Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Photo Credits coins: United States Mint, bills: Michael Houghton/StudiOhio; Cover Lori Adamski Peek/Getty Images; iv (tl bl br) File Photo, (tc tr) The McGraw-Hill Companies, (cl c) Doug Martin, (cr) Aaron Haupt; v (1 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 David Young-Wolff/PhotoEdit; Michael Houghtory/StuiOhio; 11 Stockdisc/ Superstock; 19 Christine Balderas/iStockphoto; 45 Paul Whitten/Photo Researchers,Inc.; 54–55 Michael Newman/PhotoEdit; 60 David Young-Wolff/ PhotoEdit; 110 Suzannah Skelton/iStockphoto; 112 Jeff Greenberg/PhotoEdit; 117 Steve Cole/Getty Images; 119 GK Hart/Vikki Hart/Getty Images; 125 Comstock Images/Alamy; 126 StockTrek/Getty Images; 137 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: 978-0-07-878206 MHID: 0-07-878206-6 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 2B 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 iv Instructional Planning and Support ELL Support and Vocabulary Beatrice Luchin ReLeah Cossett Lent Mathematics Consultant League City, Texas Author/Educational Consultant Alford, Florida 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 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 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 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 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 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 0.39 Combine the models Regroup 10 hundredths as tenth Regroup 10 tenths as Chapter Positive and Negative Fractions and Decimals ⎫ ⎬ ⎭ 90 ⎫ ⎬ ⎭ 1.62 + 0.39 = 2.01 Example Find the sum of 14.17 and 8.3 Write the addends vertically Line up the decimal points 3FHSPVQUFOT BTPOF + 2 Add a zero here so the place values line up 7 Bring down the decimal point to the same place in the sum Add columns from right to left The sum of 14.17 and 8.3 is 22.47 YOUR TURN! Find the sum of 36.8 and 9.52 Write the addends vertically Line up the decimal points + 2 Bring down the decimal point to the same place in the sum Copyright © by The McGraw-Hill Companies, Inc Add from right to left The sum of 36.83 and 9.52 is 46.32 Who is Correct? Find the sum of 54.68 and 13.7 Lok Monsa 54.68 + 13.7 560.5 54.68 × 13.7 749.116 Lawson 54.68 + 13.7 68.38 Circle correct answer(s) Cross out incorrect answer(s) GO ON Lesson 4-5 Add Decimals 91 Guided Practice Add using decimal models 1.45 + 0.75 = 2.20 0.54 0.03 + 0.51 = Step by Step Practice 3 Find the sum of 73.66 and 32.05 Step Write the addends vertically Line up the decimal points Step Bring down the decimal point to the same place in the sum + 6 Place the decimal here Find each sum 1.1 + 0.17 = 1.27 + 1 1 22.03 + 0.54 −−−−−− Write a zero as a placeholder 22.57 44.4 + 3.53 −−−−−− 47.93 92 3.20 + 9.11 −−−−−− 12.31 23.02 + 79.34 −−−−−−− 102.36 Chapter Positive and Negative Fractions and Decimals 78.3 + 67.18 −−−−−−− 145.48 10 5.92 + 58.24 −−−−−−− 64.16 Copyright © by The McGraw-Hill Companies, Inc Step Add Step by Step Problem-Solving Practice Problem-Solving Strategies Solve 11 BANKING Rhyan is saving for college She had $101.82 in her savings account She earned $55.15 one week and $43.89 the next Rhyan put all the money that she earned into her savings account How much does she have now? Understand Draw a diagram Act it out Guess and check Use logical reasoning ✓ Solve a simpler problem Read the problem Write what you know Rhyan had $101.82 in her account She deposited $55.15 and $43.89 into the account Pick a strategy One strategy is to solve a simpler problem Plan Add the numbers two at time Add the amounts she earned in two weeks: $55.15 + $43.89 = $99.04 Solve Add the amount she earned to the amount already in the bank to find the total amount $99.04 + $101.82 = $200.86 Did you answer the question? You can check your answer by adding the three numbers in a different order Copyright © by The McGraw-Hill Companies, Inc Check 12 BUSINESS Marcos has a business mowing lawns in the summer He mowed four lawns last week He made $25, $15.50, $21.75 and $18.75 for the lawns What were his weekly total earnings? $81 Check off each step ✔ Understand ✔ Plan ✔ Solve ✔ Check GO ON Lesson 4-5 Add Decimals 93 13 TRAVEL Corbin rode his bike 1.17 miles to visit a friend He rode it 0.68 mile to the school on the way home and then went another 2.23 miles to the library The distance he rode home from the library was 0.43 mile How far did he ride altogether? 