California math triumphs ratios, rates, and percents, volume 3b

Authors Basich Whitney • Brown • Dawson • Gonsalves • Silbey • Vielhaber Photo Credits Cover Peter Sterling/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 Digital Vision/PunchStock; viii CORBIS; ix Larry Brownstein/Getty Images; x CORBIS; 2–3 Michael A Keller/ CORBIS; 27 CORBIS; 36 Rachel Epstein/PhotoEdit; 44 Getty Images; 51 Stockdisc/SuperStock; 57 Darwin Wiggett/Getty Images; 58 David Buffington/ Getty Images; 60 Darren McCollester/Getty Images; 67 Brand X Pictures/ PunchStock; 76 Ryan McVay/Getty Images; 81 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: 978-0-07-878208 MHID: 0-07-878208-2 Printed in the United States of America 10 055/027 16 15 14 13 12 11 10 09 08 07 California Math Triumphs Volume 3B 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 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 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 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 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 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) YOUR TURN! Shane’s grandmother lives 198 miles from his house He left his home and drove 90 miles in 1.5 hours before he stopped for gas How long will it take Shane to make the trip to his grandmother’s house if he travels at the same rate for the whole trip? Write a ratio for miles to hours Set up a proportion to find the time it would take to travel 198 miles 90 mi _ 1.5h 90 mi = _ 198 mi _ t 1.5h 90t = 1.5 · 198 Cross multiply and solve 90t = 297 t = 3.3 It will take 3.3 hours for Shane to get to his grandmother’s house Who is Correct? Jerry ran miles in 35 minutes Use a proportion to find how long it would take him to run 7.5 miles at that rate Janet Copyright © by The McGraw-Hill Companies, Inc _ _ mi = x 75 35 · 75 = 35x x = 11 miles Aiden x mi = _ _ 35 7.5 mi · 35 = 7.5x x = 23 minutes Sergio 7.5 mi mi = _ _ x 35 5x = 35 · 7.5 x = 52.5 minutes Circle correct answer(s) Cross out incorrect answer(s) Guided Practice Find the value of x in each pair of similar figures x = 3.6  x = 5.2  Y Y     GO ON Lesson 4-4 Solve Problems Using Proportions 71 Step by Step Practice Raul traveled 150 miles in hours At that point, he reduced his rate of speed by 20% How far did he travel in hours? Step Find Raul’s rate of speed at the beginning of the trip Step Reduce that amount by 20% 40 mph His new rate of speed is 50 20% of 50 miles per hour = 10 Step Use the distance formula, d = r · t, to find his new distance d= Raul could travel 80 40 · miles in hours Solve Levi earns $35 for mowing lawns At that rate, how many lawns would he need to mow in order to earn $140? He earns $7 Levi needs to mow 5 = $7 for mowing one lawn = number of lawns he needs to mow to 20 lawns Savoia wants to attend a class trip to an amusement park The trip will cost $65 She has already saved $25 She can earn $4 an hour baby-sitting How many hours will she need to baby-sit to pay for the trip? 10 hours A bird flew for hours at 30 miles per hour, then slowed down and flew more hours at 25 miles per hour How far did the bird fly? 135 miles 72 Chapter Rates and Proportional Reasoning Copyright © by The McGraw-Hill Companies, Inc $ 140 ÷ earn $140 $35 ÷ Step by Step Problem-Solving Practice Problem-Solving Strategies ✓ Use a table Solve GEOMETRY times as Each side of polygon ABCD is Understand Read the problem Write what you know Look for a pattern Guess and check Solve a simpler problem Act it out long as the corresponding side of polygon FGHI Find the perimeter of polygon ABCD _ 31 Each side of polygon ABCD is times as long as the corresponding side of polygon FGHI " 
