Chapter 4 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 (0-0-0-). 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 Orion Place Columbus, OH 0 ISBN: Pre-Algebra Chapter Resource Masters

4 CONTENTS Vocabulary Builder...vii Lesson - Study Guide and Intervention... Skills Practice... Practice... Reading to Learn Mathematics... Enrichment...9 Lesson - Study Guide and Intervention...0 Skills Practice... Practice... Reading to Learn Mathematics... Enrichment... Lesson - Study Guide and Intervention... Skills Practice... Practice... Reading to Learn Mathematics... Enrichment...9 Lesson - Study Guide and Intervention...0 Skills Practice... Practice... Reading to Learn Mathematics... Enrichment... Lesson - Study Guide and Intervention... Skills Practice... Practice... Reading to Learn Mathematics... Enrichment...9 Lesson - Study Guide and Intervention...9 Skills Practice...9 Practice...9 Reading to Learn Mathematics...9 Enrichment...99 Lesson - Study Guide and Intervention...00 Skills Practice...0 Practice...0 Reading to Learn Mathematics...0 Enrichment...0 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... Chapter Vocabulary Test/Review... Chapter Quizzes &...9 Chapter Quizzes &...0 Chapter Mid-Chapter Test... Chapter Cumulative Review... Chapter Standardized Test Practice... Standardized Test Practice Student Recording Sheet...A ANSWERS...A A Lesson - Study Guide and Intervention...90 Skills Practice...9 Practice...9 Reading to Learn Mathematics...9 Enrichment...9 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 -. 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 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 A is an answer sheet for the Standardized Test Practice questions that appear in the Student Edition on pages 9 9. 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 algebraic fraction base composite number divisible expanded form exponent factor factor tree vii

9 NAME DATE PERIOD Reading to Learn Mathematics Vocabulary Builder (continued) Vocabulary Term greatest common factor (GCF) Found on Page Definition/Description/Example monomial power prime factorization prime number scientific notation simplest form standard form Venn Diagram viii

10 - Study Guide and Intervention Factors and Monomials Finding Factors Two or more numbers that are multiplied to form a product are called factors. Any number is divisible by its factors. The following rules can be used to determine mentally whether a number is divisible by,,,, or 0. A number is divisible by: if the ones digit is divisible by. if the sum of the digits is divisible by. if the ones digit is 0 or. if the number is divisible by and by. 0 if the ones digit is 0. Example Determine whether 0 is divisible by,,,, or 0. Number Divisible? Reason yes The ones digit is, and is divisible by. yes The sum of the digits is 9, and 9 is divisible by. no The ones digit is, not 0 or. yes 0 is divisible by and by. 0 no The ones digit is not 0. 0 is divisible by,, and. A monomial is a number, a variable, or a product of numbers and/or variables. So, 0 is a monomial. The expression q is also a monomial since it is the product of a number and a variable, q. However, x is not a monomial since it is the sum of two terms. Lesson - Exercises Use divisibility rules to determine whether each number is divisible by,,,, or 0.. 0,. 00,,,, 0.,,. 9 none List all the factors of each number..,,, 9,,.,,,,,,,.,,,,,, 9,. 0,,,,, 0,, 0, 0, 0 Determine whether each expression is a monomial. Explain why or why not. 9. yes; a number 0. x y no; sum of two terms. (x ) no;. st yes; product of a number difference of two terms and variables Glencoe/McGraw-Hill Glencoe Pre-Algebra

11 - Skills Practice Factors and Monomials Use divisibility rules to determine whether each number is divisible by,,,, or ,, 0.,,... 0,,,, 0. 0,, 0.,., 9.,, ,, 0 List all the factors of each number..,,,,, 9,,,. 9, 9.,,, 9,,.,, 9,,.,,,.,, 9,, 9,.,,,,.,,, 9,, Determine whether each expression is a monomial. Explain why or why not. 9. p yes; a variable 0. yes; a number. n no; sum of two terms. h w no; difference of two terms. (a ) no; sum of two terms. k yes; product of a number and a variable. q r no; sum of two terms. y no; difference of two terms. (x ) no; difference of two terms. s p yes; product of numbers and variables 9. SEATING Can graduates be seated in rows of at the graduation ceremony? Explain. Yes. Since is divisible by and by, it is divisible by. So the graduates can be seated in rows of with no extra people or empty chairs. 0. SCHOOL SUPPLIES When Alex s mother buys pencils for school, she divides them equally among Alex and his sister. Should she buy the pencils in packages of or 0? Explain. She should buy packages of 0 since 0 is divisible by, but is not. Glencoe/McGraw-Hill Glencoe Pre-Algebra

12 - Practice Factors and Monomials Use divisibility rules to determine whether each number is divisible by,,,, or 0....,,. 9 none.,.,,. 00,,,, 0. 0,,,, ,, ,,,, 0 List all the factors of each number..,,,,,,,,,.,,,,,,,.,,.,,, Lesson -.,. 9,,,,,, 9, 9, 9. 9,, 9, 9. 0,,, 0,,,, ,,,,,,,,, 0. 00,,,,, 0, 0,,,, 9 0, 0, 00, 00 Determine whether each expression is a monomial. Explain why or why not.. yes; a number. (m) yes; product of a number and a variablle. m yes; a variable. rv yes; product of variables. (x ) no; difference of two terms. n no; difference of two terms. ()()x yes; product of. w yes; product of variables numbers and a variable 9. w no; sum of two terms 0. s t no; difference of two terms NEWSPAPERS For Exercises and, refer to the following information. Brandon delivers newspapers in his neighborhood. On Sunday, he must deliver papers. Since he rides his bike, he separates the papers into smaller stacks and delivers one stack at a time.. What size stacks can he make? stacks of (or stacks of ), stacks of (or stacks of ), stacks of (or stacks of ), stacks of (or stacks of ). If Brandon can carry no more than 0 papers at a time and can return home to restock no more than times, how can he organize the papers? stacks of papers Glencoe/McGraw-Hill Glencoe Pre-Algebra

13 - Reading to Learn Mathematics Factors and Monomials Pre-Activity How are side lengths of rectangles related to factors? Do the activity at the top of page in your textbook. Write your answers below. Reading the Lesson a. Use grid paper to draw as many other rectangles as possible with an area of square units. Label the length and width of each rectangle. Students should draw rectangles with dimensions,,, and. b. Did you draw a rectangle with a length of units? Why or why not? No, if the length were, there is no whole number width that would give an area of. c. List all of the pairs of whole numbers whose product is. Compare this list to the lengths and widths of all the rectangles that have an area of square units. What do you observe? and, and, and, and 9, and ; they are the same. d. Predict the number of rectangles that can be drawn with an area of square units. Explain how you can predict without actually drawing them. rectangles; find the factor pairs whose product is :,,,.. See students work. Write a definition and give an example of each new vocabulary word. Vocabulary Definition Example. factors. divisible. monomial. Is the expression x a monomial? Explain. x is not a monomial because it is the difference of two terms. Helping You Remember. Explain in your own words how to determine whether an expression is a monomial. Sample answer: A monomial is a number, a variable, or the product of numbers and/or variables. Glencoe/McGraw-Hill Glencoe Pre-Algebra

