Launch Activity Ratios and Rates PDF

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Launch Activity Launch Activity 2 Ratios and Rates Meet Me in St. Louis Baseball teams like the St. Louis Cardinals record information about each player on the team. These statistics are used to describe a player’s performance. Statistics for a pitcher include the pitcher’s earned run average, or ERA. ERA is the number of runs, on average, a pitcher allows the opposing team to score per game. The lower the ERA, the better! More About Baseball The St. Louis Cardinals, based Statistics for a hitter include the hitter’s number of at-bats, in St. Louis, Missouri, were hits, doubles, home runs, and strikeouts. founded in 1882. In 1947, Jackie Robinson became The table shows the batting results of three baseball the first Black person to play for players who received a Most Valuable Player (MVP) a Major League baseball team. © Houghton Mifflin Harcourt Publishing Company Image credits: (t) ©Icon Sportswire/Getty Images; (b) ©Scott Kane/Getty Images Award while playing for the St. Louis Cardinals. The oldest baseball stadium Player Name Batting Results in the United States is Fenway Park, in Boston, Massachusetts, Albert Pujols (2008) 187 hits in 524 at-bats which opened in 1912 and is Stan Musial (1948) 230 hits in 611 at-bats home to the Boston Red Sox. Rogers Hornsby (1925) 203 hits in 504 at-bats Three Reads First, read to understand the situation. Next, read to understand the math. Then, read to ask what mathematical questions could be asked about the problem. One of the oldest and most widely used tools to measure a hitter’s success is batting average, or AVG. Batting average is the ratio of a player’s hits to the player’s total number of at-bats. A batting average is a number ALBERT PUJOLS between zero (shown as.000) and one (1.000). Launch Activity Ratios and Rates    167  Go Online For the interactive lesson Read the final question. Make a plan to solve the problem. One of the oldest and most widely used tools to measure a hitter’s success is batting average, or AVG. Batting average is the ratio of a player’s hits to the player’s total number of at-bats. A batting average is a number between zero (shown as.000) and one (1.000). What is each player’s batting average written as a fraction, a decimal, and a percent? Write, model, or draw to solve the problem. © Houghton Mifflin Harcourt Publishing Company Image credit: ©sirtravelalot/Shutterstock Discuss with a partner or in a group. Math Talk A baseball team’s players come up to bat in the same order for the entire game. How would you order the three players so the player with the best batting average bats first and the lowest batting average hits last? 168 Go Math! Grade 6  Chapter Name 4 Ratios and Rates Show What You Know Multiply or Divide to Find Equivalent Fractions Multiply or divide to find two equivalent fractions for the given fraction. 1​ _ 1. ​ 5_​ 2. ​ 12​ __ 3. ​ 2 6 18 ___ ___ ___ Extend Patterns Write a description of the pattern. Then find the missing numbers. 4. 3, __ , 48, 192, 768, __ 5. 625, 575, 525, __ , __ , 375 __ __ Multiply by 2-Digit Numbers Find the product. 6. ​    52 ​ 7. ​    14 ​ 8. ​    37 ​ 9. ​    45 ​ × _ 19 × _ 88 × _ 21 × _ 62 © Houghton Mifflin Harcourt Publishing Company Image Credits: (br) ©Image Source/Corbis l MATH in the Reoarld W The student council should have 1 representative for every 25 students. Which of these situations fits the description? Explain your answer. a. 5 representatives for 100 students b. 10 representatives for 250 students c. 15 representatives for 300 students Chapter 4   169  Vocabulary Builder Go Online For more help Visualize It Connect to Vocabulary Complete the bubble map with review words that are related to fractions. Review Words coordinate plane denominator ✓ equivalent fractions numerator ✓ ordered pair pattern simplify Fractions x-coordinate y-coordinate Preview Words ✓ equivalent ratios ✓ rate ✓ ratio ✓ unit rate Understand Vocabulary Complete the sentences using the checked words. 