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GU 48 feet ✔ Understand ✔ Plan ✔ Solve ✔ Check GO ON Lesson 4-4 Solve Problems Using Proportions 73 EVENTS Monica decided to participate in a walk-a-thon for charity She walked 18 miles and then took a 5-minute break She then walked another miles to complete the event It took her hours to complete the walk-a-thon from start to finish About how many miles did she travel each hour? about miles per hour List the types of problems that proportions can be used to solve 10 Sample answer: Proportions can be used to find missing lengths in similar figures, indirect measurement, percents, unit costs, and unit rates Skills, Concepts, and Problem Solving Find the value of x in each pair of similar figures 11 10.2 ft x= 12 12 mm x= Y 
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NN Solve 19 FITNESS Harry jogged miles on Saturday morning at a rate of 0.71 hours miles per hour How long did he jog? He jogged miles on Monday at a rate of miles per hour Did he jog for a longer amount of time on Saturday or Monday? He jogged for a longer amount of time on Saturday 20 SCUBA DIVING A company produces 39 wetsuits every weeks How long will it take the company to produce 429 wetsuits? 22 weeks Vocabulary Check Write the vocabulary word that completes each sentence 21 Figures whose shapes are the same but may have different sizes are similar figures 22 A(n) division 23 Writing in Math Candace says that if two figures are similar, their corresponding sides are equal and their corresponding angles are proportional Is she correct? Explain ratio is a comparison of two numbers by Sample answer: No, Candace is not correct If two figures are similar, their Copyright © by The McGraw-Hill Companies, Inc corrresponding angles are equal and their corresponding sides are proportional Spiral Review Solve (Lesson 4-3, p 61) 24 If a car travels 30 miles per hour, what is the distance it travels in 165 miles 5.5 hours? 25 If a turtle travels 7.5 feet in 15 minutes, what is its rate per minute? 26 ENTERTAINMENT Elisa sold 330 tickets to the museum in hours while working at the ticket booth Later, Ron sold 480 tickets while working an 8-hour shift Who sold tickets at a higher rate? Explain 0.5 feet per minute (Lesson 1-2, p 11) _ _ Elisa’s rate was 330 = 66 tickets/h Ron’s rate was 480 = 60 tickets/h Elisa; 66 > 60 Lesson 4-4 Solve Problems Using Proportions 75 Chapter Progress Check (Lessons 4-3 and 4-4) Find each total cost Round to the nearest cent 3AF2.1, 3AF2.2 $51.96 How much are hats? tickets cost $60 How much is ticket? One pound of nuts costs $1.99 How much pounds cost? $7.50 $9.95 Write the ratio Then find each unit rate Round to the nearest tenth 6AF2.3, 7AF4.2 904 people passed through the gate in hours 336 meters in 400 minutes 336 _ 400 ; 904 _ 0.8 m/min ; 113 people/h Find the value of x in each pair of similar figures 3AF2.1, 6NS1.3 6 in x= x= 16 mm 
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NN Use a proportion to solve each problem 3AF2.1, 6NS1.3, 6AF2.3, 7AF4.2 about 44 pounds Ricardo runs 50 meters in seconds What is his average speed? 5.6 meters per second Round to the nearest tenth 10 Two dozen shrimp cost $26 How much 3.5 dozen cost? $45.50 Solve 3AF2.1, 6NS1.3, 6AF2.3, 7AF4.2 11 TRAVEL Paloma drives at a rate of 60 miles per hour for hours Then she decreases her speed to 55 miles per hour and drives another 1.5 hours What distance will she travel altogether? 262.5 miles 12 EARTH SCIENCE Surface waves from an earthquake travel about kilometers per second through Earth’s crust How long would 250 seconds it take for a surface wave to travel 1,500 kilometers? 