Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Peter Sterling/Getty Images Photo Credits Cover, i Peter Sterling/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 Digital Vision/PunchStock; viii CORBIS; ix Larry Brownstein/Getty Images; x CORBIS; 2–3 Lisa Blumenfeld/Getty Images; (tl)Arthur Morris/CORBIS, (tr)Adam Jones/ Getty Images, (b)Mark Ransom; 10 CORBIS; 15 (t)Millard H Sharp/Photo Researchers, Inc., (b)Steve Maslowski/Visuals Unlimited; 17 Jules Frazier/CORBIS; 25 (l)Dorling Kindersley/Getty Images, (r)Dorling Kindersley/Getty Images; 32–33 Miles Ertman/Masterfile; 33 Lon C Diehl/PhotoEdit Inc.; 47 (l)Getty Images, (r)Mark A Schneider/Photo Researchers 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: 978-0-07-878207-7 MHID: 0-07-878207-4 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 3A 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 3A Ratios, Rates, and Percents Chapter Ratios and Rates 1-1 Ratios 6NS1.2 1-2 Rates and Unit Costs 11 3NS2.7, 6AF2.2 Progress Check .18 1-3 Probability as a Ratio 19 6SDAP3.3 Assessment Study Guide .26 Chapter Test .28 Standards Practice 30 Standards Addressed in This Chapter 3NS2.7 Determine the unit cost when given the total cost and number of units 6NS1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative size of two quantities, using appropriate notations (a/b, a to b, a:b) 6AF2.2 Demonstrate an understanding that rate is a measure of one quantity per unit value of another quantity 6SDAP3.3 Represent probabilities as ratios, proportions, decimals between and 1, and percentages between and 100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event, - P is the probability of an event not occurring Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Joshua Tree National Park Chapters and are contained in Volume 3A Chapters and are contained in Volume 3B vii Digital Vision/PunchStock Contents Chapter Percents, Fractions, and Decimals Standards Addressed in This Chapter 2-1 Introduction to Percents 34 5NS1.2 2-2 Percents, Fractions, and Decimals 41 5NS1.2 Progress Check .48 2-3 Compare Data Sets of Different Sizes 49 5SDAP1.3, 6NS1.2 Assessment Study Guide .56 Chapter Test .58 5NS1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number 5SDAP1.3 Use fractions and percentages to compare data sets of different sizes 6NS1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the relative size of two quantities, using appropriate notations (a/b, a to b, a:b) Standards Practice 60 Merced River near Yosemite National Park Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc viii CORBIS Contents Chapter Using Percents 3-1 Calculate Percents 5NS1.2, 6NS1.4 3-2 Solve Percent Problems 11 6NS1.3, 6NS1.4, 7NS1.7 Progress Check .20 3-3 Interest Problems 21 6NS1.4, 7NS1.7 3-4 Percent of Change 29 7NS1.6, 7NS1.7 Progress Check .36 Assessment Study Guide .37 Chapter Test .40 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Standards Practice 42 Manhattan Beach Pier Chapters and are contained in Volume 3A Chapters and are contained in Volume 3B Standards Addressed in This Chapter 5NS1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions and explain why they represent the same value; compute a given percent of a whole number 6NS1.3 Use proportions to solve problems (e.g., determine the value of N N if = _, find the length of a side of 21 a polygon simiular to a known polygon) Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse 6NS1.4 Calculate given percentages of quantities and solve problems involving discounts at sales, interest earned, and tips 7NS1.6 Calculate the percentage of increases and decreases of a quantity 7NS1.7 Solve problems that involve discounts, markups, commissions, and profit and compute simple and compound interest ix Larry Brownstein/Getty Images Contents Chapter Rates and Proportional Reasoning Standards Addressed in This Chapter 4-1 Proportions 46 6NS1.3 4-2 Unit Conversions 53 3AF1.4, 3MG1.4, 6AF2.1 Progress Check 60 4-3 Solve Rate Problems .61 3AF2.1, 3AF2.2, 6AF2.3 4-4 Solve Problems Using Proportions 69 3AF2.1, 6NS1.3, 7AF4.2 Progress Check 76 Assessment Study Guide 77 Chapter Test 80 Standards Practice 82 3AF2.1 Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit) 3AF2.2 Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4) 3MG1.4 Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes) 6NS1.3 Use proportions to solve problems (e.g., determine the value of N N if = _, find the length of a side of 21 a polygon simiular to a known polygon) Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse 6AF2.1 Convert one unit of measurement to another (e.g., from feet to