1. A comparison of one number to another by division is a ___________. ___________ are ratios that name the same comparison. 2.  ___________ are fractions that name the same 3.  amount or part. 4. A ratio that compares quantities with different units is a ___________. 5. A(n) ___________ is a rate that compares a quantity to 1 unit. 6. In a(n) ___________, the first number is the x-coodinate, and the second number is the y-coordinate. 170  Go Math! Grade 6  CHAPTER 4 Name Lesson 1 Ratios and Rates I Can write ratios and rates. UNLOCK the Problem Real World A bird rescue group is caring for 3 eagles, 2 hawks, and 5 owls in their rescue center. You can compare the numbers of different types of birds using ratios. A ratio is a comparison of two quantities by division. There are three ways to write the ratio of owls to eagles in the rescue center. Using words As a fraction With a colon 5 to 3 ​  5_3 ​ 5:3 Ratios can be written to compare a part to a part, a part to a whole, or a whole to a part. A. Use red and yellow counters to model the ratio that compares the number of owls to the number of hawks. Owls to Hawks © Houghton Mifflin Harcourt Publishing Company Image Credits: (c) ©Photodisc/Getty Images The ratio is _:_ Part to part Write each ratio using words, as a fraction, and with a colon. B. Eagles to total birds in the rescue center ____ ​ ​ Part to whole _ to _ _:_ C. Total birds in the rescue center to hawks ​____​ Whole to part _ to _ _:_ 1. The ratio of owls to total number of birds is 5:10. Explain what this ratio means. Go Online For more help Chapter 4 Lesson 1   171  Example A restaurant sells veggie burgers at the rate of $4 for 1 burger. What rate gives the cost of 5 veggie burgers? Write the rate for 5 burgers using words, as a fraction, and with a colon. A rate is a ratio that compares two quantities that have different units Math Idea of measure.  A rate can be written as a ratio, a:b, where b ≠ 0. A unit rate is a rate that makes a comparison to 1 unit. The unit rate  Multiplication can represented $4 for cost per veggie burger is $4 to 1 burger. or ​ ______ ​. in different ways such as 2 × 1 1 burger or 2 ∙ 1. Both expressions are read as “2 times 1.” Complete the table to find the rate that gives the cost of 5 veggie burgers. Think: 1 veggie burger costs $4, so 2 veggie burgers cost $4 + _ , or 2 × _. Unit 2 $4 3 $4 $4 $4 Rate Cost $4 $8 Veggie Burgers 1 2 3 4 2 1 1 4 1 1 The table shows that 5 veggie burgers cost _. So, the rate that gives the cost for 5 veggie burgers is $ $_ to _ burgers, ​ ___________ ​, or $_ : _ burgers. burgers Math Reason abstractly and Talk MP quantitatively. Describe two other ways to say “$4 per burger”. Try This! Write the rate in three different ways. A. The rate that gives the cost of 3 veggie B. The rate that gives the cost of 4 veggie burgers burgers © Houghton Mifflin Harcourt Publishing Company $4 2. Explain why the ratio ​ ______ 1 burger ​is a unit rate. 3. MP Explain the pattern you see in the table in the Example. 172 Go Math! Grade 6  Name Share and Show Math Board 1. Write the ratio of the number of red bars to blue stars. ​ _____ ​ Write the ratio in two different ways. 2. 8 to 16 4​ 3. ​ __ 4. 1:3 5. 