Chapter 3 Resource Masters

Transcription

1 Chapter Resource Masters

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3 Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks in both English and Spanish. Study Guide and Intervention Workbook Study Guide and Intervention Workbook (Spanish) Skills Practice Workbook Skills Practice Workbook (Spanish) Practice Workbook Practice Workbook (Spanish) Answers for Workbooks The answers for Chapter of these workbooks can be found in the back of this Chapter Resource Masters booklet. Spanish Assessment Masters Spanish versions of forms A and C of the Chapter Test are available in the Pre-Algebra Spanish Assessment Masters ( ). 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, teacher, and families without charge; and be used solely in conjunction with Glencoe Pre-Algebra. Any other reproduction, for use or sale, is prohibited without prior written permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 0 ISBN: Pre-Algebra Chapter Resource Masters

4 CONTENTS Vocabulary Builder...vii Lesson -1 Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics Enrichment Lesson - Study Guide and Intervention...11 Skills Practice...11 Practice...11 Reading to Learn Mathematics...11 Enrichment Lesson - Study Guide and Intervention Skills Practice Practice Reading to Learn Mathematics...10 Enrichment...11 Lesson - Study Guide and Intervention...1 Skills Practice...1 Practice...1 Reading to Learn Mathematics...1 Enrichment...16 Lesson - Study Guide and Intervention...17 Skills Practice...18 Practice...19 Reading to Learn Mathematics...10 Enrichment...11 Lesson -6 Study Guide and Intervention...1 Skills Practice...1 Practice...1 Reading to Learn Mathematics...1 Enrichment...16 Lesson -7 Study Guide and Intervention...17 Skills Practice...18 Practice...19 Reading to Learn Mathematics...10 Enrichment...11 Chapter Assessment Chapter Test, Form Chapter Test, Form A Chapter Test, Form B Chapter Test, Form C Chapter Test, Form D Chapter Test, Form Chapter Open-Ended Assessment...1 Chapter Vocabulary Test/Review...16 Chapter Quizzes 1 &...17 Chapter Quizzes &...18 Chapter Mid-Chapter Test...19 Chapter Cumulative Review Chapter Standardized Test Practice Unit 1 Test/Review (Ch 1 ) Standardized Test Practice Student Recording Sheet...A1 ANSWERS...A A0 iii

5 Teacher s Guide to Using the Chapter Resource Masters The Fast File Chapter Resource system allows you to conveniently file the resources you use most often. The Chapter Resource Masters includes the core materials needed for Chapter. These materials include worksheets, extensions, and assessment options. The answers for these pages appear at the back of this booklet. All of the materials found in this booklet are included for viewing and printing in the Pre-Algebra TeacherWorks CD-ROM. Vocabulary Builder Pages vii-viii include a student study tool that presents up to twenty of the key vocabulary terms from the chapter. Students are to record definitions and/or examples for each term. You may suggest that students highlight or star the terms with which they are not familiar. When to Use Give these pages to students before beginning Lesson -1. Encourage them to add these pages to their Pre-Algebra Study Notebook. Remind them to add definitions and examples as they complete each lesson. Study Guide and Intervention Each lesson in Pre-Algebra addresses one or two objectives. There is one Study Guide and Intervention master for each lesson. When to Use Use these masters as reteaching activities for students who need additional reinforcement. These pages can also be used in conjunction with the Student Edition as an instructional tool for students who have been absent. Skills Practice There is one master for each lesson. These provide computational practice at a basic level. When to Use These masters can be used with students who have weaker mathematics backgrounds or need additional reinforcement. Practice There is one master for each lesson. These problems more closely follow the structure of the Practice and Apply section of the Student Edition exercises. These exercises are of average difficulty. When to Use These provide additional practice options or may be used as homework for second day teaching of the lesson. Reading to Learn Mathematics One master is included for each lesson. The first section of each master asks questions about the opening paragraph of the lesson in the Student Edition. Additional questions ask students to interpret the context of and relationships among terms in the lesson. Finally, students are asked to summarize what they have learned using various representation techniques. When to Use This master can be used as a study tool when presenting the lesson or as an informal reading assessment after presenting the lesson. It is also a helpful tool for ELL (English Language Learner) students. Enrichment There is one extension master for each lesson. These activities may extend the concepts in the lesson, offer an historical or multicultural look at the concepts, or widen students perspectives on the mathematics they are learning. These are not written exclusively for honors students, but are accessible for use with all levels of students. When to Use These may be used as extra credit, short-term projects, or as activities for days when class periods are shortened. iv

6 Assessment Options The assessment masters in the Chapter Resource Masters offer a wide range of assessment tools for intermediate and final assessment. The following lists describe each assessment master and its intended use. Chapter Assessment Chapter Tests Form 1 contains multiple-choice questions and is intended for use with basic level students. Forms A and B contain multiple-choice questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Forms C and D are composed of freeresponse questions aimed at the average level student. These tests are similar in format to offer comparable testing situations. Grids with axes are provided for questions assessing graphing skills. Form is an advanced level test with free-response questions. Grids without axes are provided for questions assessing graphing skills. All of the above tests include a freeresponse Bonus question. The Open-Ended Assessment includes performance assessment tasks that are suitable for all students. A scoring rubric is included for evaluation guidelines. Sample answers are provided for assessment. A Vocabulary Test, suitable for all students, includes a list of the vocabulary words in the chapter and ten questions assessing students knowledge of those terms. This can also be used in conjunction with one of the chapter tests or as a review worksheet. Intermediate Assessment Four free-response quizzes are included to offer assessment at appropriate intervals in the chapter. A Mid-Chapter Test provides an option to assess the first half of the chapter. It is composed of both multiple-choice and free-response questions. Continuing Assessment The Cumulative Review provides students an opportunity to reinforce and retain skills as they proceed through their study of Pre-Algebra. It can also be used as a test. This master includes free-response questions. The Standardized Test Practice offers continuing review of pre-algebra concepts in various formats, which may appear on the standardized tests that they may encounter. This practice includes multiplechoice, grid-in, and open-ended questions. Bubble-in and grid-in answer sections are provided on the master. Answers Page A1 is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 1 1. This improves students familiarity with the answer formats they may encounter in test taking. The answers for the lesson-by-lesson masters are provided as reduced pages with answers appearing in red. Full-size answer keys are provided for the assessment masters in this booklet. v

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8 NAME DATE PERIOD Reading to Learn Mathematics Vocabulary Builder This is an alphabetical list of key vocabulary terms you will learn in Chapter. As you study this chapter, complete each term s definition or description. Remember to add the page number where you found the term. Add these pages to your Pre-Algebra Study Notebook to review vocabulary at the end of the chapter. Vocabulary Term Found on Page Definition/Description/Example Vocabulary Builder area coefficient koh-uh-fihsh-ehnt constant equivalent equations equivalent expressions formula vii

9 NAME DATE PERIOD Reading to Learn Mathematics Vocabulary Builder (continued) Vocabulary Term inverse operations Found on Page Definition/Description/Example like terms perimeter simplest form simplifying an expression term two-step equation viii

10 -1 Study Guide and Intervention The Distributive Property The expressions (1 ) and 1 are equivalent expressions because they have the same value, 1. The Distributive Property combines addition and multiplication. Symbols a(b c) ab ac (b c)a ba ca Model b c b a a a c The Distributive Property also combines subtraction and multiplication. Rewrite subtraction expressions as addition expressions. Example 1 Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. a. (6 ) b. (9 ) (6 ) 6 (9 ) [9 ( )] ( ) 18 ( 1) 0 The Distributive Property can also be used with algebraic expressions containing variables. Lesson -1 Example Exercises Use the Distributive Property to write each expression as an equivalent algebraic expression. a. 7(m ) b. (n 8) 7(m ) 7m 7 (n 8) [n ( 8)] 7m n ( )( 8) n Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression, if possible. 1. (8 ). (9 11). (19 6) 8 ; ; 0 19 ( 6); 6. 6( 1). (17 ) 6. ( )7 6 ( 6)(1); ( ) ; 9 7 7; 6 7. (d ) 8. (w ) 9. (c 7) d ; d 1 w ( ) ; w 0 c ( )(7); c 1 Glencoe/McGraw-Hill 107 Glencoe Pre-Algebra