4.51 miles How is adding decimals like adding whole numbers? How is adding decimals different from adding whole numbers? 14 Sample answer: It is the same in that after you line up the place values, you add the columns from right to left just as you would add whole numbers The difference is that the decimal point is placed in the sum Skills, Concepts, and Problem Solving Add using decimal models 15 1.2 + 0.03 = 1.23 16 3.64 + 1.07 = 17 44.18 + 89.13 18 133.31 19 10.19 55.78 + 13.44 12.21 20 79.41 94 11.92 + 0.29 Chapter Positive and Negative Fractions and Decimals 92.46 + 55.14 147.60 Copyright © by The McGraw-Hill Companies, Inc Find each sum 4.71 21 0.06 + 0.17 = 0.23 22 11.03 + 4.5 = 15.53 23 17.6 + 8.07 = 25.67 24 4.67 + 3.6 = 8.27 25 23.89 + 45.23 = 26 33.01 + 5.1 = 38.11 27 3.06 + 5.9 = 28 7.02 + 12.8 = 19.82 29 15.76 32.04 + 8.5 30 3.77 28.44 + 11.03 69.12 8.96 56.30 31 152.9 65.08 + 3.0 220.98 43.24 32 137.4 73.09 + 8.0 218.49 Solve Copyright © by The McGraw-Hill Companies, Inc 33 PHYSICS Aida and Kraig conducted an experiment using ramps One ramp was 16.83 centimeters long The other ramp was 5.6 centimeters long They decided to put the two ramps together How long was the combined ramp? 22.43 cm 34 EARTH SCIENCE In a science experiment, the angle of the sunshine coming through the window was measured monthly In the first month, the angle measured 38.2 degrees The next month, the angle increased by 21.03 degrees The month after that, the angle increased 45.78 degrees What was the total measure of the angle after the third month? 105.01 degrees 35 ¡ ¡ ¡ FAMILY Clarence receives $9.25 each day he dog-sits for his neighbor If he dog-sits days, how much will he earn? $46.25 GO ON Lesson 4-5 Add Decimals 95 Vocabulary Check Write the vocabulary word that completes each sentence 36 37 38 decimal A(n) numbers and fractions is a number that can represent whole When you add decimals, the first thing you is line up the decimal points Writing in Math Ethan wrote the equation: 8.9 + 14.03 = 23.2 How would you correct his mistake? The answer should be 22.93 Ethan did not line up the place values correctly for 14.03 He mistakenly used 14.3 Spiral Review Write in each circle to make a true statement Check your answer by placing the decimals on a number line (Lesson 4-3, p 73) 39 12.06 < 12.16 40 (Lesson 3-4, p 21) 41 FOOD Pete’s Pizza Place made pizzas Each serving of a pizza How many servings were there in the is pizzas? 56 42 FOOD of a pizza evenly between Paquito is trying to split himself and his parents How much of the pizza will each person get? Use a diagram to justify your answer _ Divide a figure into halves and shade part Then divide that part into thirds Each person gets _ 96 Chapter Positive and Negative Fractions and Decimals Copyright © by The McGraw-Hill Companies, Inc Solve 0.08 < 0.80 Lesson 4-6 Subtract Decimals 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 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 7NS1.2 Add, subtract, multiply, and divide rational numbers and take positive rational numbers to wholenumber powers KEY Concept Decimal models can be used to subtract decimals Copyright © by The McGraw-Hill Companies, Inc Another way to subtract decimals is to write the numbers vertically to line up the decimal points Subtract the numbers as you would with whole numbers Bring the decimal point directly down to the difference You cannot subtract 12 7.29 - 2.65 = tenths from tenths Regroup 1, - which equals 10 7.29 - 2.65 = 4.64 tenths Take from ones place and add 10 to the tenths place VOCABULARY regroup to use place value to exchange equal amounts when renaming a number Example: 12 ones = ten ones difference the answer or result of a subtraction problem When subtracting