7 to 9 24 6_MNLAESE352053_C05_001T.ai 6. Marilyn saves $15 per week. Complete the Savings $30 $45 $75 table to find the rate that gives the amount saved in 4 weeks. Write the rate in three Weeks 1 2 3 4 5 different ways. Math Talk MP Attend to precision. Are the ratios 5:2 and 2:5 the same or different? How do you know? On Your Own Write the ratio in two different ways. 16 __​ 7. ​ 8. 8:12 9. 4 to 11 10. 2:13 40 11. There are 24 baseball cards in 4 packs. Complete Cards 18 24 the table to find the rate that gives the number of cards in 2 packs. Write this rate in three different ways. Packs 1 2 3 4 © Houghton Mifflin Harcourt Publishing Company 12. MP Explain how the statement “There is 34_​ ​cup per serving” represents a rate. Chapter 4 Lesson 1   173  Problem Solving · Applications Real World Use the diagram of a birdhouse for 13–15. B 12 in. 13. Write the ratio of AB to BC in three different ways. C 28 in. 24 in. 14. Write the ratio of the shortest side length of triangle ABC to the perimeter of the triangle in three different ways. A 15. MP Write the ratio of the perimeter of triangle ABC to the longest side length of the triangle in three different ways. Show the Math Demonstrate Your Thinking 16. Leandra places 6 photos on each page in a photo album. Find the rate that gives the number of photos on 2 pages. Write the rate in three different ways. 17. The ratio of total students in Ms. Murray’s class to students in the class who have on the an older brother is 3 to 1. The answer is 1:2. Spot What is the question? 18. Write Math What do all unit rates have in common? 19. Medya has 2 green reusable shopping bags and 5 purple © Houghton Mifflin Harcourt Publishing Company reusable shopping bags. Select the ratios that compare the number of purple reusable shopping bags to the total number of reusable shopping bags. Mark all that apply. 5 to 7 5:2   2 to 7 5:7 2​ ​ _ 5  5_​7​ 174 Go Math! Grade 6  LESSON 4.1 Name Practice and Homework Ratios and Rates Go Online Interactive Examples Write the ratio in two different ways. 1. 4 _ ​5​ 2. 16 to 3 3. 9:13 15 __​ 4. ​ 8 4 to 5 4:5 _ _­_ _­__ _­__ _­__ 5. There are 20 light bulbs in 5 packages. Complete the Light Bulbs 8 16 20 table to find the rate that gives the number of light bulbs in 3 packages. Write this rate in three different Packages 1 2 3 4 5 ways. Problem Solving Real World 6. Gemma spends 4 hours each week playing 7. Armand bought 2 game controllers at Electronics soccer and 3 hours each week practicing her Plus for $36. What is the unit rate for a game clarinet. Write the ratio of hours spent practicing controller at Electronics Plus? clarinet to hours spent playing soccer three different ways. © Houghton Mifflin Harcourt Publishing Company 8. Write Math Explain how to determine if a given rate is also a unit rate. Chapter 4 Lesson 1   175 Lesson Check 9. At the grocery store, Luis bought 10 bananas 10. Rita checked out 7 books from the library. She and 4 apples. What are three different ways to had 2 nonfiction books. The rest were fiction. write the ratio of apples to bananas? What are three different ways to write the ratio of nonfiction to fiction? Spiral Review 11. Akilah bought 1.2 pounds of coffee for $11.82. ​ 9 ​ pound. 12. Efrem has a bag of flour that weighs __ 10 What was the cost per pound? He uses ​2_​of the bag to make gravy. How many 3 pounds of flour does Pedro use to make gravy? 13. Mai draws a map of her town on a coordinate 14. Compare the numbers −3.2 and −4.1. plane. The point that represents the town’s civic Write < or >. center is 1 unit to the right of the origin and 4 units above it. What are the coordinates of the point representing the civic center? © Houghton Mifflin Harcourt Publishing Company 176  Go Math! Grade 6  CHAPTER 4 Name Lesson 2 Equivalent Ratios I Can use a multiplication table to find equivalent ratios. The ratios shown in each column of the table are equivalent to the original ratio. Ratios that name the same comparison are equivalent ratios. Original 2∙1 3∙1 4∙1 5∙1 ratio Bags 1 2 3 4 5 Apples 6 12 18 24 30 2∙6 3∙6 4∙6 5∙6 You can use a multiplication table to find equivalent ratios. UNLOCK the Problem Real World The ratio of adults to students on a field trip is ​ 3_8 ​. 