11 -1 Skills Practice The Distributive Property Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. 1. 8(0 ). (0 9). (60 ). 7(0 ) 00 ; 100 ; ; ; 66. (00 ) 6. (16 ) 7. 8( 1) 8. 9( 19) ; ; 8 8; ; 9. (7 11) (1 ) 11. (1 9)( ) 1. 7(1 10) 1 ; ; ; ; 6 1. (1 6) 1. (1 ) 1. 1(100 6) 16. 1( ) 1; ; ; ; 60 Use the Distributive Property to write each expression as an equivalent algebraic expression. 17. (d ) 18. 1(u ) 19. 6(f ) 0. (g ) d 8 u 6f 0 g 6 1. (x 7). 8( b ). (9 h). (c 1)( ) x 1 8b h c. 1( y) 6. 7(a 1) 7. 11(k 0) 8. 9(r 1) y 7a 7 11k 0 9r 9 9. (1 b) 0. 8(x 1) 1. 6(p 1). (h 16) b 8x 96 6p 90 h 6. (w 10). 10(c 9). (11 q) 6. (1 f ) w 0 10c 90 q 8 f 7. 1(n ) 8. 16( g 1) 9. 8(9 b) 0. (z ) 1n 16g b z (r 0). 7( j). 1(m 1). (v 8) 6r j m 1 v 16. (q 16) 6. 10(c 7) 7. ( x 1) 8. (9 h)( ) q 80 10c 70 x 18 h Glencoe/McGraw-Hill 108 Glencoe Pre-Algebra

12 -1 Practice The Distributive Property Use the Distributive Property to write each expression as an equivalent expression. Then evaluate the expression. 1. 6(80 1). 7(70 ). (00 6). (100 10)9 80 6; ; ; ; 990. (00 90) 6. 8(700 ) 7. (0 9) 8. (100 )( 7) 000 0; ; ; 700 1; (7 9) 10. 1(1 11) 11. (80 ) 1. 1(0 18) 7 9; ; ; 00 1,90 8; 1,9 Lesson -1 Use the Distributive Property to write each expression as an equivalent algebraic expression. 1. 7( y 11) 1. 6(t 1) 1. 8(u ) 16. (r 9)( ) 7y 77 6t 6 8u 16 r ( h ) 18. ( f ) 19. (b 1) 0. 1(7 v) h f 6 b 7 v 1. (d ). (n 10). 0(z 1). 1( g 1) d 10 n 0 0z 0 1g 1. 17( p ) 6. (k 1)( 8) 7. ( s)( 9) 8. 8(a ) 17p 68 8k s 8a (19 a) 0. (d ) 1. 18( q ). 16(c ) 80 0a d 1 18q 90 16c (v 1). 1(r 7). (x 11) 6. 17( n 1) 19v 19 r 7 x 8 17n PLANTS A planter weighs pounds and holds pounds of soil. Write two equivalent expressions for the total weight of nine planters. Then find the weight. 9( ), 9() 9(); pounds 8. UNIFORMS A uniform costs $ for the sweater and $9 for the slacks. Write two equivalent expressions for the total cost of six uniforms. Then find the cost. 6( 9), 6() 6(9); $6 Glencoe/McGraw-Hill 109 Glencoe Pre-Algebra

13 -1 Reading to Learn Mathematics The Distributive Property Pre-Activity How are rectangles related to the Distributive Property? Do the activity at the top of page 98 in your textbook. Write your answers below. a. Draw a -by- and a -by- rectangle. Find the total area in two ways or 18; ( ) (9) or 18 b. Draw a -by- and a -by-1 rectangle. Find the total area in two ways or 0; ( 1) () or 0 c. Draw any two rectangles that have the same width. Find the total area in two ways. Sample answer: ( ) 1; 1 Reading the Lesson d. What did you notice about the total area in each case? The areas are equal. Write a definition and give an example of the new vocabulary term. 1. Vocabulary Definition Example equivalent See students work. expressions. In rewriting (x ), which term is distributed to the other terms in the expression? Helping You Remember. Distribute is a word that is used frequently in the English language. a. Find the definition of distribute in a dictionary. Write the definition. to give out or deliver especially to members of a group b. Explain how the English definition can help you remember how the word distributive relates to mathematics. The number outside the parentheses is distributed to each number inside. Glencoe/McGraw-Hill 110 Glencoe Pre-Algebra

14 -1 Enrichment What Day Was It? To find the day of the week on which a date occurred, follow these steps. 1) Use the formula s d m (m y y y 100 y 00 where s sum, d day of the month, using whole numbers from 1 to 1, m month, where March, April, and so on, up to December 1; then January 1 and February 1, and y year except for dates in January or February when the previous year is used. Evaluate expressions inside the special brackets [ ] by dividing, then discarding the remainder and using only the whole number part of the quotient. Lesson -1 After finding the value of s, divide s by 7 and note the remainder. The remainder 0 represents Saturday, 1 represents Sunday, represents Monday, and so on to 6 represents Friday. Example On December 7, 191, Pearl Harbor was bombed. What day of the week was that? Let d 7, m 1, and y ) s d m (m y y y 100 y 0 0 1) s 7 (1) ( s s s Now divide s by R1 Since the remainder is 1, December 7, 191, was a Sunday. Use the formula to solve each problem. 1. Verify today s date. See students work.. What will be the day of the week for April 1, 01? Friday. On what day of the week was the signing of the Declaration of Independence, July, 1776? Thursday. On what day of the week were you born? See students work. Glencoe/McGraw-Hill 111 Glencoe Pre-Algebra

15 - Study Guide and Intervention Simplifying Algebraic Expressions term: a number, a variable, or a product of numbers and variables coefficient: the numerical part of a term that also contains a variable constant: term without a variable like terms: terms that contain the same variables Example 1 Identify the terms, like terms, coefficients, and constants in the expression m m n 7. m m n 7 m ( m) n ( 7) Definition of subtraction m ( m) 1n ( 7) Identity Property terms m, m, 1n, 7; like terms: m, m; coefficients:,, 1; constants: 7 When an algebraic expression has no like terms and no parentheses, we say that it is in simplest form. Example Simplify 6x x 7. 6x x 7 6x ( ) ( x) 7 6x ( x) ( ) 7 [6 ( )]x ( ) 7 x Definition of subtraction Commutative Property Distributive Property Simplify. Exercises Identify the terms, like terms, coefficients, and constants in each expression. 1. 6a a. m m m. c d c, 6a, a; 6a, a; m, m, m, ; c, d, c, ; 6, ; m, m, m; 1,,; c, c;,, 1;. h g g h. w u 6 6. r s s r h, g,g, h;h, h and w, u, 6; none; r, s, s, r ; g, g;,,, 1; none, ; 6 r, r and s,s;,,, ; none Simplify each expression. 7. 9m m 8. x x 9. 8y y y 10. m m 1m x 1y m 11. 1a 7a a 1. y 1 y 1. 8d d s s a 7y 6 7d 1 7 s Glencoe/McGraw-Hill 11 Glencoe Pre-Algebra

16 - Skills Practice Simplifying Algebraic Expressions Simplify each expression. 1. 7a a. k k. m m 8 8a 0 m 8. 10b b 1. 9j 8j 7j 6. 6y y 6y y 9b 1 10j 1y 7. q q q x 1 x 9. 1a 18 9a q 1x 6 a c 7 c d 11. h h h 1 h 1. (v ) 7v 1c d 7 1 9v 6 1. (r 9) 1. 1 (u 1) 1. 7(w ) w 7 r 0 u w (y ) (c 1) (n ) n 7y 18c 9n 8 Lesson m 9 m 0. 7 g 1 6g 1. x 9x 8x 9m 9 g (r ) r 0 7r. a a a. 1 8(v ) 7v 6 6a 9 v. x 9 x 6 9x 6. p 1 p 1 p x 7 p 7. 11f 6 f 1f 9 8. (d ) d 1 d f s s s k 1 k (7 k) s 6k g g (g ). 7h 1 h 8h 0 h. 1 7(d 1) 1 d 6d Glencoe/McGraw-Hill 11 Glencoe Pre-Algebra

17 - Practice Simplifying Algebraic Expressions Simplify each expression. 1. 6y y. 8u u u. 1 g 8 g 7y 7u g. 1w w 1. r r r r r 6. f f f 1 18w r f 7. 8q 6 q 8. h h 6h 9. a (a 1) q a 10. b (b ) t (t ) 1. 8 ( g ) b t g 1. 1m 9 m (y ) 9 y 1. 8a b a b 10m 7 y a b x 8x x 17. 1y 1(x y) 1x 0 y g h 0( g 1) 19. (c d) d c d g h 10d 0. (8 b)( ) 6b 1 10b 1. p q (p q) p q b 1 q. n 8n 1n 7n n. 1z (z 9) 0 z 0 7z 6. 9 w v w v. 6(y 1) y 7 y v 6w y x 10 y (x y) y x 10 Write an expression in simplest form that represents the total amount in each situation. 7. LUNCH You bought pieces of chicken that cost x dollars each, a salad for $, and a drink for $1. x 8. SOCCER Sal has scored g goals this season. Ben has scored four times as many goals as Sal. Chun has scored three fewer goals than Ben. 9g Glencoe/McGraw-Hill 11 Glencoe Pre-Algebra

