $## $## $ 6. 8(#15)
7. #15(#4) 8. # $(#10) 9. ## $(#3)# $
10. # $(#2)(0)# $ 11. ## $# $ 12. ##1 $##2 $
Evaluate each expression if a $ !2.5, b $ 4.2, c $ 5.5, and d $ !0.2.
13. #2a2 14. 5(#2b) 15. #6(cd)
16. #2(3d % 2c) 17. #ad # 3c 18. b2(c # 2d)
19. #5bcd 20. #3d2 % 4 21. (#3)(#8a # 2b)
1"3
1"2
4"5
1"3
1"4
4"5
2"3
2"5
1"2
3"4
1"3
1"2
2"5
2"7
2"3
1"5
1"4
Skills PracticeMultiplying Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-32-3
© Glencoe/McGraw-Hill 89 Glencoe Algebra 1
Less
on 2
-3
Find each product.
1. 9(17) 2. #8(#7)
3. 5(#7) 4. #4(11)
5. #6(#12) 6. 7(#25)
7. # $# $ 8. ## $# $
9. ## $## $ 10. # $## $
11. ## $## $ 12. (1.5)(2.2)
13. (#2.8)(0.5) 14. (2.4)(#0.6)
15. (#4.7)(#1.3) 16. (1.1)(#1.2)
Simplify each expression.
17. 5(#2a) # 8a 18. #6(3x) % 12x
19. 3(4n # n) 20. #4(2d # d)
Evaluate each expression if a $ !1.2, b $ 0.5, c $ , and d $ ! .
21. #4ab 22. #3b2
23. #2a2 24. c2## $
25. d2 26. #3cd
27. STAIRCASES A staircase in an office building starts at ground level. Each step downlowers you by 7.5 inches. What is your height in relation to ground level after descending20 steps?
1"8
1"3
2"3
1"2
2"3
5"6
5"8
3"4
1"2
3"8
1"6
3"5
2"3
1"2
© Glencoe/McGraw-Hill 90 Glencoe Algebra 1
Find each product.
1. 42(7) 2. #28(#17) 3. 15(#34)
4. ## $# $ 5. ## $## $ 6. # $# $7. ##3 $#2 $ 8. ##2 $##1 $ 9. #1 $##1 $
10. (1.5)(8.8) 11. (6.8)(#1.3) 12. (#0.2)(2.8)
13. (#3.6)(#0.55) 14. 6.3(#0.7) 15. (#4)(9)
Simplify each expression.
16. 5(#3a) % 18a 17. #8(4c) % 12c 18. #9(2g # g)
19. 7(2b # 4b) 20. #4x(2y) % (#3b)(#2d) 21. #5p(#3q) % (4m)(#6n)
Evaluate each expression if a $ ! , b $ , c $ !3.4, and d $ 0.7.
22. b2## $ 23. 4ab 24. 5a2(#b)
25. #6d2 26. cd # 3 27. c2(#5d)
28. RECIPES A recipe for buttermilk biscuits calls for 3 cups of flour. How many cups of
flour do you need for the recipe?
COMPUTERS For Exercises 29 and 30, use the following information.
Leeza is downloading a file from a Web site at 47.3 kilobytes per second.
29. How many kilobytes of the file will be downloaded after one minute?
30. How many kilobytes will be downloaded after 4.5 minutes?
CONSERVATION For Exercises 31 and 32, use the following information.
A county commission has set aside 640 acres of land for a wildlife preserve.
31. Suppose of the preserve is marshland. How many acres of the preserve are
marshland?
32. If the forested area of the preserve is 1.5 times larger than the marshland, how manyacres of the preserve are forested?
2"5
1"2
1"3
2"3
3"4
4"5
2"3
1"5
1"4
1"6
2"3
1"2
1"4
5"7
9"10
5"6
4"5
7"8
3"4
Practice Multiplying Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-32-3
Reading to Learn MathematicsMultiplying Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-32-3
© Glencoe/McGraw-Hill 91 Glencoe Algebra 1
Less
on 2
-3
Pre-Activity How do consumers use multiplication of rational numbers?
Read the introduction to Lesson 2-3 at the top of page 79 in your textbook.
• How is the amount of the coupon shown on the sales slip?
• Besides the amount, how is the number representing the coupon differentfrom the other numbers on the sales slip?
Reading the Lesson
1. Complete: If two numbers have different signs, the one number is positive and the other
number is .
2. Complete the table.
Multiplication Are the signs of the numbers the same Is the product positive or negative?Example or different?
a. (#4)(9)
b. (#2)(#13)
c. 5(#8)
d. 6(3)
3. Explain what the term “additive inverse” means to you. Then give an example.
Helping You Remember
4. Describe how you know that the product of #3 and #5 is positive. Then describe howyou know that the product of 3 and #5 is negative.
© Glencoe/McGraw-Hill 92 Glencoe Algebra 1
Compound InterestIn most banks, interest on savings accounts is compounded at set timeperiods such as three or six months. At the end of each period, thebank adds the interest earned to the account. During the next period,the bank pays interest on all the money in the bank, including interest.In this way, the account earns interest on interest.
Suppose Ms. Tanner has $1000 in an account that is compoundedquarterly at 5%. Find the balance after the first two quarters.
Use I $ prt to find the interest earned in the first quarter if p $ 1000 and r $ 5%. Why is t equal to ?
First quarter: I $ 1000 ) 0.05 )
I $ 12.50
The interest, $12.50, earned in the first quarter is added to $1000.The principal becomes $1012.50.
Second quarter: I $ 1012.50 ) 0.05 )
I $ 12.65625
The interest in the second quarter is $12.66.
The balance after two quarters is $1012.50 % 12.66 or $1025.16.
Answer each of the following questions.
1. How much interest is earned in the third quarter of Ms. Tanner’saccount?
2. What is the balance in her account after three quarters?
3. How much interest is earned at the end of one year?
4. What is the balance in her account after one year?
5. Suppose Ms. Tanner’s account is compounded semiannually. Whatis the balance at the end of six months?
6. What is the balance after one year if her account is compoundedsemiannually?
1"4
1"4
1"4
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
2-32-3
Study Guide and InterventionDividing Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-42-4
© Glencoe/McGraw-Hill 93 Glencoe Algebra 1
Less
on 2
-4
Divide Integers The rules for finding the sign of a quotient are similar to the rules forfinding the sign of a product.
Dividing Two Numbers with the Same Sign The quotient of two numbers having the same sign is positive.
Dividing Two Numbers with Different Signs The quotient of two numbers having different signs is negative.
Find each quotient.
a. !88 ( (!4)#88 * (#4) $ 22 same signs → positive quotient
b.
$ #8 different signs → negative quotient#64"8
!64"8
Simplify .
$ .
$
$
$ #8
32"#4
32""#3 % (#1)
#4(#8)""#3 % (#1)
#4(#10 % 2)""
#3 % (#1)
!4(!10 # 2)""
!3 # (!1)Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each quotient.
1. #80 * (#10) 2. #32 * 16 3. 80 * 5
4. 18 * (#3) 5. #12 * (#3) 6. 8 * (#2)
7. #15 * (#3) 8. 121 * (#11) 9. #24 * 1.5
10. 0 * (#8) 11. #125 * (#25) 12. #104 * 4
Simplify.
13. 14. 15.
16. 17. 18. 4(#12 % 4)""
#2(8)#4(#8 % (#4))""
#3 % (#3)#12(2 % (#3))""
#4 % 1
#6(#6 % 2)""#10 % (#2)
5(#10 % (#2))""
#2 % 1#2 % (#4)""(#2) % (#1)
© Glencoe/McGraw-Hill 94 Glencoe Algebra 1
Divide Rational Numbers The rules for division with integers also apply to division
with rational numbers. To divide by any nonzero number, , multiply by the reciprocal of
that number, .
Division of Rational Numbers * $ ) d"c
a"b
c"d
a"b
d"c
c"d
Study Guide and Intervention (continued)
Dividing Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-42-4
a. Find !5 ( 8.
#5 * 8 $ # *
$ # )
$ # or #
b. Find .
$ 12.3#83.64"
#6.8
!83.64"
!6.8
2"3
16"24
1"8
16"3
8"1
16"3
1"3
1"3
Simplify .
$ (#20a % 15) * 5
$ (#20a % 15)# $$ #20a# $ % 15# $$ #4a % 3
1"5
1"5
1"5
#20a % 15""5
!20a # 15""5
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each quotient.
1. # * 2 2. #32 * 3. # *
4. 1.8 * (#3) 5. #12.9 * (#0.3) 6. * ## $7. # * ## $ 8. 52.5 * (#4.2) 9. # *
10. 105 * (#1.5) 11. #12.5 * (#2.5) 12. # *
Simplify each expression.
13. 14. 15.
16. 17. 18.
Evaluate each expression if a $ !6, b $ 2.5, c $ !3.2, and d $ 4.8.
19. 20. 21. a # 2b"c % d
a % d"b
ab"d
57y # 12""3
36a # 12""12
18a # 6b""
#3
#144a"6
16x"2
#44a"4
4"3
1"4
5"3
8"15
3"10
15"32
2"3
3"8
1"5
2"5
1"4
1"8
Skills PracticeDividing Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-42-4
© Glencoe/McGraw-Hill 95 Glencoe Algebra 1
Less
on 2
-4
Find each quotient.
1. #32 * (#4) 2. #28 * 7
3. #45 * (#15) 4. 39 * (#3)
5. #56 * 14 6. 62 * (#4)
7. #23 * (#5) 8. 52 * (#8)
9. #90 * 12 10. #16.5 * 11
11. #1.44 * 1.2 12. #16.2 * (#0.4)
13. 6 * ## $ 14. # *
15. # * ## $ 16. *
Simplify each expression.
17. 18.
19. 20.
Evaluate each expression if g $ !4, h $ 2.5, k $ 1.4, and m $ !0.8. Round to thenearest hundredth.
21. 22.
23. 24. hk * gm
25. km * gh 26. k % m"g
hk"m
hm"g
gh"m
#54z % 18""
#916c # 4"
#4
216x"12
27a"3
2"3
1"2
1"4
2"3
1"2
3"4
2"9
© Glencoe/McGraw-Hill 96 Glencoe Algebra 1
Find each quotient.
1. 75 * (#15) 2. #323 * (#17) 3. #88 * 16
4. 65.7 * (#9) 5. #36.08 * 8 6. #40.05 * (#2.5)
7. #9 * 8. # * ## $ 9. * ## $
Simplify each expression.
10. 11. 12.
13. 14. 15.
Evaluate each expression if p $ !6, q $ 4.5, r $ 3.6, and s $ !5.2. Round to thenearest hundredth.
16. 17. 18. ps * qr
19. rs * pq 20. 21.
22. EXERCISE Ashley walks 2 miles around a lake three times a week. If Ashley walks
around the lake in hour, what is her rate of speed? (Hint: Use the formula r $ ,
where r is rate, d is distance, and t is time.)
23. PUBLICATION A production assistant must divide a page of text into two columns. If
the page is 6 inches wide, how wide will each column be?
ROLLER COASTERS For Exercises 24 and 25, use the following information.
The formula for acceleration is a $ , where a is acceleration, f is final speed, s is starting speed, and t is time.
24. The Hypersonic XLC roller coaster in Virginia goes from zero to 80 miles per hour in 1.8 seconds. What is its acceleration in miles per hour per second to the nearest tenth?Source: www.thrillride.com
25. What is the acceleration in feet per second per second? (Hint: Convert miles to feet andhours to seconds, then apply the formula for acceleration. 1 mile $ 5280 feet)
f # s"t
3"4
d"t
3"4
1"2
r % s"q
p # q"r
rs"q
qr"p
#4c % (#16d)""4
8k #12h""4
18x % 12y""
#6
3t % 12"
#325 # 5x"5
168p"#14
49"54
14"63
3"8
5"6
3"5
Practice Dividing Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-42-4
Reading to Learn MathematicsDividing Rational Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-42-4
© Glencoe/McGraw-Hill 97 Glencoe Algebra 1
Less
on 2
-4
Pre-Activity How can you use division of rational numbers to describe data?
Read the introduction to Lesson 2-4 at the top of page 84 in your textbook.
• What is meant by the term mean?
• In the expression , will the numerator be positive or negative?
Reading the Lesson
1. Explain what the term inverse operations means to you.
2. Write negative or positive to describe the quotient. Explain your answer.
Expression Negative or Positive? Explanation
a.
b.
c.
Helping You Remember
3. Explain how knowing the rules for multiplying rational numbers can help you rememberthe rules for dividing rational numbers.
(#5.6)(#2.4)""1.92
#78"#13
35"#7
(#127) % 54 % (#65)"""3
© Glencoe/McGraw-Hill 98 Glencoe Algebra 1
Other Kinds of MeansThere are many different types of means besides the arithmeticmean. A mean for a set of numbers has these two properties:
a. It typifies or represents the set.b. It is not less than the least number and it is not greater than the
greatest number.
Here are the formulas for the arithmetic mean and three other means.
Enrichment
NAME ______________________________________________ DATE______________ PERIOD _____
2-42-4
Arithmetic Mean
Add the numbers in the set. Then dividethe sum by n, the number of elements inthe set.
Harmonic Mean
Divide the number of elements in the set bythe sum of the reciprocals of the numbers.
Geometric Mean
Multiply all the numbers in the set. Thenfind the nth root of their product.
n!x1 ! x2" ! x3 !"… ! xn"
Quadratic Mean
Add the squares of the numbers. Dividetheir sum by the number in the set.Then, take the square root.
#$$$x12 " x2
2 " x32 " … " xn
2
####n
n####x1
1# " #x
1
2# " #x
1
3# " … " #x
1
n#
x1 " x2 " x3 " … " xn###n
Find the four different means to the nearest hundredth for each set of numbers.
1. 10, 100 2. 50, 60
A ! 55 G ! 31.62 A ! 55 G ! 54.77
H ! 18.18 Q ! 71.06 H ! 54.55 Q ! 55.23
3. 1, 2, 3, 4, 5, 4. 2, 2, 4, 4
A ! 3 G ! 2.61 A ! 3 G ! 2.83
H ! 2.19 Q ! 3.32 H ! 2.67 Q ! 3.16
5. Use the results from Exercises 1 to 4 to compare the relative sizesof the four types of means.From least to greatest, the means are the harmonic, geometric,arithmetic, and quadratic means.
Study Guide and InterventionStatistics: Displaying and Analyzing Data
NAME ______________________________________________ DATE ____________ PERIOD _____
2-52-5
© Glencoe/McGraw-Hill 99 Glencoe Algebra 1
Less
on 2
-5
Create Line Plots and Stem-and-Leaf Plots One way to display data graphicallyis with a line plot. A line plot is a number line labeled with a scale that includes all thedata and )s placed above a data point each time it occurs in the data list. The )s representthe frequency of the data. A stem-and-leaf plot can also be used to organize data. Thegreatest common place value is called the stem, and the numbers in the next greatest placevalue form the leaves.
Draw a line plot for the data.!3 3 4 7 9 10 !2 3
6 4 3 9 !1 !2 4 2
Step 1 The value of the data ranges from#3 to 10, so construct a number linecontaining those points.
Step 2 Then place an ) above the numbereach time it occurs.
76543210!1!2!3
) ) ) ) ) ) ) ) )) ) )
) ))
)
8 9 10
76543210!1!2!3 8 9 10
Use the data below tocreate a stem-and-leaf plot.62 74 89 102 92 65 68 98 78 6578 80 83 93 87 89 104 109 104 68 97 68 64 98 93 90 102 104
The greatest common place value is tens, sothe digits in the tens place are the stems.Thus 62 would have a stem of 6 and 104would have a stem of ten. The stem-and-leafplot is shown below.Stem | Leaf
6 | 2 4 5 5 8 8 87 | 4 8 88 | 0 3 7 9 99 | 0 2 3 3 7 8 8
10 | 2 2 4 4 4 9 6⏐2 $ 62
Example 1Example 1 Example 2Example 2
ExercisesExercises
Use the table at the right for Exercises 1–3.
1. Make a line plot representing the weights of the wrestlers shown in the table at the right.
2. How many wrestlers weigh over 140 lb?
3. What is the greatest weight?
Use each set of data to make a stem-and-leaf plot.
4. 32 45 41 29 30 30 31 34 38 5. 102 104 99 109 108 112 115 120 36 32 34 41 40 42 41 29 30 112 114 98 94 96 101 100 102
200190180170160150140130120110100
) ) ) )) )
)
) ) )) )
) ))
Weights of Junior Varsity Wrestlers (pounds)
170 160 135 135 160 122 188 154108 135 140 122 103 190 154
© Glencoe/McGraw-Hill 100 Glencoe Algebra 1
Analyze Data Numbers that represent the centralized, or middle, value of a set of dataare called measures of central tendency. Three measures of central tendency are themean, median, and mode.
Definition Example
MeanSum of the data values divided by the
Data: 24, 36, 21, 30, 21, 30; $ 27number of values in the data set.
The middle number in a data set when the numbers are arranged in numerical
Median order. If there is an even number of Data: 21, 21, 25, 30, 31, 42; $ 27.5values, the median is halfway between the two middle values.
ModeThe number or numbers that occur
Data: 21, 21, 24, 30, 30, 36; 21 and 30 are modesmost often in the set of data.
Which measure of central tendency best represents the data?
Find the mean, median, and mode.
Mean $ 105
Median $ 102
Modes $ 99 and 112
The median best represents the center of the data since the mean is too high.
Find the mean, median, and mode for each data set. Then tell which bestrepresents the data.
1. 2. 3.
4. 5.
3210
) ) ) ) ) )) ) )) )
))
4 5 6 7
Month Days above 90*
May 4
June 7
July 14
August 12
September 8
Stem | Leaf 5 | 0 1 96 | 2 2 5 57 | 1 3 58 | 0 3 7 7 5 |0 $ 50
Stem | Leaf9 | 0 0 1 3 9
10 | 2 2 511 |12 | 0 3 3 8 8 9 9 |0 $ 90
Stem | Leaf2 | 4 7 73 | 1 2 6 6 6 94 | 05 | 8 8 9 2 |4 $ 24
Stem | Leaf9 | 4 6 8 9 9
10 | 0 1 2 4 8 911 | 2 212 | 0 1 9 |4 $
25 % 30"2
24 % 36 % 21 % 30 % 21 % 30""""6
Study Guide and Intervention (continued)
Statistics: Displaying and Analyzing Data
NAME ______________________________________________ DATE ____________ PERIOD _____
2-52-5
ExampleExample
ExercisesExercises
Skills PracticeStatistics: Displaying and Analyzing Data
NAME ______________________________________________ DATE ____________ PERIOD _____
2-52-5
© Glencoe/McGraw-Hill 101 Glencoe Algebra 1
Less
on 2
-5
Use each set of data to make a line plot.
1. 59 39 50 60 45 39 59 45 31 59 2. 5 #2 4 0 7 4 3 7 #1 455 43 39 42 59 35 31 55 43 52 #2 5 2 2 3 4 5 0 #2 2
INCOME For Exercises 3–5, use the list that shows the income from each assignment for a private investigator for a year.
3. Make a line plot of the data.
4. What was the median income per assignment for the investigator?
5. Does the median best represent the data?
Use each set of data to make a stem-and-leaf plot.
6. 52 68 40 74 65 68 59 75 67 73 7. 1.5 2.3 1.7 3.0 4.1 5.3 4.755 63 39 42 59 35 31 59 63 42 1.9 2.2 2.8 4.3 5.2 4.1 2.2
EMPLOYMENT For Exercises 8–10, use the list that shows the ages of employees at Watson &Sterling Publications.
8. Make a stem-and-leaf plot of the data.
9. Which age occurs most frequently?
10. Does the mode best represent the data?Explain.
Stem | Leaf
||||
20 52 21 39 40 58 27 48 36 20 51 2645 30 49 22 59 50 33 35 28 43 55 20
Stem | Leaf
|||||
Stem | Leaf
|||||
5000 5500 6000 6500 7000 7500 8000
) ) ) ) ) ))) ) )
))
6300 6100 78005600 7800 51006000 7200 63005100 6100 7800
76543210!1!2
) ) ) ) ) ) ) )) ) ) ) ) )) ) )
))
)
30 35 40 45 50 55 60
) ) ) ) ) ) )) ) ))) ) ) ) )
) ))
)
© Glencoe/McGraw-Hill 102 Glencoe Algebra 1
Use each set of data to make a line plot.
1. 72 47 62 78 49 67 80 2. #2 #1.3 1.5 0.1 #1.7 0.4 1.554 47 72 55 62 47 54 1 #1.3 #2 #2.9 0.1 1.3 1.262 80 47 78 72 46 #2.6 1.2 0.2 #1.3 #2.6
HEALTH For Exercises 3 and 4, use the list that shows the grams of saturated fat in a serving of a variety of grains such as bread, cereal, crackers, and pasta.
3. Make a line plot of the data.
4. Which measure of central tendency best describes the data? Explain.
Use each set of data to make a stem-and-leaf plot.