76 Chapter Rates and Proportional Reasoning Ryan McVay/Getty Images Copyright © by The McGraw-Hill Companies, Inc A child weighs about 20 kilograms If kilogram is about 2.2 pounds, how much does the child weigh in pounds? Chapter Study Guide Vocabulary and Concept Check proportion, p 46 Write the vocabulary word that completes each similar figures, p 69 sentence unit cost, p 61 unit rate, p 46 An equation stating that two ratios are equivalent is a proportion unit rate A describes how many units of one type of quantity are equal to unit of another type of quantity The unit cost is the cost of a single piece or item Similar figures have the same shape but may have different sizes Which of the three sets of figures below are not similar figures? " # B $ Lesson Review Copyright © by The McGraw-Hill Companies, Inc 4-1 Proportions (pp 46–52) Determine whether each pair of ratios is proportional yes = _ 18 = _ no 20 Solve each proportion x = _ x = 21 24 p _ 10 = 7.5 p=4 Example Determine whether the ratios are proportional = _ 12 Find the cross products · 12 = · 36 = 36 The cross products are equal The ratios form a proportion Example Solve for n Find the cross products Solve n =9 10 · = 5n 5n 90 _ _ = 5 18 = n 10 _ Chapter Study Guide 77 4-2 Unit Conversions (pp 53–59) Convert each unit using a proportion 282 Example 10 28,200 cm = 11 quarts = 1.25 or gallons _1 meters Solve 12 A bag weighs 48 ounces There are 16 ounces in one pound How many pounds does the bag weigh? lb 13 A piece of wood is 11 inches long One inch is about 2.54 centimeters About how long is the piece of wood in centimeters? 27.94 cm 4-3 Solve Rate Problems (pp 61–68) Solve 14 Example Julian can run miles in 27 minutes What is Julian’s average time per mile? minutes per mile 16 The Minton’s Turkey Farm tracks the number of turkeys they sell each fall They sold 444 turkeys during the last 12 falls What is the average number of turkeys sold each fall? 444 turkeys Write a ratio for turkeys to falls _ 12 falls Simplify to a unit rate 444 turkeys 444 ÷ 12 37 turkeys _ = = 12 falls 12 ÷ 12 fall The Minton Turkey Farm sold an average of 37 turkeys per fall Derek has a 286-mile drive home from college He drove 136 miles in hours Based upon this fact, about how long will it take Derek to make it home? 4.2 hours 17 It was raining at a rate of 0.8 inches per hour If it continues over the next hours, how much rain will have fallen? 6.4 inches 78 Chapter Study Guide Copyright © by The McGraw-Hill Companies, Inc An ice-cream store tracks the number of customers who come into the store After months, the count is 6,372 customers What is the average number of customers per month? 1,062 per month 15 feet to inches using a proportion Convert There are 12 inches in foot n in 12 in = _ _ Write a proportion Use ft ft the ratio of feet to inches 1=n 12 · Cross multiply Solve 42 = n feet = 42 inches 4-4 Solve Problems Using Proportions Find the value of x in the pair of similar figures 18 
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DN : The ratio of sides AC to CB in 12 triangle ABC is _ 10 The ratio of the corresponding side measures in triangle XYZ is x Set up a proportion and solve for x 12 = _ 10 x 12x = 8(10) 80 12x = _ 12 12 Find the cross products Simplify Divide by 12 Copyright © by The McGraw-Hill Companies, Inc −− centimeters The length of YZ is Use a proportion to solve the problem 20 21 A 12-oz package of chocolate chunks contains 21 pieces How many pieces would you expect to find in a 16-oz 28 package? Todd ran miles in 36 minutes Use a proportion to find how long it would take him to run miles 48 minutes Example Use a proportion to solve the problem About 17 out of every 25 customers at the bakery purchase some sort of homemade bread or rolls On a day when there are 75 customers, how many customers would be expected to purchase some bread or rolls? Write a proportion Use n to represent the number of customers to buy bread or rolls n 17 = _ _ 25 75 75(17) = 25n Solve for n On a day with 75 customers, 51 