18 - Reading to Learn Mathematics Simplifying Algebraic Expressions Pre-Activity How can you use algebra tiles to simplify an algebraic expression? Do the activity at the top of page 10 in your textbook. Write your answers below. a. x x 7x b. x x x c. x x 8 d. x x x 7x Reading the Lesson 1 6. See students work. Write a definition and give an example of each new vocabulary word or phrase. Vocabulary Definition Example 1. term. coefficient Lesson -. like terms. constant. simplest form 6. simplifying an expression 7. Is (r 1) in simplest form? Explain. No; the expression contains parentheses. Helping You Remember 8. Constant is a word used in everyday English as well as in mathematics. a. Find the definition of constant in a dictionary. Write the definition. something invariable or unchanging b. Explain how the English definition can help you remember how constant is used in mathematics. In mathematics, because a constant has no variable, its value is not subject to change. Glencoe/McGraw-Hill 11 Glencoe Pre-Algebra

19 - Enrichment Algebraic Proof Recall that properties are statements that are true for any numbers. These properties are used to prove theorems. Use the properties you have learned to complete each proof. Abbreviations for some properties you may need to use are listed below. Commutative Property Addition (CPA) Commutative Property Multiplication (CPM) Associative Property Addition (APA) Associative Property Multiplication (APM) Additive Identity Property (AIP) Multiplicative Identity Property (MIP) Inverse Property of Addition (IPA) Inverse Property of Multiplication (IPM) Multiplicative Property of Zero (MPZ) Distributive Property (DP) Write the reason for each statement. 1. Prove: (y x) x y Statement ( y x) 1( y x) 1y ( 1x) y ( x) y x x ( y) x y. Prove: x x x Statement x x x ( ) ( x) x ( x) ( ) x ( 1x) ( ) [ ( 1)]x ( ) x ( ) x. Prove: x 6 x 6 Statement x 6 x x x 6 ( )x 6 0x Reason MIP a. DP b. MIP c. Definition of Subtraction d. CPA e. Definition of Subtraction Reason a. Definition of Subtraction b. CPA c. MIP d. DP e. Simplify f. Definition of Subtraction Reason a. CPA b. DP c. IPA d. MPZ e. AIP Glencoe/McGraw-Hill 116 Glencoe Pre-Algebra

20 - Step 1 Step Step Study Guide and Intervention Solving Equations by Adding or Subtracting Identify the variable. To isolate the variable, add the same number to or subtract the same number from each side of the equation. Check the solution. Example 1 Solve x 6. x 6 x 6 x Check: x The solution is. Subtract from each side. Example x 9 1 x x Check: x The solution is. Solve x 9 1. Add 9 to each side. Exercises Solve each equation. Graph the solution of each equation on the number line. 1. x. 11 w k 1. m. a 7 6. b Lesson - 7. h y 9 9. r b k g Glencoe/McGraw-Hill 117 Glencoe Pre-Algebra

21 - Skills Practice Solving Equations by Adding or Subtracting Solve each equation. Check your solution. 1. r 1. h 8 6. t 11. p w x a m q 10. b 11. n r c v 7 1. z s y u g k w 1. z 8 8. d h r y 1 7. f d j m q. g a c. h p v x y k d 1 1. g b 1 0. f q w 1 7. r t j k 1 1. n 1 0. y Glencoe/McGraw-Hill 118 Glencoe Pre-Algebra

22 - Practice Solving Equations by Adding or Subtracting Solve each equation. Check your solution. 1. z 6. x 8. c 1. v q w z b a r p ( 9) 1. n s 1 1. t ( 1) 1 1. r m ( ) d y u k f. g. h 7. j x 1 6. c 7 7. v b h y ( 1) 0 1. g 8 9. n j ( 1) 1. p 1. k ( 1) 8 6. m Lesson - 7. SAVINGS ACCOUNT Jhumpa has $ in her savings account. This is $1 more than David. Write and solve an equation to find the amount David has in his savings account. d 1 ; $ 8. WEATHER The temperature fell 16 between noon and :00 P.M. At :00, the temperature was F. Write an equation to determine the temperature at noon. t 16 ; 1 F Glencoe/McGraw-Hill 119 Glencoe Pre-Algebra

23 - Reading to Learn Mathematics Solving Equations by Adding or Subtracting Pre-Activity How is solving an equation similar to keeping a scale in balance? Do the activity at the top of page 110 in your textbook. Write your answers below. Reading the Lesson a. Without looking in the bag, how can you determine the number of blocks in the bag? Remove blocks from each side. There are blocks left on the right, so there must be blocks in the bag. b. Explain why your method works. Removing the same number of blocks from each side keeps the scale in balance. 1. See students work. Write a definition and give an example of each new vocabulary phrase. Vocabulary Definition Example 1. inverse operations. equivalent equations. Are x 8 and x 6 equivalent equations? Explain. No; they do not have the same solution. The solution of x 8 is 10, and the solution of x 6 is 6. Helping You Remember. How is adding blocks to each side of a balanced scale like the Addition Property of Equality? Adding blocks to each side keeps the scale in balance. Adding the same number on each side of an equation keeps the two sides of the equation equal. Glencoe/McGraw-Hill 10 Glencoe Pre-Algebra

24 - Enrichment Creating a Line Design Connect each pair of equivalent expressions with a straight line segment. Describe the finished design. a (a b) a 11 a b (a ) 10 (a ) a a (a 7b) 1a b 9a b (a 6) a 1 (a 6) a a a b 7a a (b a) a 1b 6a 1 a a b a b 9 (a ) a 6b 8a 8 6a 11b (a 8) a 8a b a b 11a b 10a 8 1 (a ) a b a a 1b a (a b) a 6b (a b) a a b a 6 10(a 9) 7a (a b) 6a b a 6(a b) b 8(a ) 1 Lesson - Glencoe/McGraw-Hill 11 Glencoe Pre-Algebra

25 - Study Guide and Intervention Solving Equations by Multiplying or Dividing Step 1 Step Step Identify the variable. To isolate the variable, multiply or divide each side of the equation by the same nonzero number to get the variable by itself. Check the solution. Example 1 7x 7x 7 7 x 6 The solution is 6. Exercises Divide each side by 7. Check your solution. Example Solve 7x. Solve y. y y ( ) Multiply each side by. y Check your solution. The solution is. Solve each equation. Graph the solution of each equation on the number line. 1. a 1. t. 1 n r 8. 0 h m a 7. 11b d r p w Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

26 - Skills Practice Solving Equations by Multiplying or Dividing Solve each equation. Check your solution. m 1. x. 1. f 16. u s. 6a y 8. 7z n r h c v m w g r r 17. 1f d k 00. p 18. 7j 6 y x g 0 7. p y q c b 90. k r 0. 1t 19 n j u c q z Lesson - Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

27 - Practice Solving Equations by Multiplying or Dividing Solve each equation. Check your solution. 1. 8y 6. w 1. u 1. r n v. 9d f r p 9. 1b 10. 1h z 1. 1x g t g d 8 m k u 1. 6w 0. r q n. 16y j p Write and solve an equation for each sentence. 9. The product of a number and 6 is. 6n ; 9 0. The quotient of a number and 6 is 1. x 1; CLASS REPORTS Each student needs 1 minutes to give a report. A class period is 8 minutes long. Write and solve an equation to determine the number of students who could give a report in one class period. 1s 8; students. COOKING One pound of ground beef makes four hamburger patties. Write and solve an equation to determine how many pounds of beef are needed to make 6 hamburgers. x 6; 9 Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

28 - Reading to Learn Mathematics Solving Equations by Multiplying or Dividing Pre-Activity How are equations used to find the U.S. value of foreign currency? Do the activity at the top of page 11 in your textbook. Write your answers below. Reading the Lesson a. Suppose lunch in Mexico costs 7 pesos. Write an equation to find the cost in U.S. dollars. 9d 7 b. How can you find the cost in U.S. dollars? Divide by How do you undo multiplication in an expression? use division. What does the expression x mean? x divided by x. Explain how to find the value of x in the equation. How do you check your answer? 1 Multiply both sides by. x, x 1 Substitute 1 for the x in 1 1 the original equation to check whether this equation is correct. 1 Helping You Remember. You have learned about four properties of equalities: Addition Property of Equality, Subtraction Property of Equality, Multiplication Property of Equality, and Division Property of Equality. In each circle, write three equations that can be solved by using the given property. Include at least one negative integer in each circle. Sample answers given. These equations can be solved by using the given property. Addition Property Subtraction Property Multiplication Property Division Property Lesson - Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