5. 41 53 22 50 41 27 36 57 20 31 6. 4.1 7.3 6.9 5.7 4.8 7.3 5.628 52 41 33 28 27 41 52 22 30 6.0 4.4 7.5 4.6 7.9 5.1 7.7
EMPL0YMENT For Exercises 7–10, use the lists that show survey results ofstudents’ time spent on the Internet and on the telephone for a month.
7. Make a stem-and-leaf plot to compare the data.8. Which value appears most frequently in each set
of data?9. Is the mode the best measure to compare the data?
10. Overall, did students spend more time on the Internet or the telephone?
Internet | Stem | Telephone
| || || || || || |
Internet Telephone
42 19 28 8 35 42 20 18 36 52 40 28 43 24 8 53
51 4 7 29 14 22 6 41 26 48 35 58 8 4
Stem | Leaf
||||
Stem | Leaf
||||
0 0.5 1 1.5 2 2.5 3
)))
))))
))
) ) ))))
0.3 1.2 0.1 0.3 0.40.4 0.5 0.1 0.4 0.40.1 1.2 2.8 1.3 1.5
!3 !2.5 !2 !1.5 !1 !0.5 0 0.5 1 1.5
) ))
))
) )))
) ))
) ))
))))
45 50 55 60 65 70 75 80
)))))
) )))
)))
) ))))
)))
Practice Statistics: Displaying and Analyzing Data
NAME ______________________________________________ DATE ____________ PERIOD _____
2-52-5
Reading to Learn MathematicsStatistics: Displaying and Analyzing Data
NAME ______________________________________________ DATE ____________ PERIOD _____
2-52-5
© Glencoe/McGraw-Hill 103 Glencoe Algebra 1
Less
on 2
-5
Pre-Activity How are line plots and averages used to make decisions?
Read the introduction to Lesson 2-5 at the top of page 88 in your textbook.
• What was the number one name for boys in all five decades?
• Look at the decade in which you were born. Is your name or the names ofany of the other students in your class in the top five for that decade?
Reading the Lesson
1. Use the line plot shown below to answer the questions.
a. What are the data points for the line plot?
b. What do the three )’s above the 6 represent?
2. Explain what is meant by the frequency of a data number.
3. Use the stem-and-leaf plot shown at the right.
a. How is the number 758 represented on the plot?
b. Explain how you know there are 23 numbers in thedata.
Helping You Remember
4. Describe how you would explain the process of finding the median and mode from astem-and-leaf plot to a friend who missed Lesson 2-5.
Stem | Leaf72 | 0 1 1 2 573 | 2 2 2 7 9 974 | 1 3 375 | 6 6 8 976 | 0 1 8 8 8 74⏐2 $ 742
76543210!1!2!3!4!5!6
) ) ) ) ) ) ) ) ) ) ) ) ) )) ) ) ) ) ) ) )
) ))
))
))
© Glencoe/McGraw-Hill 104 Glencoe Algebra 1
Runs Created In The 1978 Bill James Baseball Abstract, the author introduced the “runs created” formula.
R $ where for each player h $ number of hits
w $ number of walks,
t $ number of total bases,
b $ number of at-bats, and
R $ approximate number of runs a team scores due to this player’s actions
1. As of June 29, 2001, Roberto Alomar of the Cleveland Indians and Seattle Marinersplayer Ichiro Suzuki were tied with the highest American League batting average at.351. Find the number of runs created by each player using the data below.
h w t b Runs Created
Alomar 97 37 145 276
Suzuki 121 13 159 345
Based on this information, who do you think is the more valuable American Leagueplayer? Why?
2. Carlos Lee of the Chicago White Sox and New York Yankee Bernie Williams were bothbatting .314. Find the number of runs created by each player using the data below.
h w t b Runs Created
Lee 81 13 141 258
Williams 74 31 123 236
3. Why would baseball teams want to calculate the number of runs created by each of theirplayers?
(h + w)t"(b + w)
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
2-52-5
Study Guide and InterventionProbability: Simple Probability and Odds
NAME ______________________________________________ DATE ____________ PERIOD _____
2-62-6
© Glencoe/McGraw-Hill 105 Glencoe Algebra 1
Less
on 2
-6
Probability The probability of a simple event is a ratio that tells how likely it is thatthe event will take place. It is the ratio of the number of favorable outcomes of the event tothe number of possible outcomes of the event. You can express the probability either as afraction, as a decimal, or as a percent.
Probability of a Simple Event For an event a, P(a) $ .number of favorable outcomes""""number of possible outcomes
Mr. Babcock chooses 5 out of 25 students in his algebra classat random for a special project. What isthe probability of being chosen?
P(being chosen) $
The probability of being chosen is or .1"5
5"25
number of students chosen""""total number of students
A bowl contains 3 pears,4 bananas, and 2 apples. If you take apiece of fruit at random, what is theprobability that it is not a banana?
There are 3 % 4 % 2 or 9 pieces of fruit.There are 3 % 2 or 5 pieces of fruit that arenot bananas.
P(not banana) $
$
The probability of not choosing a banana is .5"9
5"9
number of other pieces of fruit""""total number of pieces of fruit
Example 1Example 1 Example 2Example 2
ExercisesExercises
A card is selected at random from a standard deck of 52 cards. Determine eachprobability.
1. P(10) 2. P(red 2) 3. P(king or queen)
4. P(black card) 5. P(ace of spades) 6. P(spade)
Two dice are rolled and their sum is recorded. Find each probability.
7. P(sum is 1) 8. P(sum is 6) 9. P(sum is less than 4)
10. P(sum is greater than 11) 11. P(sum is less than 15) 12. P(sum is greater than 8)
A bowl contains 4 red chips, 3 blue chips, and 8 green chips. You choose one chipat random. Find each probability.
13. P(not a red chip) 14. P(red or blue chip) 15. P(not a green chip)
A number is selected at random from the list {1, 2, 3, …, 10}. Find each probability.
16. P(even number) 17. P(multiple of 3) 18. P(less than 4)
19. A computer randomly chooses a letter from the word COMPUTER. Find the probabilitythat the letter is a vowel.
© Glencoe/McGraw-Hill 106 Glencoe Algebra 1
Odds The odds of an event occurring is the ratio of the number of ways an event can occur(successes) to the number of ways the event cannot occur (failures).
Odds
A die is rolled. Find the odds of rolling a number greater than 4.
The sample space is {1, 2, 3, 4, 5, 6}. Therefore, there are six possible outcomes. Since 5 and6 are the only numbers greater than 4, two outcomes are successes and four are failures.
So the odds of rolling a number greater than 4 is , or 1:2.
Find the odds of each outcome if the spinner at the right is spun once.
1. multiple of 4 2. odd number
3. even or a 5 4. less than 4
5. even number greater than 5
Find the odds of each outcome if a computer randomly chooses a number between1 and 20.
6. the number is less than 10 7. the number is a multiple of 4
8. the number is even 9. the number is a one-digit number
A bowl of money at a carnival contains 50 quarters, 75 dimes, 100 nickels, and 125 pennies. One coin is randomly selected.
10. Find the odds that a dime will not be chosen.
11. What are the odds of choosing a quarter if all the dimes are removed?
12. What are the odds of choosing a penny?
Suppose you drop a chip onto the grid at the right. Find the odds of each outcome.
13. land on a shaded square
14. land on a square on the diagonal
15. land on square number 16
16. land on a number greater than 12
17. land on a multiple of 5
1
5
9
13
2
6
10
14
3
7
11
15
4
8
12
16
129
4
38
7
10
56
2"4
number of successes"""number of failures
Study Guide and Intervention (continued)
Probability: Simple Probability and Odds
NAME ______________________________________________ DATE ____________ PERIOD _____
2-62-6
ExampleExample
ExercisesExercises
Skills PracticeProbability: Simple Probability and Odds
NAME ______________________________________________ DATE ____________ PERIOD _____
2-62-6
© Glencoe/McGraw-Hill 107 Glencoe Algebra 1
Less
on 2
-6
One chip is randomly selected from a jar containing 8 yellow chips, 10 blue chips,7 green chips, and 5 red chips. Find each probability.
1. P(blue) 2. P(green)
3. P(yellow or green) 4. P(blue or yellow)
5. P(not red) 6. P(not blue)
Find the probability of each outcome if the spinner is spun once.
7. P(multiple of 3) 8. P(less than 7)
9. P(odd or 2) 10. P(not 1)
A person is born in the month of June. Find each probability.
11. P(date is a multiple of 6) 12. P(date is before June 15)
13. P(before June 7 or after June 24) 14. P(not after June 5)
Find the odds of each outcome if a computer randomly picks a letter in the nameThe Petrified Forest.
15. the letter f 16. the letter e
17. the letter t 18. a vowel
CLASS SCHEDULES For Exercises 19–22, use the following information.
A student can select an elective class from the following: 3 in music, 5 in physical education,2 in journalism, 8 in computer programming, 4 in art, and 6 in drama. Find each of the oddsif a student forgets to choose an elective and the school assigns one at random.
19. The class is computer programming.
20. The class is drama.
21. The class is not physical education.
22. The class is not art.
18
456 3
7 2
© Glencoe/McGraw-Hill 108 Glencoe Algebra 1
One chip is randomly selected from a jar containing 13 blue chips, 8 yellow chips,15 brown chips, and 6 green chips. Find each probability.
1. P(brown) 2. P(green)
3. P(blue or yellow) 4. P(not yellow)
A card is selected at random from a standard deck of 52 cards. Find eachprobability.
5. P(heart) 6. P(black card)
7. P(jack) 8. P(red jack)
Two dice are rolled and their sum is recorded. Find each probability.
9. P(sum less than 6) 10. P(sum less than 2)
11. P(sum greater than 10) 12. P(sum greater than 9)
Find the odds of each outcome if a computer randomly picks a letter in the nameThe Badlands of North Dakota.
13. the letter d 14. the letter a
15. the letter h 16. a consonant
CLASS PROJECTS For Exercises 17–20, use the following information.
Students in a biology class can choose a semester project from the following list: animalbehavior (4), cellular processes (2), ecology (6), health (7), and physiology (3). Find each ofthe odds if a student selects a topic at random.
17. the topic is ecology
18. the topic is animal behavior
19. the topic is not cellular processes
20. the topic is not health
SCHOOL ISSUES For Exercises 21 and 22, use the following information.
A news team surveyed students in grades 9–12 on whether to change the time school begins. One student will be selected atrandom to be interviewed on the evening news. The table gives the results.
21. What is the probability the student selected will be in the
9th grade?
22. What are the odds the student selected wants no change?
Grade 9 10 11 12
No change 6 2 5 3
Hour later 10 7 9 8
Practice Probability: Simple Probability and Odds
NAME ______________________________________________ DATE ____________ PERIOD _____
2-62-6
Reading to Learn MathematicsProbability: Simple Probability and Odds
NAME ______________________________________________ DATE ____________ PERIOD _____
2-62-6
© Glencoe/McGraw-Hill 109 Glencoe Algebra 1
Less
on 2
-6
Pre-Activity Why is probability important in sports?
Read the introduction to Lesson 2-6 at the top of page 96 in your textbook.
Look up the definition of the word probability in a dictionary. Rewrite thedefinition in your own words.
Reading the Lesson
1. Write whether each statement is true or false. If false, replace the underlined word ornumber to make a true statement.
a. Probability can be written as a fraction, a decimal, or a percent.
b. The sample space of flipping one coin is heads or tails.
c. The probability of an impossible event is 1.
d. The odds against an event occurring are the odds that the event will occur.
2. Explain why the probability of an event cannot be greater than 1 while the odds of anevent can be greater than 1.
Helping You Remember
3. Probabilities are usually written as fractions, decimals, or percents. Odds are usuallywritten with a colon (for example, 1:3). How can the spelling of the word colon helpremember this?
© Glencoe/McGraw-Hill 110 Glencoe Algebra 1
Geometric ProbabilityIf a dart, thrown at random, hits the triangular board shown at the right, what is the probability that it will hit the shaded region? Thiscan be determined by comparing the area of the shaded region to thearea of the entire board. This ratio indicates what fraction of the tosses should hit in the shaded region.
$
$ or
In general, if S is a subregion of some region R, then the probability, P(S), that a point,chosen at random, belongs to subregion S is given by the following:
P(S) $
Find the probability that a point, chosen at random, belongs to the shadedsubregions of the following figures.
1. 2. 3.
4. 5. 6.
7. 8. 9.2
2
4 48
4
4
4
4 4
6
6
66
66
6&'3 6&'3
5
5
55 55
6
6
4
4
4 4
4
6
44 4
6 63 3
5
5
area of subregion S"""area or region R
1"2
12"24
"12
"(4)(6)""12
"(8)(6)
area of shaded region"""area of triangular board
6
44
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
2-62-6
Study Guide and InterventionSquare Roots and Real Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
© Glencoe/McGraw-Hill 111 Glencoe Algebra 1
Less
on 2
-7
Square Roots A square root is one of two equal factors of a number. For example, thesquare roots of 36 are 6 and #6, since 6 ( 6 or 62 is 36 and (#6)(#6) or (#6)2 is also 36. Arational number like 36, whose square root is a rational number, is called a perfectsquare.The symbol &' is a radical sign. It indicates the nonnegative, or principal, square root of the number under the radical sign. So &36% $ 6 and #&36% $ #6. The symbol +&36%represents both square roots.
Find !%& .
#() represents the negative square root of .
$ # $2→ #() $ #
5"7
25"49
5"7
25"49
25"49
25"49
25"49 Find +'0.16(.
+&0.16% represents the positive andnegative square roots of 0.16.0.16 $ 0.42 and 0.16 $ (#0.4)2
+&0.16% $ +0.4
Example 1Example 1 Example 2Example 2
ExercisesExercises
Find each square root.
1. &64% 2. #&81% 3. &16.81%
4. +&100% 5. #() 6. #&121%
7. +() 8. #() 9. +()
10. #&3600% 11. #&6.25% 12. +&0.000%4%
13. () 14. #() 15. +&1.21%36"49
144"196
121"100
25"16
25"144
4"25
© Glencoe/McGraw-Hill 112 Glencoe Algebra 1
Classify and Order Numbers Numbers such as !2" and !3" are not perfect squares.Notice what happens when you find these square roots with your calculator. The numberscontinue indefinitely without any pattern of repeating digits. Numbers that cannot bewritten as a terminating or repeating decimal are called irrational numbers. The set ofreal numbers consists of the set of irrational numbers and the set of rational numberstogether. The chart below illustrates the various kinds of real numbers.
Natural Numbers {1, 2, 3, 4, …}
Whole Numbers {0, 1, 2, 3, 4, …}
Integers {…, !3, !2, !1, 0, 1, 2, 3, …}
Rational Numbers {all numbers that can be expressed in the form , where a and b are integers and b " 0}
Irrational Numbers {all numbers that cannot be expressed in the form , where a and b are integers and b " 0}
Name the set or sets of numbers to which each real number belongs.
a. Because 4 and 11 are integers, this number is a rational number.
b. !81" Because !81" # 9, this number is a natural number, a whole number, an integer,and a rational number.
c. !32" Because !32" # 5.656854249…, which is not a repeating or terminating decimal,this number is irrational.
Name the set or sets of numbers to which each real number belongs.
1. 2. ! 3. 4. !54"natural, whole, rational rational irrationalinteger, rational
5. 3.145 6. !25" 7. 0.62626262… 8. !22.51"rational natural, whole, rational irrational
integer, rational
Write each set of numbers in order from least to greatest.
9. ! , !5, !25", 10. !0.09", !0.3131…, 11. !1.2"5", 0.05, ! , !5"
!5, ! , , !25" !0.3131…, !0.09", !1.2"5", ! , 0.05, !5"
12. , !2, !124", !3.11 13. !!1.44", !0.35 14. 0.3"5", 2 , ! , !5"
!3.11, !2, , !124" !!1.44", !0.35, ! , 0.3"5", !5", 2 1"3
9"5
1"5
5"4
9$5
1$3
1$5
5$4
1"4
3"5
7"4
3"4
1$4
3$5
7$4
3$4
2$3
6$7
84$12
4"11
a$b
a$b
Study Guide and Intervention (continued)
Square Roots and Real Numbers
NAME ______________________________________________ DATE______________ PERIOD _____
2-72-7
ExampleExample
ExercisesExercises
Skills PracticeSquare Roots and Real Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
© Glencoe/McGraw-Hill 113 Glencoe Algebra 1
Less
on 2
-7
Find each square root. If necessary, round to the nearest hundredth.
1. &144% 2. #&36%
3. +&0.25% 4. #()5. +&17% 6. &2.25%
Name the set or sets of numbers to which each real number belongs.
7. # 8. #
9. &29% 10. &196%
11. 12. &1.8%
Graph each solution set.
13. x ' #1 14. x , 1
15. x & 1.5 16. x - #2.5
Replace each ● with %, ,, or $ to make each sentence true.
17. ● 0.4% 18. 0.0%9% ●
19. 6.2%3% ● &39% 20. ●
Write each set of numbers in order from least to greatest.
21. &5%, 2.3%6%, 22. , 0.2%1%, &0.05%
23. #&12%, #3.4%8%, #&11% 24. 0.4%3%, , 3"7
&6%"5
2"9
7"3
1"&8%
1"8
1"90
4"9
!2 !1!4 !3 0 1 2 3 4!2 !1!4 !3 0 1 2 3 4
!2 !1!4 !3 0 1 2 3 4!2 !1 0 1 2 3 4 5 6
9"13
5"6
28"7
49"100
© Glencoe/McGraw-Hill 114 Glencoe Algebra 1
Find each square root. If necessary, round to the nearest hundredth.
1. &324% 2. #&62% 3. +&25% 4. #&84%
5. +() 6. #() 7. #&0.081% 8. +&3.06%
Name the set or sets of numbers to which each real number belongs.
9. &93% 10. #&0.062%5% 11. 12. #
Graph each solution set.
13. x & #0.5 14. x - #3.5
Replace each ● with %, ,, or $ to make each sentence true.
15. 0.9%3% ● &0.93% 16. 8.1%7% ● &66% 17. ●
Write each set of numbers in order from least to greatest.
18. &0.03%, , 0.1%7% 19. # , #&8%, # 20. #&8.5%, # , #2
21. SIGHTSEEING The distance you can see to the horizon is given by the formula d $ &1.5h%, where d is the distance in miles and h is the height in feet above the horizon line. Mt. Whitney is the highest point in the contiguous 48 states. Its elevation is 14,494 feet. The lowest elevation, at #282 feet, is located near Badwater, California.With a clear enough sky and no obstructions, could you see from the top of Mt. Whitneyto Badwater if the distance between them is 135 miles? Explain.
22. SEISMIC WAVES A tsunami is a seismic wave caused by an earthquake on the oceanfloor. You can use the formula s $ 3.1&d%, where s is the speed in meters per second and d is the depth of the ocean in meters, to determine the speed of a tsunami. If anearthquake occurs at a depth of 200 meters, what is the speed of the tsunami generatedby the earthquake?
19"20
&35%"2
&7%"8
84"30
&2%"8
&5%"6
5"6
!2 !1!4 !3 0 1 2 3 4!2 !1!4 !3 0 1 2 3 4
144"3
8"7
7"12
4"289
Practice Square Roots and Real Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
Reading to Learn MathematicsSquare Roots and Real Numbers
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
© Glencoe/McGraw-Hill 115 Glencoe Algebra 1
Less
on 2
-7
Pre-Activity How can using square roots determine the surface area of thehuman body?
Read the introduction to Lesson 2-7 at the top of page 103 in your textbook.
The expression &3600% is read, “the square root of 3600.” How would youread the expression &64%?
Reading the Lesson
Complete each statement below.
1. The symbol &' is called a and is used to indicate anonnegative or principal square root of the expression under the symbol.
2. A of an irrational number is a rational number that is closeto, but not equal to, the value of the irrational number.
3. The positive square root of a number is called the squareroot of the number.
4. A number whose positive square root is a rational number is a .
5. Write each of the following as a mathematical expression that uses the &' symbol.
a. the positive square root of 1600
b. the negative square root of 729
c. the principal square root of 3025
6. The irrational numbers and rational numbers together form the set of numbers.
Helping You Remember
7. Use a dictionary to look up several words that begin with “ir-”. What does the prefix “ir-”mean? How can this help you remember the meaning of the word irrational?
© Glencoe/McGraw-Hill 116 Glencoe Algebra 1
Scale DrawingsThe map at the left below shows building lots for sale. The scale ratiois 1:2400. At the right below is the floor plan for a two-bedroomapartment. The length of the living room is 6 m. On the plan theliving room is 6 cm long.
Answer each question.
1. On the map, how many feet are represented by an inch?
2. On the map, measure the frontage of Lot 2 on Sylvan Road in inches. What is the actualfrontage in feet?
3. What is the scale ratio represented on the floor plan?
4. On the floor plan, measure the width of the living room in centimeters. What is theactual width in meters?
5. About how many square meters of carpeting would be needed to carpet the living room?
6. Make a scale drawing of your classroom using an appropriate scale.
7. Use your scale drawing to determine how many square meters of tile would be needed toinstall a new floor in your classroom.