decimals, remember to add zeros as needed so that both numbers have the same place value Example Find 1.77 – 0.9 using decimal models Model 1.77 You need to take away tenths, but there are not rods in the model Regroup Separate the one whole into 10 tenths Subtract 0.9 or tenths The remaining blocks represent the difference The model of the difference has tenths rods and hundredths blocks The difference is 0.87 1.77 - 0.9 = 0.87 GO ON Lesson 4-6 Subtract Decimals 97 YOUR TURN! Find 1.43 - 0.28 using decimal models Model 1.43 1.43 You need to take away to regroup? yes Replace hundredths units Do you need tenths rod with 10 hundredths units Subtract 0.28 The remaining blocks represent the difference The model of the difference has whole square, rod, and units The difference is 1.15 1.43 - 0.28 = 1.15 Example YOUR TURN! Find 72.40 - 59.65 16 11 Write the numbers vertically Line up the decimal points - 7 Bring down the decimal point to the same Add a zero so place in the difference that the number of place values is Subtract the the same hundredths column You need to regroup to subtract the tenths column Take one and replace it with 10 tenths You need to regroup to subtract from Take one 10 and replace it with ten 1s Write the numbers vertically Line up the decimal points 13 Bring down the decimal point to the same place in the difference Subtract the hundredths column Do you need to regroup? yes Subtract the tenths column Do you need to regroup? yes Subtract the ones column Do you need to regroup? yes Subtract the tens column Subtract the tens column 98 11 - Chapter Positive and Negative Fractions and Decimals 10 5 Copyright © by The McGraw-Hill Companies, Inc Find 47.13 - 29.7 Who is Correct? Find 20.57 - 16.98 Gabriel Theresa Dory 141 \ \20.57 - 16.98 19 \ \20\ 57 - 1698 19 41 \ \20\ 57 - 16.98 3.59 0.0359 4.59 Circle correct answer(s) Cross out incorrect answer(s) Guided Practice Copyright © by The McGraw-Hill Companies, Inc Subtract using decimal models 2.03 - 0.14 = 1.89 1.19 - 1.05 = 0.14 0.67 - 0.29 = 0.38 0.71 - 0.56 = 0.15 GO ON Lesson 4-6 Subtract Decimals 99 Step by Step Practice Find 121.09 - 85.6 Step Write the numbers vertically Line up the decimal points Add any zeros to line up place values Step Bring down the decimal point to the same place in the difference - Step Subtract the hundredths column Do you need to regroup? no Step Subtract the tenths column Do you need to regroup? yes Step Subtract the ones column Do you need to regroup? yes Step Subtract the tens column Do you need to regroup? yes Subtract 0.33 0.09 −−−−− - 0 2.06 45 −−−−− 1.61 100 16.12 3 10 $42.75 - $18.98 $23.77 Chapter Positive and Negative Fractions and Decimals 14 3.78 −−−−− 10.22 11 $13.25 - $11.26 $1.99 Copyright © by The McGraw-Hill Companies, Inc 0.24 19.77 -3.65 −−−−− Step by Step Problem-Solving Practice Problem-Solving Strategies Draw a diagram Use logical reasoning Act it out Solve a simpler problem ✓ Work backward Solve 12 GIFTS Ivan received $20 from his grandmother for his birthday He spent $5.13 on trading cards and $2.98 on a book He then gave $5 to his brother for helping him clean the garage and put the rest of the money into his savings account How much of the $20 did Ivan save? Understand Read the problem Write what you know $20 He spent $ 5.13 , $ Ivan has 5.00 and $ , and then saved the rest Pick a strategy One strategy is to work backward Plan You can begin with $20 Subtract each of the three amounts he spent The final difference is the amount he saves Ivan saved Copyright © by The McGraw-Hill Companies, Inc $14.87 - $5.13 trading cards $2.98 money left $11.89 money left book $5 money to brother = $14.87 = $11.89 = $6.89 money left money left savings $6.89 Check your answer by adding the amount he spent to the amount saved The total should be $20 Check 14 - , Fill in the blanks to find the amount he saved Solve 13 $20 birthday money 2.98 GARDENING Samili grows tomatoes She cans them in the summer to use during the winter She started with 10.25 pounds of tomatoes She canned 1.75 pounds, 2.13 pounds, and 1.98 pounds How many pounds of tomatoes did