California math triumphs fractions and decimals volume 2a

Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Lori Adamski Peek/Getty images Photo Credits Cover, i Lori Adamski Peek/Getty images; iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo; v (L to R 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo; vii Roy Ooms/Masterfile; viii Daryl Benson/Masterfile; ix Jeremy Woodhouse/Masterfile; x Daryl Benson/Masterfile; 2–3 Larry Dale Gordon/Getty Images; (t)Michael Houghton/StudiOhio, United States coin images from the United States Mint, (bl)Burke/Triolo Productions/FoodPix/Jupiter Images, (br)Burke/Triolo Productions/FoodPix/Jupiter Images; (t)Matthias Kulka/zefa/CORBIS, (b)Comstock Images/Alamy; (l)Dorling Kindersley/Getty Images, (r)Stockdisc/ PunchStock; (t)David Woolley/Getty Images, (bl bcl)Getty Images, (bcr br)CORBIS; Bonhommet/PhotoCuisine/CORBIS; 11 Envision/CORBIS; 23 Getty Images; 32–33 Boden/Ledingham/Masterfile; 33 (t)Michael Houghton/ StudiOhio, (b)Mark Ransom/RansomStudios; 40 (l)Guy Grenier/Masterfile, (r)David Young-Wolff/Photo Edit; 41 Envision/CORBIS; 49 Bonhommet/ PhotoCuisine/CORBIS; 59 Envision/CORBIS; 66 Getty Images; 69 Envision/ CORBIS; 76 CORBIS; 83 Eri Morita/Getty Images Copyright © 2008 by The McGraw-Hill Companies, Inc All rights reserved Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without prior permission of the publisher Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-07-878205-3 MHID: 0-07-878205-8 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 2A California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction 1B Chapter Multiplication 1B Chapter Division 1B Chapter Integers Volume Fractions and Decimals 2A Chapter Parts of a Whole 2A Chapter Equivalence of Fractions 2B Chapter Operations with Fractions 2B Chapter Positive and Negative Fractions and Decimals Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Volume Ratios, Rates, and Percents 3A Chapter Ratios and Rates 3A Chapter Percents, Fractions, and Decimals 3B Chapter Using Percents 3B Chapter Rates and Proportional Reasoning Volume The Core Processes of Mathematics 4A Chapter Operations and Equality 4A Chapter Math Fundamentals 4B Chapter Math Expressions 4B Chapter Linear Equations 4B Chapter Inequalities Volume Functions and Equations 5A Chapter Patterns and Relationships 5A Chapter Graphing 5B Chapter Proportional Relationships 5B Chapter The Relationship Between Graphs and Functions Volume Measurement 6A Chapter How Measurements Are Made 6A Chapter Length and Area in the Real World 6B Chapter Exact Measures in Geometry 6B Chapter Angles and Circles iii Authors and Consultants AUTHORS Frances Basich Whitney Kathleen M Brown Dixie Dawson Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Math Curriculum Leader Long Beach Unified Long Beach, California Philip Gonsalves Robyn Silbey Kathy Vielhaber Mathematics Coordinator Alameda County Office of Education Hayward, California Math Specialist Montgomery County Public Schools Gaithersburg, Maryland Mathematics Consultant St Louis, Missouri Viken Hovsepian Professor of Mathematics Rio Hondo College Whittier, California Dinah Zike Educational Consultant, Dinah-Might Activities, Inc San Antonio, Texas CONSULTANTS Assessment Donna M Kopenski, Ed.D Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Planning and Support ELL Support and Vocabulary Beatrice Luchin ReLeah Cossett Lent Mathematics Consultant League City, Texas Author/Educational Consultant Alford, Florida iv (tl)File Photo, (tc tr)The McGraw-Hill Companies, (cl c)Doug Martin, (cr)Aaron Haupt, (bl bc)File Photo Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc CONTRIBUTING AUTHORS California Advisory Board CALIFORNIA ADVISORY BOARD Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Glencoe wishes to thank the following professionals for their invaluable feedback during the development of the program They reviewed the table of contents, the prototype of the Student Study Guide, the prototype of the Teacher Wraparound