Ratios and rates grade 7

Ratios and Rates Number Mathematics in Context is a comprehensive curriculum for the middle grades It was developed in 1991 through 1997 in collaboration with the Wisconsin Center for Education Research, School of Education, University of Wisconsin-Madison and the Freudenthal Institute at the University of Utrecht, The Netherlands, with the support of the National Science Foundation Grant No 9054928 The revision of the curriculum was carried out in 2003 through 2005, with the support of the National Science Foundation Grant No ESI 0137414 National Science Foundation Opinions expressed are those of the authors and not necessarily those of the Foundation Keijzer, R., Abels, M., Wijers, M., Brinker, L J., Shew, J A., Cole, B R., and Pligge, M A (2006) Ratios and rates In Wisconsin Center for Education Research & Freudenthal Institute (Eds.), Mathematics in Context Chicago: Encyclopædia Britannica, Inc Copyright © 2006 Encyclopỉdia Britannica, Inc All rights reserved Printed in the United States of America This work is protected under current U.S copyright laws, and the performance, display, and other applicable uses of it are governed by those laws Any uses not in conformity with the U.S copyright statute are prohibited without our express written permission, including but not limited to duplication, adaptation, and transmission by television or other devices or processes For more information regarding a license, write Encyclopædia Britannica, Inc., 331 North LaSalle Street, Chicago, Illinois 60610 ISBN 0-03-039629-8 073 09 08 07 06 The Mathematics in Context Development Team Development 1991–1997 The initial version of Ratios and Rates was developed by Ronald Keijzer and Mieke Abels It was adapted for use in American schools by Laura J Brinker, Julia A Shew, and Beth R Cole Wisconsin Center for Education Freudenthal Institute Staff Research Staff Thomas A Romberg Joan Daniels Pedro Jan de Lange Director Assistant to the Director Director Gail Burrill Margaret R Meyer Els Feijs Martin van Reeuwijk Coordinator Coordinator Coordinator Coordinator Sherian Foster James A, Middleton Jasmina Milinkovic Margaret A Pligge Mary C Shafer Julia A Shew Aaron N Simon Marvin Smith Stephanie Z Smith Mary S Spence Mieke Abels Nina Boswinkel Frans van Galen Koeno Gravemeijer Marja van den Heuvel-Panhuizen Jan Auke de Jong Vincent Jonker Ronald Keijzer Martin Kindt Jansie Niehaus Nanda Querelle Anton Roodhardt Leen Streefland Adri Treffers Monica Wijers Astrid de Wild Project Staff Jonathan Brendefur Laura Brinker James Browne Jack Burrill Rose Byrd Peter Christiansen Barbara Clarke Doug Clarke Beth R Cole Fae Dremock Mary Ann Fix Revision 2003–2005 The revised version of Ratios and Rates was developed by Mieke Abels and Monica Wijers It was adapted for use in American schools by Margaret A Pligge Wisconsin Center for Education Freudenthal Institute Staff Research Staff Thomas A Romberg David C Webb Jan de Lange Truus Dekker Director Coordinator Director Coordinator Gail Burrill Margaret A Pligge Mieke Abels Monica Wijers Editorial Coordinator Editorial Coordinator Content Coordinator Content Coordinator Margaret R Meyer Anne Park Bryna Rappaport Kathleen A Steele Ana C Stephens Candace Ulmer Jill Vettrus Arthur Bakker Peter Boon Els Feijs Dédé de Haan Martin Kindt Nathalie Kuijpers Huub Nilwik Sonia Palha Nanda Querelle Martin van Reeuwijk Project Staff Sarah Ailts Beth R Cole Erin Hazlett Teri Hedges Karen Hoiberg Carrie Johnson Jean Krusi Elaine McGrath (c) 2006 Encyclopædia Britannica, Inc Mathematics in Context and the Mathematics in Context Logo are registered trademarks of Encyclopædia Britannica, Inc Cover photo credits: (all) © Getty Images Illustrations 12, 14–16, 20 © Encyclopỉdia Britannica, Inc.; 19, 22, 23, 32 Holly Cooper-Olds; 36, 37, 40, 53 Michael Nutter/© Encyclopỉdia Britannica, Inc.; 54 Christine McCabe/© Encyclopỉdia Britannica, Inc Photographs (top) Gary Russ/HRW Photo; (bottom) Victoria Smith/HRW; HRW Photo/ Sam Dudgeon; 4–6 Victoria Smith/HRW; 11 (top to bottom) © Corbis; © Corbis; © PhotoDisc/Getty Images; © Corbis; 16 (left to right) © Corbis; © Corbis; John A Rizzo/PhotoDisc/Getty Images; © Corbis; 21 Dennis MacDonald/Alamy; 22 © Corbis; 25 (left to right) PhotoDisc/Getty Images; © Corbis; 27 PhotoDisc/ Getty Images; 30 Sam Dudgeon/HRW; 35 (top) Jim Vogel; (bottom) Kalmbach Publishing Co collection; 39 © Corbis; 41 (left to right) © Digital Vision/ Getty Images; PhotoDisc/GettyImages; 42 (top, bottom) © Corel; (middle) Dynamic