Closet
Closet
Closet
Closet
Kitchen
BedroomBedroom Bath
Dining Area
Living Room
Lot 3
Lot 2
Lot 1
Suns
hine
Lak
e
Sylv
an R
oad
Enrichment
NAME ______________________________________________ DATE ____________ PERIOD _____
2-72-7
©G
lenc
oe/M
cGra
w-H
ill76
Gle
ncoe
Alg
ebra
1
Abs
olut
e Va
lue
On
a nu
mbe
r lin
e,!
3 is
thr
ee u
nits
fr
om z
ero
in t
he n
egat
ive
dire
ctio
n,an
d 3
is t
hree
uni
ts
from
zer
o in
the
pos
itiv
e di
rect
ion.
The
num
ber
line
at
the
righ
t ill
ustr
ates
the
mea
ning
of a
bsol
ute
val
ue.
The
abso
lute
val
ue o
f a
num
ber
nis
the
dis
tanc
e fr
om z
ero
on
a nu
mbe
r lin
e an
d is
rep
rese
nted
⏐n⏐
.For
thi
s ex
ampl
e,⏐!
3⏐"
3 an
d ⏐3
⏐"
3.
10
!1
!2
!3
!4
!5
23
3 un
its3
units
" d
irect
ion
! d
irect
ion
45
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Rat
iona
l Num
bers
on
the
Num
ber
Line
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-1
2-1
Fin
d e
ach
abs
olu
te v
alu
e.
a.⏐!
6⏐!
6 is
six
uni
ts f
rom
zer
o in
the
neg
ativ
edi
rect
ion.
⏐!6⏐
"6
b.⏐⏐ is
thr
ee h
alve
s un
its
from
zer
o in
the
posi
tive
dir
ecti
on.
⏐⏐"
3 # 23 # 2
3 # 23 # 2
Eva
luat
e 4
"⏐x
!2⏐
if
x"
5.
4 $
⏐x!
2⏐"
4 $
⏐5 !
2⏐R
epla
ce x
with
5.
"4
$⏐3
⏐5
!2
"3
"4
$3
⏐3⏐
"3
"7
Sim
plify
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
abs
olu
te v
alu
e.
1.⏐2
⏐2
2.⏐!
5⏐5
3.⏐!
24⏐
24
4.⏐!
1.3⏐
1.3
5.⏐!
⏐6.
⏐⏐
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
$5,
b$
,x$
8,an
d y
$2.
5.
7.18
$⏐4
!y⏐
19.5
8.⏐x
$8⏐
$12
289.
⏐x !
2⏐
$8.
214
.2
10.2
$⏐x
!5⏐
511
.⏐2.
5 $
y⏐$
1217
12.⏐
23 !
x⏐!
96
13.⏐
x!
6⏐$
4.5
6.5
14.1
0 !
⏐a!
2⏐7
15.⏐
6 $
b⏐
$6
16. ⏐
$b ⏐!
⏐!⏐0
17.⏐
3 $
b⏐$
a8
18.⏐
!b⏐
$1
13 # 4
1 # 21 # 4
1 # 21 # 4
3 # 41 # 2
1 # 4
35 # 4135 # 41
2 # 32 # 3
© Glencoe/McGraw-Hill A2 Glencoe Algebra 1
Stu
dy
Gu
ide
and I
nte
rven
tion
Rat
iona
l Num
bers
on
the
Num
ber
Line
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-1
2-1
©G
lenc
oe/M
cGra
w-H
ill75
Gle
ncoe
Alg
ebra
1
Lesson 2-1
Gra
ph R
atio
nal N
umbe
rsT
he f
igur
e at
the
rig
ht is
pa
rt o
f a
num
ber
line.
A n
umbe
r lin
e ca
n be
use
d to
sho
w
the
sets
of n
atu
ral
nu
mbe
rs,w
hol
e n
um
bers
,and
in
tege
rs.P
osit
ive
nu
mbe
rs,a
re lo
cate
d to
the
rig
ht o
f 0,
and
neg
ativ
e n
um
bers
are
loca
ted
to t
he le
ft o
f 0.
Ano
ther
set
of
num
bers
tha
t yo
u ca
n di
spla
y on
a n
umbe
r lin
e is
the
set
of r
atio
nal
nu
mbe
rs.A
rat
iona
l num
ber
can
be w
ritt
en a
s ,w
here
aan
d b
are
inte
gers
and
b%
0.So
me
exam
ples
of
rati
onal
num
bers
are
,
,,a
nd
.12 # !
3!
7# !
8!
3#5
1 # 4
a # b
10
!1
!2
!3
!4
23
Natu
ral N
umbe
rs
Posi
tive
Num
bers
Nega
tive
Num
bers
4
Who
le N
umbe
rs
Inte
gers
Nam
e th
e co
ord
inat
es o
f th
ep
oin
ts g
rap
hed
on
eac
h n
um
ber
lin
e.
a.
The
dot
s in
dica
te e
ach
poin
t on
the
gra
ph.
The
coo
rdin
ates
are
{!3,
!1,
1,3,
5}b.
The
bol
d ar
row
to
the
righ
t m
eans
the
gra
phco
ntin
ues
inde
fini
tely
in t
hat
dire
ctio
n.T
heco
ordi
nate
s ar
e {2
,2.5
,3,3
.5,4
,4.5
,5,…
}.
32.
52
1.5
13.
54
4.5
5
10
!1
!2
!3
23
45
Gra
ph
eac
h s
et o
fn
um
bers
.
a.{…
,!3,
!2,
!1,
0,1,
2}
b.!!
,0,
," 12 – 3
1 – 30
!1 – 3
!2 – 3
4 – 35 – 3
2
2 # 31 # 3
1 # 3
10
!1
!2
!3
!4
23
4
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Nam
e th
e co
ord
inat
es o
f th
e p
oin
ts g
rap
hed
on
eac
h n
um
ber
lin
e.
1.2.
{!2,
0,2,
4,6}
{1,3
,5,7
,…}
3.4.
!!,0
,,
,,1
"!!3
,!,
,2,3
"G
rap
h e
ach
set
of
nu
mbe
rs.
5.{!
3,!
1,1,
3}6.
{!5,
!2,
1,2}
7.{i
nteg
ers
less
tha
n 0}
8.{…
,!2,
!1,
0,1}
9.!!
2,!
1,!
,"
10.{
…,!
4,!
2,0,
2,…
}
!3
!4
!5
!6
!2
!1
01
2!
21 – 2!
3!
2!11 – 2!
1!
1 – 20
1 – 21
!3
!4
!2
!1
01
23
4
1 # 21 # 2
1 # 21 # 2
!3
!4
!2
!1
01
23
4!
3!
4!
5!
2!
10
12
3!
3!
4!
2!
10
12
34
1 # 31 # 2
3 # 41 # 2
1 # 41 # 4
!3
!4
!2
!1
01
23
4!
1 – 4!
1 – 20
1 – 41 – 2
3 – 41
5 – 43 – 2
0!
11
23
45
67
0!
1!
21
23
45
6
Answers (Lesson 2-1)
© Glencoe/McGraw-Hill A3 Glencoe Algebra 1
Ans
wer
s
Skil
ls P
ract
ice
Rat
iona
l Num
bers
on
the
Num
ber
Line
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-1
2-1
©G
lenc
oe/M
cGra
w-H
ill77
Gle
ncoe
Alg
ebra
1
Lesson 2-1
Nam
e th
e co
ord
inat
es o
f th
e p
oin
ts g
rap
hed
on
eac
h n
um
ber
lin
e.
1.2.
{!5,
!1,
0,2,
4}{!
6,!
5,!
4,!
1,0,
2}
3.4.
{…,!
3,!
2,!
1,0,
1}{1
.4,1
.5,1
.6,1
.7,1
.8,1
.9,2
.0,…
}
Gra
ph
eac
h s
et o
f n
um
bers
.
5.{!
8,!
5,!
3,0,
2}6.
{!9,
!6,
!4,
!3,
!1}
7.{!
3,!
2,!
1,0,
…}
8.{…
,!1,
0,1,
2,3}
9.!!
,0,
,1,
"10
.{…
,!3,
!2.
5,!
2,!
1.5,
!1}
Fin
d e
ach
abs
olu
te v
alu
e.
11.⏐
!9⏐
912
.⏐15
⏐15
13.⏐
!30
⏐30
14. ⏐!
⏐15
.⏐2.
4⏐2.
416
. ⏐⏐
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
"3,
b"
!10
,c"
,x"
9,y
"1.
5,an
d z
"12
.
17.2
6 !
⏐x"
6⏐11
18.1
1 "
⏐10
!x⏐
12
19.⏐
12 !
a⏐"
514
20.⏐
a"
20⏐
!4
19
21.4
.5 !
⏐y⏐
322
.⏐z
!7⏐
"5
10
23.1
4 !
⏐b⏐
424
.⏐b⏐
!2
8
25. ⏐c
"⏐"
23
26.9
"⏐3
.5 !
y⏐11
1 # 2
1 # 2
9 # 119 # 11
5 # 75 # 7
!3
!2
!1
01
2!
1!
1 – 20
1 – 21
3 – 22
5 – 23
7 – 24
5 # 21 # 2
1 # 2
!1
01
23
45
67
89
!10
!9
!8
!7
!6
!5
!4
!3
!2
!1
0
!5
!6
!7
!8
!9
!10
!4
!3
!2
!1
0!
5!
6!
7!
8!
4!
3!
2!
10
12
1.4
1.3
1.2
1.1
1.0
1.5
1.6
1.7
1.8
1.9
2.0
32
10
!1
!2
!3
45
67
10
!1
!2
!3
!4
!5
!6
!7
23
10
!1
!2
!3
!4
!5
!6
23
4
©G
lenc
oe/M
cGra
w-H
ill78
Gle
ncoe
Alg
ebra
1
Nam
e th
e co
ord
inat
es o
f th
e p
oin
ts g
rap
hed
on
eac
h n
um
ber
lin
e.
1.2.
!…,!
,!,!
,!1,
!"
{2.4
,2.8
,3.2
,3.6
,4,…
}
Gra
ph
eac
h s
et o
f n
um
bers
.
3.!…
,!,!
,!1,
!,!
"4.
{int
eger
s le
ss t
han
!4
or g
reat
er t
han
2}
Fin
d e
ach
abs
olu
te v
alu
e.
5.⏐!
11⏐
116.
⏐100
⏐10
07.
⏐!0.
35⏐
0.35
8.⏐!
⏐E
valu
ate
each
exp
ress
ion
if
a"
4,b
",c
",x
"14
,y"
2.4,
and
z"
!3.
9.41
!16
!⏐z
⏐22
10.⏐
3a"
20⏐
!15
1711
.⏐2x
"4⏐
!6
2612
.2.5
!⏐3
.8 !
y⏐1.
1
13. #b
!$"
⏐!⏐14
."
⏐b!
⏐15
.⏐c
!1⏐
!16
.⏐!
c⏐!
AST
RO
NO
MY
For
Exe
rcis
es 1
7–19
,use
th
e fo
llow
ing
info
rmat
ion
.
The
abs
olut
e m
agni
tude
of a
sta
r is
how
bri
ght
the
star
wou
ld
appe
ar f
rom
a s
tand
ard
dist
ance
of
10 p
arse
cs,o
r 32
.6 li
ght
year
s.T
he lo
wer
the
num
ber,
the
grea
ter
the
mag
nitu
de,o
r br
ight
ness
,of
the
sta
r.T
he t
able
giv
es t
he m
agni
tude
s of
sev
eral
sta
rs.
17.U
se a
num
ber
line
to o
rder
the
mag
nitu
des
from
leas
t to
gre
ates
t.
18.W
hich
of
the
star
s ar
e th
e br
ight
est
and
the
leas
t br
ight
?br
ight
est:
Rig
el;l
east
bri
ght:
Alta
ir19
.Wri
te t
he a
bsol
ute
valu
e of
the
mag
nitu
de o
f ea
ch s
tar
2.3,
7.2,
0.5,
4.7,
0.7,
0.3,
8.1,
1.4
Sour
ce:w
ww.as
tro.w
isc.ed
u
20.C
LIM
ATE
The
tab
le s
how
s th
e m
ean
win
d sp
eeds
in
mile
s pe
r ho
ur a
t D
ayto
naB
each
,Flo
rida
.So
urce
:Nati
onal
Clim
atic D
ata C
ente
r
Gra
ph t
he w
ind
spee
ds o
n a
num
ber
line.
Whi
ch
mon
th h
as t
he g
reat
est
mea
n w
ind
spee
d?M
arch
7.1
7.4
7.9
8.3
8.7
9.1$
2$
2
9.7
10.1
77.
58
8.5
99.
510
10.5
Jan
Feb
Mar
Apr
May
June
July
Aug
Sep
Oct
Nov
Dec
9.0
9.7
10.1
9.7
9.0
7.9
7.4
7.1
8.3
9.1
8.7
8.5
!6
!7
!8
!8.
1!
7.2
!4.
7!
0.3
2.3
1.4
0.5
0.7
!9
!5
!4
!3
!2
!1
01
23
Sta
rM
agni
tude
Alta
ir2.
3
Bet
elge
use
!7.
2
Cas
tor
0.5
Den
eb!
4.7
Pol
lux
0.7
Reg
ulus
!0.
3
Rig
el!
8.1
Siri
us1.
4
3 # 41 # 6
1 # 37 # 10
3 # 41 # 3
2 # 52 # 15
3 # 101 # 5
3 # 23 # 5
28 # 5328 # 53
!6
!5
!4
!3
!2
!1
01
23
4!
7 – 5!
6 – 5!
1!
3 – 5!
4 – 5!
2 – 5!
1 – 51 – 5
2 – 53 – 5
0
3 # 54 # 5
6 # 57 # 5
3 # 45 # 4
3 # 27 # 4
00.
40.
81.
21.
62
2.4
2.8
3.2
3.6
4!
7 – 4!
3 – 2!
5 – 4!
1!
3 – 4!
1 – 2!
1 – 41 – 4
1 – 23 – 4
0
Pra
ctic
e (A
vera
ge)
Rat
iona
l Num
bers
on
the
Num
ber
Line
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-1
2-1
Answers (Lesson 2-1)
© Glencoe/McGraw-Hill A4 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csR
atio
nal N
umbe
rs o
n th
e N
umbe
r Li
ne
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-1
2-1
©G
lenc
oe/M
cGra
w-H
ill79
Gle
ncoe
Alg
ebra
1
Lesson 2-1
Pre-
Act
ivit
yH
ow c
an y
ou u
se a
nu
mbe
r li
ne
to s
how
dat
a?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 2-
1 at
the
top
of
page
68
in y
our
text
book
.
In t
he t
able
,wha
t do
es t
he n
umbe
r "
0.2
tell
you?
The
leve
l of
the
Bra
zos
Riv
er in
crea
sed
by 0
.2 fo
ot in
24
hou
rs.
Read
ing
the
Less
on
1.R
efer
to
the
num
ber
line
on p
age
68 in
you
r te
xtbo
ok.W
rite
tru
eor
fal
sefo
r ea
ch o
f th
efo
llow
ing
stat
emen
ts.
a.A
ll w
hole
num
bers
are
inte
gers
.tr
ue
b.A
ll na
tura
l num
bers
are
inte
gers
.tr
ue
c.A
ll w
hole
num
bers
are
nat
ural
num
bers
.fa
lse
d.A
ll na
tura
l num
bers
are
who
le n
umbe
rs.
true
e.A
ll w
hole
num
bers
are
pos
itiv
e nu
mbe
rs.
fals
e
2.U
se t
he w
ords
den
omin
ator
,fra
ctio
n,an
d nu
mer
ator
to c
ompl
ete
the
follo
win
g se
nten
ce.
You
know
tha
t a
num
ber
is a
rat
iona
l num
ber
if it
can
be
wri
tten
as
a
that
has
a
and
that
are
inte
gers
,whe
re t
he d
enom
inat
or is
not
equ
al t
o ze
ro.
3.E
xpla
in w
hy
,0.6 %
,and
15
are
rati
onal
num
bers
.
Eac
h nu
mbe
r is
in o
r ca
n be
wri
tten
in t
he fo
rm
,whe
re a
and
bar
e
inte
gers
and
b%
0.0.
6#ca
n be
wri
tten
as
,and
15
can
be w
ritt
en a
s .
Hel
ping
You
Rem
embe
r
4.C
onne
ctin
g a
mat
hem
atic
al c
once
pt t
o so
met
hing
in y
our
ever
yday
life
is o
ne w
ay o
fre
mem
beri
ng.D
escr
ibe
a si
tuat
ion
or s
etti
ng in
you
r lif
e th
at r
emin
ds y
ou o
f ab
solu
teva
lue.
Sam
ple
answ
er:T
he d
ista
nce
from
eac
h go
al li
ne t
o th
e 50
-yar
d lin
e is
50
yard
s.
15 # 12 # 3
a # b
!3
#7
deno
min
ator
num
erat
orfr
actio
n
©G
lenc
oe/M
cGra
w-H
ill80
Gle
ncoe
Alg
ebra
1
Inte
rsec
tion
and
Uni
onT
he in
ters
ecti
on o
f tw
o se
ts is
the
set
of e
lem
ents
tha
t ar
e in
bot
h se
ts.
The
inte
rsec
tion
of s
ets
A a
nd B
is w
ritt
en A
!B
.The
uni
on o
f tw
o se
tsis
the
set
of e
lem
ents
in e
ithe
r A
,B,o
r bo
th.T
he u
nion
is w
ritt
en A
"B
.
In t
he d
raw
ings
bel
ow,s
uppo
se A
is t
he s
et o
f po
ints
insi
de t
he c
ircl
ean
d B
is t
he s
et o
f po
ints
insi
de t
he s
quar
e.T
hen,
the
shad
ed a
reas
show
the
inte
rsec
tion
in t
he f
irst
dra
win
g an
d th
e un
ion
in t
he s
econ
ddr
awin
g.
Wri
te A
#B
an
d A
$B
for
eac
h o
f th
e fo
llow
ing.
1.A
${p
,q,r
,s,t
}A
#B
"{q
,r,s
}B
${q
,r,s
}A
$B
"{p
,q,r
,s,t
}
2.A
${t
he in
tege
rs b
etw
een
2 an
d 7}
A #
B "
{3}
B $
{0,3
,8}
A $
B "
{0,3
,4,5
,6,8
}
3.A
${t
he s
tate
s w
hose
nam
es s
tart
wit
h K
}A
#B
"{K
ansa
s}B
${t
he s
tate
s w
hose
cap
ital
s ar
e H
onol
ulu
or T
opek
a}A
$B
"{H
awai
i,K
ansa
s,K
entu
cky}
4.A
${t
he p
osit
ive
inte
ger
fact
ors
of 2
4}A
#B
"{1
,2,3
,4,6
,8}
B $
{the
cou
ntin
g nu
mbe
rs le
ss t
han
10}
A $
B "
{1,2
,3,4
,5,6
,7,8
,9,1
2,24
}
Su
pp
ose
A "
{nu
mbe
rs x
such
th
at x
&3}
,B "
{nu
mbe
rs x
such
as
x'
!1}
,an
d
C "
{nu
mbe
rs x
such
th
at x
(1.
5}.G
rap
h e
ach
of
the
foll
owin
g.
5.A
!B
6.A
"B
7.B
"C
8.B
!C
9.(A
!C
) !
B10
.A !
(B "
C)
!2
!1
!4
!3
01
23
4!
2!
1!
4!
30
12
34
!2
!1
!4
!3
01
23
4!
2!
1!
4!
30
12
34
!2
!1
!4
!3
01
23
4!
2!
1!
4!
30
12
34
Inte
rsec
tion
A !
B
AB
Unio
nA
" B
AB
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-1
2-1
Answers (Lesson 2-1)
© Glencoe/McGraw-Hill A5 Glencoe Algebra 1
Ans
wer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Add
ing
and
Sub
trac
ting
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-2
2-2
©G
lenc
oe/M
cGra
w-H
ill81
Gle
ncoe
Alg
ebra
1
Lesson 2-2
Add
Rat
iona
l Num
bers
Add
ing
Rat
iona
l Num
bers
,A
dd th
e nu
mbe
rs. I
f bot
h ar
e po
sitiv
e, th
e su
m is
pos
itive
; if b
oth
are
nega
tive,
S
ame
Sig
nth
e su
m is
neg
ativ
e.
Add
ing
Rat
iona
l Num
bers
,S
ubtr
act t
he n
umbe
r w
ith th
e le
sser
abs
olut
e va
lue
from
the
num
ber
with
the
Diff
eren
t S
igns
grea
ter
abso
lute
val
ue. T
he s
ign
of th
e su
m is
the
sam
e as
the
sign
of t
he n
umbe
rw
ith th
e gr
eate
r ab
solu
te v
alue
.
Use
a n
um
ber
lin
e to
fin
d t
he
sum
!2
)(!
3).
Step
1D
raw
an
arro
w f
rom
0 t
o !
2.St
ep 2
Fro
m t
he t
ip o
f the
firs
t ar
row
,dra
wa
seco
nd a
rrow
3 u
nits
to
the
left
to
repr
esen
t ad
ding
!3.
Step
3T
he s
econ
d ar
row
end
s at
the
sum
!5.
So !
2 "
(!3)
$!