Edition, and the professional development plan Linda Anderson Cheryl L Avalos Bonnie Awes Kathleen M Brown 4th/5th Grade Teacher Oliveira Elementary School, Fremont, California Mathematics Consultant Retired Teacher Hacienda Heights, California Teacher, 6th Grade Math Monroe Clark Middle School San Diego, California Math Curriculum Staff Developer Washington Middle School Long Beach, California Carol Cronk Audrey M Day Jill Fetters Grant A Fraser, Ph.D Mathematics Program Specialist San Bernardino City Unified School District San Bernardino, California Classroom Teacher Rosa Parks Elementary School San Diego, California Math Teacher Tevis Jr High School Bakersfield, California Professor of Mathematics California State University, Los Angeles Los Angeles, California Eric Kimmel Donna M Kopenski, Ed.D Michael A Pease Chuck Podhorsky, Ph.D Mathematics Department Chair Frontier High School Bakersfield, California Math Coordinator K–5 City Heights Educational Collaborative San Diego, California Instructional Math Coach Aspire Public Schools Oakland, California Math Director City Heights Educational Collaborative San Diego, California Arthur K Wayman, Ph.D Frances Basich Whitney Mario Borrayo Melissa Bray Professor Emeritus California State University, Long Beach Long Beach, California Project Director, Mathematics K–12 Santa Cruz County Office of Education Capitola, CA Teacher Rosa Parks Elementary San Diego, California K–8 Math Resource Teacher Modesto City Schools Modesto, California v (L to R 11 12)The McGraw-Hill Companies, (5 10 13 14)File Photo California Reviewers CALIFORNIA REVIEWERS Each California Reviewer reviewed at least two chapters of the Student Study Guides, providing feedback and suggestions for improving the effectiveness of the mathematics instruction Melody McGuire Math Teacher California College Preparatory Academy Oakland, California 6th and 7th Grade Math Teacher McKinleyville Middle School McKinleyville, California Eppie Leamy Chung Monica S Patterson Teacher Modesto City Schools Modesto, California Educator Aspire Public Schools Modesto, California Judy Descoteaux Rechelle Pearlman Mathematics Teacher Thornton Junior High School Fremont, California 4th Grade Teacher Wanda Hirsch Elementary School Tracy, California Paul J Fogarty Armida Picon Mathematics Lead Aspire Public Schools Modesto, California 5th Grade Teacher Mineral King School Visalia, California Lisa Majarian Anthony J Solina Classroom Teacher Cottonwood Creek Elementary Visalia, California Lead Educator Aspire Public Schools Stockton, California vi Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Bobbi Anne Barnowsky Volume 2A Fractions and Decimals Chapter Parts of a Whole 1-1 Parts of a Whole and Parts of a Set 2NS4.0, 4NS1.5 1-2 Recognize, Name, and Compare Unit Fractions 11 2NS4.1 Progress Check .18 1-3 Representing Fractions 19 2NS4.3, 4NS1.7 Assessment Study Guide .26 Chapter Test .28 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Standards Practice 30 Bixby Creek Bridge on Highway 1, south of Carmel Chapters and are contained in Volume 2A Chapters and are contained in Volume 2B Standards Addressed in This Chapter 2NS4.0 Students understand that fractions and decimals may refer to parts of a set and parts of a whole 2NS4.1 Recognize, name, and 1 compare unit fractions from _ to 12 2NS4.3 Know that when all fractional parts are included, such as fourfourths, the result is equal to the whole and to one 4NS1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalence of fractions (see Standard 4.0) 4NS1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line vii Roy Ooms/Masterfile Contents Chapter Equivalence of Fractions Standards Addressed in This Chapter 2-1 Equivalent Fractions and Equivalent Forms of One 34 2NS4.3, 3NS3.1, 4NS1.5 2-2 Mixed Numbers and Improper Fractions 41 2NS4.3, 4NS1.5, 5NS1.5 Progress Check .50 2-3 Least Common Denominator and Greatest Common Factors 51 4NS1.5 2-4 Compare and Order Fractions 59 3NS3.1, 6NS1.1 Progress Check .68 2-5 