29 - Enrichment Puzzling Equations Solve each equation. Notice that the first equation is completed. m v 78 c d w g p(8) x 66 k z q y 1608 a k 1. m ( 10) I. A. E 10. J. A M R 8 8. S Y R O 1 1. N 8 1. R 8 1. S H 80 Use the letter beside each of your answers to decode the answer to this question. What woman led a 1-mile march from Pennsylvania to Long Island in 190 to bring the practice of child labor to the attention of President Theodore Roosevelt? Glencoe/McGraw-Hill 16 Glencoe Pre-Algebra

30 - Study Guide and Intervention Solving Two-Step Equations A two-step equation contains two operations. To solve two-step equations, use inverse operations to undo each operation in reverse order. First, undo addition/subtraction. Then, undo multiplication/division. Example c 1 7 Solve c 1 7. c Add 1 to each side. c 0 c (0) Multiply each side by. c 0 Check: c The solution is 0. For some problems, it may be necessary to combine like terms before solving. Exercises Solve each equation. Check your solution. 1. t 7. x 9. 6u m w d k 8. a c m h x 1. m p g 6 n m k a 0. c v x 16 8x 16. 1a 1a 8. 7c 8 c y y r r 1 1 Lesson - Glencoe/McGraw-Hill 17 Glencoe Pre-Algebra

31 - Skills Practice Solving Two-Step Equations Solve each equation. Check your solution. 1. x a w 1 1. r q 6. j u p d c n b w 1. h k y g 18. 1s r 19. z z h w. a a k 8k f 6. 6 m d x x 0 9. t a q 16. m b 6 6b Glencoe/McGraw-Hill 18 Glencoe Pre-Algebra

32 - Practice Solving Two-Step Equations Solve each equation. Check your solution. 1. 6p 10. r. d 9 18 v. 1q h k w s 1 7 x z r q n w r y 11 y d 9 1 u h h p p x j b 9 b b a w w y y RENTAL AGREEMENTS A furniture rental store charges a down-payment of $100 and $7 per month for a table. Hilde paid $0 to rent the table. Solve 7n to find the number of months Hilde rented the table. 6 months 9. BUSINESS At work, Jack must stuff 1000 envelopes with advertisements. He can stuff 1 envelopes in one minute, and he has 11 envelopes already finished. Solve n 11 to find how many minutes it will take Jack to complete the task. 7 min Lesson - Glencoe/McGraw-Hill 19 Glencoe Pre-Algebra

33 - Reading to Learn Mathematics Solving Two-Step Equations Pre-Activity How can algebra tiles show the properties of equality? Do the activity at the top of page 10 in your textbook. Write your answers below. Reading the Lesson a. What property is shown by removing a tile from each side? Subtraction Property of Equality b. What property is shown by separating the tile into two groups? Division Property of Equality c. What is the solution of x 1 9? Write a definition and give an example of the new vocabulary phrase. 1. Vocabulary Definition Example two-step equation See students work.. To solve two-step equations, use inverse operations to undo each operation in reverse order. Helping You Remember Suppose you start with a number x, multiply it by, add three, and the result is 17. The top row of boxes at the right represents the equation x 17. To solve the equation, you undo the operations in reverse order. This is shown in the bottom row of boxes. Start x? 7 1 So, x Complete the bottom row of boxes in each figure. Then find the value of x... Start x? 10 Start x?. 6. Start x? 7 Start x? Glencoe/McGraw-Hill 10 Glencoe Pre-Algebra

34 - Enrichment Al-Khowarizmi: The Father of Algebra The title Father of Algebra should be awarded to the Arabian mathematician Al-Khowarizmi. In the ninth century, he wrote a work entitled Hisab al-jabr-w al muqubalah, meaning the science of restoring and canceling. In this work, he gave a clear and complete explanation of how to solve an equation by performing the same operation on both sides of the equation. In the thirteenth century, Al-Khowarizmi s work was translated into Latin, the language of educated people in Europe, which launched algebra into the Western world. It is from the title of his work that we get the word algebra. Here is an example of how Al-Khowarizmi solved an equation like x 10. To solve this equation, must be added, or restored, to each side. Thus, x 10, or x 1. Another example of restoring can be used to solve x 10. To solve this equation, must be restored to each side. This is the same as subtracting from each side. Thus, x 10, or x. Here is an example of solving an equation by canceling (or dividing). To solve x 9, each side must be canceled by a factor of. Thus, x 9, or x. Solve each equation and label it with an R for restoring or with a C for canceling. 1. x y. x 1 x 0; R y ; R x ; C. y 1. y 6 6. x 18 y ; C y 11; R x 6; C 7. x 8. y y 1 x 1; R y ; C y 7; C 10. Make up your own equations to solve. Three should use restoring and three canceling. See students work. Lesson - Glencoe/McGraw-Hill 11 Glencoe Pre-Algebra

35 -6 Study Guide and Intervention Writing Two-Step Equations You can use two-step equations to represent situations in which you start with a given amount and then increase it at a certain rate. Example PRINTING: A laser printer prints 9 pages per minute. Liza refilled the paper tray after it had printed 9 pages. In how many more minutes will there be a total of pages printed? EXPLORE You know the number of pages printed and the total number of pages to be printed. You need to find the number of minutes required to print the remaining pages. PLAN Let m = the number of minutes. Write and solve an equation. The remaining pages to print is 9m. remaining pages pages printed total pages 9m 9 SOLVE 9m 9 9m m 1 9m 1 9 m 17 EXAMINE The remaining 1 pages will print in 17 minutes. Since 1 = 9, the answer is correct. Exercises Solve each problem by writing and solving an equation. 1. METEOROLOGY During one day in 1918, the temperature in Granville, North Dakota, began at and rose for 1 hours. The high temperature was about 1. About how many degrees per hour did the temperature rise? 1d 1; about 7 degrees. SAVINGS John has $8 in his savings account. He has decided to deposit $6 per month until he has a total of $1800. In how many months will this occur? 6m ; 1 months. SKYDIVING A skydiver jumps from an airplane at an altitude of 1,000 feet. After seconds, she reaches 608 feet and opens her parachute. What was her average velocity during her descent? 1,000 f 608; 176 feet per second. FLOODING The water level of a creek has risen inches above its flood stage. If it continues to rise steadily at inches per hour, how long will it take for the creek to be 1 inches above its flood stage? h 1; hours Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

36 -6 Skills Practice Writing Two-Step Equations Translate each sentence into an equation. Then find each number. 1. Eleven less than times a number is. n 11 ; 7. The quotient of a number and 9 increased by 10 is 11. n 10 11; 9 9. Five less than the product of and a number is. n ; 1 Lesson -6. Fifteen more than twice a number is. 1 n ; 19. The difference between times a number and is 16. n 16; 6. Nine more than 8 times a number is n 7; 7. The difference between 1 and ten times a number is n 8; 8. Seven more than three times a number is. n 7 ; 1 9. Eleven less than five times a number is 19. n 11 19; Thirteen more than four times a number is 91. n 1 91; Seven less than twice a number is. n 7 ; Solve each problem by writing and solving an equation. 1. SHOPPING The total cost of a suit and ties is $9. The suit cost $00. Each tie cost the same amount. Find the cost of one tie. x 00 9; $ 1. AGES Mary s sister is 7 years older than Mary. Their combined ages add up to. How old is Mary? x 7 ; 1 Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

37 -6 Practice Writing Two-Step Equations Translate each sentence into an equation. Then find each number. 1. Eight less than 7 times a number is 9. 7n 8 9;. Twenty more than twice a number is. 0 n ; 16. The difference between three times a number and 11 is 10. n 11 10; 7. One more than the difference between 18 and seven times a number is n 9;. Eight times a number plus 6 less than twice the number is. 8n n 6 ; 6. 6 more than the product of a number and 17 is. 17n 6 ; 7. Twelve less than the quotient of a number and 8 is 1. n 1 1; 88 8 Solve each problem by writing and solving an equation. 8. ANIMAL TRAINING Last summer, Gary trained more dogs than Zina. Together they trained 16 dogs. How many dogs did Gary train? g (g ) 16; 79 dogs 9. SALES Julius sold five times as many computers as Sam sold last year. In total, they sold 78 computers. How many computers did Julius sell? s s 78; 6 computers 10. TRACK In one season, Ana ran 18 races. This was four fewer races than twice the number of races Kelly ran. How many races did Kelly run? 18 r ; 11 races 11. BASEBALL André hit four more home runs than twice the number of home runs Larry hit. Together they hit 10 home runs. How many home runs did André hit? h h 10; 8 home runs Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