Graphics Group/Creatas /Alamy; 43 (top) James F Snyder; (bottom) Artville/Getty Images; 45 (left to right) © Corbis; Georgette Douwma/PhotoDisc/Getty Images; Russell Illig/PhotoDisc/Getty Images; 47 (top) Su Davies/PhotoDisc/Getty Images; (bottom) PhotoDisc/Getty Images; 49 Artville/Getty Images; 54 Andrew Ward/ Life File/PhotoDisc/Getty Images Contents Letter to the Student Section A Single Number Ratios Car Pooling? Miles per Gallon Miles per Hour Cruise Control Summary Check Your Work Section B 21 23 25 28 29 Scale and Ratio Scale Drawings Scale Models Maps Summary Check Your Work Section E 11 15 16 18 19 Different Kinds of Ratios Too Fast Percent Part-Part and Part-Whole Summary Check Your Work Section D Comparisons Telephones and Populations Television Sets Cell Phones Summary Check Your Work Section C vi 30 35 36 38 39 Scale Factor Smaller or Larger Enlarged or Reduced Summary Check Your Work 41 43 48 49 Additional Practice 50 Answers to Check Your Work 55 Contents v Dear Student, Welcome to the unit Ratios and Rates In this unit you will learn many different ways to make comparisons Do you have more boys or girls in your class? If you count, you might use a ratio to describe this situation You can make comparisons using different types of ratios You might have noticed speed limit signs posted along highways and streets The rate a car travels on a highway is usually greater than the rate a car travels on a street You can make comparisons using rates You use ratios to make scale drawings Architects use scale drawings to design and build buildings They create sets of working documents, which contain a floor plan, site plan, and elevation plan Maps are also scale drawings Have you ever looked at a cell through a microscope? The magnification of the lens sets the ratio between what you see and the actual size of the cell Architects, engineers, and artists often make scale models of objects they want to construct Many people have hobbies creating miniature worlds using trains, planes, ships, and automobiles When you look through a microscope, you see enlargements of small objects In all instances, ratios keep everything real We hope you learn efficient ways to work with ratios and rates Sincerely, The Mathematics in Context Development Team vi Ratios and Rates A Single Number Ratios Car Pooling? The students in Ms Cole’s science class are concerned about the air quality around Brooks Middle School They noticed that smog frequently hangs over the area They just finished a science project where they investigated the ways smog destroys plants, corrodes buildings and statues, and causes respiratory problems The students hypothesize that the city has so much smog because of the high number of cars on the roads Students think there are so many cars because most people not carpool They want to find out if people carpool They set up an experiment to count the number of cars and people on the East Side Highway adjacent to the school Section A: Single Number Ratios A Single Number Ratios One group spent exactly one minute and counted 10 cars and 12 people a How many of these cars could have carried more than one person? Give all possible answers b Find the average number of people per car and explain how you found your answer At the same time, at a different point on the highway, a second group of students counts cars and people for two minutes A third group counts cars and people for three minutes The second and third groups each calculate the average number of people per car They are surprised to find that both groups got an average of 1.2 people per car How many cars and how many people might each group have counted? Ratios and Rates Single Number Ratios A A fourth group counts cars and people for one minute on the north side of the school They count 18 cars and 21 people Compare the results of the fourth group of students with those of the other three groups What conclusions can you draw? For the first group of students, the ratio of people to cars was 12 people to 10 cars or 12:10 Another way to describe this is it to use the average number of people per car The first three groups calculated an average of 1.2 people per car They might have found this average by calculating the result of the division 12 ، 10 You can show both the ratio and the average in a ratio table Number of People 12 1.2 Number of Cars 10 a How can you use the ratio table to find the average number of people per car? b You can also write the average number of people per car in a ratio What ratio is