Simplify Fractions 69 3NS3.1, 4NS1.5 Assessment Chapter Test .82 Standards Practice 84 Alabama Hills, Owens Valley viii Daryl Benson/Masterfile 3NS3.1 Compare fractions represented by drawings or concrete materials to show equivalency and to add and subtract simple fractions in context (e.g., of a 2 pizza is the same amount as of another pizza that is the same size; show that is larger than ) 4NS1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain the equivalence of fractions (see Standard 4.0) 5NS1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers 6NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Study Guide .77 2NS4.3 Know that when all fractional parts are included, such as fourfourths, the result is equal to the whole and to one Contents Chapter Operations with Fractions 3-1 Add Fractions with Like Denominators .4 3NS3.2, 6NS2.1 3-2 Subtract Fractions with Like Denominators .11 3NS3.2, 6NS2.1 Progress Check .18 3-3 Multiply Fractions 19 5NS2.0, 5NS2.5, 6NS2.1 3-4 Divide Fractions 25 5NS2.5, 6NS2.1 Progress Check .32 3-5 Add Fractions with Unlike Denominators 33 3NS3.2, 5NS2.0, 6NS2.1 3-6 Subtract Fractions with Unlike Denominators 39 3NS3.2, 5NS2.0, 6NS2.1 Chapters and are contained in Volume 2A Chapters and are contained in Volume 2B Standards Addressed in This Chapter 3NS3.2 Add and subtract simple fractions (e.g., determine that + is the 8 same as ) 5NS2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals 5NS2.5 Compute and perform simple multiplication and division of fractions and apply these procedures to solving problems 6NS2.1 Solve problems involving addition, subtraction, multiplication, and division of positive fractions and explain why a particular operation was used for a given situation Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Progress Check .45 Assessment Study Guide .46 Chapter Test .50 San Diego Harbor Standards Practice 52 ix Jeremy Jeremy Woodhouse/Masterfile Woodhouse/Masterfile Contents Chapter Positive and Negative Fractions and Decimals 4-1 Introduction to Decimals .56 3NS3.4, 4NS1.6, 4NS1.7 4-2 Decimals and Money 63 2NS5.1, 2NS5.2 Progress Check .72 4-3 Compare and Order Decimals 73 5NS1.5, 6NS1.1 4-4 Compare and Order Fractions and Decimals 81 5NS1.5, 6NS1.1, 4NS1.7 Progress Check .88 4-5 Add Decimals 89 4NS2.0, 5NS2.0, 5NS2.1, 7NS1.2 4-6 Subtract Decimals 97 4NS2.0, 5NS2.0, 5NS2.1, 7NS1.2 Progress Check 104 5NS2.0, 5NS2.1, 7NS1.2 4-8 Divide Decimals 113 5NS2.0, 5NS2.1, 7NS1.2 Progress Check 120 4-9 Operations with Positive and Negative Numbers 121 4NS1.8, 5NS2.1, 6NS2.3, 7NS1.2 Assessment Study Guide 128 Chapter Test 134 Standards Practice 136 Antelope Valley x Daryl Benson/Masterfile 3NS3.4 Know and understand that fractions and decimals are two different representations of the same concept (e.g., 50 cents is of a dollar, 75 cents is of a dollar) 4NS1.6 Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (e.g., _ = 0.5 or 0.50; = 1_ = 1.75) 4 4NS1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line 2NS5.1 Solve problems using combinations of coins and bills 2NS5.2 Know and use the decimal notation and the dollar and cent symbols for money 5NS1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative integers 6NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line 4NS2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple decimals 5NS2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication and division of fractions and decimals 7NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers 5NS2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive integers from negative integers; and verify the reasonableness of the results 4NS1.8 Use concepts of negative numbers (e.g., on a number line, in counting, in temperature, in “owing”) 6NS2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations, that use positive and negative integers and combinations of these operations Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc 4-7 Multiply Decimals .105 Standards Addressed in This Chapter