miles, from centimeters to inches) 6AF2.3 Solve problems involving rates, average speed, distance, and time 7AF4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation x CORBIS Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc Reconstructed house in a restored Hoopa Valley Tribe village, Humboldt County 3AF1.4 Express simple unit conversions in symbolic form (e.g., _ inches = _ feet × 12) Lesson 2-3 Compare Data Sets of _ Different Sizes KEY Concept Percents can be used to compare ratios from sets of data that have different sizes When you compare ratios written as percents, you are comparing numerators of fractions that have the same denominator of 100 Consider the ratios of out of and out of × 20 40 = _ = = 40% 5 × 20 100 × 50 50 = _ = = 50% × 50 6NS1.2 Interpret and use ratios in different contexts to show the relative sizes of two quantities using appropriate a notations ( , a to b, a:b) b 5SDAP1.3 Use fractions and percentages to compare data sets of different sizes VOCABULARY compare to look closely at numbers or objects to find similarities and differences Example: is less than (difference) and are numbers (similarity) 100 Since 40% < 50%, < Copyright © by The McGraw-Hill Companies, Inc When you compare numbers, write them in the same form Example YOUR TURN! Express the circled data as a fraction and a percent of the entire data set Express the circled data as a fraction and a percent of the entire data set 2, 4, 7, 8, How many numbers are in the data set? How many numbers are circled? 3 Write the ratio as a fraction Write the ratio as a percent 60% 1, 3, 5, 6, 10, 11, 12, 15 How many numbers are in the data set? How many numbers are circled? Write the ratio as a fraction Write the ratio as a percent GO ON Lesson 2-3 Compare Data Sets of Different Sizes 49 Example YOUR TURN! Use fractions to compare the ratios of the number of red triangles to the number of blue triangles for each set of figures Set A Set B Write the ratio of red triangles to blue triangles for Set A as a fraction in simplest form Write the ratio of red triangles to blue triangles for Set B as a fraction in simplest form > Compare the fractions So, Set A has the greater ratio of red triangles to blue triangles Use fractions to compare the number of green circles to the number of red circles for each set of figures Set A Set B Write the ratio of the number of green circles to the number of red circles for Set A as a fraction in simplest form Write the ratio of the number of green circles to the number of red circles for Set B as a fraction in simplest form Compare the fractions > has a greater ratio of the So, number of green circles to the number of red circles One bag contains 50 marbles Thirty of them are red Another bag contains 35 marbles and 28 of them are red Use percents to compare the ratios of the red marbles to the entire bag of marbles to determine which bag has the greater percentage of red marbles Write the ratio of the red marbles to the entire bag of marbles as a 30 percent for the first bag _ = 60% 50 Write the ratio of the red marbles to the entire bag of marbles as a 28 percent for the second bag _ = 80% 35 Compare the percents 80% > 60% The second bag has a greater percentage of red marbles 50 Chapter Percents, Fractions, and Decimals Copyright © by The McGraw-Hill Companies, Inc Example YOUR TURN! One package of socks contains blue socks A second package of 15 socks contains blue socks Use percents to compare the ratios of the number of blue socks to the entire package to determine which package has the greater percentage of blue socks Write the ratio of the number of blue socks to the entire package as a percent for the first package = % Write the ratio of the number of blue socks to the entire package as a percent for the second package = % > Compare the percents The package has a greater percentage of blue socks to the entire package Who is Correct? Compare 28 _ and 55% Sara 14 28 = _ _ 50 25 0.56 25 14.00 -125 150 -150 28 > 55% _ 50 50 Copyright © by The McGraw-Hill Companies, Inc Paquito A.J 56_ × 2_ = _ 28 = 28 _ 10 × 50 50 56_ × 2_ = _ 28 = 28 _ 10 × 50 50 28 > 55% _ 28 < 55% _ 50 50 Circle correct answer(s) Cross out incorrect answer(s) Guided Practice Express the shaded areas of the figures as a fraction and as a percent of the area of the entire figure 0.6 GO ON Lesson 2-3 Compare Data Sets of Different Sizes 51 Step by Step Practice Your sister gave you two bags of pens One bag contained blue pens and red pens The other bag contained red pens and green pens Which bag had the greater percentage of red pens? red pens and a total Step In the first bag, there were