would be expected to purchase bread or rolls 1,275 = 25n 25n 1275 = _ 25 25 51 = n Chapter Study Guide 79 Chapter Chapter Test Determine whether the ratios are proportional Write = or ≠ in each circle 3AF2.2, 5SDAP1.3 15 ≠ 10 ≠ = _ 27 Solve each proportion 3AF2.2, 5SDAP1.3 p 3 _ = p = 27 18 36 _ = _ 25 f 135 = 135 f = 100 Convert each unit using a proportion Round to the nearest tenth if necessary 3AF1.4, 3MG1.4, 6AF2.1 16 ounces = pint; 48 ounces = in ≈ 2.54 cm; in ≈ 20.3 cm mi = 5,280 ft; 15,840 ft = 3 mi pints 1,000 m = km; 2,050 m = 2.1 km lb = 16 oz; 56 oz = 3.5 lbs 10 T = 2,000 lb; 7,000 lb = 3.5 T Find each total cost 3AF2.1, 3AF2.2 One ticket costs $7.75 How much are 12 tickets? $93 12 $98.85 buys admissions to the theme park How much is admission? $32.95 Write a ratio Then find each unit rate Round to the nearest tenth if necessary 3AF2.1, 3AF2.26AF2.3 13 $75 earned in hours 14 296 miles in hours 80 Chapter Test 75 , $12.50/h _ 296 , 49.3 mi/h _ Copyright © by The McGraw-Hill Companies, Inc 11 15 Find the value of x in each pair of similar figures 6NS1.3 
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DN x = 7.2 Solve 3AF2.1, 5SDAP1.3, 3AF2.2, 6AF2.3, 3AF1.4, 6NS1.3, 7AF4.2 17 SPORTS A group of friends jogged during lunch time After 60 minutes, they had jogged miles If they kept a fairly steady pace, then how far had they jogged after 45 minutes? 4.5 miles 18 ART The two frames shown are proportional What is the width of the second frame? _ Copyright © by The McGraw-Hill Companies, Inc 13 inches Correct the mistakes 19 pounds of walnuts for a recipe She Jeremy’s mother needed looked at the store’s ad and saw that walnuts were on sale for $6.99 per pound She gave Jeremy a 10-dollar bill to buy the walnuts What mistake did she make? He would need more than $10 in order to purchase the amount his mother requested He would need about $0.50 more 20 Roberta wanted to make lemonade The recipe called for gallons of water Roberta had only a 2-cup measuring cup for measuring She filled the measuring cup times with water to make the lemonade What mistake did she make? Roberta should have filled the measuring cup 16 times Chapter Test Getty Images 81 Chapter Standards Practice Choose the best answer and fill in the corresponding circle on the sheet at right A group of students wants to ride on the newest roller coaster at the amusement park The height requirement is feet Which students will be allowed on the ride? 3MG1.4 Student Height (inches) Isabelle Brady Omar Frankie 52 61 58 63 A family’s meal totals $43.80, including tax After a 15% tip is added, what is the total cost of the meal? 7NS1.7 F $6.57 H $50.37 G $43.80 J $52.56 A store buys DVDs of new movies for $6 each It marks up the price 350% At what price does this store sell these DVDs? 7NS1.7 A Isabelle and Omar A $7.17 C $21 B Brady and Frankie B $18 D $27 C Brady and Omar D Isabelle and Frankie F 200 feet H 1,200 feet F $25,017 H $50,035 G 900 feet J 1,800 feet G $38,473 J $5,003,500 Hector ran 116 laps during track practice this week LaShawn ran 75% of Hector’s total laps How many laps did LaShawn run this week? 6NS1.4 A 58 laps C 143 laps B 87 laps D 203 laps How many grams equal milligrams? 3MG1.4 A 0.007 g C 700 g B 0.7 g D 7,000 g GO ON 82 Chapter Standards Practice Copyright © by The McGraw-Hill Companies, Inc Naomi is running the 600-yard medley How many feet is this? 3MG1.4 Mr Alvarez earns a 4% commission on each home he sells Last year, his home sales totaled $1,250,875 How much did Mr Alvarez make in commission? 7NS1.7 Copyright © by The McGraw-Hill Companies, Inc 10 Juanita uses 12.5 cups of mashed bananas to make loaves of banana bread How many cups of mashed bananas does she need to make loaves? 6NS1.3 F 2.5 cups H cups G 4.17 cups J 7.5 cups Antonio needs feet of rope Which package of rope should he purchase? 