Step by Step Practice 12 in simplest form Use prime factorization Write _ 16 Step Write the numerator as a product of prime numbers Step Write the denominator as a product of prime numbers 16 12 4 Step Replace the numerator with its prime factors Replace the denominator with its prime factors Find and eliminate all equivalent forms of · · · · = _ = · 12 is Step The simplest form of _ 16 Copyright © by The McGraw-Hill Companies, Inc Write each fraction in simplest form Use prime factorization · · · · 12 = _ = _ 30 10 _ 15 15 _ 18 Write each fraction in simplest form Divide by the GCF 10 24 _ 10 _ 25 32 21 _ 11 21 _ 28 49 GO ON Lesson 2-5 Simplify Fractions 73 Step by Step Problem-Solving Practice Problem-Solving Strategies Solve 12 LANDSCAPING Doris wants a border around her flower bed She can choose brown or red bricks of the same size If she uses brown bricks, she will use 54 of the 72 brown bricks she has Write the fraction of the brown bricks she will use in simplest form Understand Look for a pattern ✓ Use logical reasoning Solve a simpler problem Work backward Draw a diagram Read the problem Write what you know She would use of the brown bricks Plan Pick a strategy One strategy is to use logical reasoning Simplify the fraction that shows how many brown bricks she would use Solve Find the GCF of 54 and 72 Divide the numerator and denominator by the GCF Factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 ÷ = _ = ÷ Check Use another method Use prime factorization Simplify the fraction Does your answer make sense? Did you answer the question? 74 Chapter Equivalence of Fractions Copyright © by The McGraw-Hill Companies, Inc Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 13 James and Nat run on the track after school each day 18 16 James runs _ of a mile in minutes Nat runs _ of a mile in 27 24 the same time James says he ran faster Is he correct? Explain FITNESS Check off each step Understand Plan Solve Check 14 SCHOOL Omar correctly answered 54 out of 60 questions on his last test What fraction of the questions did he answer correctly? Simplify your answer to its simplest form What fraction of the questions did he answer incorrectly? Simplify your answer to its simplest form Explain which method used for simplifying fractions you prefer and why Copyright © by The McGraw-Hill Companies, Inc 15 Skills, Concepts, and Problem Solving Write each fraction in simplest form Use models Shade an equivalent area and name the simplified fraction 16 = 17 _ = 12 Write each fraction in simplest form Use the GCF 18 36 _ = 60 19 32 _ = 40 20 60 = 144 21 45 _ = 90 GO ON Lesson 2-5 Simplify Fractions 75 Write each fraction in simplest form Use prime factorization 22 18 _ = 27 23 25 _ = 24 30 16 _ = 48 25 27 = _ 39 Solve 26 FOOD Ti took 48 cookies to a picnic He brought cookies home Write the fraction of cookies that were eaten in simplest form 27 SPORTS Mario and Byron are playing a game where they each get 10 chances to throw a basketball into a hoop After of the balls they throw playing games, they both make How many throws they each make? Vocabulary Check sentence Write the vocabulary word that completes each 28 A fraction in is a fraction in which the numerator and the denominator have no common factor greater than 29 The is the greatest number that divides evenly into two or more numbers 30 Writing in Math Spiral Review Find the LCM of each set of numbers 31 2, 10, and 25 Solve 33 76 Corbis (Lesson 2-4, p 59) 32 2, 3, and (Lesson 2-3, p 51) A potato soup recipe needs cups of milk A cups of milk broccoli soup recipe needs Which recipe requires more milk? COOKING Chapter Equivalence of Fractions Copyright © by The McGraw-Hill Companies, Inc Suppose that you had a fraction that had a 12x What you think this fraction is in symbol in it, such as 15x simplest form? Explain your reasoning The boys each made of the baskets attempted Chapter Study Guide Vocabulary and Concept Check common denominators, p 59 composite numbers, p 51 equivalent forms of one, p 34 Write