38 -6 Reading to Learn Mathematics Writing Two-Step Equations Pre-Activity How are equations used to solve real-world problems? Do the activity at the top of page 16 in your textbook. Write your answers below. a. Let n represent the number of minutes. Write an expression that represents the cost when your call lasts n minutes n 99 b. Suppose your monthly cost was 99. Write and solve an equation to find the number of minutes you used the calling card. n c. Why is your equation considered to be a two-step equation? It has two operations, multiplication and addition. Lesson -6 Reading the Lesson Refer to Example on page 17. Read the Explore and Plan steps. Then complete the following. 1. Suppose you have already saved $7 and plan to save $ a week. a. Complete the table below. Week Amount Saved ($). Suppose you have already saved $ and plan to save $10 each week. a. Complete the table below. Week Amount Saved ($) 0 1 (0) 7 7 (1) 7 80 () 7 8 () (0) 1 10(1) 10() 10() n (n) 7 n 7 n 10 (n) 10n b. Write an equation that represents how many weeks it will take you to save $100. n b. Write an equation that represents how many weeks it will take you to save $17. 10n 17 Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

39 -6 Enrichment Systems of Equations A system of equations is a set of equations with the same variables. The equations shown below are an example of one kind of system of equations. y x x = 16 The solution of this system must be a pair of numbers, x and y, that make both equations true. To solve this type of system, first solve the equation that contains only one variable. Then substitute that answer into the second equation and solve for the remaining variable. Example a. y x x 16 Solve each system of equations. b. d 1 19 c d Solve x 16 first. x 16 x 16 x 1 x 1 x 7 Substitute 7 for x in the other equation. y x y 7 or 9 The solution is x 7 and y 9. Solve d 1 19 first. d 1 19 d d 0 d 0 d Substitute for d in the other equation. c d c or The solution is c and d. Solve each system of equations t 10. a b s t s 11a 8 d s t 1, s 10 a, b s, d 00. m 1.. 6x y 6. c p 7m n 17. x 0 p m., n 0 x 7, y p.7, c 8.7 Glencoe/McGraw-Hill 16 Glencoe Pre-Algebra

40 -7 Study Guide and Intervention Using Formulas The formula d = rt relates distance d, rate r, and time t, traveled. Example 1 d rt Find the distance traveled if you drive at 0 miles per hour for hours. d 0 Replace r with 0 and t with. d 10 The distance traveled is 10 miles. The formula P ( w) relates perimeter P, length, and width w for a rectangle. The formula A w relates area A, length, and width w for a rectangle. Example P ( w) P (7 ) P (9) P 18 The perimeter is 18 feet. Find the perimeter and area of a rectangle with length 7 feet and width feet. A w A 7 A 1 The area is 1 square feet. Lesson -7 Exercises 1. TRAIN TRAVEL How far does a train travel in 1 hours at 8 miles per hour? 76 miles. TRAVEL How long does it take a car traveling 0 miles per hour to go 00 miles? hours. BICYCLING What is the rate, in miles per hour, of a bicyclist who travels 6 miles in hours? 1 miles per hour. RACING How long will it take a driver to finish a 980-mile rally race at 70 miles per hour? 1 hours Find the perimeter and area of each rectangle.. P 0 in.; in. A 1 in. 7 in. 7. ft P 0 ft; 1 ft A 6 ft 6. 6 m P 0 m; 9 m A m 8. P 16 cm; cm A 1 cm cm 9. P 0 yd; 10 yd A 10 yd 1 yd 10. P 76 cm; 18 cm A 60 cm 0 cm Glencoe/McGraw-Hill 17 Glencoe Pre-Algebra

41 -7 Skills Practice Using Formulas 1. AIR TRAVEL A plane is traveling 9 miles per minute. How much time is needed to travel 16 miles? min. JOGGING What is the rate, in feet per second, of a girl who jogs 1 feet in seconds? 7 ft/sec Find the perimeter and area of each rectangle... mm 6 mm 16 mm; 1 mm ft ft 18 ft; 0 ft. 6. m 8 mi 7 m 16 mi 0 m; 7 m 0 mi; 10,8 mi 7. a rectangle that is 1 inches long and 1 inches wide perimeter: 68 in; area: 7 in 8. a square that is centimeters on each side perimeter: 100 cm; area: 6 cm Find the missing dimension of each rectangle. 0 in ft Area 10 m 10 m 6 mi Perimeter 08 in. 8 in 1 m Perimeter 0 mi Area 16 ft 76 mi 7 ft 1. The perimeter of a rectangle is 100 centimeters. Its width is 9 centimeters. Find its length. 1 cm 1. The area of a rectangle is 19 square kilometers. Its width is 11 kilometers. Find its length. 9 km Glencoe/McGraw-Hill 18 Glencoe Pre-Algebra

42 -7 Practice Using Formulas 1. AIR TRAVEL What is the rate, in miles per hour, of a plane that travels 1680 miles in hours? 60 mph. TRAVEL A train is traveling at miles per hour. How long will it take to go 78 miles? 7 h. SWIMMING What is the rate, in feet per second, of a swimmer who crosses a 16-foot-long pool in 1 seconds? ft/sec. BALLOONING A balloon is caught in a wind traveling at feet per second. If the wind is constant, how long will it take the balloon to travel 1000 feet? 0 seconds Find the perimeter and area of each rectangle. Lesson cm 1 cm yd yd 8 cm; area: 10 cm 88 yd; area: 8 yd mm 61 mi 8 mm mi 0 mi; area: 9 mi 19 m; area: 0 m 9. a rectangle that is 9 meters long and 18 meters wide 0 m; area: 166 m 10. a rectangle that is 0 inches long and 9 inches wide 118 in; area: 870 in Find the missing dimension in each rectangle mi mi 1. 1 cm cm Perimeter 6 mi Area 76 cm 1. ft 1. Area 11 ft ft 1 m 1. GEOMETRY The area of a rectangle is 160 square inches. Its length is 6 inches. Find the width. in. Glencoe/McGraw-Hill 19 Glencoe Pre-Algebra 1 m Perimeter 68 m

43 -7 Reading to Learn Mathematics Using Formulas Pre-Activity Why are formulas important in math and science? Do the activity at the top of page 11 in your textbook. Write your answers below. a. Write an expression for the distance traveled by a duck in t hours. 6t b. What disadvantage is there in showing the data in a table? You cannot show all of the possible relationships in a table. c. Describe an easier way to summarize the relationship between the speed, time, and distance. Write an equation that relates Reading the Lesson 1. See students work. speed, time, and distance. Vocabulary Definition Example 1. formula. perimeter. area Write a definition and give an example of each new vocabulary word. Helping You Remember. The word perimeter is composed of the prefix peri- and the suffix -meter. a. Find the definitions of peri- and -meter in a dictionary. Write their definitions. Enclosing or surrounding; means for measuring b. Find two other words in a dictionary that begin with the prefix peri-. Write their definitions. Sample answers: peripheral: of, relating to, or being the outer part of the field of vision; pericardium: the membrane that encloses the heart of vertebrates c. Explain how your definitions can help you remember how perimeter is used in mathematics. The definitions relate to the outer edge of something, just as perimeter is a measure of the distance around a figure. Glencoe/McGraw-Hill 10 Glencoe Pre-Algebra

44 -7 Enrichment Mathematics and Social Studies Since the discovery that Earth is round, people have been fascinated with the prospect of making ever faster trips around the world. Ferdinand Magellan s ship Victoria set sail on September 0, 119, and completed the first voyage around the world about three years later on September 6, 1. With more consistent modes of transportation came new records in circling Earth. Solve each problem by finding the average speed it took to circle Earth. Use,900 miles to approximate the distance around Earth. 1. DIRIGIBLE In 199, Graf Zeppelin made the first round-the-world dirigible flight in 1 days, 8 hours on the LZ17.What was the Zeppelin s average speed in miles per hour? about 8.6 mph Lesson -7. AIRPLANE Air Force bomber Lucky Lady II made the first nonstop flight around the world in 199. The flight took 9 hours. What was the average speed of the Lucky Lady II on that trip? about 6.9 mph. SPACESHIP In 1961, Yuri Gagarin and Bherman Titov of Russia each circled Earth in a little over an hour and minutes. At what speed must one travel to circle Earth at its surface in an hour and a half? 1,8.6 mph AIRCRAFT In Exercises 6, assume that each aircraft travels at a constant rate. Use,900 miles as the distance traveled. How long would it take each aircraft to circle Earth?. a commercial plane of the 190s traveling at 168 mph about 18. hours. a Boeing 707 cruising at 60 mph about 8.9 hours 6. a Concorde flying at 10 mph about 17. hours 7. BALLOONING Jules Verne wrote about circling Earth in a hot air balloon in his novel (187). Suppose it were possible for a hot air balloon to circle Earth in 80 days. What would be the average speed in miles per hour? about 1.0 mph Glencoe/McGraw-Hill 11 Glencoe Pre-Algebra