5.
10
!1
!2
!3
!4
!5
!6
!7
!8
!9
23
!3
!2
Fin
d e
ach
su
m.
a.!
8 )
5!
8 "
5$
!(⏐
!8⏐
!⏐5
⏐)$
!(8
!5)
$!
3
b.)
$!%
"#!
$$"
#!$
$"# ⏐
⏐!⏐!
⏐$$
"#
!$
$1 # 4
2 # 43 # 4
2 # 43 # 4
2 # 43 # 4
1 # 23 # 4
1 # 23 # 4
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
su
m.
1.12
"24
362.
!6
"14
83.
!12
"(!
15)
!27
4.!
21.5
"34
.212
.75.
8.2
"(!
3.5)
4.7
6.23
.5 "
(!15
.2)
8.3
7.90
"(!
105)
!15
8.10
8 "
(!62
)46
9.!
84 "
(!90
)!
174
10.
"or
111
."
12.!
"
13.!
"#!
$!
14.!
"15
.!"
#!$!
16.!
"#!
$17
.!1.
6 "
(!1.
8)18
.!0.
008
"(!
0.25
)
!or
!1
!3.
4!
0.25
813 # 30
43 # 30
5 # 63 # 5
19 # 2010 # 20
18 # 4024 # 55
7 # 111 # 5
11 # 121 # 4
2 # 3
7 # 453 # 5
4 # 913
5# 23
86 # 17
3 # 141 # 21
22 # 211 # 3
5 # 7
©G
lenc
oe/M
cGra
w-H
ill82
Gle
ncoe
Alg
ebra
1
Subt
ract
Rat
iona
l Num
bers
Eve
ry p
osit
ive
rati
onal
num
ber
can
be p
aire
d w
ith
ane
gati
ve r
atio
nal n
umbe
r so
tha
t th
eir
sum
is 0
.The
num
bers
,cal
led
opp
osit
es,a
read
dit
ive
inve
rses
of e
ach
othe
r.
Add
itive
Inve
rse
Pro
pert
yF
or e
very
num
ber
a, a
"(!
a) $
0.
To s
ubtr
act
a ra
tion
al n
umbe
r,ad
d it
s in
vers
e an
d us
e th
e ru
les
for
addi
tion
giv
en o
n pa
ge 8
1.
Sub
trac
tion
of R
atio
nal N
umbe
rsF
or a
ny n
umbe
rs a
and
b, a
!b
$a
"(!
b).
Fin
d 8
.5 !
10.2
.
8.5
!10
.2 $
8.5
"( !
10.2
)To
sub
trac
t 10.
2, a
dd it
s in
vers
e.
$!
(⏐!
10.2
⏐!
⏐8.5
⏐)⏐!
10.2
⏐is
gre
ater
, so
the
resu
lt is
neg
ativ
e.
$!
1.7
Sim
plify
.
Fin
d e
ach
dif
fere
nce
.
1.11
!41
2.15
!(!
21)
3.!
33 !
(!17
)
!30
36!
16
4.18
!(!
12)
5.15
.5 !
(!2.
5)6.
65.8
!(!
23.5
)
3018
89.3
7.90
!(!
15)
8.!
10.8
!(6
.8)
9.!
84 !
(!72
)
105
!17
.6!
12
10.5
8.8
!(!
11.2
)11
.!18
.2 !
3.2
12.!
9 !
(!5.
6)
70!
21.4
!3.
4
13.!
! #!
$14
.!!
#!$
15.
!
or 1
16.
!#!
$17
.!!
#!$
18.
!
or 1
!or
1
19.S
anel
le w
as p
layi
ng a
vid
eo g
ame.
Her
sco
res
wer
e "
50,"
75,!
18,a
nd !
22.W
hat
was
her
fina
l sco
re?
)85
20.T
he f
ootb
all t
eam
off
ense
beg
an a
dri
ve f
rom
the
ir 2
0-ya
rd li
ne.T
hey
gain
ed 8
yar
ds,l
ost
12 y
ards
and
lost
2 y
ards
bef
ore
havi
ng t
o ki
ck t
he b
all.
Wha
t ya
rd li
ne w
ere
they
on
whe
n th
ey h
ad t
o ki
ck t
he b
all?
14-y
ard
line
1 # 23 # 2
13 # 241 # 46
47 # 46
18 # 2024 # 10
3 # 97 # 8
1 # 212 # 23
25 # 3661 # 36
13 # 355 # 12
5 # 99 # 4
4 # 71 # 5
3 # 41 # 3
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Add
ing
and
Sub
trac
ting
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-2
2-2
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 2-2)
© Glencoe/McGraw-Hill A6 Glencoe Algebra 1
Skil
ls P
ract
ice
Add
ing
and
Sub
trac
ting
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-2
2-2
©G
lenc
oe/M
cGra
w-H
ill83
Gle
ncoe
Alg
ebra
1
Lesson 2-2
Fin
d e
ach
su
m.
1.28
"13
2.18
"54
3.!
6 "
15
4172
9
4.!
12 "
255.
!14
"11
6.!
42 "
18
13!
3!
24
7.!
19 "
(!3)
8.!
9 "
(!17
)9.
25 "
(!30
)
!22
!26
!5
10.1
6 "
(!20
)11
."
#!$
12.!
2.5
"3.
2
!4
!0.
7
Fin
d e
ach
dif
fere
nce
.
13.3
1 !
1214
.53
!47
15.1
7 !
20
196
!3
16.2
8 !
3917
.!15
!65
18.!
27 !
13
!11
!80
!40
19.!
11 !
(!12
)20
.!25
!(!
36)
21.!
9 !
(!7)
111
!2
22.!
14 !
(!8)
23.!
1.5
!1
24.3
.6 !
4.8
!6
!2.
5!
1.2
25.!
!#!
$26
.!!
27.!
"
0!
28.W
EATH
ERA
t 6:
00 P
.M.,
the
tem
pera
ture
in N
orth
For
k w
as 2
8 de
gree
s Fa
hren
heit
.Sh
ortl
y af
terw
ard,
a st
rong
col
d fr
ont
pass
ed t
hrou
gh,a
nd t
he t
empe
ratu
re d
ropp
ed
36 d
egre
es b
y 8:
00 A
.M.t
he n
ext
mor
ning
.Wha
t w
as t
he t
empe
ratu
re a
t 8:
00 A
.M.?
!8*
F
3 # 41 # 2
3 # 23 # 4
1 # 61 # 3
1 # 21 # 2
1 # 2
3 # 41 # 4
©G
lenc
oe/M
cGra
w-H
ill84
Gle
ncoe
Alg
ebra
1
Fin
d e
ach
su
m.
1.!
82 "
14!
682.
!33
"47
143.
!17
"(!
39)
!56
4.8
"(!
11)
!3
5.!
1.7
"3.
21.
56.
!13
.3 "
(!0.
9)!
14.2
7.!
51.8
"29
.7!
22.1
8.7.
34 "
(!9.
06)
!1.
729.
"or
1
10.!
"11
.!"
#!$
12.
"#!
$!
or !
1!
Fin
d e
ach
dif
fere
nce
.
13.6
5 !
93!
2814
.!42
!(!
17)
!25
15.1
3 !
(!19
)32
16.!
8 !
43!
5117
.82.
8 !
(!12
.4)
95.2
18.1
.27
!2.
34!
1.07
19.!
9.26
!12
.05
!21
.31
20.!
18.1
!(!
4.7)
!13
.421
.!!
!
22.
!23
.!!
#!$
24.
!#!
$!
or !
2
FIN
AN
CE
For
Exe
rcis
es 2
5–27
,use
th
e fo
llow
ing
info
rmat
ion
.
The
tab
le s
how
s ac
tivi
ty in
Ben
’s c
heck
ing
acco
unt.
The
bal
ance
bef
ore
the
acti
vity
was
$200
.00.
Dep
osit
s ar
e ad
ded
to a
n ac
coun
t an
d ch
ecks
are
sub
trac
ted.
Num
ber
Dat
eTr
ansa
ctio
nA
mou
ntB
alan
ce
5/2
depo
sit
52.5
025
2.50
101
5/10
chec
k to
Cas
tle M
usic
25.5
0?
102
6/1
chec
k to
Com
p U
Sav
e23
5.40
?
25.W
hat
is t
he a
ccou
nt b
alan
ce a
fter
wri
ting
che
ck n
umbe
r 10
1?$2
27.0
0
26.W
hat
is t
he a
ccou
nt b
alan
ce a
fter
wri
ting
che
ck n
umbe
r 10
2?!
$8.4
0
27.R
ealiz
ing
that
he
has
just
wri
tten
a c
heck
for
mor
e th
an is
in t
he a
ccou
nt,B
enim
med
iate
ly d
epos
its
$425
.Wha
t w
ill t
his
mak
e hi
s ne
w a
ccou
nt b
alan
ce?
$416
.60
28.C
HEM
ISTR
YT
he m
elti
ng p
oint
s of
kry
pton
,rad
on,a
nd s
ulfu
r in
deg
rees
Cel
sius
are
!15
6.6,
!61
.8,a
nd 1
12.8
,res
pect
ivel
y.W
hat
is t
he d
iffe
renc
e in
mel
ting
poi
nts
betw
een
rado
n an
d kr
ypto
n an
d be
twee
n su
lfur
and
kry
pton
?94
.8*C
and
269
.4*C
23 # 241 # 14
29 # 141 # 2
5 # 61 # 8
3 # 75 # 2
5 # 64 # 3
13 # 152 # 3
1 # 57 # 247 # 20
27 # 201 # 15
2 # 33 # 8
3 # 53 # 4
2 # 33 # 5
7 # 1825 # 18
5 # 65 # 9
Pra
ctic
e (A
vera
ge)
Add
ing
and
Sub
trac
ting
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-2
2-2
Answers (Lesson 2-2)
© Glencoe/McGraw-Hill A7 Glencoe Algebra 1
Ans
wer
s
Rea
din
g t
o L
earn
Math
emati
csA
ddin
g an
d S
ubtr
actin
g R
atio
nal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-2
2-2
©G
lenc
oe/M
cGra
w-H
ill85
Gle
ncoe
Alg
ebra
1
Lesson 2-2
Pre-
Act
ivit
yH
ow c
an a
nu
mbe
r li
ne
be u
sed
to
show
a f
ootb
all
team
’s p
rogr
ess?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 2-
2 at
the
top
of
page
73
in y
our
text
book
.
Use
pos
itiv
eor
neg
ativ
eto
com
plet
e th
e fo
llow
ing
sent
ence
s.
The
fiv
e-ya
rd p
enal
ty is
sho
wn
by t
he
num
ber
!5.
The
13-
yard
pas
s is
sho
wn
by t
he
num
ber
13.
Read
ing
the
Less
on
1.To
add
tw
o ra
tion
al n
umbe
rs,y
ou c
an u
se a
num
ber
line.
Eac
h nu
mbe
r w
ill b
ere
pres
ente
d by
an
arro
w.
a.W
here
on
the
num
ber
line
does
the
arr
ow f
or t
he f
irst
num
ber
begi
n? a
t 0
b.A
rrow
s fo
r ne
gati
ve n
umbe
rs w
ill p
oint
to
the
(lef
t/ri
ght)
.Arr
ows
for
posi
tive
num
bers
will
poi
nt t
o th
e (l
eft/
righ
t).
2.T
wo
stud
ents
add
ed t
he s
ame
pair
of
rati
onal
num
bers
.Bot
h st
uden
ts g
ot t
he c
orre
ctsu
m.O
ne s
tude
nt u
sed
a nu
mbe
r lin
e.T
he o
ther
stu
dent
use
d ab
solu
te v
alue
.The
n th
eyco
mpa
red
thei
r w
ork.
a.H
ow d
o th
e ar
row
s sh
ow w
hich
num
ber
has
the
grea
ter
abso
lute
val
ue?
The
num
ber
with
the
gre
ater
abs
olut
e va
lue
mat
ches
the
long
er a
rrow
.
b.If
the
long
er a
rrow
poi
nts
to t
he le
ft,t
hen
the
sum
is
(pos
itiv
e/ne
gati
ve).
If t
he lo
nger
arr
ow p
oint
s to
the
rig
ht,t
hen
the
sum
is
(pos
itiv
e/ne
gati
ve).
3.If
tw
o nu
mbe
rs a
re a
ddit
ive
inve
rses
,wha
t m
ust
be t
rue
abou
t th
eir
abso
lute
val
ues?
The
abso
lute
val
ues
of t
he t
wo
num
bers
are
equ
al.
4.W
rite
eac
h su
btra
ctio
n pr
oble
m a
s an
add
itio
n pr
oble
m.
a.12
!4
12 !
("4)
b.!
15 !
7"
15 !
("7)
c.0
!9
0 !
("9)
d.!
20 !
34"
20 !
("34
)
Hel
ping
You
Rem
embe
r
5.E
xpla
in w
hy k
now
ing
the
rule
s fo
r ad
ding
rat
iona
l num
bers
can
hel
p yo
u to
sub
trac
tra
tion
al n
umbe
rs.
Sam
ple
answ
er:S
ince
sub
trac
tion
is t
he s
ame
as a
ddin
g th
e op
posi
te,
you
can
chan
ge e
very
sub
trac
tion
prob
lem
to
an a
dditi
on p
robl
em.T
hen
you
can
use
the
rule
s fo
r ad
ding
rat
iona
l num
bers
to
get
the
final
ans
wer
.
posi
tive
nega
tive
righ
tle
ft
posi
tive
nega
tive
©G
lenc
oe/M
cGra
w-H
ill86
Gle
ncoe
Alg
ebra
1
Rou
ndin
g Fr
actio
nsR
ound
ing
frac
tion
s is
mor
e di
ffic
ult
than
rou
ndin
g w
hole
num
bers
or
de
cim
als.
For
exam
ple,
thin
k ab
out
how
you
wou
ld r
ound
in
ches
to
the
near
est
quar
ter-
inch
.Thr
ough
est
imat
ion,
you
mig
ht r
ealiz
e th
at
is le
ss t
han
.But
,is
it c
lose
r to
or
to
?
Her
e ar
e tw
o w
ays
to r
ound
fra
ctio
ns.E
xam
ple
1 us
es o
nly
the
frac
tion
s;E
xam
ple
2 us
es d
ecim
als.
1 " 41 " 2
1 " 24 " 9
4 " 9
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-2
2-2
Subt
ract
the
fra
ctio
n tw
ice.
Use
the
tw
one
ares
t qu
arte
rs.
!#
!#
Com
pare
the
dif
fere
nces
.
$
The
sm
alle
r di
ffer
ence
sho
ws
you
whi
chfr
acti
on t
o ro
und
to.
roun
ds t
o .
1 " 24 " 9
7 " 361 " 18
7 " 361 " 4
4 " 91 " 18
4 " 91 " 2
Cha
nge
the
frac
tion
and
the
tw
o ne
ares
tqu
arte
rs t
o de
cim
als.
#0.
44!,
#0.
5,#
0.25
Fin
d th
e de
cim
al h
alfw
ay b
etw
een
the
two
near
est
quar
ters
.
(0.5
%0.
25)
#0.
375
If t
he f
ract
ion
is g
reat
er t
han
the
half
way
deci
mal
,rou
nd u
p.If
not
,rou
nd d
own.
0.44!
&0.
3675
.So,
is m
ore
than
hal
f w
ay
betw
een
and
.
roun
ds t
o .
1 " 24 " 9
1 " 21 " 4
4 " 9
1 " 2
1 " 41 " 2
4 " 9
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Rou
nd
eac
h f
ract
ion
to
the
nea
rest
on
e-qu
arte
r.U
se e
ith
er m
eth
od.
1.2.
3.4.
5.6.
7.8.
Rou
nd
eac
h d
ecim
al o
r fr
acti
on t
o th
e n
eare
st o
ne-
eigh
th.
9.0.
610
.0.1
11.0
.45
12.0
.85
13.
14.
15.
16.
1 # 25 " 9
7 # 823 " 25
1 # 83 " 20
3 # 45 " 7
7 # 81 # 2
1 # 85 # 8
3 # 423 " 30
1 # 49 " 25
1 # 231 " 50
1 # 47 " 20
1 # 44 " 15
3 # 47 " 11
1 # 23 " 7
1 # 41 " 3
Answers (Lesson 2-2)
© Glencoe/McGraw-Hill A8 Glencoe Algebra 1
Stu
dy
Gu
ide
and I
nte
rven
tion
Mul
tiply
ing
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-3
2-3
©G
lenc
oe/M
cGra
w-H
ill87
Gle
ncoe
Alg
ebra
1
Lesson 2-3
Mul
tipl
y In
tege
rsYo
u ca
n us
e th
e ru
les
belo
w w
hen
mul
tipl
ying
inte
gers
and
rat
iona
lnu
mbe
rs.
Mul
tiply
ing
Num
bers
with
the
Sam
e S
ign
The
pro
duct
of t
wo
num
bers
hav
ing
the
sam
e si
gn is
pos
itive
.
Mul
tiply
ing
Num
bers
with
Diff
eren
t S
igns
The
pro
duct
of t
wo
num
bers
hav
ing
diffe
rent
sig
ns is
neg
ativ
e.
Fin
d e
ach
pro
du
ct.
a.!
7(6)
The
sig
ns a
re d
iffe
rent
,so
the
prod
uct
isne
gati
ve.
!7(
6) $
!42
b.!
18(!
10)
The
sig
ns a
re t
he s
ame,
so t
he p
rodu
ct is
posi
tive
.!
18(!
10)
$18
0
Sim
pli
fy t
he
exp
ress
ion
(!2x
)5y.
(!2x
)5y
$(!
2)(5
)x%
yC
omm
utat
ive
Pro
pert
y (&
)
$(!
2 %
5)xy
Ass
ocia
tive
Pro
pert
y
$!
10xy
Sim
plify
.
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
pro
du
ct.
1.11
(4)
2.!
5(!
3)3.
(!24
)(!
2)
4415
48
4.(6
0)(!
3)5.
(!2)
(!3)
(!4)
6.8(
!15
)
!18
0!
24!
120
7.!
15(3
)8.
(12)
(!10
)9.
(!22
)(!
3)(2
)
!45
!12
013
2
10.(
5)(!
5)(0
)(4)
11.(
!15
)(45
)12
.(!
12)(
!23
)
0!
675
276
Sim
pli
fy e
ach
exp
ress
ion
.
13.4
(!2x
) !8x
14.6
(!2n
) !10
n15
.6(3
y!
y)
!16
x!
22n
12y
16.!
3(3d
"2d
)17
.!2x
(2)
"2x
(3y)
18.4
m(!
2n) "
2d(!
4e)
!15
d!
4x)
6xy
!8m
n!
8de
19.!
5(2x
"x)
!3(
!xy
)20
.(2)
(!4x
"2x
)21
.(!
3)(!
8n!
6m)
!15
x)
3xy
!4x
24n
)18
m
©G
lenc
oe/M
cGra
w-H
ill88
Gle
ncoe
Alg
ebra
1
Mul
tipl
y Ra
tion
al N
umbe
rsM
ulti
plyi
ng a
rat
iona
l num
ber
by !
1 gi
ves
you
the
addi
tive
inve
rse
of t
he n
umbe
r.
Mul
tiplic
ativ
e P
rope
rty
of !
1T
he p
rodu
ct o
f any
num
ber
and
!1
is(!
1)(5
) $
5(!
1) $
!5
its a
dditi
ve in
vers
e.
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Mul
tiply
ing
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-3
2-3
Eva
luat
e a
3 b2
if a
"!
2an
d b
"!
5.
a3b2
$(!
2)3 (
!5)
2S
ubst
itutio
n
$(!
8)(2
5)(!
2)3
$!
8 an
d (!
5)2
$25
$!
200
diffe
rent
sig
ns →
nega
tive
prod
uct
Eva
luat
e n
2 $!%if
n"
!.
n2#!
$$#!
$2 #!$S
ubst
itutio
n
$#
$#!$
#!$2
$#!
$#!$o
r
$!
diffe
rent
sig
ns →
nega
tive
prod
uct
3 # 20
1 # 41 # 2
1 # 21 # 2
3 # 51 # 4
3 # 51 # 2
3 # 5
1 # 23 # 5
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
pro
du
ct.
1.(!
12)
2.#!
$#!$
3.#!
$#$
!3
!
4.(6
.0)(
!0.
3)5.
#!$#!
$#!$
6.8(
!15
)
!1.
8!
!12
0
7.!
15(!
4)8.
#$(!
10)
9.#!
$(!3)#
$60
!5
10. #
$(!2)
(0) #
$11
. #!$#
$12
. #!1
$#!2
$0
!3
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
"!
2.5,
b"
4.2,
c"
5.5,
and
d"
!0.
2.
13.!
2a2
14.5
(!2b
)15
.!6(
cd)
!12
.5!
426.
6
16.!
2(3d
"2c
)17
.!ad
!3c
18.b
2 (c
!2d
)
!20
.8!
1710
4.07
6
19.!
5bcd
20.!