the vocabulary word that completes each sentence The least common multiple of the denominators (bottom numbers) of two or more fractions is the The is the least whole number greater than that is a common multiple of two or more numbers A(n) is any whole number with exactly two factors, and itself equivalent fractions, p 34 greatest common factor (GCF), p 51 improper fraction, p 41 least common denominator (LCD), p 51 least common multiple (LCM), p 51 prime factorization, p 51 The greatest number that is a factor of two or more numbers is known as the A fraction is in when the numerator and the denominator have no common factor greater than prime number, p 51 simplest form, p 69 value, p 34 Copyright © by The McGraw-Hill Companies, Inc = is an example of mixed number, p 41 Label each diagram below Write the correct vocabulary term in each blank Chapter Study Guide 77 Lesson Review 2-1 Equivalent Fractions and Equivalent Forms of One (pp 34–40) Complete to name an equivalent fraction Example 10 Complete to name an equivalent fraction = 11 _1 = _2 Ask yourself, “What can I multiply the denominator by to get 8”? = Multiply by to get Multiply the fraction by · 1 = = · 42 = So, Mixed Numbers and Improper Fractions Name two equivalent fractions 12 13 (pp 41–49) Example _2 as an improper fraction Write Multiply × Add 12 + Write the total number of fourths as an improper fraction 14 as an improper fraction Write 15 73 Write _ as a mixed number 78 Chapter Study Guide · + 12 + 14 = _ = _ 4 Copyright © by The McGraw-Hill Companies, Inc 2-2 2-3 Least Common Denominator (LCD) and Greatest Common Factors (pp 51–58) Find the least common multiple (LCM) of each set of numbers 16 2, 4, and 17 2, 5, and 18 9, 8, and 36 19 4, 26, and 52 Example Find the least common multiple (LCM) of 3, 4, and List the multiples of each number Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, … Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, … Multiples of 6: 6, 12, 18, 24, … Find the numbers that are common in all three lists The least of these numbers is the LCM Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, … Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, … Multiples of 6: 6, 12, 18, 24, … The LCM of 3, 4, and is 12 Copyright © by The McGraw-Hill Companies, Inc Find the greatest common factor (GCF) of each set of numbers 20 14 and 70 21 20 and 75 22 48 and 80 23 45 and 120 Example Find the greatest common factor (GCF) of 32 and 56 by using prime factors 32 56 2 2 2 The common factors are 2, 2, and So, the GCF of 32 and 56 is × × or Chapter Study Guide 79 2-4 24 and Use to compare Shade the models given _1 25 _2 and Use to compare Rename the fractions using a common denominator _1 26 Compare and Order Fractions (pp 59–67) _2 11 Order the fractions , , and _ 12 from least to greatest Example _ Use to compare and Shade the models given The circle on the left has four sections Use it to model Shade sections The circle on the right has five sections Shade sections Use it to model Compare the shaded areas 3 C < B = D + 84 G J Chapter Standards Practice , , B , , D _ Rachel finished of her homework before dinner Her sister Sonia finished of her homework before dinner Which math sentence is correct? 6 < 4 > H F 8 6 = J Which fraction is equal to the fraction at point C on the number line? 10 H , C ,7 " Which mixed number does the model represent? F , A ,1 < G _ 10 # $ 10 10 % 10 A C B _ 10 D 10 _ Write in simplest form 10 F H 2 G J GO ON Copyright © by The McGraw-Hill Companies, Inc 12 Order these fractions from least to greatest: , , _ Which symbol makes the sentence true? _7 □ _5 10 Copyright © by The McGraw-Hill Companies, Inc 11 Which fraction does the model represent? A C 8 B _ 12 D _ 12 Which shows one-fifth written in fraction form? F 1 H _ 15 G J _ 50 Which fraction is equal to the number at point C on the number line? " 12 # $ 10 10 10 10 10 10 10 10 10 A C _ 12 B D ANSWER SHEET Directions: Fill in the circle of each correct answer A B C D F G H J A B C D F G H J