14 - Enrichment Divisibility Divisibility rule for Determine whether 0 is divisible by. 0 X Cross out the ones digit. Subtract twice the value of the ones digit from the rest of the number. 99 X If the difference is a number that you know is divisible by, stop. If not, repeat. Since is divisible by, 0 is divisible by. Divisibility rule for Determine whether 9 is divisible by. Method 9 X Cross out the ones digit. 9 Subtract the value of the ones digit from the rest of the number. 0 X If the difference is a number that you know is divisible by, stop. If not, repeat. Since is divisible by, 9 is divisible by. Method 9 0 Add the odd-numbered digits (first and third). 9 0 Add the even-numbered digits (second and fourth). 0 Subtract the sums. If the difference is divisible by, the number is divisible by. Since 0 is divisible by, 9 is divisible by. Lesson - Determine whether, is divisible by. Add the odd-numbered digits. 0 Add the even-numbered digits. Subtract the sums. Since is not divisible by,, is not divisible by. Determine whether each number is divisible by or... 9 neither. 9 neither. and., neither 9. and Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

15 - Study Guide and Intervention Powers and Exponents A number that is expressed using an exponent is called a power. The base is the number that is multiplied. The exponent tells how many times the base is used as a factor. So, has a base of and an exponent of, and. Example Write each expression using exponents. a The base is 0. It is a factor times, so the exponent is b. ( p )( p )(p ) The base is p. It is a factor times, so the exponent is. ( p )( p )( p ) ( p ) Expressions involving powers are evaluated using order of operations. Powers are repeated multiplications. They are evaluated after any grouping symbols and before other multiplication or division operations. Example x = () Exercises Evaluate x if x. Replace x with. = ()() is a factor times. = Multiply. = Subtract. Write each expression using exponents... ( )( )( ) (). d d d d d. x x y y x y. (z )(z ) (z ). ( t)( t)( t) (t ) Evaluate each expression if g, h, and m 9.. g. g 9. g m 0 0. hm. g h. m hg Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

16 - Skills Practice Powers and Exponents Write each expression using exponents... ()()()()() ( ).. (k k)(k k)(k k) k. p p p p p p p.. (a)(a)(a)(a) ( a) y z z z yz. s s s s t u u s tu. q q q Express each number in expanded form... ( 0 ) ( 0 ) ( 0 0 ) ( 0 ) ( 0 ) ( 0 ) ( 0 0 ) ( 0 ) (0 0 ) (9 0 ) ( 0 ) (9 0 0 ) (0 0 ) ( 0 0 ) Lesson - Evaluate each expression if b, c, and d.. c. c 0 9. b 0. c c. c 9. c. c d. b. b c. d 9. d. b d 9. b d 9 0. (b c) Glencoe/McGraw-Hill Glencoe Pre-Algebra

17 - Practice Powers and Exponents Write each expression using exponents..... ()() (). a a a a a. n n n n n n.. (b b)(b b)(b b) b 9. (v)(v)(v)(v) (v) 0. x x z z z x z. t t t. m m m n p p m np Express each number in expanded form ( 0 ) ( 0 0 ) ( 0 ) (0 0 ) (0 0 ) ( 0 0 ).,9 ( 0 ) ( 0 ). 9 ( 0 ) (9 0 ) ( 0 ) ( 0 ) (9 0 0 ) ( 0 0 ) Evaluate each expression if x, y, and z.. y x z 0. x 9. 9 x 9. z. y. z y 0. x y z 9. z x FAMILY TREE For Exercises and, refer to the following information. When examining a family tree, the branches are many. You are generation now. One generation ago, your parents were born. Two generations ago your grandparents were born.. How many great-grandparents were born three generations ago? or. How many great grandparents were born ten generations ago? 0 or 0 Glencoe/McGraw-Hill Glencoe Pre-Algebra

18 - Reading to Learn Mathematics Powers and Exponents Pre-Activity Why are exponents important in comparing computer data? Do the activity at the top of page in your textbook. Write your answers below. a. Write as a product of factors of. How many factors are there? ; factors b. How many factors of form the product? factors c. One megabyte is 0 kilobytes. How many factors of form the product 0? 0 factors Reading the Lesson. See students work. Write a definition and give an example of each new vocabulary word or phrase. Vocabulary Definition Example. base. exponent Lesson -. power. standard form. expanded form. Write each expression using exponents. a. b. x x x y y x y c. ()()() () d. r r m m m r m. The number ( 0 ) ( 0 ) (0 0 ) ( 0 0 ) is written in expanded form, while 0 is written in standard form. Helping You Remember. Explain how the terms base, power, and exponent are related. Provide an example. Sample answer: A power is an expression with two parts a base and an exponent. For example, the power has a base of and an exponent of. Glencoe/McGraw-Hill Glencoe Pre-Algebra

19 - Enrichment Exponents Numbers can be expressed in several ways. Some numbers are expressed as sums. Some numbers are expressed as products of factors, while other numbers are expressed as powers. Two ways to express are and. The number million can be expressed in the following ways.,000, ,000, Write names for each number below using the given exponents.. ; exponents: and,. ; exponents: and 9,. ; exponents: and,. ; exponents: and,. ; exponents: and,. 9; exponents: and,. 0; exponents: and 9,. 09; exponents: and, 9. ; exponents: and, 0. 90,; exponents: and, Numbers that can be named as powers with like bases can be multiplied by adding the exponents. Write the product of each pair of factors in exponential form Glencoe/McGraw-Hill Glencoe Pre-Algebra

20 - Study Guide and Intervention Prime Factorization A prime number is a whole number that has exactly two factors, and itself. A composite number is a whole number that has more than two factors. Zero and are neither prime nor composite. Example Determine whether 9 is prime or composite. Find the factors of The only factors of 9 are and 9, therefore 9 is a prime number. Any composite number can be written as a product of prime numbers. A factor tree can be used to find the prime factorization. Example Find the prime factorization of. is the number to be factored. Find any pair of whole number factors of. Continue to factor any number that is not prime. The factor tree is complete when there is a row of prime numbers. The prime factorization of is or. In algebra, monomials can be factored as a product of prime numbers and variables with no exponent greater than. So, x factors as x x. Exercises Determine whether each number is prime or composite.. composite. prime. composite. composite Lesson - Write the prime factorization for each number. Use exponents for repeated factors Factor each monomial. 9. m m m m 0. 0xy x y y. a b c a a b b c c c. h h Glencoe/McGraw-Hill Glencoe Pre-Algebra