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46 NAME DATE PERIOD Chapter Test, Form 1 SCORE Write the letter for the correct answer in the blank at the right of each question. 1. Which property of equality is used to solve k 7 1? A. addition B. distributive C. multiplication D. division 1.. Rewrite (7 ) using the Distributive Property. A. 7 B. 7 C. 7 D. (7 ) ( ).. Which expression is equivalent to (x )? A. x 1 B. x 1 C. x 1 D. x ( 1).. Translate the sentence the product of m and is 0 into an equation. A. m 0 B. m 0 C. m 0 D. m 0.. Simplify 1n n. A. 1n B. 17n C. 17n D. 17n. 6. Find the area of a rectangle with length 9 feet and width feet. A. 7 ft B. ft C. 1 ft D. ft 6. Assessment 7. Choose the equation whose solution is graphed below. A. x 19 B. x 19 C. x 11 D. x Solve y A. 1 B. C. D Find the solution of h 1 7. A. 6 B. 0 C. 0 D What is the solution of d 9? A. B. 1 C. 1 D A rectangle has a length of 1 centimeters and a width of 7 centimeters. What is its perimeter? A. 8 cm B. 8 cm C. 19 cm D. 1 cm 11. Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

47 NAME DATE PERIOD Chapter Test, Form 1 (continued) 1. Find the solution of 6w 7. A. 1 B. 16 C. D Solve 8 8m. A. 8 B. 6 C. 0 D k 1. What is the solution of 1? A. B. C. 96 D Suppose a race car travels at an average rate of 16 miles per hour for hours. What distance did the race car travel? A. 9 mi B. 168 mi C. 0 mi D. mi What is the speed in miles per hour of a cyclist who travels 6 miles in 7 hours? A. 7 mph B. 9 mph C. 6 mph D. 8 mph Simplify m 9m. A. m 1 B. m 1 C. m 1 D. m What is the solution of 6h h? A. 1 B. 1 C. D The wingspan of a ghost bat is 1 more than twice that of a vampire bat. Suppose a ghost bat has a wingspan of 8 inches. Which equation can be used to find the wingspan of a vampire bat? A. x 1 8 B. x 1 8 C. x 1 8 D. 1x A true crab has fewer than twice the number of legs that a hermit crab has. The hermit crab has 6 legs. How many legs does the true crab have? A. B. 6 C. 1 D Bonus Which runs faster, a reindeer that covers 9 miles in 1 minutes or a zebra that covers 0 miles in 0 minutes? B: Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

48 NAME DATE PERIOD Chapter Test, Form A SCORE Write the letter for the correct answer in the blank at the right of each question. 1. Name the property of equality that is used to solve 8x 7. A. addition B. subtraction C. distributive D. division 1.. Translate the difference of a number and 7 is 8 into an equation. A. 7 n 8 B. n 8 C. n 7 8 D. n ( 7) Rewrite ( 6) using the Distributive Property. A. 6 B. 6 C. 6 D. 6.. Which expression is equivalent to (m )? A. m 1 B. m 1 C. m 7 D. m 1. Simplify each expression.. x y x y A. y B. 6x y C. 6x y D. 6x y. 6. (x ) x A. x 8 B. x C. x D. x 8 6. Solve each equation. Assessment 7. n 1 A. 8 B. 18 C. 8 D h A. 8 B. 8 C. D k 16 A. 1 B. 1 C. 19 D Ryan studied x hours for his history exam. His twin brother Rick studied hours more. Which expression represents how long Rick studied? A. x B. x C. x D. x ( ) Which expression has a constant of? A. x y B. m C. y y D. a Find the perimeter of a square that is 1 centimeters on each side. A. cm B. 8 cm C. 60 cm D. 1 cm The area of a rectangle is 168 square feet. If its length is 1 feet, what is its width? A. 1 ft B. 70 ft C. 6 ft D. 1 ft 1. Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

49 NAME DATE PERIOD Chapter Test, Form A (continued) 1. How far does a jet travel if it flies 0 miles per hour for hours? A. 6 mi B. 100 mi C mi D. 0 mi How long will it take a plane to fly 10 miles at 1 miles per hour? A. h B.. h C. h D.. h 1. Solve each equation. 16. q A. 18 B. 17 C. 18 D g A. 98 B. 98 C. 1 D Name the first step in solving x 7. A. Add to each side. B. Subtract from each side. C. Divide each side by x. D. Subtract x from each side. 18. Solve each equation. 19. c A. B. 7 C. 18 D w A. B. 18 C. D m 6 1 A. 60 B. 9 C. 8 D d d 6 A. 9 B. 8 C. 8 D. 9.. A racquetball court has an area of 800 square feet. Its width is 0 feet. What is the length of the racquetball court? A. 60 ft B. 16,000 ft C. 80 ft D. 0 ft.. Elisa has $ and saves an additional $1 per week. Which equation can be used to find how many weeks it will take until she has $? A. 1w B. 1w C. 1w D. w.. Refer to Question. How long will take Elisa to save $17? A. 10 weeks B. weeks C. 19 weeks D. 1 weeks. Bonus A rectangle whose length is inches has an area of 0 square inches. What is the perimeter of the rectangle? B: Glencoe/McGraw-Hill 16 Glencoe Pre-Algebra

50 NAME DATE PERIOD Chapter Test, Form B SCORE Write the letter for the correct answer in the blank at the right of each question. 1. Name the property of equality that is used to solve 10 x 8. A. addition B. subtraction C. multiplication D. division 1.. Translate the sum of a number and is into an equation. A. n B. n C. n D. n ( ).. Rewrite ( 7) using the Distributive Property. A. 7 B. 7 C. 7 D. 7.. Which expression is equivalent to 8(k )? A. 8k 16 B. 8k 16 C. 8k 6 D. 8k 16. Simplify each expression.. x 7y x y A. y x B. y x C. x y D. x y. 6. x (x 8) A. x B. 9x 1 C. 9x 8 D. 9x 6. Assessment Solve each equation. 7. n 6 1 A. 9 B. 1 C. 9 D k 8 A. B. 9 C. 9 D m A. B. 0 C. D Consuela worked on her art project for h hours. Dion worked on his art project hours less. Which expression represents how long Dion worked? A. h B. h C. h D. h ( ) Which expression has a constant of 6? A. m m B. 6n C. 6n 6m D. 6n Find the perimeter of a square that is 11 centimeters on each side. A. 11 cm B. cm C. cm D. cm The area of a rectangle is 18 square feet. If its width is 8 feet, what is its length? A. 1 ft B. 16 ft C. 6 ft D. 10 ft 1. Glencoe/McGraw-Hill 17 Glencoe Pre-Algebra

51 NAME DATE PERIOD Chapter Test, Form B (continued) 1. How far does a jet travel if it flies miles per hour for hours? A. 11 mi B. 906 mi C. 19 mi D. 19 mi How long will it take a plane to fly 18 miles at 1 miles per hour? A. 1 h B. 1. h C. h D.. h 1. Solve each equation. 16. q A. 1 B. 1 C. 1 D g A. 6 B. C. D Name the first step in solving x 6. A. Add 6 to each side. B. Subtract 6 from each side. C. Multiply each side by. D. Subtract x from each side. 18. Solve each equation. 19. c 1 A. 8 B. 7 C. 9 D w A. 7 B. 8 C. 7 D m 1 8 A. 6 B. 16 C. 6 D k k 9 7 A. 7 B. 1 C. 1 D... A billiards table has an area of 000 square inches. Its width is 0 inches. What is the length of the billiards table? A. in. B. 00 in. C. 100 in. D. 0 in... Ana has $7 and saves an additional $1 per week. Which equation can be used to find how many weeks it will take until she has $? A. 7 w B. 7 1w C. 1w 7 D. 1w 7.. Refer to Question. How long will take Ana to save $? A. weeks B. 7 weeks C. 0 weeks D. 9 weeks. Bonus If a baseball mitt costs m dollars and a cap costs b dollars, write two expressions that show the cost of mitts and caps for 1 players. B: Glencoe/McGraw-Hill 18 Glencoe Pre-Algebra