A B C D F G H J A B C D F G H J A B C D 10 F G H J 11 A B C D 12 F G H J Success Strategy If you not know the answer to a question, go on to the next question Come back to the problem, if you have time You might find another question later in the test that will help you figure out the skipped problem Which symbol makes the sentence true? _1 □ _1 12 F > H < G = J + Chapter Standards Practice 85 Index A Answer sheet, 31, 85 ascending order, 59–67 models, 19–25, 34–40, 41–49 ordering, 59–67 simplest form, 69–76 simplifying, 69–76 unit, 11–17 Assessment, 28–29, 82–83 C California Mathematics Content Standards, 4, 11, 19, 34, 41, 51, 59, 69 G N number line, 41–49, 50, 67 Number Sense, 4, 11, 19, 34, 41, 51, 59, 69 numerator, 4–10, 11–17, 19–25, 51–58, 59–67, 69–76 greater than, 59–67 O greatest common factor (GCF), 51–58, 69–76 order, 59–67 I Chapter Preview, 3, 33 order fractions, 59–67 Chapter Test, 28–29, 82–83 common denominators, 51–58, 59–67 improper fraction, 41–49 K compare, 59–67 composite number, 51 Correct the Mistakes, 29, 83 descending order, 59–67 equivalent forms of one, 34–40, 59–67 Progress Check, 18, 50, 68 L least common denominator (LCD), 51–58 least common multiple (LCM), 51–58, 59–67 less than, 59–67 like fractions, 67–69 M equivalent fractions, 34–40, 51–58, 59–67, 69–76 F fraction, 4–10, 11–17, 19–25 common denominators, 51–58, 59–67 comparing, 59–67 equivalent, 34–40, 51–58, 59–67, 69–76 improper fractions, 41–49 least common denominator (LCD), 51–58 like, 59–67 mixed numbers, 41–49 86 Index Problem-Solving See Step-byStep Problem Solving Manipulatives fraction circle, 5, 9, 10, 11, 12, 13, 14, 15, 17, 18, 20, 24, 25, 34, 35, 36, 60, 63, 65, 69, 75, 78, 80, 81 fraction strip (tiles), 3, 5, 6, 7, 9, 11, 13, 14, 15, 16, 19, 20, 22, 34, 35, 43, 60, 63, 65, 75 Math Reasoning See Step-byStep Problem Solving mixed number, 41–49 money, R Real-World Applications baking, 22, 66, 67 baseball, 49 basketball, 57 business, 17, 83 cafeteria, 29 carpentry, 49 cleaning, 40 community service, 23, 49 construction, 39, 83 cooking, 48, 76 crafts, 48 entertainment, 66, 83 farming, 16 finance, 29 fitness, 18, 64, 75 flowers, 56 food, 18, 25, 38, 49, 56, 65, 76 food service, 83 groceries, 67 hobbies, 39, 50, 83 invitations, 49 jobs, 24 Copyright © by The McGraw-Hill Companies, Inc E prime factorization, 51–58 prime number, 51–58 Key Concept, 4, 11, 19, 34, 41, 51, 59, 69 D denominator, 4–10, 11–17, 19–25, 51–58, 59–67, 69–76 P kites, 38 landscaping, 74 manufacturing, 48 money, 55, 56 music, 29 nature, 24 number sense, 47 nutrition, 17, 37, 40 online shopping, pets, 10 population, 58 reading, 16 school, 8, 10, 17, 23, 75 shopping, 10 snacks, sports, 39, 66, 76 weather, 65 words, 10, 18 Reflect, 9, 16, 23, 38, 48, 56, 65, 75 S Standards Practice, 30–31, 84–85 Step-by-Step Practice, 7, 15, 21, 36, 46, 54, 63, 73 Step-by-Step Problem Solving Practice, 8, 16, 22–23, 37–38, 47–48, 55–56, 64–65, 74–75 Draw a diagram, 16, 37, 64 Draw a picture, Use a model, 22 Use logical reasoning, 55, 74 Work backward, 47 V value, 34 Vocabulary, 4, 11, 19, 34, 41, 51, 59, 69 Vocabulary and Concept Check, 26, 77 Vocabulary Check, 10, 17, 25, 40, 49, 57, 66, 76 W Study Guide, 26–27, 77–81 Success Strategy, 31, 85 whole, 4–10 U unit fraction, 11–17 Who is Correct?, 6, 14, 20, 36, 45, 54, 63, 72 whole numbers, 41–48 Writing in Math, 10, 17, 25, 40, 49, 57, 67, 76 simplest form, 69–76 Copyright © by The McGraw-Hill Companies, Inc Spiral Review, 17, 25, 40, 49, 57, 67, 76 Index 87 ... Integers Volume Fractions and Decimals 2A Chapter Parts of a Whole 2A Chapter Equivalence of Fractions 2B Chapter Operations with Fractions 2B Chapter Positive and Negative Fractions and Decimals. .. 10 09 08 07 California Math Triumphs Volume 2A California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction... and are contained in Volume 2A Chapters and are contained in Volume 2B Standards Addressed in This Chapter 2NS4.0 Students understand that fractions and decimals may refer to parts of a set and