21 - Skills Practice Prime Factorization Determine whether each number is prime or composite.. prime. 9 prime. composite. composite. composite. prime. prime. 0 prime 9. 9 composite 0. 9 composite. prime. prime Write the prime factorization of each number. Use exponents for repeated factors Factor each monomial.. t t. r r r. m m m. 9y y y y. ab a b. xyz x y z 9. j k j j k 0. u v u u v v. d d d d d. cd c d d Glencoe/McGraw-Hill Glencoe Pre-Algebra

22 - Practice Prime Factorization Determine whether each number is prime or composite.. prime. composite. prime. composite. 9 composite. 9 composite. prime. prime Write the prime factorization of each number. Use exponents for repeated factors Factor each monomial. 9. v v 0. 9c c c. b b b b. h h h. wz w z. ghj g h j. NUMBER THEORY Twin primes are a pair of consecutive odd primes, which differ by. For example, and are twin primes. Find the twin primes less than 00. (Hint: There are pairs of twins less than 00.), ;, ;, ;, 9; 9, ;, ; 9, ;, Lesson - Glencoe/McGraw-Hill Glencoe Pre-Algebra

23 - Reading to Learn Mathematics Prime Factorization Pre-Activity How can models be used to determine whether numbers are prime? Do the activity at the top of page 9 in your textbook. Write your answers below. a. Use grid paper to draw as many different rectangular arrangements of,,,,,,, and 9 squares as possible. See students answers. b. Which numbers of squares can be arranged in more than one way?,,, 9 c. Which numbers of squares can only be arranged one way?,,, d. What do all rectangles that you listed in part c have in common? Explain. They all have a width of because no other pair of factors can be found. Reading the Lesson. See students work. Write a definition and give an example of each new vocabulary word or phrase. Vocabulary Definition Example. composite number. factor. factor tree. prime factorization. prime number Helping You Remember. Composite is a word used in everyday English. a. Find the definition of composite in the dictionary. Write the definition. made up of distinct parts b. Explain how the English definition can help you remember how composite is used in mathematics. Sample answer: Composite numbers are made up of many distinct parts, or factors. Glencoe/McGraw-Hill Glencoe Pre-Algebra

24 - Enrichment Prime Pyramid A prime number is a whole number that has exactly two factors itself and. The pyramid below is called a prime pyramid. Each row begins with and ends with the number of that row. So, row begins with and ends with, row begins with and ends with, and so on. In each row, the numbers from to the row number are arranged such that the sum of any two adjacent numbers is a prime number. For example, look at row : It must contain the numbers,,, and. It must begin with and end with. The sum of adjacent pairs must be a prime number:,, * 9 0 Lesson -. Complete the pyramid by filling in the missing numbers.. Extend the pyramid to row.,,,,,,, 0, 9,,,,. Explain the patterns you see in the completed pyramid. Sample answer: Each row alternates odd and even numbers. Multiples of form diagonals that are constant. Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

25 - Study Guide and Intervention Greatest Common Factor (GCF) The greatest number that is a factor of two or more numbers is the greatest common factor (GCF). Two ways to find the GCF are shown below. Example Find the GCF of and. Method List the factors. factors of :,,,,,,, Look for factors common to both lists,,,, and. factors of :,,,,, The greatest common factor of and is. Method Use prime factorization. Find the common prime factors of and. Multiply the common prime factors. The greatest common factor of and is or. In algebra, greatest common factors are used to factor expressions. Example Factor x 0. First, find the GCF of x and 0. x x 0 The GCF is. Now write each term as a product of the GCF and its remaining factors. x 0 (x) () (x ) So, x 0 (x ). Exercises Distributive Property Find the GCF of each set of numbers.. 0,.,., 0., Factor each expression.. g (g ). d (d ). a (a ). f f f (f ) 9. j ( j ) 0. n 0n n(n ) Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

26 - Skills Practice Greatest Common Factor (GCF) Find the GCF of each set of numbers or monomials.., 0.,., 9.,., 0., 9.,., 9. 0, ,., 0.,. 0t, 0t 0t., 9t. k,0k k. 9m, n. pq, q q. p, 9 Factor each expression. 9. b (b ) 0. t 9 (t ). w (w ). 00 0x 0( x). x (x ). n 0 (n ). g ( g ). 0 f (0 f ). n (n ). 9 9(l ) 9. u (u ) 0. 0 c (0 c). x ( x). y (y ). p (p ). 9r 9(r 9). q ( q ). x (x ) Lesson - Glencoe/McGraw-Hill Glencoe Pre-Algebra

27 - Practice Greatest Common Factor (GCF) Find the GCF of each set of numbers or monomials.. 9, 9., 0., 0. 9, 9.,. 90, ,. 00, , 0.,,., 0.,. p, 0p p. a, 9ab a. b, c. a,b. s t,0st st. a b,0ab ab Factor each expression. 9. 0x 0 0. v. 9t 9 9(t. m n. p 0. r. z. q. h 9. a 0. 0 s. 0n 0. d. m 0. 9b. d (d 9). m. SCHOOL TRIP Thirty-two seventh graders, eighth graders, and 0 ninth graders are taking a ski trip. In order to help students get better acquainted, students from each grade level are to ride each bus. What is the greatest number of buses that can be used if students from each grade level are divided equally among the buses? buses Glencoe/McGraw-Hill Glencoe Pre-Algebra

28 - Reading to Learn Mathematics Greatest Common Factor (GCF) Pre-Activity How can a diagram be used to find the greatest common factor? Do the activity at the top of page in your textbook. Write your answers below. a. Which numbers are in both circles?, b. Find the product of the numbers that are in both circles. c. Is the product also a factor of and 0? yes d. Make a Venn diagram showing the prime factors of and. Then use it to find the common factors of the numbers., Reading the Lesson. See students work. Write a definition and give an example of each new vocabulary word or phrase. Vocabulary Definition Example. Venn diagram. greatest common factor Helping You Remember. Summarize in your own words how to find the greatest common factor of two numbers using each method. a. prime factorization Write the prime factorization of each number, then look for the prime factors common to both numbers. The greatest common factor is the product of the common factors. b. lists of factors Make a list of all factors of both numbers. The largest factor that is in both lists is the greatest common factor. c. a Venn diagram Make a Venn diagram with the prime factors of each number in a circle. The GCF is the product of the factors in the overlapping section of the diagram. Lesson - Glencoe/McGraw-Hill Glencoe Pre-Algebra