3MG1.4 A 36 inches C 55 inches B 48 inches D 60 inches Marissa has a picture measuring 100 mm by 150 mm Which frame will best fit this picture? 3MG1.4 F cm by 1.5 cm G 100 cm by 150 cm H 10 cm by 15 cm 12 If inch equals 2.54 centimeters, how many inches equal 12.7 centimeters? F inches H inches G inches J 32.258 inches 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 J 0.10 cm by 0.15 cm Success Strategy 11 A bird flew at 13 miles per hour for hours Then the bird flew at 15 miles per hour for hours How far did the bird fly in all? 7AF4.2 A 26 miles C 71 miles B 45 miles D 195 miles After you select your answer, reread the question to check that the answer is reasonable Check for careless mistakes, like skipping over words that change the meaning of the question Chapter Standards Practice 83 Index A Algebra and Functions, 46, 53, 61, 69 K Key Concept, 4, 11, 21, 29, 46, 53, 61, 69 Answer sheet, 43, 83 Assessment, 40–41, 80–81 C California Mathematics Content Standards, 4, 11, 21, 29, 46, 53, 61, 69 Chapter Preview, 3, 45 M Mathematical Reasoning, see Step-by-Step Problem Solving Measurement and Geometry, 53 metric system of measurement, 53–59 Chapter Test, 40–41, 80–81 commission, 11–19 compound interest, 21–28 Correct the Mistakes, 41, 81 N Number Sense, 4, 11, 21, 29, 69 cross multiply, 11–19 cross products, 11–19, 46–52 customary system of measurement, 53–59 D P percent, 4–10, 11–19, 21–28, 29–35 percent of change, 29–35 distance, 61–68 Problem-Solving, see Step-byStep Problem Solving Progress Check, 20, 36, 60, 76 E equation, 11–19, 21–28, 29–35, 46–52, 53–59, 61–68, 69–75 I increase, 29–35 interest compound, 21–28 simple, 21–28 84 Index proportion, 11–19, 46–52, 53– 59, 61–68, 69–75 R rate, 21–28, 46–52 ratio, 4–10, 11–19, 21–28, 29–35 Real-World Applications art, 81 astronomy, babies, 58 baking, 58 baseball, 59 biking, 50 books, 35 Reflect, 9, 17, 26, 34, 51, 57, 67, 73 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc principal, 21–28 decrease, 29–35 business, 10, 27, 33, 36, 51, 52, 57, 68 cell phones, 17 chess, 10 commission, 18 community service, 68 computers, 16 construction, 58 contact lenses, 35 cooking, 56 discount, 16, 18 earth science, 68 eating out, 10 education, 59 elections, 36 entertainment, 75 events, 74 fashion, 10, 19, 28, 34, 52, 68 finance, 26, 27 finances, 26, 41 fitness, 75 food, 51 geography, 60 geometry, 73 hiking, 66 life science, 68 loans, 27 money, 20, 25 movies, 17, 20, 36, 66 nature, 57 packaging, 41 painting, 67 pets, 50 proportions, 73 reading, 51 sales, 35, 38 school, 9, 28, 50 scuba diving, 75 shopping, 38 snow, 67 sports, 10, 33, 41, 81 studying, 19 surveys, 18 taxes, 14, 16, 18 tennis, tests, 18 tipping, 14, 16, 18 travel, 60, 67, 76 S scale, 69–75 similar figures, 69–75 simple interest, 21–28 Spiral Review, 10, 19, 28, 35, 52, 59, 68, 74 Standards Practice, 42–43, 82–83 Statistics, Data Analysis, and Probability, 4, 46 Step-by-Step Practice, 7, 15, 24, 32, 49, 55, 65, 72 Step-by-Step Problem Solving Practice, 8–9, 16–17, 25–26, 33, 50, 56–57, 66, 73 Look for a pattern, 56 Make a table, 50 Solve a simpler problem, 8, 16, 25 Use a table, 73 Use logical reasoning, 33 Write an equation, 66 V Vocabulary, 4, 11, 21, 29, 46, 53, 61, 69 Vocabulary and Concept Check, 37, 77 Vocabulary Check, 10, 19, 28, 35, 52, 59, 68, 75 Study Guide, 37–39, 77–79 Success Strategy, 43, 83 U unit cost, 61–68 W Who is Correct?, 6, 14, 24, 31, 48, 55, 64, 71 Writing in Math, 10, 19, 28, 35, 52, 59, 68, 74 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc unit rate, 46–52, 53–59, 61–68 Index 85 ... 10 09 08 07 California Math Triumphs Volume 3B 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. .. 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