3d2
"4
21.(
!3)
(!8a
!2b
)
23.1
3.88
!34
.8
1 # 24 # 15
1 # 31 # 2
4 # 51 # 3
1 # 44 # 5
4 # 5
2 # 32 # 5
1 # 2
1 # 8
3 # 41 # 3
1 # 2
4 # 352 # 15
2 # 52 # 7
2 # 31 # 5
1 # 4
Answers (Lesson 2-3)
© Glencoe/McGraw-Hill A9 Glencoe Algebra 1
Ans
wer
s
Skil
ls P
ract
ice
Mul
tiply
ing
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-3
2-3
©G
lenc
oe/M
cGra
w-H
ill89
Gle
ncoe
Alg
ebra
1
Lesson 2-3
Fin
d e
ach
pro
du
ct.
1.9(
17)
153
2.!
8(!
7)56
3.5(
!7)
!35
4.!
4(11
)!
44
5.!
6(!
12)
726.
7(!
25)
!17
5
7.#
$#$
8.#!
$#$!
9.#!
$#!$
10. #
$#!$!
11. #!
$#!$
12.(
1.5)
(2.2
)3.
3
13.(
!2.
8)(0
.5)
!1.
414
.(2.
4)(!
0.6)
!1.
44
15.(
!4.
7)(!
1.3)
6.11
16.(
1.1)
(!1.
2)!
1.32
Sim
pli
fy e
ach
exp
ress
ion
.
17.5
(!2a
) !8a
!18
a18
.!6(
3x) "
12x
!6x
19.3
(4n
!n)
9n20
.!4(
2d!
d)!
4d
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
"!
1.2,
b"
0.5,
c"
,an
d d
"!
.
21.!
4ab
2.4
22.!
3b2
!0.
75
23.!
2a2
!2.
8824
.c2 #!
$!
25.
d226
.!3c
d1
27.S
TAIR
CA
SES
A s
tair
case
in a
n of
fice
bui
ldin
g st
arts
at
grou
nd le
vel.
Eac
h st
ep d
own
low
ers
you
by 7
.5 in
ches
.Wha
t is
you
r he
ight
in r
elat
ion
to g
roun
d le
vel a
fter
des
cend
ing
20 s
teps
?!
150
in.o
r !
12 f
t 6
in.
1 # 181 # 8
1 # 121 # 3
2 # 31 # 2
5 # 92 # 3
5 # 6
15 # 325 # 8
3 # 43 # 16
1 # 23 # 8
1 # 101 # 6
3 # 51 # 3
2 # 31 # 2
©G
lenc
oe/M
cGra
w-H
ill90
Gle
ncoe
Alg
ebra
1
Fin
d e
ach
pro
du
ct.
1.42
(7)
294
2.!
28(!
17)
476
3.15
(!34
)!
510
4.#!
$#$!
5.#!
$#!$
6.#
$#$
7.#!
3$#2
$!or
!8
8.#!
2$#!
1$
or 3
9.#1
$#!1
$!or
!1
10.(
1.5)
(8.8
)13
.211
.(6.
8)(!
1.3)
!8.
8412
.(!
0.2)
(2.8
)!
0.56
13.(
!3.
6)(!
0.55
)1.
9814
.6.3
(!0.
7)!
4.41
15.
(!4)
(9)
!24
Sim
pli
fy e
ach
exp
ress
ion
.
16.5
(!3a
) "18
a3a
17.!
8(4c
) "12
c!
20c
18.!
9(2g
!g)
!9g
19.7
(2b
!4b
)20
.!4x
(2y)
"(!
3b)(
!2d
)21
.!5p
(!3q
) "(4
m)(
!6n
)
!14
b!
8xy
)6b
d15
pq)
(!24
mn)
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
"!
,b"
,c"
!3.
4,an
d d
"0.
7.
22.b
2 #!$!
23.4
ab!
or !
224
.5a2
(!b)
!or
!2
25.!
6d2
!2.
9426
.cd
!3
!5.
3827
.c2 (
!5d
)!
40.4
6
28.R
ECIP
ESA
rec
ipe
for
butt
erm
ilk b
iscu
its
calls
for
3cu
ps o
f fl
our.
How
man
y cu
ps o
f
flou
r do
you
nee
d fo
r th
e re
cipe
?1
c
CO
MPU
TER
SF
or E
xerc
ises
29
and
30,
use
th
e fo
llow
ing
info
rmat
ion
.
Lee
za is
dow
nloa
ding
a f
ile f
rom
a W
eb s
ite
at 4
7.3
kilo
byte
s pe
r se
cond
.
29.H
ow m
any
kilo
byte
s of
the
file
will
be
dow
nloa
ded
afte
r on
e m
inut
e?28
38 k
iloby
tes
30.H
ow m
any
kilo
byte
s w
ill b
e do
wnl
oade
d af
ter
4.5
min
utes
?12
,771
kilo
byte
s
CO
NSE
RVA
TIO
NF
or E
xerc
ises
31
and
32,
use
th
e fo
llow
ing
info
rmat
ion
.
A c
ount
y co
mm
issi
on h
as s
et a
side
640
acr
es o
f la
nd f
or a
wild
life
pres
erve
.
31.S
uppo
se
of t
he p
rese
rve
is m
arsh
land
.How
man
y ac
res
of t
he p
rese
rve
are
mar
shla
nd?
256
acre
s
32.I
f th
e fo
rest
ed a
rea
of t
he p
rese
rve
is 1
.5 t
imes
larg
er t
han
the
mar
shla
nd,h
ow m
any
acre
s of
the
pre
serv
e ar
e fo
rest
ed?
384
acre
s
2 # 5
2 # 31 # 2
1 # 3
2 # 512 # 5
2 # 512 # 5
3 # 82 # 3
3 # 44 # 5
2 # 3
1 # 23 # 2
1 # 51 # 4
1 # 928 # 9
1 # 62 # 3
1 # 865 # 8
1 # 21 # 4
9 # 145 # 7
9 # 102 # 3
5 # 64 # 5
21 # 327 # 8
3 # 4
Pra
ctic
e (A
vera
ge)
Mul
tiply
ing
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-3
2-3
Answers (Lesson 2-3)
© Glencoe/McGraw-Hill A10 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csM
ultip
lyin
g R
atio
nal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-3
2-3
©G
lenc
oe/M
cGra
w-H
ill91
Gle
ncoe
Alg
ebra
1
Lesson 2-3
Pre-
Act
ivit
yH
ow d
o co
nsu
mer
s u
se m
ult
ipli
cati
on o
f ra
tion
al n
um
bers
?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 2-
3 at
the
top
of
page
79
in y
our
text
book
.
•H
ow is
the
am
ount
of
the
coup
on s
how
n on
the
sal
es s
lip?
!1.
00•
Bes
ides
the
am
ount
,how
is t
he n
umbe
r re
pres
enti
ng t
he c
oupo
n di
ffer
ent
from
the
oth
er n
umbe
rs o
n th
e sa
les
slip
?
It is
neg
ativ
e.
Read
ing
the
Less
on
1.C
ompl
ete:
If t
wo
num
bers
hav
e di
ffer
ent
sign
s,th
e on
e nu
mbe
r is
pos
itiv
e an
d th
e ot
her
num
ber
is
.
2.C
ompl
ete
the
tabl
e.
Mul
tiplic
atio
nA
re t
he s
igns
of
the
num
bers
the
sam
e
Is t
he p
rodu
ct p
ositi
ve o
r ne
gativ
e?E
xam
ple
or d
iffer
ent?
a.(!
4)(9
)di
ffer
ent
nega
tive
b.(!
2)(!
13)
the
sam
epo
sitiv
e
c.5(
!8)
diff
eren
tne
gativ
e
d.6(
3)th
e sa
me
posi
tive
3.E
xpla
in w
hat
the
term
“ad
diti
ve in
vers
e”m
eans
to
you.
The
n gi
ve a
n ex
ampl
e.Th
e pr
oduc
t of
any
num
ber
and
!1
is it
s ad
ditiv
e in
vers
e;!
+(!
1) "
.
Hel
ping
You
Rem
embe
r
4.D
escr
ibe
how
you
kno
w t
hat
the
prod
uct
of !
3 an
d !
5 is
pos
itiv
e.T
hen
desc
ribe
how
you
know
tha
t th
e pr
oduc
t of
3 a
nd !
5 is
neg
ativ
e.
Sam
ple
answ
er:T
he s
igns
are
the
sam
e;th
e si
gns
are
diff
eren
t.
2 # 32 # 3
nega
tive
©G
lenc
oe/M
cGra
w-H
ill92
Gle
ncoe
Alg
ebra
1
Com
poun
d In
tere
stIn
mos
t ba
nks,
inte
rest
on
savi
ngs
acco
unts
is c
ompo
unde
d at
set
tim
epe
riod
s su
ch a
s th
ree
or s
ix m
onth
s.A
t th
e en
d of
eac
h pe
riod
,the
bank
add
s th
e in
tere
st e
arne
d to
the
acc
ount
.Dur
ing
the
next
per
iod,
the
bank
pay
s in
tere
st o
n al
l the
mon
ey in
the
ban
k,in
clud
ing
inte
rest
.In
thi
s w
ay,t
he a
ccou
nt e
arns
inte
rest
on
inte
rest
.
Supp
ose
Ms.
Tann
er h
as $
1000
in a
n ac
coun
t th
at is
com
poun
ded
quar
terl
y at
5%
.Fin
d th
e ba
lanc
e af
ter
the
firs
t tw
o qu
arte
rs.
Use
I$
prt
to f
ind
the
inte
rest
ear
ned
in t
he f
irst
qua
rter
if p
$10
00
and
r$
5%.W
hy is
teq
ual t
o ?
Fir
st q
uart
er:
I$
1000
&0.
05 &
I$
12.5
0
The
inte
rest
,$12
.50,
earn
ed in
the
fir
st q
uart
er is
add
ed t
o $1
000.
The
pri
ncip
al b
ecom
es $
1012
.50.
Seco
nd q
uart
er:I
$10
12.5
0 &
0.05
&
I$
12.6
5625
The
inte
rest
in t
he s
econ
d qu
arte
r is
$12
.66.
The
bal
ance
aft
er t
wo
quar
ters
is $
1012
.50
"12
.66
or $
1025
.16.
An
swer
eac
h o
f th
e fo
llow
ing
ques
tion
s.
1.H
ow m
uch
inte
rest
is e
arne
d in
the
thi
rd q
uart
er o
f M
s.Ta
nner
’sac
coun
t?I"
$12.
81
2.W
hat
is t
he b
alan
ce in
her
acc
ount
aft
er t
hree
qua
rter
s?$1
037.
97
3.H
ow m
uch
inte
rest
is e
arne
d at
the
end
of
one
year
?I"
$12.
97
4.W
hat
is t
he b
alan
ce in
her
acc
ount
aft
er o
ne y
ear?
$105
0.94
5.Su
ppos
e M
s.Ta
nner
’s a
ccou
nt is
com
poun
ded
sem
iann
ually
.Wha
tis
the
bal
ance
at
the
end
of s
ix m
onth
s?$1
025.
00
6.W
hat
is t
he b
alan
ce a
fter
one
yea
r if
her
acc
ount
is c
ompo
unde
dse
mia
nnua
lly?
$105
0.63
1 # 4
1 # 4
1 # 4
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-3
2-3
Answers (Lesson 2-3)
© Glencoe/McGraw-Hill A11 Glencoe Algebra 1
Ans
wer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Div
idin
g R
atio
nal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-4
2-4
©G
lenc
oe/M
cGra
w-H
ill93
Gle
ncoe
Alg
ebra
1
Lesson 2-4
Div
ide
Inte
gers
The
rul
es f
or f
indi
ng t
he s
ign
of a
quo
tien
t ar
e si
mila
r to
the
rul
es f
orfi
ndin
g th
e si
gn o
f a
prod
uct.
Div
idin
g Tw
o N
umbe
rs w
ith t
he S
ame
Sig
nT
he q
uotie
nt o
f tw
o nu
mbe
rs h
avin
g th
e sa
me
sign
is p
ositi
ve.
Div
idin
g Tw
o N
umbe
rs w
ith D
iffer
ent
Sig
nsT
he q
uotie
nt o
f tw
o nu
mbe
rs h
avin
g di
ffere
nt s
igns
is n
egat
ive.
Fin
d e
ach
qu
otie
nt.
a.!
88 ,
(!4)
!88
'(!
4) $
22sa
me
sign
s →
posi
tive
quot
ient
b.
$!
8di
ffere
nt s
igns
→ne
gativ
e qu
otie
nt!
64#
8
!64
#8
Sim
pli
fy
.
$.
$ $ $!
832 # !4
32#
#!
3 "
(!1)
!4(
!8)
##
!3
"(!
1)!
4(!
10 "
2)#
#!
3 "
(!1)
!4(
!10
)2)
##
!3
)(!
1)Ex
ampl
e1Ex
ampl
e1Ex
ampl
e2Ex
ampl
e2
Exer
cises
Exer
cises
Fin
d e
ach
qu
otie
nt.
1.!
80 '
(!10
)2.
!32
'16
3.80
'5
8!
216
4.18
'(!
3)5.
!12
'(!
3)6.
8 '
(!2)
!6
4!
4
7.!
15 '
(!3)
8.12
1 '
(!11
)9.
!24
'1.
5
5!
11!
16
10.0
'(!
8)11
.!12
5 '
(!25
)12
.!10
4 '
4
05
!26
Sim
pli
fy.
13.
14.
15.
260
!2
16.
17.
18.
!4
!8
24(!
12 "
4)#
#!
2(8)
!4(
!8
"(!
4))
##
!3
"(!
3)!
12(2
"(!
3))
##
!4
"1
!6(
!6
"2)
##
!10
"(!
2)5(
!10
"(!
2))
##
!2
"1
!2
"(!
4)#
#(!
2) "
(!1)
©G
lenc
oe/M
cGra
w-H
ill94
Gle
ncoe
Alg
ebra
1
Div
ide
Rati
onal
Num
bers
The
rul
es f
or d
ivis
ion
wit
h in
tege
rs a
lso
appl
y to
div
isio
n
wit
h ra
tion
al n
umbe
rs.T
o di
vide
by
any
nonz
ero
num
ber,
,mul
tipl
y by
the
rec
ipro
cal o
f
that
num
ber,
.
Div
isio
n of
Rat
iona
l Num
bers
'$
&d # c
a # bc # d
a # b
d # c
c # d
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Div
idin
g R
atio
nal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-4
2-4
a.F
ind
!5
,8.
!5
'8
$!
'
$!
&
$!
or !
b.F
ind
.
$12
.3!
83.6
4#
!6.
8
!83
.64
#!
6.8
2 # 316 # 24
1 # 816 # 3
8 # 116 # 3
1 # 3
1 # 3
Sim
pli
fy
.
$(!
20a
"15
) '
5
$(!
20a
"15
) #$
$!
20a #
$"15
#$
$!
4a "
3
1 # 51 # 5
1 # 5
!20
a"
15#
# 5
!20
a)
15#
# 5Ex
ampl
e1Ex
ampl
e1Ex
ampl
e2Ex
ampl
e2
Exer
cises
Exer
cises
Fin
d e
ach
qu
otie
nt.
1.!
'2
!2.
!32
'!
128
3.!
'!
2
4.1.
8 '
(!3)
!0.
65.
!12
.9 '
(!0.
3)43
6.'
#!$!
7.!
'#!
$ or
18.
52.5
'(!
4.2)
!12
.59.
!'
!
10.1
05 '
(!1.
5)!
7011
.!12
.5 '
(!2.
5)5
12.!
'!
Sim
pli
fy e
ach
exp
ress
ion
.
13.
!11
a14
.8x
15.
!24
a
16.
!6a
)2b
17.
3a!
118
.19
y!
4
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
"!
6,b
"2.
5,c
"!
3.2,
and
d"
4.8.
19.
!3.
125
20.
!0.
4821
.!
6.87
5a
!2b
# c"
da
"d
#b
ab # d
57y
!12
## 3
36a
!12
## 12
18a
!6b
##
!3
!14
4a#
616
x#
2!
44a
#4
3 # 164 # 3
1 # 4
8 # 255 # 3
8 # 159 # 16
25 # 163 # 10
15 # 32
9 # 162 # 3
3 # 8
1 # 52 # 5
1 # 41 # 16
1 # 8
Answers (Lesson 2-4)
© Glencoe/McGraw-Hill A12 Glencoe Algebra 1
Skil
ls P
ract
ice
Div
idin
g R
atio
nal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-4
2-4
©G
lenc
oe/M
cGra
w-H
ill95
Gle
ncoe
Alg
ebra
1
Lesson 2-4
Fin
d e
ach
qu
otie
nt.
1.!
32 "
(!4)
82.
!28
"7
!4
3.!
45 "
(!15
)3
4.39
"(!
3)!
13
5.!
56 "
14!
46.
62 "
(!4)
!15
.5
7.!
23 "
(!5)
4.6
8.52
"(!
8)!
6.5
9.!
90 "
12!
7.5
10.!
16.5
"11
!1.
5
11.!
1.44
"1.
2!
1.2
12.!
16.2
"(!
0.4)
40.5
13.6
"!!
"!27
14.!
"!
or !
1
15.!
"!!
"or
216
."
Sim
pli
fy e
ach
exp
ress
ion
.
17.
9a18
.18
x
19.
!4c
"1
20.
6z"
(!2)
Eva
luat
e ea
ch e
xpre
ssio
n i
f g
#!
4,h
#2.
5,k
#1.
4,an
d m
#!
0.8.
Rou
nd
to
the
nea
rest
hu
nd
red
th.
21.
12.5
22.
0.5
23.
!4.
3824
.hk
"gm
1.09
25.k
m"
gh0.
1126
.!
0.15
k#
m$
g
hk $ m
hm $g
gh $ m
!54
z#
18$
$!
916
c!
4$
!4
216x
$12
27a
$3
3 $ 42 $ 3
1 $ 22 $ 3
8 $ 31 $ 4
2 $ 3
1 $ 23 $ 2
1 $ 23 $ 4
2 $ 9
©G
lenc
oe/M
cGra
w-H
ill96
Gle
ncoe
Alg
ebra
1
Fin
d e
ach
qu
otie
nt.
1.75
"(!
15)
!5
2.!
323
"(!
17)
193.
!88
"16
!5.
5
4.65
.7 "
(!9)
!7.
35.
!36
.08
"8
!4.
516.
!40
.05
"(!
2.5)
16.0
2
7.!
9 "
8.!
"!!
"9.
"!!
"!
15$2 90 $
or 2
!
Sim
pli
fy e
ach
exp
ress
ion
.
10.
!12
p11
.5
!x
12.
!t
"(!
4)
13.
14.
15.
!3x
"(!
2y)
2k!
3h!
c"
(!4d
)
Eva
luat
e ea
ch e
xpre
ssio
n i
f p
#!
6,q
#4.
5,r
#3.
6,an
d s
#!
5.2.
Rou
nd
to
the
nea
rest
hu
nd
red
th.
16.
!2.
717
.!
4.16
18.p
s"
qr1.
93
19.r
s"
pq0.
6920
.!
2.92
21.
!0.
36
22.E
XER
CIS
EA
shle
y w
alks
2m
iles
arou
nd a
lake
thr
ee t
imes
a w
eek.
If A
shle
y w
alks
arou
nd t
he la
ke in
ho
ur,w
hat
is h
er r
ate
of s
peed
? (H
int:
Use
the
form
ula
r%
,
whe
re r
is r
ate,
dis
dis
tanc
e,an
d t
is t
ime.
)3
mi/h
23.P
UB
LIC
ATI
ON
A p
rodu
ctio
n as
sist
ant
mus
t di
vide
a p
age
of t
ext
into
tw
o co
lum
ns.I
f
the
page
is 6
inch
es w
ide,
how
wid
e w
ill e
ach
colu
mn
be?
3in
.
RO
LLER
CO
AST
ERS
For
Exe
rcis
es 2
4 an
d 2
5,u
se t
he
foll
owin
g in
form
atio
n.
The
for
mul
a fo
r ac
cele
rati
on is
a%
,whe
re a
is a
ccel
erat
ion,
fis
fin
al s
peed
,sis
st
arti
ng s
peed
,and
tis
tim
e.
24.T
he H
yper
soni
c X
LC
rol
ler
coas
ter
in V
irgi
nia
goes
fro
m z
ero
to 8
0 m
iles
per
hour
in
1.8
seco
nds.
Wha
t is
its
acce
lera
tion
in m
iles
per
hour
per
sec
ond
to t
he n
eare
st t
enth
?So
urce
: www
.thrill
ride.c
omab
out
44.4
mi/h
per
sec
ond
25.W
hat
is t
he a
ccel
erat
ion
in f
eet
per
seco
nd p
er s
econ
d? (H
int:
Con
vert
mile
s to
fee
t an
dho
urs
to s
econ
ds,t
hen
appl
y th
e fo
rmul
a fo
r ac
cele
rati
on.1
mile
%52
80 f
eet)
abou
t 39
11.1
ft/s
per
sec
ondf!
s$
t
3 $ 83 $ 4
1 $ 3
d $ t3 $ 4
1 $ 2
r#
s$
qp
!q
$r
rs $ qqr $ p
!4c
#(!