52 NAME DATE PERIOD Chapter Test, Form C SCORE For Questions 1, use the Distributive Property to write each expression as an equivalent expression. 1. (9 ) 1.. (a 1).. (x 7).. Identify the like terms in 1q r 6 q... List the constant(s) in x y.. Solve each equation. 6. t m c r 9. Assessment a 10. h k r x y b y Glencoe/McGraw-Hill 19 Glencoe Pre-Algebra

53 NAME DATE PERIOD Chapter Test, Form C (continued) Simplify each expression. 18. n 7 n (b 1) 6b 19. For Questions 0 and 1, translate each sentence into an equation. Then find each number. 0. Nineteen is less than twice a number Four more than the quotient of a number and is How far does a train travel if it goes 90 miles per hour for hours?.. In 1978, a powerboat broke the water speed record by traveling approximately 17 miles in 1 hours. About how fast was the average speed of the boat?. Find the perimeter and area of each rectangle.. 9 cm. cm. 6 yd. 17 yd Bonus Tiger Woods won $1,008,000 for his first place win of B: the Masters Tournament in 001. This was about double what he received in 1997 for winning the same tournament. Write and solve an equation to find the amount of his winnings for the Masters Tournament in Glencoe/McGraw-Hill 10 Glencoe Pre-Algebra

54 NAME DATE PERIOD Chapter Test, Form D SCORE For Questions 1, use the Distributive Property to write each expression as an equivalent expression. 1. ( 7) 1.. 6(n ).. (y 9).. Identify the like terms in 8 r r 1... List the constant(s) in 6 a a b.. Solve each equation. 6. x h d Assessment 9. t y b g 6 1. k t x w n Glencoe/McGraw-Hill 11 Glencoe Pre-Algebra

55 NAME DATE PERIOD Chapter Test, Form D (continued) Simplify each expression m 8 m c (c ) 19. For Questions 0 and 1, translate each sentence into an equation. Then find each number. 0. Translate the following sentence into an equation and solve. 0. Thirteen more than 8 times a number is. 1. Six less than the quotient of a number and is How far does a cyclist travel if she rides 1 miles per hour. for hours?. How long would it take a stagecoach to travel 6 miles if its. rate is 16 miles per hour? Find the perimeter and area of each rectangle... in. 7 in.. 1 cm. cm Bonus The area of Lake Michigan is 90 square miles less B: than the area of Lake Superior, which is about one-fifth the size of the Caspian Sea (about 10,000 sq mi). Write and solve an equation to find the approximate area of Lake Michigan. Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

56 NAME DATE PERIOD Chapter Test, Form SCORE Use the Distributive Property to write each expression as an equivalent expression. 1. 6(n ) 1.. (k 8).. (r 7).. 9(x y). Simplify each expression.. x 9 6x h g h (r ) 8r a (b a) x (y x) 9. Solve each equation. Check your solution. Assessment b m r x g q Translate each sentence into an equation. Then find each number. 16. Forty-eight equals the product of 6 and a number A number plus 1 equals The quotient of a number and equals Twelve less than twice a number equals Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

57 NAME DATE PERIOD Chapter Test, Form (continued) Solve each equation. 0. t k c y 6 y r r.. x Translate the following sentence into an equation and solve. 6. Sixteen less than the quotient of a number and 7 is. 7. Antonio is saving money to buy a CD player that costs $ He has already saved $0 and plans to save $10 each week. How many weeks will Antonio need to save? 8. How far does a motorist travel if he drives miles per hour 8. for hours? 9. What is the speed in miles per hour of a train that travels 9. 0 miles in hours? Find the perimeter and area of each rectangle in. 7 in. 1 cm 16 cm 1.. a square that is 1 meters on each side.. a 1-foot by 8-foot rectangle. Bonus Tanya and Jason went to the library, which was miles B: away.tanya left on her bike at :00 P.M. She traveled at a rate of 1 mph. Jason left at :1 P.M. by car. He traveled at 0 mph. Who got to the library first? Explain. Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

58 NAME DATE PERIOD Chapter Open-Ended Assessment SCORE Demonstrate your knowledge by giving a clear, concise solution to each problem. Be sure to include all relevant drawings and justify your answers. You may show your solution in more than one way or investigate beyond the requirements of the problems. 1. Consider the equation 10x a. Add to each side of the equation. Tell, in your own words, how you know that the two sides of the equation are still equal. b. How are the solutions of the original equation and the equation in part a related? What does the term equivalent equations mean? c. Use subtraction, multiplication, and division to form three equations equivalent to the original equation. d. Solve the original equation. Explain each step in finding the solution.. Solve ay b c for y. Explain each step in the process.. Poloma is planning a new vegetable garden. She has 70 feet of fencing with which to enclose the garden. If she wants to obtain the greatest possible area, what are the dimensions of the garden? Explain your reasoning. Assessment. Make up a problem that can be represented by the equation x 10. Glencoe/McGraw-Hill 1 Glencoe Pre-Algebra

59 NAME DATE PERIOD Chapter Vocabulary Test/Review SCORE Addition Property of Equality area coefficient constant Distributive Property Division Property of Equality equivalent equations equivalent expressions formula inverse operations like terms Multiplication Property of Equality perimeter simplest form simplifying an expression Subtraction Property of Equality term two-step equation Underline the term that best completes each statement. 1. The statement a(b c) ab ac is an example of the (Distributive Property, Multiplication Property of Equality).. A term without a variable is a (coefficient, constant).. The expression x 8 x x has three (like terms, terms).. An algebraic expression is in simplest form if it has no parentheses and no (like terms, constants).. To undo the addition of in the expression x, you would subtract. This is an example of (inverse operations, simplest form). 6. The equations x 9 and x are equivalent equations because they have the same (solution, variable). 7. The number in front of a variable is the (constant, coefficient). 8. A two-step equation contains two (operations, like terms). 9. The (area, perimeter) of a figure is the measure of the distance around it. 10. The (area, perimeter) of a figure is measured in square units. In your own words Define each term. 11. formula 1. equivalent expressions Glencoe/McGraw-Hill 16 Glencoe Pre-Algebra

60 NAME DATE PERIOD Chapter Quiz (Lessons 1 and ) SCORE Use the Distributive Property to write each expression. 1. ( 8) 1.. (n ).. (x 6).. (t 7). Identify the like terms in each expression.. 1n 6 p 6n. 6. a 9a 6. Simplify each expression. 7. x x r r y (a ) a 10. NAME DATE PERIOD Chapter Quiz (Lessons and ) SCORE Assessment Solve each equation. 1. c 1. 7 t x q... n 8 6. y. 6. z a Write and solve an equation for the sentence. The sum of 10 and a number is Standardized Test Practice What value of x makes x 1 a true statement? A. B. 6 C. D Glencoe/McGraw-Hill 17 Glencoe Pre-Algebra

61 NAME DATE PERIOD Chapter Quiz (Lessons and 6) SCORE Solve each equation. 1. n x x.. 19 r 7 r.. Courtney paid $1. to mail some photographs to her friend first-class. The Post Office charges cents for the first ounce, and cents for each additional ounce. Solve w 1 to find how much Courtney s package weighed.. Translate each sentence into an equation. Then find the number. 6. Five more than twice a number is Three times a number less 1 is Sixteen decreased by three times a number is Nine more than the quotient of a number and is An electrician charges $ to make a house call. For each hour of labor, she charges an additional $0. How many hours did she work if the repair bill was $19? 10. NAME DATE PERIOD Chapter Quiz (Lesson 7) SCORE 1. How far does a truck driver travel if he drives 6 miles per 1. hour for hours?. What is the speed in miles per hour of a balloon that travels. miles in hours? Find the perimeter and area of each rectangle.. a rectangle that is 1 meters long and 8 meters wide.. a square that is 6 centimeters on each side.. a -inch by 7-inch rectangle. Glencoe/McGraw-Hill 18 Glencoe Pre-Algebra