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 Write three ratios that are equivalent to ​ 3_8 ​. 2 2 4 6 8 10 12 14 16 18 Use a multiplication table. 3 3 6 9 12 15 18 21 24 27 STEP 1 Shade the rows in the multiplication table that 4 4 8 12 16 20 24 28 32 36 show the original ratio. 5 5 10 15 20 25 30 35 40 45 6 6 12 18 24 30 36 42 48 54 Think: The original ratio is ____ ​ ​. Shade the row for _ and 7 7 14 21 28 35 42 49 56 63 the row for _ on the multiplication table. 8 8 16 24 32 40 48 56 64 72 9 9 18 27 36 45 54 63 72 81 STEP 2 Complete a table of equivalent ratios. Think: Use rows from the multiplication table to help you complete a table of equivalent ratios. 2 3 3∙3 ∙3 © Houghton Mifflin Harcourt Publishing Company 3 12 8 24 2∙8 ∙8 4∙8 Math Talk MP Attend to precision. So, _, _, and _ are equivalent to ​ 3_8 ​. Explain whether the multiplication table shown represents all of the ratios that are equivalent to 3:8. Go Online For more help Chapter 4 Lesson 2   177 connect You can find equivalent ratios by multiplying or dividing by a form of one. Example 1 Multiply or divide by a form of one. Write two equivalent ratios for ​ 6_8.​ A. Multiply by a form of one. Common Error Multiply the numerator and denominator by the same number. Be sure to multiply or divide the numerator and the denominator 6 ​ × _____ = ____ ​ by the same number. 8× B. Divide by a form of one. Divide the numerator and denominator by the same number. ​ 6 ÷ ______ = ___ ​ 8÷ So, 6_8​  ​, _, and _ are equivalent ratios. Example 2 A paint store makes rose-pink paint by mixing 3 parts red paint to 5 parts white paint. A clerk mixes 4 parts red paint to 7 parts white paint. Did the clerk mix the paint correctly to make rose-pink paint? Use tables of equivalent ratios. Rose-Pink Paint Clerk’s Paint Mixture Parts Red 3 6 9 12 Parts Red 4 Parts White 5 Parts White 7 14 21 28 Look for a pattern to determine whether the ratios in the first table are equivalent to the ratios in the second table. Think: The number 12 appears in the first row of both tables. ​  12 ​ ​  12 ​is/is not equivalent to _____ _____ © Houghton Mifflin Harcourt Publishing Company The ratios have the same numerator and denominators. So, the clerk mix the paint correctly. Math Talk MP Model with mathematics. MP Explain how ratios are similar to fractions. Explain how How can you check that your answer is correct? they are different. 178 Go Math! Grade 6  Name Share and Show Math Board Write two equivalent ratios. 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 1. Use a multiplication table to write two ratios that are equivalent to ​ 4_7 ​. 2 2 4 6 8 10 12 14 16 18 Find the rows that show ​ 4_7 ​. 3 6 9 12 15 18 21 24 27 3 4 4 8 12 16 20 24 28 32 36 Find columns that show equivalent ratios. 4_ ​ ​= = 7 _ _ 5 5 10 15 20 25 30 35 40 45 6 6 12 18 24 30 36 42 48 54 7 7 14 21 28 35 42 49 56 63 2. 3. 8 8 16 24 32 40 48 56 64 72 3 5 9 9 18 27 36 45 54 63 72 81 7 2 4 _​ 12 __​ 2_ 4. ​ 5. ​ 6. ​ ​ 5 30 9 Math Use appropriate tools Talk MP strategically. Explain how the multiplication table helps you find equivalent ratios. On Your Own Write two equivalent ratios. 7. 8. 9. 9 5 6 8 4 9 8 _​ 2_ 4 10. ​ 11. ​ ​ 12. ​ __​ 7 6 11 © Houghton Mifflin Harcourt Publishing Company Determine whether the ratios are equivalent. 