16d)
$$ 4
8k!
12h
$$ 4
18x
#12
y$
$!
6
3t#
12$
!3
25 !
5x$
516
8p$ !
14
12 $ 492 $ 9
49 $ 5414 $ 63
3 $ 85 $ 6
3 $ 5Pra
ctic
e (A
vera
ge)
Div
idin
g R
atio
nal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-4
2-4
Answers (Lesson 2-4)
© Glencoe/McGraw-Hill A13 Glencoe Algebra 1
Ans
wer
s
Rea
din
g t
o L
earn
Math
emati
csD
ivid
ing
Rat
iona
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-4
2-4
©G
lenc
oe/M
cGra
w-H
ill97
Gle
ncoe
Alg
ebra
1
Lesson 2-4
Pre-
Act
ivit
yH
ow c
an y
ou u
se d
ivis
ion
of
rati
onal
nu
mbe
rs t
o d
escr
ibe
dat
a?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 2-
4 at
the
top
of
page
84
in y
our
text
book
.
•W
hat
is m
eant
by
the
term
mea
n?
the
sum
of
a se
t of
dat
a ite
ms
divi
ded
by t
he n
umbe
r of
da
ta it
ems.
•In
the
exp
ress
ion
,will
the
num
erat
or b
e po
siti
ve o
r ne
gati
ve?
nega
tive
Read
ing
the
Less
on
1.E
xpla
in w
hat
the
term
inve
rse
oper
atio
nsm
eans
to
you.
Sam
ple
answ
er:I
nver
se o
pera
tions
are
ope
ratio
ns t
hat
undo
on
e an
othe
r.
2.W
rite
neg
ativ
eor
pos
itiv
eto
des
crib
e th
e qu
otie
nt.E
xpla
in y
our
answ
er.
Exp
ress
ion
Neg
ativ
e or
Pos
itive
?E
xpla
natio
n
a.ne
gativ
eTh
e si
gns
of t
he t
wo
num
bers
are
diff
eren
t.
b.po
sitiv
eTh
e si
gns
of t
he t
wo
num
bers
are
the
sa
me.
c.po
sitiv
eA
fter
mul
tiply
ing,
the
sign
s of
the
num
bers
bein
g di
vide
d ar
e th
e sa
me.
Hel
ping
You
Rem
embe
r
3.E
xpla
in h
ow k
now
ing
the
rule
s fo
r m
ulti
plyi
ng r
atio
nal n
umbe
rs c
an h
elp
you
rem
embe
rth
e ru
les
for
divi
ding
rat
iona
l num
bers
.
Sam
ple
answ
er:B
oth
rule
s st
ate
that
the
ans
wer
(pro
duct
for
mul
tiplic
atio
n,qu
otie
nt fo
r di
visi
on)
is p
ositi
ve if
the
sig
ns a
re t
he s
ame
and
nega
tive
if th
e si
gns
are
diff
eren
t.
(!5.
6)(!
2.4)
""
1.92
!78
" !13
35 " !7
(!12
7) #
54 #
(!65
)"
""
3
©G
lenc
oe/M
cGra
w-H
ill98
Gle
ncoe
Alg
ebra
1
Oth
er K
inds
of
Mea
nsT
here
are
man
y di
ffer
ent
type
s of
mea
ns b
esid
es t
he a
rith
met
icm
ean.
A m
ean
for
a se
t of
num
bers
has
the
se t
wo
prop
erti
es:
a.It
typ
ifie
s or
rep
rese
nts
the
set.
b.It
is n
ot le
ss t
han
the
leas
t nu
mbe
r an
d it
is n
ot g
reat
er t
han
the
grea
test
num
ber.
Her
e ar
e th
e fo
rmul
as fo
r th
e ar
ithm
etic
mea
n an
d th
ree
othe
r m
eans
.
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-4
2-4
Ari
thm
etic
Mea
n
Add
the
num
bers
in t
he s
et.T
hen
divi
deth
e su
m b
y n,
the
num
ber
of e
lem
ents
inth
e se
t.
Har
mon
ic M
ean
Div
ide
the
num
ber
of e
lem
ents
in t
he s
et b
yth
e su
m o
f th
e re
cipr
ocal
s of
the
num
bers
.
Geo
met
ric
Mea
n
Mul
tipl
y al
l the
num
bers
in t
he s
et.T
hen
find
the
nth
roo
t of
the
ir p
rodu
ct.
n !x 1
$x 2
"$
x 3$
"…
$x n
"
Qu
adra
tic
Mea
n
Add
the
squ
ares
of
the
num
bers
.Div
ide
thei
r su
m b
y th
e nu
mbe
r in
the
set
.T
hen,
take
the
squ
are
root
.
#$$
$x 12
#x 22
#x 32
#…
#x n2
""
""
n
n"
""
" x1 1"#
" x1 2"#
" x1 3"#
…#
" x1 n"
x 1#
x 2#
x 3#
…#
x n"
""
n
Fin
d t
he
fou
r d
iffe
ren
t m
ean
s to
th
e n
eare
st h
un
dre
dth
for
eac
h s
et o
f n
um
bers
.
1.10
,100
2.50
,60
A!
55G
!31
.62
A!
55G
!54
.77
H!
18.1
8Q
!71
.06
H!
54.5
5Q
!55
.23
3.1,
2,3,
4,5,
4.2,
2,4,
4
A!
3G
!2.
61A
!3
G!
2.83
H!
2.19
Q!
3.32
H!
2.67
Q!
3.16
5.U
se t
he r
esul
ts f
rom
Exe
rcis
es 1
to
4 to
com
pare
the
rel
ativ
e si
zes
of t
he f
our
type
s of
mea
ns.
From
leas
t to
gre
ates
t,th
e m
eans
are
the
har
mon
ic,g
eom
etri
c,ar
ithm
etic
,and
qua
drat
ic m
eans
.
Answers (Lesson 2-4)
© Glencoe/McGraw-Hill A14 Glencoe Algebra 1
Stu
dy
Gu
ide
and I
nte
rven
tion
Sta
tistic
s:D
ispl
ayin
g an
d A
naly
zing
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-5
2-5
©G
lenc
oe/M
cGra
w-H
ill99
Gle
ncoe
Alg
ebra
1
Lesson 2-5
Crea
te L
ine
Plot
s an
d St
em-a
nd-L
eaf
Plot
sO
ne w
ay t
o di
spla
y da
ta g
raph
ical
lyis
wit
h a
lin
e p
lot.
A li
ne p
lot
is a
num
ber
line
labe
led
wit
h a
scal
e th
at in
clud
es a
ll th
eda
ta a
nd &
s pl
aced
abo
ve a
dat
a po
int
each
tim
e it
occ
urs
in t
he d
ata
list.
The
&s
repr
esen
tth
e fr
equ
ency
of t
he d
ata.
A s
tem
-an
d-l
eaf
plo
tca
n al
so b
e us
ed t
o or
gani
ze d
ata.
The
grea
test
com
mon
plac
e va
lue
is c
alle
d th
e st
em,a
nd t
he n
umbe
rs in
the
nex
t gr
eate
st p
lace
valu
e fo
rm t
he le
aves
.
Dra
w a
lin
e p
lot
for
the
dat
a.!
33
47
910
!2
36
43
9!
1!
24
2
Step
1T
he v
alue
of
the
data
ran
ges
from
!3
to 1
0,so
con
stru
ct a
num
ber
line
cont
aini
ng t
hose
poi
nts.
Step
2T
hen
plac
e an
&ab
ove
the
num
ber
each
tim
e it
occ
urs.
76
54
32
10
!1
!2
!3$
$$
$$
$$
$$
$$
$$
$$
$
89
10
76
54
32
10
!1
!2
!3
89
10
Use
th
e d
ata
belo
w t
ocr
eate
a s
tem
-an
d-l
eaf
plo
t.62
74
89
102
92
65
68
98
78
65
78 8
0 8
3
93 8
7 8
9 1
04 1
09 1
04
68 9
7 6
8
64 9
8 9
3
90 1
02 1
04
The
gre
ates
t co
mm
on p
lace
val
ue is
ten
s,so
the
digi
ts in
the
ten
s pl
ace
are
the
stem
s.T
hus
62 w
ould
hav
e a
stem
of
6 an
d 10
4w
ould
hav
e a
stem
of
ten.
The
ste
m-a
nd-l
eaf
plot
is s
how
n be
low
.S
tem
|Lea
f6
|24
55
88
87
|48
88
|03
79
99
|02
33
78
810
|22
44
49
6⏐2
$62
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Use
th
e ta
ble
at t
he
righ
t fo
r E
xerc
ises
1–3
.
1.M
ake
a lin
e pl
ot r
epre
sent
ing
the
wei
ghts
of
the
wre
stle
rs s
how
n in
the
tab
le a
t th
e ri
ght.
2.H
ow m
any
wre
stle
rs w
eigh
ove
r 14
0 lb
?7
3.W
hat
is t
he g
reat
est
wei
ght?
190
lb
Use
eac
h s
et o
f d
ata
to m
ake
a st
em-a
nd
-lea
f p
lot.
4.32
4541
2930
3031
3438
5.10
210
499
109
108
112
115
120
36
3234
4140
4241
2930
112
114
9894
9610
110
010
2
Ste
m|L
eaf
9|4
68
910
|01
22
48
911
|22
45
12|0
9| 4
"94
Ste
m|L
eaf
2|9
93
|00
01
22
44
68
4|0
11
12
52
| 9"
29
200
190
180
170
160
150
140
130
120
110
100$
$$
$$
$$
$$
$$
$$
$$
Wei
ghts
of
Juni
or V
arsi
ty W
rest
lers
(po
unds
)
170
160
135
135
160
122
188
154
108
135
140
122
103
190
154
©G
lenc
oe/M
cGra
w-H
ill10
0G
lenc
oe A
lgeb
ra 1
Ana
lyze
Dat
aN
umbe
rs t
hat
repr
esen
t th
e ce
ntra
lized
,or
mid
dle,
valu
e of
a s
et o
f da
taar
e ca
lled
mea
sure
s of
cen
tral
ten
den
cy.T
hree
mea
sure
s of
cen
tral
ten
denc
y ar
e th
em
ean
,med
ian
,and
mod
e.
Def
initi
onE
xam
ple
Mea
nS
um o
f the
dat
a va
lues
div
ided
by
the
Dat
a: 2
4, 3
6, 2
1, 3
0, 2
1, 3
0;
$27
num
ber
of v
alue
s in
the
data
set
.
The
mid
dle
num
ber
in a
dat
a se
t whe
n th
e nu
mbe
rs a
re a
rran
ged
in n
umer
ical
M
edia
nor
der.
If th
ere
is a
n ev
en n
umbe
r of
D
ata:
21,
21,
25,
30,
31,
42;
$
27.5
valu
es, t
he m
edia
n is
hal
fway
bet
wee
n th
e tw
o m
iddl
e va
lues
.
Mod
eT
he n
umbe
r or
num
bers
that
occ
urD
ata:
21,
21,
24,
30,
30,
36;
21
and
30 a
re m
odes
mos
t ofte
n in
the
set o
f dat
a.
Wh
ich
mea
sure
of
cen
tral
ten
den
cy b
est
rep
rese
nts
th
e d
ata?
Fin
d th
e m
ean,
med
ian,
and
mod
e.
Mea
n $
105
Med
ian
$10
2
Mod
es $
99 a
nd 1
12
The
med
ian
best
rep
rese
nts
the
cent
er o
f the
dat
a si
nce
the
mea
n is
too
high
.
Fin
d t
he
mea
n,m
edia
n,a
nd
mod
e fo
r ea
ch d
ata
set.
Th
en t
ell
wh
ich
bes
tre
pre
sen
ts t
he
dat
a.
1.2.
3.
mea
n "
38.7
;m
ean
"10
8.8
mea
n "
69.3
;m
edia
n "
36;
med
ian
"10
3.5
med
ian
"68
;m
ode
"36
;m
odes
"90
,102
,123
,m
ode
"62
,65,
87;
med
ian
or m
ode
128;
mea
n or
med
ian
mea
n or
med
ian
4.5.
mea
n "
9;m
ean
"3.
7;m
edia
n "
8;m
edia
n "
4;m
ode
"no
ne;
mod
e "
1 an
d 5;
mea
n or
med
ian
med
ian
32
10
$$
$$
$$
$$
$$
$$
$
45
67
Mon
thD
ays
abov
e 90
*
May
4
June
7
July
14
Aug
ust
12
Sep
tem
ber
8
Ste
m|L
eaf
5|0
19
6|2
25
57
|13
58
|03
77
5|0
$50
Ste
m|L
eaf
9|0
01
39
10|2
25
11|
12|0
33
88
99
|0$
90
Ste
m|L
eaf
2|4
77
3|1
26
66
94
|05
|88
92
|4$
24
Ste
m|L
eaf
9|4
68
99
10|0
12
48
911
|22
12|0
19
|4$
94
25 "
30#
2
24 "
36 "
21 "
30 "
21 "
30#
##
#6
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Sta
tistic
s:D
ispl
ayin
g an
d A
naly
zing
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-5
2-5
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 2-5)
© Glencoe/McGraw-Hill A15 Glencoe Algebra 1
Ans
wer
s
Skil
ls P
ract
ice
Sta
tistic
s:D
ispl
ayin
g an
d A
naly
zing
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-5
2-5
©G
lenc
oe/M
cGra
w-H
ill10
1G
lenc
oe A
lgeb
ra 1
Lesson 2-5
Use
eac
h s
et o
f d
ata
to m
ake
a li
ne
plo
t.
1.59
3950
6045
3959
4531
592.
5!
24
07
43
7!
14
5543
3942
5935
3155
4352
!2
52
23
45
0!
22
INC
OM
EF
or E
xerc
ises
3–5
,use
th
e li
st t
hat
sh
ows
the
inco
me
from
eac
h a
ssig
nm
ent
for
a p
riva
te i
nve
stig
ator
for
a y
ear.
3.M
ake
a lin
e pl
ot o
f th
e da
ta.
4.W
hat
was
the
med
ian
inco
me
per
assi
gnm
ent
for
the
inve
stig
ator
?$6
200
5.D
oes
the
med
ian
best
rep
rese
nt t
he d
ata?
Yes;
the
inco
mes
of
$780
0 (t
he m
ode)
are
far
to
the
righ
t on
the
plo
t,an
dal
so m
ake
the
mea
n to
o hi
gh.
Use
eac
h s
et o
f d
ata
to m
ake
a st
em-a
nd
-lea
f p
lot.
6.52
6840
7465
6859
7567
737.
1.5
2.3
1.7
3.0
4.1
5.3
4.7
5563
3942
5935
3159
6342
1.9
2.2
2.8
4.3
5.2
4.1
2.2
EMPL
OY
MEN
TF
or E
xerc
ises
8–1
0,u
se t
he
list
th
at s
how
s th
e ag
es o
f em
plo
yees
at
Wat
son
&S
terl
ing
Pu
blic
atio
ns.
8.M
ake
a st
em-a
nd-l
eaf
plot
of
the
data
.
9.W
hich
age
occ
urs
mos
t fr
eque
ntly
?20
10.D
oes
the
mod
e be
st r
epre
sent
the
dat
a?E
xpla
in.
No;
the
mod
e is
the
lo
wes
t va
lue
of t
he d
ata.
Ste
m|L
eaf
2|0
00
12
67
83
|03
56
94
|03
58
95
|01
25
89
4 ⏐5
"45
2052
2139
4058
2748
3620
5126
4530
4922
5950
3335
2843
5520
Ste
m|L
eaf
1|5
79
2|2
23
83
|04
|11
37
5|2
32 ⏐
2"
2.2
Ste
m|L
eaf
3|1
59
4|0
22
5|2
59
99
6|3
35
78
87
|34
56 ⏐
5"
65
5000
5500
6000
6500
7000
7500
8000
$$
$$
$$
$$
$$$
$
6300
6100
7800
5600
7800
5100
6000
7200
6300
5100
6100
7800
76
54
32
10
!1
!2$
$$
$$
$$
$$
$$
$$
$$
$$$
$$
3035
4045
5055
60
$$
$$
$$
$$
$$
$$
$$
$$
$$$
$
©G
lenc
oe/M
cGra
w-H
ill10
2G
lenc
oe A
lgeb
ra 1
Use
eac
h s
et o
f d
ata
to m
ake
a li
ne
plo
t.
1.72
4762
7849
6780
2.!
2!
1.3
1.5
0.1
!1.
70.
41.
554
4772
5562
4754
1!
1.3
!2
!2.
90.
11.
31.
262
8047
7872
46!
2.6
1.2
0.2
!1.
3!
2.6
HEA
LTH
For
Exe
rcis
es 3
an
d 4
,use
th
e li
st t
hat
sh
ows
the
gram
s of
sat
ura
ted
fat
in
a s
ervi
ng
of a
var
iety
of
grai
ns
such
as
brea
d,c
erea
l,cr
ack
ers,
and
pas
ta.
3.M
ake
a lin
e pl
ot o
f th
e da
ta.
4.W
hich
mea
sure
of
cent
ral t
ende
ncy
best
des
crib
es t
he d
ata?
Exp
lain
.Th
e m
ode
and
med
ian,
both
0.4
.The
mea
n is
too
hig
h be
caus
e of
the
val
ue 2
.8.
Use
eac
h s
et o
f d
ata
to m
ake
a st
em-a
nd
-lea
f p
lot.
5.41
5322
5041
2736
5720
316.
4.1
7.3
6.9
5.7
4.8
7.3
5.6
2852
4133
2827
4152
2230
6.0
4.4
7.5
4.6
7.9
5.1
7.7
EMPL
0YM
ENT
For
Exe
rcis
es 7
–10,
use
th
e li
sts
that
sh
ow s
urv
ey r
esu
lts
ofst
ud
ents
’ tim
e sp
ent
on t
he
Inte
rnet
an
d o
n t
he
tele
ph
one
for
a m
onth
.
7.M
ake
a st
em-a
nd-l
eaf
plot
to
com
pare
the
dat
a.8.
Whi
ch v
alue
app
ears
mos
t fr
eque
ntly
in e
ach
set
of d
ata?
Inte
rnet
:42;
tele
phon
e:8
9.Is
the
mod
e th
e be
st m
easu
re t
o co
mpa
re t
he d
ata?
Exp
lain
.N
o;it
is t
oo h
igh
for
the
Inte
rnet
and
too
low
for
the
tele
phon
e.10
.Ove
rall,
did
stud
ents
spe
nd m
ore
tim
e on
the
In
tern
et o
r th
e te
leph
one?
tele
phon
e
Inte
rnet
|Ste
m|T
elep
hone
87
64
|0
|48
89
84
|1
|9
82
0|
2|4
68
5|
3|5
62
2|
4|0
13
81
|5
|23
85 ⏐
1"
512 ⏐
6"
26
Inte
rnet
Tele
phon
e
4219
288
3542
2018
3652
4028
4324
853
514
729
1422
641
2648
3558
84
Ste
m|L
eaf
4|1
46
85
|16
76
|09
7|3
35
79
7 ⏐7
"7.
7
Ste
m|L
eaf
2|0
22
77
88
3|0
13
64
|11
11
5|0
22
37
3 ⏐3
"330
0.5
11.
52
2.5
3
$$$
$$
$$$$
$$
$$
$$
0.3
1.2
0.1
0.3
0.4
0.4
0.5
0.1
0.4
0.4
0.1
1.2
2.8
1.3
1.5
!3
!2.
5!
2!
1.5
!1
!0.
50
0.5
11.
5
$$$
$$$
$$$
$$$
$$$
$$
$$
4550
5560
6570
7580
$$$$$
$$$$
$$$
$$
$$
$$
$$Pra
ctic
e (A
vera
ge)
Sta
tistic
s:D
ispl
ayin
g an
d A
naly
zing
Dat
a
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-5
2-5
Answers (Lesson 2-5)
© Glencoe/McGraw-Hill A16 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csS
tatis
tics:
Dis
play
ing
and
Ana
lyzi
ng D
ata
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-5
2-5
©G
lenc
oe/M
cGra
w-H
ill10
3G
lenc
oe A
lgeb
ra 1
Lesson 2-5
Pre-
Act
ivit
yH
ow a
re l
ine
plo
ts a
nd
ave
rage
s u
sed
to
mak
e d
ecis
ion
s?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 2-
5 at
the
top
of
page
88
in y
our
text
book
.
•W
hat
was
the
num
ber
one
nam
e fo
r bo
ys in
all
five
dec
ades
?M
icha
el•
Loo
k at
the
dec
ade
in w
hich
you
wer
e bo
rn.I
s yo
ur n
ame
or t
he n
ames
of
any
of t
he o
ther
stu
dent
s in
you
r cl
ass
in t
he t
op f
ive
for
that
dec
ade?
See
stu
dent
s’w
ork.
Read
ing
the
Less
on
1.U
se t
he li
ne p
lot
show
n be
low
to
answ
er t
he q
uest
ions
.
a.W
hat
are
the
data
poi
nts
for
the
line
plot
?!
6,!
5,!
4,!
3,!
2,!
1,0,
1,2,
3,4,
5,6,
7
b.W
hat
do t
he t
hree
&’s
abo
ve t
he 6
rep
rese
nt?