of pens red pens and a In the second bag, there were total of pens Step Write each ratio as a percent = % = < Step Compare the percents Step The of red pens % had the greater percentage In Amira’s box of 15 party hats, of them are silver In Lupe’s box of 30 hats, 21 of them are silver Which girl has the greater ratio of the number of silver party hats to the total number of hats? What is the ratio in simplest form of the number of silver hats to the total number of hats in Lupe’s box? has the greater ratio of the number of silver hats to the total number of hats in her box 52 Jaime has two binders that are filled with CDs One can hold 50 CDs, and the other can hold 30 CDs The first one contains 26 hip-hop CDs, and the second one contains 16 hip-hop CDS Which binder has the greater ratio of the number of hip-hop CDs to the total number of CDs? Chapter Percents, Fractions, and Decimals Copyright © by The McGraw-Hill Companies, Inc What is the ratio in simplest form of the number of silver hats to the total number of hats in Amira’s box? Step by Step Problem-Solving Practice Problem-Solving Strategies Solve SPORTS Bianca and Chris played darts Bianca hit the bull’s-eye out of 18 times Chris missed the bull’s-eye out of 15 times Who hit the bull’s-eye a greater percent of the time? Use a table Look for a pattern Write an equation Guess and check ✓ Use logical reasoning Understand Read the problem Write what you know Bianca hit the bull’s-eye out of times Chris did not hit the bull’s-eye out of times Plan Pick a strategy One strategy is to use logical reasoning Solve Write the fraction of Bianca’s hits to attempts Write the fraction of Chris’s misses to attempts Write each fraction as a decimal rounded to the nearest hundredth, then as a percent .28 _ = 18 5.00 = 28% 18 33 _ = 15 5.00 = 33% 15 Copyright © by The McGraw-Hill Companies, Inc Chris missed the bull’s-eye 33% of the time, so he hit the bull’s-eye 100% - 33% = % of the time Compare the percents hit the bull’s-eye a greater percent of the time Does the answer make sense? Look over your solution Did you answer the question? Check WEATHER The table shows how much rain fell in Albuquerque and Denver for the given number of days Which city had the greater fraction of inches of rain per day? Check off each step City Rain (in.) Days (#) Albuquerque, NM 60 Denver, CO 15 90 Understand Plan Solve Check GO ON Lesson 2-3 Compare Data Sets of Different Sizes 53 Nestor is using two different recipes for a cake The first recipe calls for cup of sugar and eggs The other recipe calls for cups of sugar and eggs Name the ratios of eggs to sugar for each recipe Which recipe has the smaller ratio of eggs to sugar? Mrs Rodriguez just returned from the grocery store Her first bag of groceries contains 12 items, and of them are frozen Her second bag of groceries contains 18 items, and 10 of them are frozen Which bag has the greater percentage of frozen items in it? Do you prefer to compare sets of data of different sizes by using ratios written as fractions or as percents? Explain 10 Skills, Concepts, and Problem Solving Compare Circle the greater value 11 and 40% _ 12 13 _ and 62% 10 and 81% Express the shaded area of the figures as a fraction and a percent of the area of the entire figure 14 15 Express the circled data as a fraction and as a percent of the entire data set 16 1, 3, 5, 6, 10, 11 18 54 17 19 Chapter Percents, Fractions, and Decimals 10, 20, 30, 40, 50, 60, 70, 80 Copyright © by The McGraw-Hill Companies, Inc 25 Solve 20 For the fall school concert, the music director purchased 60 bottles of juice for refreshments Of those, 25 bottles were apple juice For the spring concert, she purchased 75 bottles of juice, and 35 bottles were apple juice Which concert had the greater ratio of the number of bottles of apple juice to the total number of bottles of juice? 21 One spinner is divided into equal parts Two of the parts are green, of the parts are red, and part is yellow Another spinner is divided into equal parts Two of the parts are green, of the parts are red and part is yellow Which spinner has the greater percentage of red parts? Copyright © by The McGraw-Hill Companies, Inc Vocabulary Check sentence Write the vocabulary word that completes each 22 When you , you look closely at numbers or objects to find similarities and differences 23 If numbers ascend from least to greatest, or descend from greatest to least, they are said to be in 24 Writing in Math Which of these ratios does not equal the value of the others? How you know? out of 15 0.06 60% Spiral Review Solve (Lesson 2-1, p 34) 25 FITNESS Miriam ran miles in 35 