this? c Given this average, how many people would you expect to see if you counted 15 cars? d What can you say about the number of people in each of the 15 cars? In order to lessen air pollution, the students investigate ways to increase the average number of people per car Explain why a higher average of people per car will result in fewer cars You may use examples in your explanation Section A: Single Number Ratios A Single Number Ratios Some students recommend that the average number of people per car should increase from 1.2 to 1.5 people per car a Find different groups of cars and people that will give you an average of 1.5 people per car Put your findings in a table b Work with a group of your classmates to make a poster that will show the city council how raising the average number of people per car from 1.2 to 1.5 will lessen traffic congestion and improve the quality of air Miles per Gallon Another way to reduce air pollution is to encourage drivers to use automobiles that are more efficient A local TV station decides to a special series on how to reduce air pollution In one report, the newscaster mentions, “Cars with high gas mileage pollute less than cars with low gas mileage.” Gas mileage is the average number of miles (mi) a car can travel on gallon (gal) of gasoline It is represented by the ratio of miles per gallon (mpg) John says, “My car’s gas mileage is 25 mpg.” How many miles can John travel on 12 gal of gas? Ratios and Rates E Scale Factor A scale factor tells you how you enlarged or reduced every measurement of the original picture or object Note that a scale factor is always expressed as a multiplier If a scale factor is greater than one, it is an enlargement If a scale factor is between zero and one, it is a reduction You can work with scale factors using arrow language or a ratio table These tools help organize your work and make calculations easier For example, an enlargement with a scale factor of 2: Using arrow language: scale factor Length of Original Drawing (in cm) ؋2 Length Enlargement (in cm) Using a ratio table: scale factor Length of Original Drawing (in cm) Length of Enlargement 10 (in cm) ؋2 For example, a reduction with a scale factor of 0.25: Using arrow language: scale factor Length of Original Drawing (in cm) ؋ 0.25 Length Reduction (in cm) Using a ratio table: scale factor Length of Original Drawing (in cm) 12 Length of Reduction 0.25 (in cm) ؋ 0.25 Note that the scale factor is always a multiplication factor To make the calculations you can use division as well 48 Ratios and Rates Four pictures are reduced One measurement of the original pictures and the reductions are listed in the table below Length of Original (in cm) Length of Reduction (in cm) Picture A Picture B 24 Picture C 35 8.5 Picture D 30 7.5 a For which two pictures are the scale factors the same? b Are the two remaining pictures reduced more or less than the two pictures with the same scale factor? How you know? The actual length of an ant is about mm What is the scale factor for the drawing of the ant shown on the right? Copy and complete the table below Scale Factor Enlargement or Reduction? Length 0.1 ᎑᎑ enlargement Binoculars have a scale ratio Describe in your own words what a scale ratio of 1:35 would mean for binoculars Section E: Scale Factor 49 Additional Practice Section A Single Number Ratios Mr Adams asked his students to conduct a survey to find the average number of children in a family Sarah surveyed 12 families in her neighborhood and counted a total of 28 children a In your opinion, how many of the families Sarah surveyed you think had exactly two children? Why you think so? b What is the average number of children per family in Sarah’s neighborhood survey? c What are some other numbers of families and children that produce this same average? Dennis surveyed his neighborhood He found an average of 2.5 children per family List some different possibilities for the numbers of families and children that Dennis could have counted Dave has a car He made three different trips Trip A: 112 miles Trip B: 70 miles Trip C: 21 miles The gas mileage of Dave’s car is 28 mpg For each of the trips calculate how many gallons of gas Dave used Dave traveled non-stop for each trip and made a record of the times listed below Trip A: hours (112 miles) Trip B: 1.5 hours (70 miles) Trip C: 20 minutes (21 miles) For each trip, calculate Dave’s average speed in miles per hour 50 Ratios and Rates Section B Comparisons The table below lists just a few of the countries