29 - Enrichment GCFs by Successive Division Another way to find the greatest common factor (GCF) of two numbers is to use successive division. This method works well for large numbers. Find the GCF of and. Step Divide the smaller number into the greater number. R Step Divide the remainder into the divisor. Repeat this step until you get a remainder of 0. R R0 R R The last divisor is the GCF of the two original numbers. So the GCF of and is. Use the method above to find the GCF of each pair of numbers.. ;. ; 9. ; 9. ;. ;. 9; 0. ; 9. 90; 9. ; ; 0 0.,; 9,.,; 0,00 Glencoe/McGraw-Hill Glencoe Pre-Algebra

30 - Study Guide and Intervention Simplifying Algebraic Fractions A fraction is in simplest form when the GCF of the numerator and the denominator is. One way to write a fraction in simplest form is to write the prime factorization of the numerator and the denominator. Then divide the numerator and denominator by the GCF. Example Write in simplest form. Write the prime factorization of the numerator and the denominator. Divide the numerator and denominator by the GCF,. / / or Simplify. Algebraic fractions can also be written in simplest form. Again, you can write the prime factorization of the numerator and the denominator, then divide by the GCF. Example Simplify ab. a ab a b b a / / / / Divide the numerator and denominator by the GCF, a. / / / a/ a Exercises b b a or b a Simplify. Simplify each fraction. If the fraction is already in simplest form, write simplified c. c c. r r r 9. b b 0. w w. s t simplified simplified d. d d Lesson - Glencoe/McGraw-Hill Glencoe Pre-Algebra

31 - Skills Practice Simplifying Algebraic Fractions Write each fraction in simplest form. If the fraction is already in simplest form, write simplified simplified. d d d y. y y. q q q. s s s. x y 9a simplified. a. t t. g g 9. j 0 j 00p 0. 00p p n k. 00n n. k k. a b simplified. b d b d. a a. t t t Glencoe/McGraw-Hill Glencoe Pre-Algebra

32 - Practice Simplifying Algebraic Fractions Write each fraction in simplest form. If the fraction is already in simplest form, write simplified simplified simplified. x x x. m a m. m a a. u u u. y y. q q. x x c. c 9. v v v 0. b 9 b. e f f m e. f e p simplified. b a 0a b b a. SKI RESORT A local ski resort is open for business weeks in the winter. Write a fraction in simplest form that represents the fraction of a year the resort is open. Lesson - Glencoe/McGraw-Hill Glencoe Pre-Algebra

33 - Reading to Learn Mathematics Simplifying Algebraic Fractions Pre-Activity How are simplified fractions useful in representing measurements? Do the activity at the top of page 9 in your textbook. Write your answers below. a. Are the three fractions equivalent? Explain your reasoning. Yes; the same portion of each circle is shaded. b. Which figure is divided into the least number of parts? the third figure c. Which fraction would you say is written in simplest form? Why? ; The shaded part is not divided into smaller parts. Reading the Lesson. See students work. Write a definition and give an example of each new vocabulary phrase. Vocabulary Definition Example. simplest form. algebraic fraction. Use a Venn diagram to explain how to simplify. The prime factors of the numerator are,, and. The prime factors of the denominator are,, and. The GCF of the numbers, 9, is shown by the intersection. So, the simplified fraction is. Helping You Remember. Explain the similarities and differences between simplifying a numerical fraction and simplifying an algebraic fraction. Both fractions are simplified by dividing the numerator and denominator by the GCF. The only difference is that an algebraic fraction has variables as factors in the numerator and/or the denominator. Glencoe/McGraw-Hill Glencoe Pre-Algebra

34 - Enrichment Matching Equivalent Fractions Cut out the pieces below and match the edges so that equivalent fractions meet. The pieces form a rectangle. The outer edges of the rectangle formed will have no fractions Lesson - Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

35 - Study Guide and Intervention Multiplying and Dividing Monomials When multiplying powers with the same base, add the exponents. Symbols Example a m a n a m + n + or When dividing powers with the same base, subtract the exponents. Symbols Example a m an a m n, where a 0 or Example a (a) ( )(a a) Example ( ) ( ) () () Exercises Find a (a). Express your answer using exponents. ()(a ) The common base is a. a Use the Commutative and Associative Properties. Add the exponents. Find ( ). ( ) Express your answer using exponents. The common base is. Subtract the exponents. Find each product or quotient. Express your answer using exponents... v v v 9. ( f )( f 9 ) f. 0. h(h ) h. 0x (x ) 0x.. 9. ( ) ( ) 0 () 0 or 0.. c c c. ( p) ( p) (p). u (u ) u. w w. m (m ) 0m 9 w. the product of two cubed and two squared. the quotient of six to the eighth power and six squared Glencoe/McGraw-Hill 90 Glencoe Pre-Algebra

36 - Skills Practice Multiplying and Dividing Monomials Find each product or quotient. Express your answer using exponents () () (). (9) (9) (9) Lesson -. a a a. n n n 9. ( p )(p ) p 0. (z )(z ) z. (b )(b ) b. (v) (v) (v) 0. a a a. 0t t 0 0t. (c )(9c) c. (f )(f ) 0f r r 9 00 or 00. ( ) r or r. z z 0 0 () z. q q q. g g g. ( y) ( y) (y). ( ( z) z) (z) 9. the product of two squared and two to the sixth power 0. the quotient of ten to the seventh power and ten cubed 0. the product of y squared and y cubed y. the quotient of a to the twentieth power and a to the tenth power a 0 Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

37 - Practice Multiplying and Dividing Monomials Find each product or quotient. Express your answer using exponents () () (). () 9 () (). t 9 t t. h h h 9. (m )(m ) m 0. (u )(u 0 ) u. (r) (r) 0 (r). (w)(w) 9 (w) 0. d d d. j 0 j 0 j 00. b 9 b 0b ( ) ( ) 0 or 0 or () or v v0 v 0. n n n. the product of five cubed and five to the fourth power. the quotient of eighteen to the ninth power and eighteen squared. the product of z cubed and z cubed z. the quotient of x to the fifth power and x cubed x 9. SOUND Decibels are units used to measure sound. The softest sound that can be heard is rated as 0 decibels (or a relative loudness of ). Ordinary conversation is rated at about 0 decibels (or a relative loudness of 0 ). A rock concert is rated at about 0 decibels (or a relative loudness of 0 ). How many times greater is the relative loudness of a rock concert than the relative loudness of ordinary conversation? 0 or,000,000 times 9 Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