minutes Terry ran miles in 36 minutes Who ran at a slower rate? 26 NATURE During a 30-minute walk, Alma identified bird species During an hour walk, Kota identified 10 bird species Who identified birds at a faster rate? Find each unit rate (Lesson 1-2, p 11) 27 15 inches every 30 seconds 28 150 miles every hours Lesson 2-3 Compare Data Sets of Different Sizes 55 Chapter Study Guide Vocabulary and Concept Check compare, p 49 Write the vocabulary word that completes each sentence equivalent fractions, p 34 order, p 49 percent, p 34 To is to look closely at numbers or objects to find similarities and differences means hundredths or out of 100 ratio, p 34 When numbers ascend from least to greatest, or descend from greatest to least, they are in A(n) numbers by division is a comparison of two Write the correct vocabulary term in each blank 6 and < 0.5 20% < Lesson Review Introduction to Percents Identify each percent that is modeled (pp 34–40) Example Identify the percent that is modeled The model has 100 squares 20 squares are shaded The ratio as a fraction of shaded squares to 20 total squares is 100 The fraction written as a percent is 20% 56 Chapter Study Guide Copyright © by The McGraw-Hill Companies, Inc 2-1 Write each percent as a fraction with a denominator of 100 and as a decimal 44% Write 84% as a fraction with a denominator of 100 and as a decimal 10 13% 11 26% Write 84% as a fraction 84 100 Write 84% as a decimal 0.84 2-2 Percents, Fractions, and Decimals (pp 41–47) Write each fraction as a decimal and as a percent 12 13 14 _ Example Write _5 as a decimal and as a percent 0.625 5.000 -48 20 -16 40 -40 Divide to convert to a decimal Move the decimal point two places to the right and add the percent symbol 62.5% 2-3 Copyright © by The McGraw-Hill Companies, Inc Example Compare Data Sets of Different Sizes (pp 49–55) Compare the ratios described as a fraction in simplest form and as a percent Use the following data sets Set A 2, 3, 5, 7, 11, 13 Example Compare the ratio of the number of blue squares to the total number of squares as a fraction in simplest form and as a percent Set A Set B Set B 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 15 16 17 The number of even numbers to the number of odd numbers for each data set The number of blue numbers to the total numbers for each data set Write as a fraction and as a percent the ratio of the number of blue squares to the total number of squares for each set Set A = 66 2% 3 Set B = 80% %, so Set B has a greater Compare 80% > 66 ratio of the number of blue squares to the total number of squares The number of odd numbers to the total numbers for each data set Chapter Study Guide 57 Chapter Chapter Test Identify the percent that is modeled Write each percent as a decimal and as a fraction in simplest form 55% 28% 125% 107% A small bag of snack mix has pretzels, 12 peanuts, 10 cheese crackers, and raisins Write the ratios of the pretzels to the total number of pieces and peanuts to the total number of pieces as fractions in simplest form, as percents, and as decimals number of pretzels to total number of pieces number of peanuts to total number of pieces 12 _ _ 15 Copyright © by The McGraw-Hill Companies, Inc Write each fraction as a decimal and as a percent 10 11 12 13 14 Use the spinner to write each ratio as a fraction in simplest form Then write the ratio as a percent and as a decimal 15 number of orange sections to total number of sections fraction 16 percent decimal number of blue sections to number of nonblue sections fraction 58 decimal number of yellow sections to the number of orange sections fraction 17 percent Chapter Test percent decimal GO ON Express the circled data as a fraction in simplest form and as a percent of the entire data set 18 a, b, c, d, e, f, g, h, i, j 19 20 LeBron made 49 free throws out of 70 attempts Donyell made 39 free throws out of 59 attempts Which player made the greater percentage of free throws? Solve 21 GAMES At one video-game store, 29% of the sales of the newrelease video games were sold by presale orders At a larger store in town, 54% of the new-release sales were sold to customers who were waiting in line outside the store for several hours Write each percent as a decimal and as a fraction in simplest form 22 BASEBALL Matthew got 24 hits out of his last 75 at bats Write his batting average as a decimal and as a fraction in simplest form Copyright © by The McGraw-Hill Companies, Inc Correct the mistakes 23 Thomas wanted to purchase an MP3 player The regular price was $59.99 It was on sale for 10% off When Thomas’s mother asked him about the sale price, he told her that the discount perentage was equal to 0.12 What did Thomas wrong? 