you saw in the table on page 11 Country Population Number of Telephones Number of Radios Bolivia 8.4 million 1.26 million 5.5 million Chad 9.0 million 44,000 1.9 million Finland 5.2 million 6.3 million 8.4 million Tonga 102,000 14,500 61,000 Solomon Islands 450,000 7,600 36,000 United States 292.6 million 317 million 598 million Source: Encyclopaedia Britannica Almanac 2005 (Chicago: Encyclopaedia Britannica, Inc., 2005) A fourth column with the number of radios has been added a Which country has the fewest number of radios? b Do any countries have more telephones than radios? If so, which ones? c Which country has the largest number of radios per person? a Choose two countries and compare the numbers of people per telephone in an absolute and in a relative way b For the same two countries you choose in part a, compare the numbers of people per radio in these countries, both in an absolute and in a relative way Additional Practice 51 Additional Practice Section C Different Kinds of Ratios There are four city recreation centers where girls can participate in after-school sports Because funding is limited, only one recreation center will have a girls’ basketball coach The following table shows the number of girls involved in basketball and the number involved in sports other than basketball at each recreation center Recreation Center Girls Involved in Basketball Girls Involved in Other Sports 16 13 12 35 22 23 20 Compare the four centers a Which center has the highest number of girls participating in after-school sports? b Which center has the highest number of girls involved in basketball? c Which center has the highest percent of its participating girls involved in basketball? Explain Write a percent for each of the following: a One out of every four girls in the seventh grade plays volleyball b Three out of every five boys in the sixth grade play soccer c Eleven out of every 15 students like to participate in sports events d Thirty-two out of the 78 boys in our school are on the football team 52 Ratios and Rates Additional Practice Section D Scale and Ratio Members of the Lewis and Clark expedition (1804–1806) searched for an overland route from the Mississippi River to the Pacific Ocean nsi n o rad lo o C atte Pl GE RAN ba W isc o s te i L ake Michigan St Louis A sas an rk : 25,000,000 pp ou r i Miss l at S VE DESERT M i s si N P ED I NT T PA ES E R D DEATEHY VALL Lewis's MOHA return route si S IN RA SIER DA A NEV Clark's return route L ak e S up e r i o r I N TA Lewis and Clark S Fort Mandan BLACK H I LL S ny Al Re d e wston Yello E Lake Winnipeg Missouri B I G S N OW MTS UN LEWIS AND CLARK ROUTES W A P L ADE wan BEAR PAW MTS RANGE SC N MO Sna A ST RANG E CA S KY CO ke S a s k a tc he OT BITTERRO C RO IC OLYMP MTS Fort Clatsop skatc hew an T E A G R Columbia P A C I F I C O C E A N N S a O ZA RK U TEA PLA O hio The scale of this map is 1:25,000,000 Estimate the distance Lewis and Clark covered when they traveled from St Louis to Fort Clatsop Here is an excerpt from a journal May 14, 1804 Expedition begins in St Louis October 24, 1804 Expedition discovers earth lodge villages of the Mandan and Hidatsas Indians The captains decide to build Fort Mandan across the river from the main village a Use the information in the journal to estimate the average distance the expedition covered per month during this period Note that Fort Mandan is about halfway between St Louis and Fort Clatsop b Also find the average distance per day Additional Practice 53 Additional Practice Eiffel Tower Puzzle The wrought-iron original has attracted millions of visitors and is the symbol of Paris Now you can construct your own Eiffel Tower to a scale of 1:500 The height of the actual tower is 312 meters What is the height of the model? Section E Scale Factor Some ponds become green in the summer because of the large number of algae in the water Algae are actually very small plants The simplified drawing on the left shows the Scenedesmus alga This is the size they would appear to be if seen through a microscope that enlarges 250x Tamar wants to make a life-sized drawing of one alga She begins by calculating the actual length of this type of alga She is suddenly very surprised Why? Algae (250؋) Would you be able to see a Scenedesmus alga with a microscope that enlarges 80x? Why or why not? Electron microscopes are more powerful than ordinary microscopes This picture from an electron microscope shows a blood cell enlarged by a scale factor of 10,000 a Which are larger Scenedesmus algae or