38 - Reading to Learn Mathematics Multiplying and Dividing Monomials Pre-Activity How are powers of monomials useful in comparing earthquake magnitudes? Do the activity at the top of page in your textbook. Write your answers below. a. Examine the exponents of the factors and the exponents of the products in the last column. What do you observe? The exponents of the factors are added to get the exponent of the product. b. Make a conjecture about a rule for determining the exponent of the product when you multiply powers with the same base. Test your rule by multiplying using a calculator. Sample answer: Add the exponents. Lesson - Reading the Lesson. When multiplying powers with like bases, add the exponents.. When dividing powers with like bases, subtract the exponents.. Write a division expression whose quotient is. Sample answer:. Write a multiplication expression whose product is v. Sample answer: v v. Find each product. a. b. y y y c. (x )(x ) 0x d. r r r. Find each quotient. a. b. v v v c. or d. a b Helping You Remember 9 b a. Explain how dividing powers is related to simplifying fractions. Provide an example as part of your explanation. Sample answer: When dividing powers with like bases, subtracting the exponents is equivalent to simplifying fractions. For example, or by the Quotient of Powers rule. When simplifying, divide the numerator and denominator by the GCF,,to get or. Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

39 - Enrichment Dividing Powers with Different Bases Some powers with different bases can be divided. First, you must be able to write both as powers of the same base. An example is shown below. ( ) or To find the power of a power, multiply the exponents. This method could not have been used to divide 9, since 9 cannot be written as a power of using integers. Simplify each fraction using the method shown above. Express the solution without exponents , Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

40 - Study Guide and Intervention Negative Exponents Extending the pattern below shows that = or. 0 This suggests the following definition. a n = a n, for a 0 and any integer n. Example Write each expression using a positive exponent. a. b. y y y Lesson - We can evaluate algebraic expressions with negative exponents using the definition of negative exponents. Example Evaluate b if b. b Replace b with. 9 Find. Definition of negative exponent Exercises Write each expression using a positive exponent... () ( ). b b. n n or n Write each fraction as an expression using a negative exponent other than Evaluate each expression if m, n, and p. 9. p 0. m. (np). m Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

41 - Skills Practice Negative Exponents Write each expression using a positive exponent () ( ). (0) ( 0). () ( ). n 0 n 0. b b 9. q q 0. m m. v v. p p Write each fraction as an expression using a negative exponent other than Evaluate each expression if x, y, and z.. y z. z 9. x. y 9. z 0. y. z. z. x99. z. z. yz Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

42 - Practice Negative Exponents Write each expression using a positive exponent () ( ). () 0 ( ) 0. m m. () ( ). c c 9. p p 0. g g. z z. t t Write each fraction as an expression using a negative exponent m 9. x 0. x a a. 9 m Lesson Evaluate each expression if x, y, and z.. x. y. y. z 9. y 0. 0 y 00. z. zy. (xz). HAIR Hair grows at a rate of inch per day. Write this number using negative exponents. or or Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

43 - Reading to Learn Mathematics Negative Exponents Pre-Activity How do negative exponents represent repeated division? Do the activity at the top of page in your textbook. Write your answers below. a. Describe the pattern of powers in the first column. Continue the pattern by writing the next two powers in the table. The exponents decrease by ; 0,. b. Describe the pattern of values in the second column. Then complete the second column. Each number is divided by ;,. c. Verify that the powers you wrote in part a are equal to the values that you found in part b. See students work. d. Determine how should be defined. Reading the Lesson. Explain the value of using a pattern. Sample answer: The value in each row is the previous value divided by, so is. Power Value 0. Using what you know about the Quotient of Powers rule, fill in the missing number.? = Helping You Remember. Are x and x equivalent? Explain. Sample answer: No; let x =. = 9, but 9. Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

44 - Enrichment Proving Definitions of Exponents Recall the rules for multiplying and dividing powers with the same base. Use these rules, along with other properties you have learned, to justify each definition. Abbreviations for some properties you may wish to use are listed below. Associative Property of Multiplication (APM) Additive Identity Property (AIP) Multiplicative Identity Property (MIP) Inverse Property of Addition (IPA) Inverse Property of Multiplication (IPM) Write the reason for each statement.. Prove: a 0 Statement Let m be an integer, and let a be any nonzero number. a m a 0 a m 0 a m a 0 a m a m (am a 0 ) a m am a m am a0 a m am a 0 a 0 Reason a. Given b. Product of Powers c. IPA d. Mult. Prop. Equality e. APM f. IPM g. MIP Lesson -. Prove: a n a n Statement Let n be an integer, and let a be any nonzero number. a n a n a n n a n a n a 0 a n a n (a n a n ) a n a n a n an a n an a n a n a n a n Reason a. Given b. Product of Powers c. IPA d. Def. Zero Exponents e. Mult. Prop. Equality f. APM g. IPM h. MIP Glencoe/McGraw-Hill 99 Glencoe Pre-Algebra

45 - Study Guide and Intervention Scientific Notation When you deal with very large numbers like,000,000 or very small numbers like 0.000, it is difficult to keep track of place value. Numbers such as these can be written in scientific notation. A number is expressed in scientific notation when it is written as a product of a factor and a power of 0. The factor must be greater than or equal to and less than 0. By definition, a number in scientific notation is written as a 0 n, where a 0 and n is an integer. Example a.. 0 Express each number in standard form.. 0,000 Move the decimal point places to the right. b Move the decimal point places to the left. Example a.,000,00 Express each number in scientific notation. To write in scientific notation, place the decimal point after the first nonzero digit, then find the power of 0.,000, The decimal point moves places. The power of 0 is. b Place the decimal point after the first nonzero digit. The power of 0 is. Exercises.. 0,0, , Express each number in scientific notation..,000,000, , Choose the greater number in each pair...9 0, , , ,. 0 Glencoe/McGraw-Hill 00 Glencoe Pre-Algebra

46 - Skills Practice Scientific Notation Express each number in standard form , ,9, ,000, ,900, ,00.. 0, , ,,000 Express each number in scientific notation..,000, , , ,000,000, ,00. 0.,0, ,, Lesson - Choose the greater number in each pair... 0, , , , , , 9 Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

47 - Practice Scientific Notation Express each number in standard form... 0, ,0, ,000, ,00,000, ,000, , Express each number in scientific notation.. 0, ,000, ,000, , ,000,000,000, NIAGARA FALLS For Exercises and, use the following information. Every minute, 0,000,000,000 drops of water flow over Niagara Falls.. Write this number in scientific notation.. 0. How many drops flow over the falls in a day?.09 0 Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