6 oc
curs
in t
he d
ata
set
3 tim
es.
2.E
xpla
in w
hat
is m
eant
by
the
freq
uenc
y of
a d
ata
num
ber.
how
man
y tim
es t
he d
ata
num
ber
occu
rs
3.U
se t
he s
tem
-and
-lea
f pl
ot s
how
n at
the
rig
ht.
a.H
ow is
the
num
ber
758
repr
esen
ted
on t
he p
lot?
75⏐8
b.E
xpla
in h
ow y
ou k
now
the
re a
re 2
3 nu
mbe
rs in
the
data
.
Ther
e ar
e 23
leav
es.
Hel
ping
You
Rem
embe
r
4.D
escr
ibe
how
you
wou
ld e
xpla
in t
he p
roce
ss o
f fi
ndin
g th
e m
edia
n an
d m
ode
from
ast
em-a
nd-l
eaf
plot
to
a fr
iend
who
mis
sed
Les
son
2-5.
Sam
ple
answ
er:T
o fin
d th
e m
edia
n,co
unt
the
num
ber
of le
aves
,the
nfin
d th
e nu
mbe
r in
the
mid
dle.
To f
ind
the
mod
e,id
entif
y th
e le
af t
hat
occu
rs m
ost
freq
uent
ly a
nd u
se t
he s
tem
and
key
to
iden
tify
the
data
num
ber.
Ste
m|L
eaf
72|0
11
25
73|2
22
79
974
|13
375
|66
89
76|0
18
88
74⏐2
$74
2
76
54
32
10
!1
!2
!3
!4
!5
!6$
$$
$$
$$
$$
$$
$$
$$
$$
$$
$$
$$
$$$$
$$
©G
lenc
oe/M
cGra
w-H
ill10
4G
lenc
oe A
lgeb
ra 1
Run
s C
reat
ed
In T
he 1
978
Bil
l Ja
mes
Bas
ebal
l Abs
trac
t,th
e au
thor
intr
oduc
ed t
he “
runs
cre
ated
”fo
rmul
a.
R$
whe
re f
or e
ach
play
erh
$nu
mbe
r of
hit
s
w$
num
ber
of w
alks
,
t$
num
ber
of t
otal
bas
es,
b$
num
ber
of a
t-ba
ts,a
nd
R$
appr
oxim
ate
num
ber
of r
uns
a te
am
scor
es d
ue t
o th
is p
laye
r’s a
ctio
ns
1.A
s of
Jun
e 29
,200
1,R
ober
to A
lom
ar o
f th
e C
leve
land
Ind
ians
and
Sea
ttle
Mar
iner
spl
ayer
Ich
iro
Suzu
ki w
ere
tied
wit
h th
e hi
ghes
t A
mer
ican
Lea
gue
batt
ing
aver
age
at.3
51.F
ind
the
num
ber
of r
uns
crea
ted
by e
ach
play
er u
sing
the
dat
a be
low
.
hw
tb
Run
s C
reat
ed
Alo
mar
9737
145
276
62
Suz
uki
121
1315
934
560
Bas
ed o
n th
is in
form
atio
n,w
ho d
o yo
u th
ink
is t
he m
ore
valu
able
Am
eric
an L
eagu
epl
ayer
? W
hy?
Sam
ple
answ
er:A
lom
ar,b
ecau
se h
e cr
eate
s m
ore
runs
.
2.C
arlo
s L
ee o
f th
e C
hica
go W
hite
Sox
and
New
Yor
k Ya
nkee
Ber
nie
Will
iam
s w
ere
both
batt
ing
.314
.Fin
d th
e nu
mbe
r of
run
s cr
eate
d by
eac
h pl
ayer
usi
ng t
he d
ata
belo
w.
hw
tb
Run
s C
reat
ed
Lee
8113
141
258
49
Will
iam
s74
3112
323
648
3.W
hy w
ould
bas
ebal
l tea
ms
wan
t to
cal
cula
te t
he n
umbe
r of
run
s cr
eate
d by
eac
h of
the
irpl
ayer
s?
Sam
ple
answ
er:T
o he
lp m
ake
deci
sion
s ab
out
star
ting
line-
ups;
To h
elp
mak
e de
cisi
ons
abou
t tr
adin
g pl
ayer
s.
(h+
w)t
# (b+
w)En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-5
2-5
Answers (Lesson 2-5)
© Glencoe/McGraw-Hill A17 Glencoe Algebra 1
Ans
wer
s
Stu
dy
Gu
ide
and I
nte
rven
tion
Pro
babi
lity:
Sim
ple
Pro
babi
lity
and
Odd
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-6
2-6
©G
lenc
oe/M
cGra
w-H
ill10
5G
lenc
oe A
lgeb
ra 1
Lesson 2-6
Prob
abili
tyT
he p
roba
bili
tyof
a s
imp
le e
ven
tis
a r
atio
tha
t te
lls h
ow li
kely
it is
tha
tth
e ev
ent
will
tak
e pl
ace.
It is
the
rat
io o
f th
e nu
mbe
r of
fav
orab
le o
utco
mes
of
the
even
t to
the
num
ber
of p
ossi
ble
outc
omes
of
the
even
t.Yo
u ca
n ex
pres
s th
e pr
obab
ility
eit
her
as a
frac
tion
,as
a de
cim
al,o
r as
a p
erce
nt.
Pro
babi
lity
of a
Sim
ple
Eve
ntF
or a
n ev
ent a
, P(a
) $
.nu
mbe
r of
favo
rabl
e ou
tcom
es#
##
#nu
mbe
r of
pos
sibl
e ou
tcom
es
Mr.
Bab
cock
ch
oose
s 5
out
of 2
5 st
ud
ents
in
his
alg
ebra
cla
ssat
ran
dom
for
a s
pec
ial
pro
ject
.Wh
at i
sth
e p
roba
bili
ty o
f be
ing
chos
en?
P(b
eing
cho
sen)
$
The
pro
babi
lity
of b
eing
cho
sen
is
or
.1 # 5
5 # 25
num
ber
of s
tude
nts
chos
en#
##
#to
tal n
umbe
r of
stu
dent
s
A b
owl
con
tain
s 3
pea
rs,
4 ba
nan
as,a
nd
2 a
pp
les.
If y
ou t
ake
ap
iece
of
fru
it a
t ra
nd
om,w
hat
is
the
pro
babi
lity
th
at i
t is
not
a ba
nan
a?
The
re a
re 3
"4
"2
or 9
pie
ces
of f
ruit
.T
here
are
3 "
2 or
5 p
iece
s of
fru
it t
hat
are
not
bana
nas.
P(n
ot b
anan
a)$ $
The
pro
babi
lity
of n
otch
oosi
ng a
ban
ana
is.
5 # 9
5 # 9num
ber
of o
ther
pie
ces
of f
ruit
##
##
tota
l num
ber
of p
iece
s of
fru
it
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
A c
ard
is
sele
cted
at
ran
dom
fro
m a
sta
nd
ard
dec
k o
f 52
car
ds.
Det
erm
ine
each
pro
babi
lity
.
1.P
(10)
2.P
(red
2)
3.P
(kin
g or
que
en)
4.P
(bla
ck c
ard)
5.P
(ace
of
spad
es)
6.P
(spa
de)
Tw
o d
ice
are
roll
ed a
nd
th
eir
sum
is
reco
rded
.Fin
d e
ach
pro
babi
lity
.
7.P
(sum
is 1
)0
8.P
(sum
is 6
)9.
P(s
um is
less
tha
n 4)
10.P
(sum
is g
reat
er t
han
11)
11.P
(sum
is le
ss t
han
15)
12.P
(sum
is g
reat
er t
han
8)
1
A b
owl
con
tain
s 4
red
ch
ips,
3 bl
ue
chip
s,an
d 8
gre
en c
hip
s.Yo
u c
hoo
se o
ne
chip
at r
and
om.F
ind
eac
h p
roba
bili
ty.
13.P
(not
a r
ed c
hip)
14.P
(red
or
blue
chi
p)15
.P(n
ot a
gre
en c
hip)
A n
um
ber
is s
elec
ted
at
ran
dom
fro
m t
he
list
{1,
2,3,
…,1
0}.F
ind
eac
h p
roba
bili
ty.
16.P
(eve
n nu
mbe
r)17
.P(m
ulti
ple
of 3
)18
.P(l
ess
than
4)
19.A
com
pute
r ra
ndom
ly c
hoos
es a
lett
er f
rom
the
wor
d C
OM
PU
TE
R.F
ind
the
prob
abili
tyth
at t
he le
tter
is a
vow
el.
3 # 8
3 # 103 # 10
1 # 2
7 # 157 # 15
11 # 15
5 # 181 # 36
1 # 125 # 36
1 # 41 # 52
1 # 2
2 # 131 # 26
1 # 13
©G
lenc
oe/M
cGra
w-H
ill10
6G
lenc
oe A
lgeb
ra 1
Odd
sT
he o
dds
of a
n ev
ent
occu
rrin
g is
the
rat
io o
f th
e nu
mbe
r of
way
s an
eve
nt c
an o
ccur
(suc
cess
es)
to t
he n
umbe
r of
way
s th
e ev
ent
cann
ot o
ccur
(fa
ilure
s).
Odd
s
A d
ie i
s ro
lled
.Fin
d t
he
odd
s of
rol
lin
g a
nu
mbe
r gr
eate
r th
an 4
.
The
sam
ple
spac
e is
{1,
2,3,
4,5,
6}.T
here
fore
,the
re a
re s
ix p
ossi
ble
outc
omes
.Sin
ce 5
and
6 ar
e th
e on
ly n
umbe
rs g
reat
er t
han
4,tw
o ou
tcom
es a
re s
ucce
sses
and
fou
r ar
e fa
ilure
s.
So t
he o
dds
of r
ollin
g a
num
ber
grea
ter
than
4 is
,o
r 1:
2.
Fin
d t
he
odd
s of
eac
h o
utc
ome
if t
he
spin
ner
at
the
righ
t is
sp
un
on
ce.
1.m
ulti
ple
of 4
1:4
2.od
d nu
mbe
r1:
1
3.ev
en o
r a
53:
24.
less
tha
n 4
3:7
5.ev
en n
umbe
r gr
eate
r th
an 5
3:7
Fin
d t
he
odd
s of
eac
h o
utc
ome
if a
com
pu
ter
ran
dom
ly c
hoo
ses
a n
um
ber
betw
een
1 an
d 2
0.
6.th
e nu
mbe
r is
less
tha
n 10
9:11
7.th
e nu
mbe
r is
a m
ulti
ple
of 4
1:3
8.th
e nu
mbe
r is
eve
n1:
19.
the
num
ber
is a
one
-dig
it n
umbe
r9:
11
A b
owl
of m
oney
at
a ca
rniv
al c
onta
ins
50 q
uar
ters
,75
dim
es,1
00 n
ick
els,
and
12
5 p
enn
ies.
On
e co
in i
s ra
nd
omly
sel
ecte
d.
10.F
ind
the
odds
tha
t a
dim
e w
ill n
ot b
e ch
osen
.11
:3
11.W
hat
are
the
odds
of
choo
sing
a q
uart
er if
all
the
dim
es a
re r
emov
ed?
2:9
12.W
hat
are
the
odds
of
choo
sing
a p
enny
?5:
9
Su
pp
ose
you
dro
p a
ch
ip o
nto
th
e gr
id a
t th
e ri
ght.
Fin
d t
he
odd
s of
eac
h o
utc
ome.
13.l
and
on a
sha
ded
squa
re1:
1
14.l
and
on a
squ
are
on t
he d
iago
nal
1:1
15.l
and
on s
quar
e nu
mbe
r 16
1:15
16.l
and
on a
num
ber
grea
ter
than
12
1:3
17.l
and
on a
mul
tipl
e of
53:
13
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
12
9
4
38 7
10
56
2 # 4
num
ber
of s
ucce
sses
##
#nu
mbe
r of
failu
res
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Pro
babi
lity:
Sim
ple
Pro
babi
lity
and
Odd
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-6
2-6
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 2-6)
© Glencoe/McGraw-Hill A18 Glencoe Algebra 1
Skil
ls P
ract
ice
Pro
babi
lity:
Sim
ple
Pro
babi
lity
and
Odd
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-6
2-6
©G
lenc
oe/M
cGra
w-H
ill10
7G
lenc
oe A
lgeb
ra 1
Lesson 2-6
On
e ch
ip i
s ra
nd
omly
sel
ecte
d f
rom
a j
ar c
onta
inin
g 8
yell
ow c
hip
s,10
blu
e ch
ips,
7 gr
een
ch
ips,
and
5 r
ed c
hip
s.F
ind
eac
h p
roba
bili
ty.
1.P
(blu
e)&
33%
2.P
(gre
en)
&23
%
3.P
(yel
low
or
gree
n)"
50%
4.P
(blu
e or
yel
low
)"
60%
5.P
(not
red
)&
83%
6.P
(not
blu
e)&
67%
Fin
d t
he
pro
babi
lity
of
each
ou
tcom
e if
th
e sp
inn
er i
s sp
un
on
ce.
7.P
(mul
tipl
e of
3)
"25
%8.
P(l
ess
than
7)
"75
%
9.P
(odd
or
2)"
62.5
%10
.P(n
ot 1
)"
87.5
%
A p
erso
n i
s bo
rn i
n t
he
mon
th o
f Ju
ne.
Fin
d e
ach
pro
babi
lity
.
11.P
(dat
e is
a m
ulti
ple
of 6
)12
.P(d
ate
is b
efor
e Ju
ne 1
5)
&17
%&
47%
13.P
(bef
ore
June
7 o
r af
ter
June
24)
14.P
(not
aft
er J
une
5)
"40
%&
17%
Fin
d t
he
odd
s of
eac
h o
utc
ome
if a
com
pu
ter
ran
dom
ly p
ick
s a
lett
er i
n t
he
nam
eT
he
Pet
rifi
ed F
ores
t.
15.t
he le
tter
f2
:16
or 1
:816
.the
lett
er e
4:1
4 or
2:7
17.t
he le
tter
t3
:15
or 1
:518
.a v
owel
7:1
1
CL
AS
S S
CH
ED
UL
ES
For
Exe
rcis
es 1
9–22
,use
th
e fo
llow
ing
info
rmat
ion
.
A s
tude
nt c
an s
elec
t an
ele
ctiv
e cl
ass
from
the
fol
low
ing:
3 in
mus
ic,5
in p
hysi
cal e
duca
tion
,2
in jo
urna
lism
,8 in
com
pute
r pr
ogra
mm
ing,
4 in
art
,and
6 in
dra
ma.
Fin
d ea
ch o
f th
e od
dsif
a s
tude
nt f
orge
ts t
o ch
oose
an
elec
tive
and
the
sch
ool a
ssig
ns o
ne a
t ra
ndom
.
19.T
he c
lass
is c
ompu
ter
prog
ram
min
g.8
:20
or 2
:5
20.T
he c
lass
is d
ram
a.6
:22
or 3
:11
21.T
he c
lass
is n
ot p
hysi
cal e
duca
tion
.23
:5
22.T
he c
lass
is n
ot a
rt.
24:4
or
6:1
1 # 62 # 5
7 # 151 # 6
7 # 85 # 8
3 # 41 # 4
18
45
63
72
2 # 35 # 6
3 # 51 # 2
7 # 301 # 3
©G
lenc
oe/M
cGra
w-H
ill10
8G
lenc
oe A
lgeb
ra 1
On
e ch
ip i
s ra
nd
omly
sel
ecte
d f
rom
a j
ar c
onta
inin
g 13
blu
e ch
ips,
8 ye
llow
ch
ips,
15 b
row
n c
hip
s,an
d 6
gre
en c
hip
s.F
ind
eac
h p
roba
bili
ty.
1.P
(bro
wn)
&36
%2.
P(g
reen
)&
14%
3.P
(blu
e or
yel
low
)"
50%
4.P
(not
yel
low
)&
81%
A c
ard
is
sele
cted
at
ran
dom
fro
m a
sta
nd
ard
dec
k o
f 52
car
ds.
Fin
d e
ach
pro
babi
lity
.
5.P
(hea
rt)
"25
%6.
P(b
lack
car
d)"
50%
7.P
(jack
)&
8%8.
P(r
ed ja
ck)
&4%
Tw
o d
ice
are
roll
ed a
nd
th
eir
sum
is
reco
rded
.Fin
d e
ach
pro
babi
lity
.
9.P
(sum
less
tha
n 6)
&28
%10
.P(s
um le
ss t
han
2)0
"0%
11.P
(sum
gre
ater
tha
n 10
)&
8%12
.P(s
um g
reat
er t
han
9)&
17%
Fin
d t
he
odd
s of
eac
h o
utc
ome
if a
com
pu
ter
ran
dom
ly p
ick
s a
lett
er i
n t
he
nam
eT
he
Ba
dla
nd
s of
Nor
th D
ako
ta.
13.t
he le
tter
d3
:21
or 1
:714
.the
lett
er a
4:2
0 or
1:5
15.t
he le
tter
h2
:22
or 1
:11
16.a
con
sona
nt16
:8 o
r 2
:1
CLA
SS P
RO
JEC
TSF
or E
xerc
ises
17–
20,u
se t
he
foll
owin
g in
form
atio
n.
Stud
ents
in a
bio
logy
cla
ss c
an c
hoos
e a
sem
este
r pr
ojec
t fr
om t
he f
ollo
win
g lis
t:an
imal
beha
vior
(4)
,cel
lula
r pr
oces
ses
(2),
ecol
ogy
(6),
heal
th (
7),a
nd p
hysi
olog
y (3
).F
ind
each
of
the
odds
if a
stu
dent
sel
ects
a t
opic
at
rand
om.
17.t
he t
opic
is e
colo
gy6
:16
or 3
:8
18.t
he t
opic
is a
nim
al b
ehav
ior
4:1
8 or
2:9
19.t
he t
opic
is n
ot c
ellu
lar
proc
esse
s20
:2 o
r 10
:1
20.t
he t
opic
is n
ot h
ealt
h15
:7
SC
HO
OL
IS
SU
ES
For
Exe
rcis
es 2
1 an
d 2
2,u
se t
he
foll
owin
g in
form
atio
n.
A n
ews
team
sur
veye
d st
uden
ts in
gra
des
9–12
on
whe
ther
to
ch
ange
the
tim
e sc
hool
beg
ins.
One
stu
dent
will
be
sele
cted
at
rand
om t
o be
inte
rvie
wed
on
the
even
ing
new
s.T
he t
able
giv
es
the
resu
lts.
21.W
hat
is t
he p
roba
bilit
y th
e st
uden
t se
lect
ed w
ill b
e in
the
9th
grad
e?"
32%
22.W
hat
are
the
odds
the
stu
dent
sel
ecte
d w
ants
no
chan
ge?
16:3
4 or
8:1
7
8 # 25
Gra
de9
1011
12
No
chan
ge6
25
3
Hou
r la
ter
107
98
1 # 61 # 12
5 # 18
1 # 261 # 13
1 # 21 # 4
17 # 211 # 2
1 # 75 # 14
Pra
ctic
e (A
vera
ge)
Pro
babi
lity:
Sim
ple
Pro
babi
lity
and
Odd
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-6
2-6
Answers (Lesson 2-6)
© Glencoe/McGraw-Hill A19 Glencoe Algebra 1
Ans
wer
s
Rea
din
g t
o L
earn
Math
emati
csP
roba
bilit
y:S
impl
e P
roba
bilit
y an
d O
dds
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-6
2-6
©G
lenc
oe/M
cGra
w-H
ill10
9G
lenc
oe A
lgeb
ra 1
Lesson 2-6
Pre-
Act
ivit
yW
hy
is p
roba
bili
ty i
mp
orta
nt
in s
por
ts?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 2-
6 at
the
top
of
page
96
in y
our
text
book
.
Loo
k up
the
def
init
ion
of t
he w
ord
prob
abil
ity
in a
dic
tion
ary.
Rew
rite
the
defi
niti
on in
you
r ow
n w
ords
.
Sam
ple
answ
er:t
he li
kelih
ood
of s
omet
hing
hap
peni
ng
Read
ing
the
Less
on
1.W
rite
whe
ther
eac
h st
atem
ent
is t
rue
or fa
lse.
If fa
lse,
repl
ace
the
unde
rlin
ed w
ord
ornu
mbe
r to
mak
e a
true
sta
tem
ent.
a.P
roba
bilit
y ca
n be
wri
tten
as
a fr
acti
on,a
dec
imal
,or
a pe
rcen
t.tr
ue
b.T
he s
ampl
e sp
ace
of f
lippi
ng o
ne c
oin
is h
eads
or
tails
.tr
ue
c.T
he p
roba
bilit
y of
an
impo
ssib
le e
vent
is 1
.fa
lse;
0
d.T
he o
dds
agai
nst
an e
vent
occ
urri
ng a
re t
he o
dds
that
the
eve
nt w
ill o
ccur
.fa
lse;
will
not
2.E
xpla
in w
hy t
he p
roba
bilit
y of
an
even
t ca
nnot
be
grea
ter
than
1 w
hile
the
odd
s of
an
even
t ca
n be
gre
ater
tha
n 1.