blood cells? Explain your reasoning Blood Cell (10,000؋) b Could you make a drawing of the blood cell if it was enlarged by a factor of 250? Why or why not? c How would a magnification of 80x work for looking at blood cells? Explain your answer 54 Ratios and Rates Section A Single Number Ratios a There are 2.5 people per car There are different ways to find this answer Using a ratio table: Number of People 40 20 10 2.5 Number of Cars 16 Using division: 40 ، 16 ‫ ؍‬2.5 b About 35.6 students per class Using a calculator, 320 ، ‫ ؍‬35.5555, and rounding to one decimal is 35.6 18 mpg Sample strategy: Miles Gallons of Gas 108 54 18 3 The mechanic charged $60 per hour Here are two ratio table strategies Charge $90 $900 $180 $60 Hours 1.5 15 or Charge $90 $30 $60 Hours 1.5 0.5 25:15 written as a single number is 1.7 Here is one ratio table strategy Number of People 25 1.7 Number of Cars 15 Answers to Check Your Work 55 Answers to Check Your Work Ask a classmate to your problem Check and discuss the answer Here is one possible problem Talia makes about 82% of her free throws This season she shot 40 free throws How many free throws did she make? Solution: 82% is 82:100, so setting up a ratio table, she made about 33 free throws Section B Number of Free Throws Made 82 8.2 ≈33 Number of Free Throws Shot 100 10 40 Comparisons Two different answers are possible Your explanation is critical Tom is correct: I start with the ratio 14.2 million: 43.6 million This is the same ratio as 14.2:43.6 I use a ratio table to get a ratio of phones per person Then I find the number of telephones per 100 people Number of Telephones 14.2 ≈0.33 33 Number of People 43.6 100 Tom is incorrect: I start with Tom’s statement that the ratio is 33 telephones for every 100 people Then I use the ratio table to build up to 43.6 million people Number of Telephones (in millions) 33 3.3 0.33 14.4 Number of People 100 10 43.6 (in millions) This doesn’t match the data since 14.4 phones is not the same as 14.2 phones a Texas, with 13.6 million cows b The comparison is absolute because the number of people is not involved c Kansas has 244 cows per 100 people while Montana has 278 cows for every 100 people, so Montana has more cows for every 100 people 56 Ratios and Rates Answers to Check Your Work Kansas: 6.6 million cows per 2.7 million people; I calculated 6.6 ، 2.7 ➝ 2.44 This is 244 cows per 100 people For this calculation, you can also use a ratio table Number of Cows (in millions) 6.6 66 2.44 244 Number of People (in millions) 2.7 27 100 Montana: 2.5 million cows per 0.9 million people; I calculated 2.5 ، 0.9 ➝ 2.78 This is 278 cows per 100 people d The comparison is relative, because the number of cows is in relation to the number of people Different answers are possible depending on how you compared the data If you made a relative comparison your can compare the area per person, or you can compare the number of people per square mile For either strategy, the conclusion is that Japan is the most populated Japan, compared to Argentina and Brazil, has more people per square mile and each person has the least area available to them Here are the results for both strategies Country Area (sq mi) Population Square Miles Population per per Person Square Mile Argentina 1.1 million 36.8 million 0.030 33.5 Japan 146,000 127 million 0.001 869.9 Brazil 3.3 million 176 million 0.019 53.3 If you made an absolute comparison, Brazil has the largest population with 176 million people Answers to Check Your Work 57 Answers to Check Your Work Section C Different Kinds of Ratios Discuss the examples you found with a classmate and check whether they are right Here is one example This season, our baseball team won 23 games and lost 20 games The win: loss ratio is 23:20, which is a part-part ratio The win: total ratio is 23:43, which is a part-whole ratio With the part-part ratio, you can see they won games more than they lost Using the part-whole ratio, the team win average is over 500 (0.535) You can use this average to compare our school to other schools across the country that might play more or fewer games than we a 3:5 b 3:8 (people with side effects) or 5:8 (people without side effects) c Only a part-whole ratio can be written as a percent This is the is 0.125; this helps me with ratio in 2b I always remember ᎐᎐ other eighths , which is 0.375 or 37.5% 3:8 written as a fraction is ᎐᎐ 5:8 written as a fraction is , which is 0.625 or 62.5% ᎐᎐ or 20% a 1:5 written as a fraction is ᎐᎐ or 75% b 3:4 written as a fraction is ᎐᎐ 21 