she not can? 4.39 lb Check off each step ✔ Understand ✔ Plan ✔ Solve ✔ Check COMMUNITY SERVICE Ian and Tito participated in a walk-a-thon to raise money for charity Together, they walked a total of 33.08 miles Their goal was 20.5 miles How much farther than their 12.58 miles goal did they walk? GO ON Lesson 4-6 Subtract Decimals 101 Write a few sentences for a student who was absent from class explaining how to decide whether you have to regroup when subtracting decimals 15 Sample answer: After the numbers are written vertically, look at each column of numbers If the second number in the column is greater than the first number, then you have to regroup Skills, Concepts, and Problem Solving Subtract using decimal models 16 1.11 - 99 = 12 17 2.13 - 0.03 = 2.10 Subtract 18 1.0 0.73 −−−−− 19 0.27 14.89 0.7 −−−−− 20 14.19 88.06 1.75 −−−−− 21 86.31 9.75 0.17 - 0.06 = 0.11 23 11.03 - 4.5 = 6.53 24 17.6 - 8.07 = 9.53 25 25.4 - 7.98 = 17.42 26 CIVICS In a local election, one candidate received 24.85 percent of the vote Another candidate received 33.13 percent What percent more votes did the second 8.28 candidate receive than the first? 27 FOOD The cafeteria had 36 cups of flour at the beginning of the week One day 10.33 cups of flour were used, and another day 5.25 cups were used On Friday, the chef wanted to make a recipe yes that needed 16.75 cups of flour Did she have enough? If so, how much flour was left at the end of the day on Friday? 3.67 cups 102 Chapter Positive and Negative Fractions and Decimals Copyright © by The McGraw-Hill Companies, Inc 22 Solve 20.96 11.21 −−−−−− 28 ENGINEERING An engineer designed a machine that weighed 2.75 tons The owner of the factory that will use the machine wanted it to weigh 0.06 ton less How many tons did the owner want the machine to weigh? 2.69 tons Vocabulary Check Write the vocabulary word that completes each sentence 29 regroup When you rename a number 30 The answer to a subtraction problem is called the 31 Writing in Math Write about a real-life situation in which you would subtract decimals , you exchange equal amounts to difference Answers will vary Sample answer: making a withdrawal from a bank account Spiral Review Solve 32 (Lesson 4-5, p 89) SCIENCE A compound contains 0.08 liter of acid, 1.16 liters of water, and 0.78 liter base How many total liters are in the compound? Copyright © by The McGraw-Hill Companies, Inc 2.02 L 33 ASTRONOMY A comet traveled across the sky 0.16 million miles from Earth Five years later the same comet was 0.07 million miles farther from Earth How far was the comet from Earth the second time? 0.23 million miles Add Write the sum in simplest form (Lesson 3-5, p 28) 23 10 24 =1 34 _ + = 35 _ + _ = 10 100 50 12 24 24 _ _ Divide Write the quotient in simplest form (Lesson 3-4, p 21) 37 ÷ = 38 ÷ = 8 _ _ 36 1= _ + _7 39 2= _ ÷ 35 _ 16 12 16 24 Lesson 4-6 Subtract Decimals 103 Chapter Progress Check (Lessons 4-5 and 4-6) Add using decimal models 4NS2.0, 5NS2.0, 5NS2.1, 7NS1.2 0.07 + 0.94 = 1.01 0.11 + 1.03 = 1.14 Add 4NS2.0, 5NS2.0, 5NS2.1, 7NS1.2 4.95 + 56.03 = 60.98 13.07 + 0.29 = 13.36 6.92 + 11.08 = 18 24.85 + 4.76 = 29.61 Subtract using decimal models 4NS2.0, 5NS2.0, 5NS2.1, 7NS1.2 0.17 - 0.10 = 0.07 1.03 - 0.2 = 0.83 48.09 - 10.7 = 37.39 10 8.11 - 0.73 = 7.38 11 78.03 - 19.5 = 58.53 12 34.13 - 6.89 = 27.24 Solve 4NS2.0, 5NS2.0, 5NS2.1, 7NS1.2 13 ART A fifth-grade class is making a mural Three groups of students are creating different parts of the mural Then the three parts will be combined to make the mural One group makes a piece 3.50 yards long The other two groups make pieces that are each 4.22 11.94 yards yards long How long will the mural be? 14 MONEY Sharika and her friend set up lemonade stands at opposite sides of the neighborhood Sharika made $43.12 Her friend made $36.83 How much more did Sharika make? $6.29 104 Chapter Positive and Negative Fractions and Decimals Copyright © by The McGraw-Hill Companies, Inc Subtract 4NS2.0, 5NS2.0, 5NS2.1, 7NS1.2 ... 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 2B 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