24 Jamal plays soccer in a league with 100 other students, 53 of which are girls Ito plays in a different league, and 27 out of 80 students are girls Heather said the percentage of girls in each league was equal since 100 - 53 = 47 and 80 - 27 = 47 What did Heather wrong? Chapter Test 59 Chapter Standards Practice Choose the best answer and fill in the corresponding circle on the sheet at right Which model represents 74%? Which statement is correct? = 0.24 = 24% = 0.20 = 20% C A = 0.75 = 7.5% = 1.0 = 10% D B _ 10 Dominic watches a quiz show on TV every night He guesses correctly on 70% of the questions What fraction of the questions does Dominic answer correctly? 7 H _ F 10 G J 4 A B C D A 70% C 80% B 75% D 90% Which percent represents the shaded portion of the model? Damian read 320 pages of his novel this week Eli read 80% of Damian’s total pages How many pages did Eli read this week? F 50% H 112% F 26 pages H 256 pages G 100% J 150% G 240 pages J 260 pages GO ON 60 Chapter Standards Practice Copyright © by The McGraw-Hill Companies, Inc _ Ayden scored 16 on his math quiz 20 What is his percent? A meal totals $22.60, including tax After a 20% tip is added, what is the total cost of the meal? 10 A $4.52 Tisha flew 2,496 miles across the country The flight lasted hours At what rate was the plane traveling? F hours B $18.08 G 416 miles/hour C $22.60 H 419 miles/hour D $27.12 J 2,496 miles This sweater is priced at $38 What is the price after the discount? Copyright © by The McGraw-Hill Companies, Inc Sweaters 25% off ANSWER SHEET Directions: Fill in the circle of each correct answer A B C D F G H J A B C D F $9.50 F G H J G $25 A B C D H $28.50 F G H J J $950 A B C D F G H J A B C D 10 F G H J What is the ratio of striped marbles to solid-colored marbles? Success Strategy Read the entire question before looking at the answer choices Make sure you know what the question is asking , 5:3, or to A , 4:5, or to B , 4:3, or to C 3 , 3:5, or to D Chapter Standards Practice 61 Index A Algebra and Functions, 11 Answer sheet, 31, 61 Assessment, 28–29, 58–59 C California Mathematics Content Standards, 4, 11, 19, 34, 41, 49 Chapter Preview, 3, 33 Chapter Test, 28–29, 58–59 M Manipulatives base-ten blocks, 34, 35, 39, 47, 48, 54, 56, 58, 60 fraction circles and strips, 51, 54 Mathematical Reasoning See Step-by-Step Problem Solving N Number Sense, 4, 11, 34, 41, 49 compare, 49–55 Correct the Mistakes, 29, 59 D decimals, 41–47 E O outcomes, 19–25 P probability, 19–25 Standards Practice, 30–31, 60–61 event, 19–25 Progress Check, 18, 48 K Key Concept, 4, 19, 34, 41, 49 62 Index R rate, 4–10, 11–17 ratio, 4–10, 19–25, 34–40 Real-World Applications ages, archeology, 47 baseball, 59 basketball, 39 business, 15 chemistry, 44 cooking, 54 dogs, 38 education, 40 entertainment, 48 exercise, 48 fitness, 10, 40, 55 food, 23, 40, 46, 48 Statistics, Data Analysis, and Probability, 19, 34, 49 Step-by-Step Practice, 7, 14, 21, 36, 43, 52 Step-by-Step Problem Solving Practice, 8–9, 15, 23, 38, 44, 53 Look for a pattern, 44 Solve a simpler problem, 8, 15 Use a table, 38 Use logical reasoning, 23, 44, 53 Study Guide, 26–27, 56–57 Success Strategy, 31, 61 U unit cost, 11–17 unit rate, 11–17 Copyright © by The McGraw-Hill Companies, Inc fraction comparing, 49–55 decimals to, 41–47 equivalent, 4–10, 11–17, 34–40 percents to, 41–47 probability, 19–25 ratios as, 4–10, 11–17 to decimals, 41–47 to percents, 41–47 S Spiral Review, 17, 25, 40, 47, 55 equivalent ratios, 4–10, 11–17 F Reflect, 9, 16, 24, 39, 45, 54 percent, 34–40, 41–47, 49–55 Problem-Solving See Step-byStep Problem Solving equivalent fractions, 34–40 football, fund-raiser, 16 games, 24 genetics, 23 health, 25 insects, 25 language, 25 life science, 17 movies, 45 music, 38 nature, 15, 47, 55 population, 16, 17 reading, 29 sewing, 25 spelling, 18, 29 sports, 10, 18, 53 tennis, travel, 29 weather, 53 V Vocabulary, 4, 19, 34, 41, 49 Vocabulary and Concept Check, 26, 56 Vocabulary Check, 10, 17, 25, 40, 47, 55 W Who is Correct?, 6, 13, 21, 35, 43, 51 Copyright © by The McGraw-Hill Companies, Inc Writing in Math, 10, 17, 25, 40, 47, 55 Index 63 ... 10 09 08 07 California Math Triumphs Volume 3A California Math Triumphs Volume Place Value and Basic Number Skills 1A Chapter Counting 1A Chapter Place Value 1A Chapter Addition and Subtraction... 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. .. National Park Chapters and are contained in Volume 3A Chapters and are contained in Volume 3B vii Digital Vision/PunchStock Contents Chapter Percents, Fractions, and Decimals Standards Addressed in