48 - Reading to Learn Mathematics Scientific Notation Pre-Activity Why is scientific notation an important tool in comparing real-world data? Reading the Lesson Do the activity at the top of page in your textbook. Write your answers below. a. Write the track length in millimeters.,000,000 mm b. Write the track width in millimeters. ( micron 0.00 millimeter) mm Write a definition and give an example of the new vocabulary phrase.. Vocabulary Definition Example slope intercept form See students work.. To multiply by a power of 0, move the decimal point to the right if the exponent is positive.. Which is larger,. 0 or. 0? Explain.. x 0 is larger, since the numbers are negative and it is closer to zero. Lesson - Helping You Remember. Explain how to express each number in scientific notation. a. a number greater than Place the decimal point after the first nonzero digit, then multiply by the appropriate positive power of 0. b. a number less than one Place the decimal point after the first nonzero digit, then multiply by the appropriate negative power of 0. c. the number Place the decimal point after the, then multiply by 0 0 (.0 x 0 0 ). Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

49 - Enrichment Scientific Notation It is sometimes necessary to multiply and divide very large or very small numbers using scientific notation. To multiply numbers in scientific notation, use the following rule. For any numbers a and b, and any numbers c and d, (c 0 a )(d 0 b ) (c d) 0 a b. Example (.0 0 )(.0 0 ) [.0 (.0)] 0 () or 00 To divide numbers in scientific notation, use the following rule. For any numbers a and b, and any numbers c and d, (d 0) (c 0 a ) (d 0 b ) (c d) 0 a b. Example ( 0 ) (. 0 ) (.) or Multiply or divide. Express each product or quotient in scientific notation.. (. 0 9 ) (. 0 ). 0. (. 0 ) (. 0 ).9 0. (. 0 ) (. 0 ).0 0. (.9 0 ) (.0 0 ). 0. (. 0 ) (9.9 0 ) ( ) (.0 0 ).0 0 Solve. Write your answers in standard form.. The distance from Earth to the Moon is about.0 0 miles. The distance from Earth to the Sun is about 9. 0 miles. How many times farther is it to the Sun than to the Moon?. If each of the.0 0 people employed by Sunny Motors earned.0 0 dollars last year, how much money did the company pay out to its employees? $,00,000,000 Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

50 NAME DATE PERIOD Chapter Test, Form SCORE Write the letter for the correct answer in the blank at the right of each question.. Use divisibility rules to determine which number is a factor of 9. A. B. C. D. 0.. Determine which expression is not a monomial. A. B. x C. x D. k.. Write ()()() using exponents. A. B. C. D... Evaluate k if k. A. B. C. D... Write the prime factorization of. A. 9 B. C. D... Factor x y completely. A. x x y B. x x y C. x y y D. x y. For Questions and, find the GCF of each set of numbers or monomials.., 0 A. B. C. 0 D..., A. B. C. D.. Assessment 9. Factor b. A. (b ) B. (b ) C. (b ) D. b( ) 9. For Questions 0 and, write each fraction in simplest form. 0. A. B. C. D. 0.. a a A. B. a C. a a D.. a Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

51 NAME DATE PERIOD Chapter Test, Form (continued). Eight inches is what part of foot? A. 9 B. C. D.. Find each product.. A. B. C. 0 D... m m A. m B. m C. m D. m. For Questions and, find each quotient.. A. B. C. D... t t A. B. t C. t D. t.. Write using a negative exponent. A. B. C. D... Evaluate y if y. A. B. C. D.. 9. The speed of light is 00,000,000 meters per second. Express this number in scientific notation. A B C..0 0 D Choose the true statement. A B C D Bonus Dyenitha is renting tables for her wedding reception. B: She can choose from tables that seat or. If she is expecting people and wants the same number of people at each table, which size table should she order? Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

52 NAME DATE PERIOD Chapter Test, Form A SCORE Write the letter for the correct answer in the blank at the right of each question.. Use divisibility rules to determine which number is a factor of. A. B. 0 C. D... Determine which expression is not a monomial. A. xyz B. (x y) C. D. u.. Write ( y)( y)( y)( y)( y) using exponents. A. y B. y C. y D. y.. Evaluate m if m. A. B. 0 C. D... Write the prime factorization of. A. 9 B. C. D... Factor 0x y completely. A. x x y B. x y C. x x y D. 0 x x y.. Find the GCF of x and x. A. 90x B. x C. 90x D. x.. Factor 0y. A. y( ) B. ( 0y) C. ( y) D. y( y). For Questions 9 and 0, write each fraction in simplest form. Assessment 9. A. B. C. D ab 0ab A. a b b B. C. ab a a b D. b 0.. Twenty centimeters is what part of a meter? A. B. C. D Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

53 NAME DATE PERIOD Chapter Test, Form A (continued) Find each product.. A. B. C. D... x x A. 9x B. 9x C. 0x D. 0x. For Questions and, find each quotient.. m m A. m B. C. m D... A. B. C. D... Write as an expression using a negative exponent. A. B. C. D.. For Questions and, evaluate each expression if a and b.. b. a A. B. 9 C. D.. A. B. C. D.. 9. A red blood cell is about. 0 centimeter long. Express this number in standard form. A B C. 00 D Choose the number that is greater than. 0. A.,000 B.. 0 C.. 0 D Bonus Order the planets in Planet Diameter (mi) B: the table at the right from least to greatest diameter. Venus Uranus Neptune Earth Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

54 NAME DATE PERIOD Chapter Test, Form B SCORE Write the letter for the correct answer in the blank at the right of each question.. Use divisibility rules to determine which number is a factor of 0. A. B. C. D. 0.. Determine which expression is not a monomial. A. (x y) B. xyz C. D. w.. Write (m)(m)(m)(m) using exponents. A. m B. m C. m D. m.. Evaluate m if m. A. B. C. D... Write the prime factorization of. A. B. C. D... Factor xy completely. A. x y y B. x y y C. x y y D. x y.. Find the GCF of x and x. A. x B. x C. x D. x.. Factor y. A. ( y) B. ( y) C. ( y) D. (y). Assessment For Questions 9 and 0, write each fraction in simplest form. 9. A. B. C. D a 0a A. B. a C. 0 a 0 D. 0.. Twenty-five centimeters is what part of a meter? A. B. C. D. 0. Glencoe/McGraw-Hill 09 Glencoe Pre-Algebra

55 NAME DATE PERIOD Chapter Test, Form B (continued) Find each product A B. 0 C. 0 D (y )(y ) A. y B. 9y C. y D. 9y. For Questions and, find each quotient.. x x A. B. C. x D. x.. ( ) ( ) A. B. C. () D. ().. Write as an expression using a negative exponent. A. B. C. D.. For Questions and, evaluate each expression if s and t.. t A. B. 9 C. 9 D.. 9. A. B. C. D.. 9. Bacteria are among the smallest living things. Some of the largest bacteria measure. 0 inch across. Express this number in standard form. A B.,000 C D Choose the number that is less than. 0. A.. 0 B.. 0 C.,000 D Bonus Order the planets in the table at the right from least to greatest diameter. Planet Saturn Uranus Jupiter Neptune Diameter (mi) B: Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