c 21:130 written as a fraction is ᎐᎐᎐ 130 Using a calculator 21 ، 130 ≈ 0.16153 or about 16% (or 16.2%) 58 Ratios and Rates Answers to Check Your Work Scale and Ratio Here is one sample drawing Your room dimensions should be cm by cm Door Bed Window Section D cm Desk Chair Dresser cm The scale ratio of 1:50, means cm on the map is 50 cm in reality Working up to 300 cm (3 m) and 400 cm (4 m), you can get the drawing dimensions needed ➝ 50, cm ➝ 100 cm, cm ➝ 400 cm and cm ➝ 300 cm a Yes, a life-size drawing of the butterfly would fit on a page in this book because it is 10 cm Here is how 10 cm looks 10 cm b About 2.5 cm c The scale ratio is 1:4 Sample strategy using a double number line: 2.5 In Drawing (in cm) 10 20 Actual (in cm) Sample strategy using a ratio table: In Drawing (in cm) 2.5 25 Actual 10 100 (in cm) Answers to Check Your Work 59 Answers to Check Your Work d The actual length of the body of the butterfly is 3.6 cm Here is one strategy The body length in the reduction is about 0.9 cm Since this of the length, the body length is about 3.6 cm represents ᎐᎐ (0.9 ؋ ➝ 3.6) a cm represents kilometer, which is 1,000 meters b The scale ratio is 1:100,000 On the map, cm represents 1,000 m In reality, 1,000 m is 100,000 cm So cm on the map represents 100,000 cm in reality The scale ratio is 1:100,000 a On Map (in cm) In Reality (in cm) 1,000 1,000 In Reality (in cm) 100,000 Distance on a Map (in cm) Actual Distance (in cm) 5,000 b About 385 m or 0.385 km The distance on the map is about 7.7 cm Since cm represents 5,000 cm, you can calculate 7.7 ؋ 5,000 ➝ 38,500 cm or 385 m If you measured a distance between 7.3 cm and 7.8 cm on the map, your answer must be between 365 m and 390 m a The map is designed to be used by someone who is walking Here is one way of reasoning cm on the map represents 20,000 cm in reality This is about 200 m If cm represents 200 m then 10 cm represents 2,000 m, which is km I chose 10 cm, because that fits nicely on a page The map is not for driving because you would be off the map before you knew it km is a short distance 60 Ratios and Rates Answers to Check Your Work b Here is one possible scale line meters 1,000 200 Your scale line might look different You might have other distances indicated like 400 m (at cm); 600 m (at cm); etc Instead of meters, it may show kilometers, and every cm is km Note that for a scale line to be correct, cm must represent 200 m Section E Scale Factor a Pictures A and D have the same scale factor, 0.25 Here are two strategies Calculating the scale factor of each: Scale Ratio Scale Factor Picture A 2: 0.25 Picture B : 24 about 0.33 Picture C 8.5 : 35 about 0.24 Picture D 7.5 : 30 0.25 Finding the scale factor using ratio tables: Picture A Original (cm) Reduction (cm) 0.25 (cm) 24 Reduction (cm) 0.33- (cm) 35 70 Reduction (cm) 8.5 17 0.24- (in cm) 30 60 20 Reduction (in cm) 7.5 15 0.25 ؋ 0.25 Picture B Original Ӎ؋ 0.33 Picture C Original Ӎ؋ 0.24 Picture D Original Ӎ؋ 0.25 Answers to Check Your Work 61 Answers to Check Your Work b Picture B is reduced less, and picture C is reduced a little more Sample Explanation: Pictures A and D are one-fourth of their original size Picture B is one-third its original size So picture B is not reduced as much as pictures A and D Similarly picture C is reduced a little more than the other two because 0.24 is less than 0.25 Note: When a reduction is minor (reduced less), the scale factor is closer to When a reduction is extensive (reduced more), the scale factor is closer to The scale factor is 10 Here is one sample strategy The measured length in the picture is about cm or 40 mm I set up an arrow string to find the scale factor ؋⎯⎯→ ? 40 mm mm ⎯⎯⎯ I found ؋ 10 ‫ ؍‬40, so the scale factor is 10 62 Ratios and Rates Scale Factor Enlargement or Reduction? enlargement 0.1 reduction ᎐᎐ reduction Any number that is greater than enlargement Neither; 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ISBN 0-03-039629-8 073 09 08 07 06 The Mathematics in Context Development Team Development 1991–19 97 The initial version of Ratios and Rates was developed by Ronald Keijzer and Mieke Abels It... Denmark United States Canada Taiwan Poland World 74 0 440 320 970 260 160 Number of Cell Phones per 1,000 People CANADA UNITED STATES 16 Ratios and Rates DENMARK POLAND TAIWAN Comparisons B 11 a Can... comparison be a better choice? 14 Ratios and Rates Comparisons B Television Sets CANADA FRANCE BRAZIL TV Sets there are 3 17 TVs Brazil has about 176 million people, and e are about for every 1,000