62 NAME DATE PERIOD Chapter Mid-Chapter Test (Lessons 1 through ) SCORE Part I Write the letter for the correct answer in the blank at the right of each question. x 1. Name the property of equality that is used to solve 16. A. addition B. subtraction C. multiplication D. division 1.. Translate the product of and a number is into an equation. A. n B. n C. n D. n.. Rewrite (8 ) using the Distributive Property. A. 8 B. 8 C. 8 8 D. 8.. Which expression is equivalent to (r 8)? A. r 16 B. r 16 C. r 6 D. r 6. Simplify each expression.. m n m 6n A. n B. 10m n C. 10m n D. 10m n. 6. x (x ) A. x 6 B. 8x 6 C. 8x D. x 6. Assessment Part II Solve each equation. 7. y k z t A tool kit costs $1 for a hammer, $0 for a screwdriver set, 11. and $11 for a measuring tape. Write two equivalent expressions for the total cost of tool kits. Then find the cost. 1. In 1997, people living in Alaska used about 100 million 1. BTUs of energy per person, which was about times as many BTUs as the people living in California used. Write and solve an equation to find how many BTUs Californians used per person in Glencoe/McGraw-Hill 19 Glencoe Pre-Algebra

63 NAME DATE PERIOD Chapter Cumulative Review (Chapters 1 ) 1. The temperature drops an average of 1 C for every 100 meters that a hot air balloon rises. If the temperature is C on the ground, what is the approximate temperature 100 meters above the ground? (Lesson 1-1) 1.. Find the value of 0. (Lesson 1-).. Evaluate 1 c d if c 6 and d. (Lesson 1-).. Name the property shown by (8 ) 8 ( ). (Lesson 1-).. Name the ordered pair for point P. y (Lesson -6) P. 6. State whether a scatter plot showing age and height of students would show a positive, negative, or no relationship. (Lesson 1-7) Simplify 6 7. (Lesson -1) 7. Simplify each expression. (Lessons - and -) 8. 7m ( 1)m c ( c) 9. Find each product or quotient. (Lessons - and -) 10. 8( ) Name the quadrant in which P(, ) lies. (Lesson -) Use the Distributive Property to rewrite (p ). (Lesson -1) Simplify y 8 7y 1. (Lesson -) 1. For Questions 1 17, solve each equation. (Lessons -, -, and -) 1. 1 t w n Nine more than times a number is 11. Write an equation and find the number. (Lesson -6) Find the perimeter and area of a 6-inch by 7-inch rectangle. (Lesson -7) 19. O x Glencoe/McGraw-Hill 160 Glencoe Pre-Algebra

64 NAME DATE PERIOD Standardized Test Practice (Chapters 1 ) Part 1: Multiple Choice Instructions: Fill in the appropriate oval for the best answer. 1. Evaluate r s if r and s 18. (Lesson 1-) A. B. 1 C. 9 D A B C D. Rewrite the expression (9 p) using the Commutative Property. (Lesson 1-) E. 9 p F. p (9 ) G. 9 (p ) H. (9 p). E F G H. Choose an inequality that compares the number of days in a month and days. (Lesson -1) A. m B. m C. m D. none of these. A B C D. Find the product of and x. (Lesson -) E. 0x F. 0x G. x H. x.. Evaluate the expression ac bc if a, b, and c. (Lesson -) A. 9 B. 1 C. D.. E A F B G C H D Assessment 6. Find the average of the test scores:, 7, 7, 70, 7. (Lesson -) E. 0 F. 7. G. 70 H E F G H 7. Name the quadrant in which the graph of (, ) lies. (Lesson -6) A. I B. II C. III D. IV 7. A B C D 8. Which is the simplified form of (1z 7) z? (Lesson -) E. 1z 7 F. 9z 7 G. 9z 7 H. z 1 8. E F G H 9. Solve 8 6m. (Lesson -) A. 6 B. 8 C. D A B C D 10. Solve a 1. (Lesson -) E. 6 F. 7 G. 7 H E F G H 11. Which expression is equivalent to (n ) (n )? (Lesson -) A. n B. n 16 C. n D. n 11. A B C D 1. What is the perimeter of the rectangle? (Lesson -7) E. 60 ft F. 17 ft 1 ft ft G. ft H. 9 ft 1. E F G H Glencoe/McGraw-Hill 161 Glencoe Pre-Algebra

65 NAME DATE PERIOD Standardized Test Practice (continued) 1. What is the solution of 6 m 8? (Lesson -) A. B. 1 C. 1 D. 1. A B C D 1. Solve n. (Lesson -) E. 1 F. 1 G. 6 H E F G H 1. Find the area of a square that is 1 centimeters on each side. (Lesson -7) A. cm B. 8 cm C. 1 cm D. 196 cm 1. A B C D 16. What is the solution of 6w 7? (Lesson -) E. 1 F. G. 1 H. 16. E F G H Part : Grid In Instructions: Enter your answer by writing each digit of the answer in a column box and then shading in the appropriate oval that corresponds to that entry. 17. Find the next number in the pattern. (Lesson 1-1) ,,,,. 18. Evaluate st if s and t 6. (Lesson -) / / / / Part : Short Response Instructions: Write your answer in the blank at the right of each question. 19. A water company charges a family a $10.0 monthly service 19. fee, plus $.00 for each unit of water used. (Lesson 1-) a. Let n represent the number of units. Write an expression that represents the total monthly cost when the family uses n units of water. b. Suppose the family has a water bill of $6.0 for one month. Write and solve an equation to find the number of units used that month. 0. The ordered pairs ( 1, ), (, ), and (, ) are coordinates 0. of three of the vertices of a rectangle. Find the area of the rectangle. (Lesson -6) Glencoe/McGraw-Hill 16 Glencoe Pre-Algebra

66 NAME DATE PERIOD Unit 1 Test (Chapters 1 ) SCORE 1. Bacterial populations can grow to enormous numbers in a 1. matter of a few hours with the right conditions. If a bacterial colony doubles its size every 1 minutes, how many bacteria will be present after 1 hour if the colony began with bacteria?. Find the value of 6[(0 ) (8 )].. For Questions and, evaluate each expression if m, p 7, and t... t p m. 8p (t m).. Name the property shown by the statement Write an equation and solve. A number increased by 7 is Express the relation {(0, ), (, 1), (, 1), (, )} as a table 7. and as a graph. The table shows SAT test scores for a group of students who took an SAT review course together. 8. Make a scatter plot of the 8. Student English Math data. Does there appear to Jerrod be a relationship between the scores? Explain. Becca Wallace David Raul Keesha 0 10 Math Scores y 1 O y O 100 SAT Scores English Scores x x Assessment Replace each with,, or to make a true sentence Glencoe/McGraw-Hill 16 Glencoe Pre-Algebra

67 NAME DATE PERIOD Unit 1 Test (continued) (Chapters 1 ) 11. What is the sum of 9 ( 1)? 11. For Questions 1 and 1, evaluate each expression if x, y, and z. 1. z x y z Simplify 9j()(k) Find the average (mean) of 6, 11, 0, 1, 9,,. 1. Name the ordered pair for each y point graphed on the coordinate G B plane at the right. C 1 F 16. A 16. O 1 x E D 17. C 17. A 18. A package of soccer accessories costs 18. $ for cleats, $1 for shin guards, and $1 for a ball. Write two equivalent expressions for the total cost of 9 accessory packages. Then find the cost. 19. Salvador bought pounds of oranges that cost x cents per 19. pound, a cucumber for 9, and bananas for. Write an expression in simplest form that represents the amount he spent. 0. The difference between the highest and lowest elevations in 0. Africa is 601 meters. The lowest elevation is 16 meters. Write and solve an equation to find the highest elevation in Africa. 1. When you divide a number by 7, the result is 6. Write and 1. solve an equation for this sentence. Solve each equation.. 7z z.. 11 r 7 r.. The quotient of a number and 6, plus 9, is. Translate. this sentence into an equation, then find the number.. An 800-gallon water tank is being drained at the rate. of 00 gallons per hour. How long will it take the tank to empty? Glencoe/McGraw-Hill 16 Glencoe Pre-Algebra

68 Standardized Test Practice Student Record Sheet (Use with pages 1 1 of the Student Edition.) Glencoe/McGraw-Hill A1 Glencoe Pre-Algebra NAME DATE PERIOD Answers Select the best answer from the choices given and fill in the corresponding oval Solve the problem and write your answer in the blank. For Questions 1 16 and 18, also enter your answer by writing each number or symbol in a box. Then fill in the corresponding oval for that number or symbol (grid in) 1 (grid in) 1 (grid in) 16 (grid in) (grid in) 19 Record your answers for Questions 0 1 on the back of this paper / / / / / / / / / / D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A D C B A Part Short Response/Grid In Part Short Response/Grid In Part 1 Multiple Choice Part 1 Multiple Choice Part Open Ended Part Open Ended