56 NAME DATE PERIOD Chapter Test, Form C SCORE Use divisibility rules to determine whether each number is divisible by,,,, or For Questions and, determine whether each expression is a monomial.. 0m(n ).. 9b(e).. Write ()()()()() using exponents... Evaluate a if a.. Write the prime factorization of each number or monomial.... a x. For Questions 9 and 0, find the GCF of each set of numbers or monomials. 9. 0,, y, 0y 0. Assessment. Factor b 9.. For Questions and, write each fraction in simplest form r. 0r. Forty minutes is what part of an hour?. Glencoe/McGraw-Hill Glencoe Pre-Algebra

57 NAME DATE PERIOD Chapter Test, Form C (continued) Find each product. Express using exponents.. m m.. (x y)(y). Find each quotient. Express using exponents.. ( ) ( ).. b. b For Questions 9 and 0, write each expression using a negative exponent other than Evaluate b if b... Express.09 0 in standard form... Scientists have discovered that many mammals can expect. to live for. billion heartbeats. Write this number in scientific notation.. The distance between Saturn and Mars is. 0 miles.. The distance between Mars and Mercury is. 0 miles. Is Mars closer to Saturn or to Mercury?. David is packing bundles of -inch-by--inch cards, face up,. into a square box. He places the cards side-by-side so that there is no wasted space. Find the smallest possible measure for the edge of the box. Bonus Write the prime factorization of. Use exponents B: for repeated factors. Glencoe/McGraw-Hill Glencoe Pre-Algebra

58 NAME DATE PERIOD Chapter Test, Form D SCORE Use divisibility rules to determine whether each number is divisible by,,,, or For Questions and, determine whether each expression is a monomial.. 9k(p ).. a(c).. Write ()()()()()() using exponents... Evaluate y if y.. Write the prime factorization of each number or monomial.... p x. For Questions 9 and 0, find the GCF of each set of numbers or monomials. 9. 0, 0, 9. Assessment 0. x,x 0.. Factor 0a.. Write each fraction in simplest form.... a. 0a. Forty-five seconds is what part of a minute?. Glencoe/McGraw-Hill Glencoe Pre-Algebra

59 NAME DATE PERIOD Chapter Test, Form D (continued) Find each product. Express using exponents.. d d.. (x y)(y). Find each quotient. Express using exponents.. ( ) ( ).. a. a For Questions 9 and 0, write each expression using a negative exponent other than Evaluate a if a... Express. 0 in standard form... The number of different hands possible in the game of. bridge is about billion. Write this number in scientific notation.. The number of neurons in the neocortex of the human. brain is The neocortex of a gorilla contains. 0 neurons. Which mammal has more neurons?. Scott is packing bundles of -inch-by--inch cards, face up,. into a square box. He places the cards side-by-side so that there is no wasted space. Find the smallest possible measure for the edge of the box. Bonus Write the prime factorization of. Use exponents B: for repeated factors. Glencoe/McGraw-Hill Glencoe Pre-Algebra

60 NAME DATE PERIOD Chapter Test, Form SCORE Use divisibility rules to determine whether each number is divisible by,,,, or ,0..,. Determine whether each expression is a monomial. Explain why or why not.. a b.. (x)(y).. k(p ).. 9c d(c ). Write each expression using exponents.. x x y. 9. ( d) ( d) 9. Evaluate each expression if a, b, and c. 0. a b 0.. (a c). Assessment Determine whether each number is prime or composite..... Factor each number or monomial completely qr s. Find the GCF of each set of numbers or monomials..,, 9.. a c,0a b. Glencoe/McGraw-Hill Glencoe Pre-Algebra

61 NAME DATE PERIOD Chapter Test, Form (continued) Factor each expression.. x x. 9. y 9. For Questions 0 and, write each fraction in simplest form. If already in simplest form, write simplified p. 9pq.. Forty-four feet is what part of a mile?.. Twelve inches is what part of one yard?. For Questions, find each product or quotient. Express using exponents.. (x )(x ).. (s t)(st ). a b. b a.. m m m.. Write using a negative exponent other than.. Evaluate each expression if a, b, and c. 9. (b )( c ) (bc) 0.. Express.0 0 in standard form... To find how many seconds it takes light to travel from the. Sun to Earth, divide the total distance, 9,000,000 miles, by the distance light travels in one second,,000 miles. Write the result in scientific notation... Order. 0,0.0,.0 0,0.000, and.0 0 from least to greatest. Bonus Write all of the prime numbers between and 0. B: Glencoe/McGraw-Hill Glencoe Pre-Algebra

62 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 problem.. Methods of finding prime numbers have intrigued mathematicians for years. For example, Goldbach s conjecture states that every even number greater than can be written as the sum of two prime numbers. Choose three even numbers greater than 0 and less than 00. Write each as the sum of two prime numbers.. Write an argument or counterexample to support your answers to the following questions. a. Are all numbers that are divisible by 9 also divisible by? b. Are all numbers that are divisible by also divisible by 9?. The Warrior High School band and drill team have been invited to participate in the Thanksgiving parade. There are 0 members in the band and 0 members in the drill team. a. Can the band march in a rectangular formation having band members in each row? Why or why not? If not, give an example of a rectangular formation that would be possible. b. Twenty-six drill team members and 0 band members turned in their permission slips for the Thanksgiving trip. Explain how to tell whether a greater fractional part of the drill team or band turned in their slips. Find which part is greater.. To understand mathematics, you must understand the language or symbols used. a. Explain the difference in the meanings of a and a. b. Explain the difference in the meanings of b and b. Assessment Glencoe/McGraw-Hill Glencoe Pre-Algebra

63 NAME DATE PERIOD Chapter Vocabulary Test/Review SCORE algebraic fraction base base two binary divisible expanded form exponent factor greatest common factor (GCF) monomial power prime number scientific notation simplest form Venn diagram Write the letter of the term that best matches each statement or phrase.. shows relationships among sets of numbers or objects using overlapping circles in a rectangle. a whole number with exactly two factors, and itself. tells how many times a number is used as a factor. GCF of the numerator and denominator is. ( 0 ) ( 0 ) ( 0 ) ( 0 0 ). language that uses a base two system of numbers. a number, variable, or product of numbers and/or variables a. power b. binary c. exponent d. Venn diagram e. monomial f. GCF g. expanded form h. simplest form i. prime number. the greatest number that is a factor of two or more numbers 9. a number that is expressed using an exponent In your own words Define each term. 0. scientific notation. base. algebraic fraction Glencoe/McGraw-Hill Glencoe Pre-Algebra