Sam
ple
answ
er:T
o fin
d th
e pr
obab
ility
of
an e
vent
,you
com
pare
a p
art
ofth
e sa
mpl
e sp
ace
to t
he w
hole
sam
ple
spac
e.W
hen
you
find
the
odds
of
an e
vent
,you
com
pare
the
num
ber
of f
avor
able
out
com
es t
o th
e nu
mbe
rof
unf
avor
able
out
com
es.I
n so
me
situ
atio
ns,t
here
may
be
mor
efa
vora
ble
than
unf
avor
able
out
com
es.
Hel
ping
You
Rem
embe
r
3.P
roba
bilit
ies
are
usua
lly w
ritt
en a
s fr
acti
ons,
deci
mal
s,or
per
cent
s.O
dds
are
usua
llyw
ritt
en w
ith
a co
lon
(for
exa
mpl
e,1:
3).H
ow c
an t
he s
pelli
ng o
f th
e w
ord
colo
nhe
lpre
mem
ber
this
?
Sam
ple
answ
er:T
he w
ord
colo
nha
s th
e le
tter
“o”
as it
s on
ly v
owel
,and
the
wor
d od
dsal
so h
as t
he le
tter
“o”
as it
s on
ly v
owel
.
©G
lenc
oe/M
cGra
w-H
ill11
0G
lenc
oe A
lgeb
ra 1
Geo
met
ric
Pro
babi
lity
If a
dar
t,th
row
n at
ran
dom
,hit
s th
e tr
iang
ular
boa
rd s
how
n at
the
ri
ght,
wha
t is
the
pro
babi
lity
that
it w
ill h
it t
he s
hade
d re
gion
? T
his
can
be d
eter
min
ed b
y co
mpa
ring
the
are
a of
the
sha
ded
regi
on t
o th
ear
ea o
f th
e en
tire
boa
rd.T
his
rati
o in
dica
tes
wha
t fr
acti
on o
f th
e to
sses
sho
uld
hit
in t
he s
hade
d re
gion
. ! !or
In g
ener
al,i
f Sis
a s
ubre
gion
of
som
e re
gion
R,t
hen
the
prob
abili
ty,P
(S),
that
a p
oint
,ch
osen
at
rand
om,b
elon
gs t
o su
breg
ion
Sis
giv
en b
y th
e fo
llow
ing:
P(S
) !
Fin
d t
he
pro
babi
lity
th
at a
poi
nt,
chos
en a
t ra
nd
om,b
elon
gs t
o th
e sh
aded
subr
egio
ns
of t
he
foll
owin
g fi
gure
s.
1.2.
3.
4.5.
6.
7.8.
9.3 ! 4
2 2
44
" ! 4
8
4
" ! 44 4
44
2 ! 36 6
66
66
6!"3
6!"3
!3 "
"4
5 5
55
55
1 ! 2
6
6
4
" ! 4
4
44
45 ! 9
644
46
6
1 ! 23
3
5 5
area
of
subr
egio
n S
""
"ar
ea o
r re
gion
R
1 " 212 " 24"1 2" (
4)(6
)" "1 2" (
8)(6
)
area
of
shad
ed r
egio
n"
""
area
of
tria
ngul
ar b
oard
6
44
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-6
2-6
Answers (Lesson 2-6)
© Glencoe/McGraw-Hill A20 Glencoe Algebra 1
Stu
dy
Gu
ide
and I
nte
rven
tion
Squ
are
Roo
ts a
nd R
eal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-7
2-7
©G
lenc
oe/M
cGra
w-H
ill11
1G
lenc
oe A
lgeb
ra 1
Lesson 2-7
Squa
re R
oots
A s
quar
e ro
otis
one
of
two
equa
l fac
tors
of
a nu
mbe
r.Fo
r ex
ampl
e,th
esq
uare
roo
ts o
f 36
are
6 a
nd !
6,si
nce
6 %
6 or
62
is 3
6 an
d (!
6)(!
6) o
r (!
6)2
is a
lso
36.A
rati
onal
num
ber
like
36,w
hose
squ
are
root
is a
rat
iona
l num
ber,
is c
alle
d a
per
fect
squ
are.
The
sym
bol &
'is
a r
adic
al s
ign
.It
indi
cate
s th
e no
nneg
ativ
e,or
pri
nci
pal
,squ
are
root
of
the
num
ber
unde
r th
e ra
dica
l sig
n.So
&36%
$6
and
!&
36%$
!6.
The
sym
bol (
&36%
repr
esen
ts b
oth
squa
re r
oots
.
Fin
d !'(
.
!()
repr
esen
ts t
he n
egat
ive
squa
re r
oot
of
.
$#
$2→
!()
$!
5 # 725 # 49
5 # 725 # 49
25 # 4925 # 49
25 # 49F
ind
-)
0.16
#.
(&
0.16
%re
pres
ents
the
pos
itiv
e an
dne
gati
ve s
quar
e ro
ots
of 0
.16.
0.16
$0.
42an
d 0.
16 $
(!0.
4)2
(&
0.16
%$
(0.
4
Exam
ple1
Exam
ple1
Exam
ple2
Exam
ple2
Exer
cises
Exer
cises
Fin
d e
ach
squ
are
root
.
1.&
64%8
2.!
&81%
!9
3.&
16.8
1%
4.1
4.(
&10
0%
-10
5.!()
!6.
!&
121
%!
11
7.(()
-8.
!()
!9.
(()
-
10.!
&36
00%
!60
11.!
&6.
25%
!2.
512
.(&
0.00
0%
4%-
0.02
13.()
14.!
()!
15.(
&1.
21%
-1.
16 # 7
36 # 496 # 7
144
# 196
11 # 1012
1# 10
05 # 4
25 # 165 # 12
25 # 144
2 # 54 # 25
©G
lenc
oe/M
cGra
w-H
ill11
2G
lenc
oe A
lgeb
ra 1
Clas
sify
and
Ord
er N
umbe
rsN
umbe
r su
ch a
s &
2%an
d &
3%ar
e no
t pe
rfec
t sq
uare
s.N
otic
e w
hat
happ
ens
whe
n yo
u fi
nd t
hese
squ
are
root
s w
ith
your
cal
cula
tor.
The
num
bers
cont
inue
inde
fini
tely
wit
hout
any
pat
tern
of
repe
atin
g di
gits
.Num
bers
tha
t ca
nnot
be
wri
tten
as
a te
rmin
atin
g or
rep
eati
ng d
ecim
al a
re c
alle
d ir
rati
onal
nu
mbe
rs.T
he s
et o
fre
al n
um
bers
cons
ists
of
the
set
of ir
rati
onal
num
bers
and
the
set
of
rati
onal
num
bers
toge
ther
.The
cha
rt b
elow
illu
stra
tes
the
vari
ous
kind
s of
rea
l num
bers
.
Nat
ural
Num
bers
{1, 2
, 3, 4
, …}
Who
le N
umbe
rs{0
, 1, 2
, 3, 4
, …}
Inte
gers
{…, !
3, !
2, !
1, 0
, 1, 2
, 3, …
}
Rat
iona
l Num
bers
{all
num
bers
that
can
be
expr
esse
d in
the
form
, w
here
aan
d b
are
inte
gers
and
b)
0}
Irra
tiona
l Num
bers
{all
num
bers
that
can
not b
e ex
pres
sed
in th
e fo
rm
, whe
re a
and
bar
e in
tege
rs a
nd b
)0}
Nam
e th
e se
t or
set
s of
nu
mbe
rs t
o w
hic
h e
ach
rea
l n
um
ber
belo
ngs
.
a.B
ecau
se 4
and
11
are
inte
gers
,thi
s nu
mbe
r is
a r
atio
nal n
umbe
r.
b.)
81#B
ecau
se &
81%$
9,th
is n
umbe
r is
a n
atur
al n
umbe
r,a
who
le n
umbe
r,an
inte
ger,
and
a ra
tion
al n
umbe
r.
c.)
32#B
ecau
se &
32%$
5.65
6854
249…
,whi
ch is
not
a r
epea
ting
or
term
inat
ing
deci
mal
,th
is n
umbe
r is
irra
tion
al.
Nam
e th
e se
t or
set
s of
nu
mbe
rs t
o w
hic
h e
ach
rea
l n
um
ber
belo
ngs
.
1.2.
!3.
4.&
54%na
tura
l,w
hole
,ra
tiona
lra
tiona
lir
ratio
nal
inte
ger,
ratio
nal
5.3.
145
6.&
25%7.
0.62
6262
62…
8.&
22.5
1%
ratio
nal
natu
ral,
who
le,
ratio
nal
irra
tiona
l in
tege
r,ra
tiona
l
Wri
te e
ach
set
of
nu
mbe
rs i
n o
rder
fro
m l
east
to
grea
test
.
9.!
,!5,
&25%
,10
.&0.
09%
,!0.
3131
…,
11.!
1.2%5%
,0.0
5,!
,&5%
!5,
!,
,)25#
!0.
3131
…,)
0.09
#,
!1.
2#5#,!
,0.0
5,)
5#
12.
,!2,
&12
4%
,!3.
1113
.!&
1.44
%,!
0.35
14
.0.3%
5%,2
,!,&
5%
!3.
11,!
2,,)
124
#!
)1.
44#
,!0.
35,
!,0
.3#5#,
)5#,
21 # 3
9 # 51 # 5
5 # 4
9 # 51 # 3
1 # 55 # 4
1 # 43 # 5
7 # 43 # 4
1 # 43 # 5
7 # 43 # 4
2 # 36 # 7
84 # 124 # 11
a # b
a # b
Stu
dy
Gu
ide
and I
nte
rven
tion
(c
onti
nued
)
Squ
are
Roo
ts a
nd R
eal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-7
2-7
Exam
ple
Exam
ple
Exer
cises
Exer
cises
Answers (Lesson 2-7)
© Glencoe/McGraw-Hill A21 Glencoe Algebra 1
Ans
wer
s
Skil
ls P
ract
ice
Squ
are
Roo
ts a
nd R
eal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-7
2-7
©G
lenc
oe/M
cGra
w-H
ill11
3G
lenc
oe A
lgeb
ra 1
Lesson 2-7
Fin
d e
ach
squ
are
root
.If
nec
essa
ry,r
oun
d t
o th
e n
eare
st h
un
dre
dth
.
1.&
144
%12
2.!
&36%
!6
3.(
&0.
25%
-0.
54.
!()
!
5.(
&17%
-4.
126.
&2.
25%
1.5
Nam
e th
e se
t or
set
s of
nu
mbe
rs t
o w
hic
h e
ach
rea
l n
um
ber
belo
ngs
.
7.!
8.!
inte
ger,
ratio
nal
ratio
nal
9.&
29%10
.&19
6%
irra
tiona
lna
tura
l,w
hole
,int
eger
,rat
iona
l
11.
12.&
1.8
%ra
tiona
lir
ratio
nal
Gra
ph
eac
h s
olu
tion
set
.
13.x
*!
114
.x+
1
15.x
,1.
516
.x-
!2.
5
Rep
lace
eac
h ●
wit
h &
,.,o
r "
to m
ake
each
sen
ten
ce t
rue.
17.
●0.
4 %"
18.0
.0%9%
●.
19.6
.2%3%
●&
39%&
20.
●&
Wri
te e
ach
set
of
nu
mbe
rs i
n o
rder
fro
m l
east
to
grea
test
.
21. &
5%,2.
3%6%,
)5#,
,2.3#
6#22
.,0
.2%1%,
&0.
05%
0.2#1#
,,)
0.05
#
23.!
&12%
,!3.
4%8%,!
&11%
24.0
.4%3%,
,,0
.43,
!3.
4 #8#,!
)12#
,!)
11#
)6#
#5
3 # 73 # 7
&6%
#5
2 # 92 # 9
7 # 37 # 3
1# &
8%1 # 8
1 # 904 # 9
!2
!1
!4
!3
01
23
4!
2!
1!
4!
30
12
34
!2
!1
!4
!3
01
23
4!
2!
10
12
34
56
9 # 13
5 # 628 # 7
7 # 1049 # 10
0
©G
lenc
oe/M
cGra
w-H
ill11
4G
lenc
oe A
lgeb
ra 1
Fin
d e
ach
squ
are
root
.If
nec
essa
ry,r
oun
d t
o th
e n
eare
st h
un
dre
dth
.
1.&
324
%2.
!&
62%3.
(&
25%4.
!&
84%18
!7.
87-
5!
9.17
5.(()
6.!()
7.!
&0.
081
%8.
(&
3.06
%
-!
0.76
!0.
28-
1.75
Nam
e th
e se
t or
set
s of
nu
mbe
rs t
o w
hic
h e
ach
rea
l n
um
ber
belo
ngs
.
9.&
93%10
.!&
0.06
2%
5%11
.12
.!
irra
tiona
lra
tiona
lra
tiona
lin
tege
r,ra
tiona
l
Gra
ph
eac
h s
olu
tion
set
.
13.x
,!
0.5
14.x
-!
3.5
Rep
lace
eac
h ●
wit
h &
,.,o
r "
to m
ake
each
sen
ten
ce t
rue.
15.0
.9 %3%
●&
0.93
%&
16.8
.1%7%
●&
66%.
17.
●.
Wri
te e
ach
set
of
nu
mbe
rs i
n o
rder
fro
m l
east
to
grea
test
.
18. &
0.03
%,
,0.1%
7%19
.!,!
&8%,
!20
.!&
8.5
%,!
,!2
0.1#7#
,)
0.03
#,
!)
8#,!
,!!
,!2
,!)
8.5
#
21.S
IGH
TSEE
ING
The
dis
tanc
e yo
u ca
n se
e to
the
hor
izon
is g
iven
by
the
form
ula
d$
&1.
5h%
,whe
re d
is t
he d
ista
nce
in m
iles
and
his
the
hei
ght
in f
eet
abov
e th
e ho
rizo
n lin
e.M
t.W
hitn
ey is
the
hig
hest
poi
nt in
the
con
tigu
ous
48 s
tate
s.It
s el
evat
ion
is 1
4,49
4 fe
et.T
he lo
wes
t el
evat
ion,
at !
282
feet
,is
loca
ted
near
Bad
wat
er,C
alif
orni
a.W
ith
a cl
ear
enou
gh s
ky a
nd n
o ob
stru
ctio
ns,c
ould
you
see
fro
m t
he t
op o
f M
t.W
hitn
eyto
Bad
wat
er if
the
dis
tanc
e be
twee
n th
em is
135
mile
s? E
xpla
in.
Yes;
you
can
see
abou
t 14
9 m
iles
from
the
top
of
Mt.
Whi
tney
to
an e
leva
tion
of !
282
feet
.
22.S
EISM
IC W
AV
ESA
tsu
nam
iis
a s
eism
ic w
ave
caus
ed b
y an
ear
thqu
ake
on t
he o
cean
floo
r.Yo
u ca
n us
e th
e fo
rmul
a s
$3.
1 &d%,
whe
re s
is t
he s
peed
in m
eter
s pe
r se
cond
and
d
is t
he d
epth
of
the
ocea
n in
met
ers,
to d
eter
min
e th
e sp
eed
of a
tsu
nam
i.If
an
eart
hqua
ke o
ccur
s at
a d
epth
of
200
met
ers,
wha
t is
the
spe
ed o
f th
e ts
unam
i gen
erat
edby
the
ear
thqu
ake?
abou
t 43
.8 m
/s
19 # 20)
35##
2)
7##
884 # 30
)2#
#8
19 # 20&
35%#
2&
7%#
884 # 30
&2%
#8
&5%
#6
5 # 6
!2
!1
!4
!3
01
23
4!
2!
1!
4!
30
12
34
144
#3
8 # 7
2 # 17
7 # 124
# 289P
ract
ice
(Ave
rage
)
Squ
are
Roo
ts a
nd R
eal N
umbe
rs
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-7
2-7
Answers (Lesson 2-7)
© Glencoe/McGraw-Hill A22 Glencoe Algebra 1
Rea
din
g t
o L
earn
Math
emati
csS
quar
e R
oots
and
Rea
l Num
bers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-7
2-7
©G
lenc
oe/M
cGra
w-H
ill11
5G
lenc
oe A
lgeb
ra 1
Lesson 2-7
Pre-
Act
ivit
yH
ow c
an u
sin
g sq
uar
e ro
ots
det
erm
ine
the
surf
ace
area
of
the
hu
man
bod
y?
Rea
d th
e in
trod
ucti
on t
o L
esso
n 2-
7 at
the
top
of
page
103
in y
our
text
book
.
The
exp
ress
ion
&36
00%
is r
ead,
“the
squ
are
root
of
3600
.”H
ow w
ould
you
read
the
exp
ress
ion
&64%
?
the
squa
re r
oot
of 6
4
Read
ing
the
Less
on
Com
ple
te e
ach
sta
tem
ent
belo
w.
1.T
he s
ymbo
l &'
is c
alle
d a
and
is u
sed
to in
dica
te a
nonn
egat
ive
or p
rinc
ipal
squ
are
root
of
the
expr
essi
on u
nder
the
sym
bol.
2.A
of
an
irra
tion
al n
umbe
r is
a r
atio
nal n
umbe
r th
at is
clo
seto
,but
not
equ
al t
o,th
e va
lue
of t
he ir
rati
onal
num
ber.
3.T
he p
osit
ive
squa
re r
oot
of a
num
ber
is c
alle
d th
e sq
uare
root
of
the
num
ber.
4.A
num
ber
who
se p
osit
ive
squa
re r
oot
is a
rat
iona
l num
ber
is a
.
5.W
rite
eac
h of
the
fol
low
ing
as a
mat
hem
atic
al e
xpre
ssio
n th
at u
ses
the
&'
sym
bol.
a.th
e po
siti
ve s
quar
e ro
ot o
f 16
00)
1600
#b.
the
nega
tive
squ
are
root
of
729
!)
729
#c.
the
prin
cipa
l squ
are
root
of
3025
)30
25#
6.T
he ir
rati
onal
num
bers
and
rat
iona
l num
bers
tog
ethe
r fo
rm t
he s
et o
f nu
mbe
rs.
Hel
ping
You
Rem
embe
r
7.U
se a
dic
tion
ary
to lo
ok u
p se
vera
l wor
ds t
hat
begi
n w
ith
“ir-
”.W
hat
does
the
pre
fix
“ir-
”m
ean?
How
can
thi
s he
lp y
ou r
emem
ber
the
mea
ning
of
the
wor
d ir
rati
onal
?
Sam
ple
answ
er:T
he p
refix
“ir
-”m
eans
not
.So
an ir
ratio
nal n
umbe
r is
anu
mbe
r th
at is
not
a r
atio
nal n
umbe
r.
real
perf
ect
squa
re
prin
cipa
l
ratio
nal a
ppro
xim
atio
n
radi
cal s
ign
©G
lenc
oe/M
cGra
w-H
ill11
6G
lenc
oe A
lgeb
ra 1
Sca
le D
raw
ings
The
map
at
the
left
bel
ow s
how
s bu
ildin
g lo
ts f
or s
ale.
The
sca
le r
atio
is 1
:240
0.A
t th
e ri
ght
belo
w is
the
flo
or p
lan
for
a tw
o-be
droo
map
artm
ent.
The
leng
th o
f th
e liv
ing
room
is 6
m.O
n th
e pl
an t
heliv
ing
room
is 6
cm
long
.
An
swer
eac
h q
ues
tion
.
1.O
n th
e m
ap,h
ow m
any
feet
are
rep
rese
nted
by
an in
ch?
200
ft
2.O
n th
e m
ap,m
easu
re t
he f
ront
age
of L
ot 2
on
Sylv
an R
oad
in in
ches
.Wha
t is
the
act
ual
fron
tage
in f
eet?
200
ft
3.W
hat
is t
he s
cale
rat
io r
epre
sent
ed o
n th
e fl
oor
plan
?1
:100
4.O
n th
e fl
oor
plan
,mea
sure
the
wid
th o
f th
e liv
ing
room
in c
enti
met
ers.
Wha
t is
the
actu
al w
idth
in m
eter
s?4
m
5.A
bout
how
man
y sq
uare
met
ers
of c
arpe
ting
wou
ld b
e ne
eded
to
carp
et t
he li
ving
roo
m?
24 m
2
6.M
ake
a sc
ale
draw
ing
of y
our
clas
sroo
m u
sing
an
appr
opri
ate
scal
e.A
nsw
ers
will
var
y.
7.U
se y
our
scal
e dr
awin
g to
det
erm
ine
how
man
y sq
uare
met
ers
of t
ile w
ould
be
need
ed t
oin
stal
l a n
ew f
loor
in y
our
clas
sroo
m.
Ans
wer
s w
ill v
ary.
Clos
et
Clos
et
Clos
et
Clos
et
Kitc
hen
Bedr
oom
Bedr
oom
Bath
Dini
ng A
rea
Livi
ng R
oom
Lot 3
Lot 2
Lot 1
Sunshine Lake
Sylvan Road
En
rich
men
t
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
PE
RIO
D__
___
2-7
2-7
Answers (Lesson 2-7)