64 NAME DATE PERIOD Chapter Quiz (Lessons and ) SCORE Use divisibility rules to determine whether each number is divisible by,,,, or Determine whether each expression is a monomial. Explain why or why not... xy. x y. Write each expression using exponents.. x x x.. (9 9 9) (9 9). Evaluate each expression if x, a, and b. 9. x a b NAME DATE PERIOD Chapter Quiz (Lessons and ) Write the prime factorization of each number. Use exponents for repeated factors SCORE Assessment Factor each monomial completely.. b... 0x y. Find the GCF of each set of numbers or monomials..,.. 0, 0, 0.. x,x. Factor each expression. 9. a y 0. Glencoe/McGraw-Hill 9 Glencoe Pre-Algebra

65 NAME DATE PERIOD Chapter Quiz (Lessons and ) SCORE Write each fraction in simplest form. If the fraction is already in simplest form, write simplified x 0x. Fifteen centimeters is what part of a meter?. Standardized Test Practice Which fraction is r r written in simplest form? r A. B. r C. D. r r Find each product or quotient. Express using exponents... x x x. (x )(x ) 9. ( ) ( ) 0. x x NAME DATE PERIOD Chapter Quiz (Lesson and ) SCORE Write each expression using a positive exponent... y Evaluate each expression if x and y.. x. (xy) Write each number in scientific notation ,000,000.,000,000,000 Choose the greater number in each pair... 0, , The table at the right shows the masses of three subatomic particles. Write the names of the particles in order from least to greatest mass. Particle electron neutron proton Mass Glencoe/McGraw-Hill 0 Glencoe Pre-Algebra

66 NAME DATE PERIOD Chapter Mid-Chapter Test (Lessons through ) SCORE Part I Write the letter for the correct answer in the blank at the right of each question.. Determine which expression is not a monomial. A. 9(a b) B. 9x yz C. D. k.. Evaluate x if x. A. B. C. D... Write the prime factorization of. A. B. C. D... Factor b. A. (b ) B. (b ) C. b( ) D. ( b).. Factor y. A. y B. ( y) C. 0y D. y( ).. Choose the number that is prime. A. B. C. D. 9. Part II. Determine whether is divisible by,,,, or 0... Write ()()()()() using exponents.. Factor each number or monomial completely Assessment 0. x y 0. In Questions and, find the GCF of each set of numbers or monomials..,.. 0x,x.. Amy raised chickens for her -H project. The chickens have. laid 0 eggs. Does Amy have enough eggs to completely fill cartons that contain eggs each? Why or why not? Glencoe/McGraw-Hill Glencoe Pre-Algebra

67 NAME DATE PERIOD Chapter Cumulative Review (Chapters ). State the domain and range of the relation. {(., ), (,.), (.,.)}. (Lesson ). Determine whether a scatter plot of the outside temperatures. and the corresponding air conditioning bills might show a positive, negative, or no relationship. Explain your answer. (Lesson ) For Questions and, simplify each expression... m (m). 9x (x). (Lesson ) (Lesson ). Evaluate h if h and k. (Lesson ). k. Find the average (mean) of,,, 9,. (Lesson ).. Name the quadrant in which the graph of (, ) lies.. (Lesson ). When you divide a number by 9, the result is.. Write and solve an equation to find the number. (Lesson ) Graph the solution of each equation on a number line. 9. y (Lesson ) z (Lesson ) 0. 0 For Questions and, evaluate each expression if n and r.. n (Lesson ).. r (Lesson ).. Write the prime factorization of. (Lesson ).. Factor 0abc completely. (Lesson ). For Questions and, find the GCF of each set of numbers or monomials..,, 90 (Lesson ).. r s t,r t (Lesson ).. Factor y. (Lesson ). Glencoe/McGraw-Hill Glencoe Pre-Algebra

68 NAME DATE PERIOD Standardized Test Practice (Chapters ) Part : Multiple Choice Instructions: Fill in the appropriate oval for the best answer.. Lenora wants to buy a CD player that costs $9 (including tax). She has $0 in the bank, she earns $0 babysitting, $ taking care of a neighbor s pet, and receives $ in allowance. How much more money does she need to buy the CD player? (Lesson ) A. $ B. $ C. $ D. none. A B C D. Simplify (k ) 9k. (Lesson ) E. k F. 0k G. k H. k. E F G H. Simplify ()(a)(b). (Lesson ) A. ab B. ab C. ab D. ab. A B C D. Evaluate the expression x if x 0 and y. (Lesson ) y E. F. G. H.. E F G H. Name the ordered pair for the point A graphed on the coordinate plane at the right. (Lesson ) A. (, ) B. (, ) C. (, ) D. (, ).. In the school cafeteria, an apple costs a cents and a carton of milk costs 0 cents. Which expression represents the total cost of an apple and cartons of milk for s students? (Lesson ) A E. a 0 s F. s(a 0) G. sa 0 H. s(a 0). O y x A E B F C G D H Assessment. Wanda drove for w hours on a trip. Her husband drove hours more than Wanda. Which expression represents the total time they spent driving? (Lesson ) A. w B. w C. w D. w. A B C D. If z 9, find the numerical value of z. (Lesson ) E. F. G. H.. E F G H 9. Nine more than eight times a number is. Translate this sentence into an equation. (Lesson ) A. n 9 B. 9n C. (n 9). D. 9( n) 9. A B C D 0. The formula d rt can be rewritten as (Lesson ) t E. dr t. F. r. G. t d d r. H. r dt. 0. E F G H Glencoe/McGraw-Hill Glencoe Pre-Algebra

69 NAME DATE PERIOD Standardized Test Practice (continued). Choose the expression that is not a monomial. (Lesson ) A. (k )(9m) B. r s s C. 9xy D.. c A B C D. Write (a)(a)(a)(b)(b) using exponents. (Lesson ) E. a b F. a b G. a b H. a b. E F G H. Write the prime factorization of. (Lesson ) A. B. C. D.. A B C D. Find the GCF of and. (Lesson ) E. F. G. H.. E F G H. Simplify c c A. c. (Lesson ) B. c C. c D. c. A B C D. Which is written with a negative exponent? (Lesson ) E. F. G. H.. 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.. The end zone of a football field is 0 feet wide.. and 0 feet long. What is its area in / / square feet? (Lesson )..... What is the least -digit number that is divisible by and? (Lesson ) / / Part : Short Response Instructions: Write your answer in the blank at the right of each question. 9. Order the integers {,,,, 0,, } from least to 9. greatest. (Lesson ) 0. Saturn is about 99,00,000 miles from Earth. Write this 0. number in scientific notation. (Lesson ) Glencoe/McGraw-Hill Glencoe Pre-Algebra