2 ​ 8 ​ _​and __ 13. ​ 8 14. ​ __ ​ 6 ​ ​and __ 16 ​ 4 ​ __​and __ 15. ​ 3 16. ​ __ ​ 8 ​ ​and __ 3 12 10 10 60 15 14 28 Chapter 4 Lesson 2   179  Problem Solving · Applications Real World Use the multiplication table for 18 and 19. 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 17. In Keith’s baseball games this year, the ratio of times he has 2 2 4 6 8 10 12 14 16 18 gotten on base to the times he has been at bat is ​ __ 4 ​. Write 14 3 3 6 9 12 15 18 21 24 27 two ratios that are equivalent to ​ __ 14 4 ​. 4 4 8 12 16 20 24 28 32 36 5 5 10 15 20 25 30 35 40 45 6 6 12 18 24 30 36 42 48 54 18. Use the multiplication table to write a new problem 7 7 14 21 28 35 42 49 56 63 involving equivalent ratios. Then solve the problem. 8 8 16 24 32 40 48 56 64 72 on the 9 18 27 36 45 54 63 72 81 Spot 9 19. For every $10 that Jawan makes, she saves $3. For every $15 Liam makes, he saves $6. Is Jawan’s ratio of money saved to money earned equivalent to Liam’s ratio of money saved to money earned? Explain. 20. Determine whether each ratio is equivalent to ​ 1_3 ​, ​  __ 5 ​, or ​  3_ ​. Write the ratio in the 10 5 correct box. 2 __ 3 __ 7 18 10 6 1 8 ​​ ​​ ​ ___ ​ ___ ​ ​ ___ ​ ​ ​ ___ ​ __ ​​ ​ ___​ 4 9 21 30 30 10 2 16 1 5 _ ​​ ​ __​ ​3_​ 3 10 5 © Houghton Mifflin Harcourt Publishing Company 180 Go Math! Grade 6  LESSON 4.2 Name Practice and Homework Equivalent Ratios Go Online Interactive Examples Write two equivalent ratios. 1. Use a multiplication table to write two ratios that are equivalent to ​ 5_3 ​. 5 10 ​  ​, 15 ​_​ ∙ __ ​__ ​ 3 ____ 6 9 2. 3. 4. 6__ ​​ 11 ​ ___ 5. ​ 6 6 8 1 7 4 Determine whether the ratios are equivalent. 2​ and __5​ ​ __ 6. ​ 5 ​ and __1​ ​ 7. ​ ___ 8​ and ___ __ 8. ​ 32 ​ ​ 9 ​ and __3​ ​ 9. ​ ___ 3 6 10 6 3 12 12 4 Problem Solving Real World 10. Tristan uses 7 stars and 9 diamonds to make a 11. There are 12 blue seats and 16 red seats in design. Write two ratios that are equivalent to ​ 7_9 ​. Javier’s math class. There are 26 blue seats and 14 red seats in Javier’s choir class. Are the ratios of blue seats to red seats in the two classes equivalent? Explain. © Houghton Mifflin Harcourt Publishing Company 12. Write Math Explain how to determine whether two ratios are equivalent. Chapter 4 Lesson 2   181 Lesson Check 13. A pancake recipe calls for 4 cups of flour and 14. A bracelet is made of 14 red beads and 19 gold 3 cups milk. Does a recipe calling for 2 cups beads. A necklace is made of 84 red beads and flour and 1.5 cups milk use the same ratio of 133 gold beads. Do the two pieces of jewelry flour to milk? have the same ratio of red beads to gold beads? Spiral Review 15. Scissors come in packages of 3. Glue sticks 16. Bruno had __3​ ​hour of free time before dinner. He 4 come in packages of 10. Sarai wants to buy the spent 2​__​of the time playing the guitar. How long 3 same number of each. What is the fewest glue did he play the guitar? sticks Sarai can buy? 17. Delia has 3​__5​yards of ribbon. About how many ​ 18. Which point is located at –1.1? 8 1__​-yard-long pieces can she cut? 4 A B C D -2 -1 0 1 © Houghton Mifflin Harcourt Publishing Company 182  Go Math! Grade 6  CHAPTER 4 Name Lesson 3 Use Equivalent Ratios I Can use tables to solve problems involving equivalent ratios. UNLOCK the Problem Real World In warm weather, the Hernandez family likes to spend time on the family’s boat. The boat uses 2 What are you asked to find? gallons of gas to travel 12 miles on the lake. How much gas would the boat use to travel 48 miles? Solve by finding equivalent ratios. Let represent the unknown number of gallons. gallons gallons _______​   ​ ___ ​ ​ ​  ​ 2 ​= ___ _______​ miles 12 48 miles Make a table of equivalent ratios. Original 2∙2 ∙2 ∙2 ratio Gas used (gallons) 2 6 Distance (miles) 12 24 48 ∙ 12 3 ∙ 12 ∙ 12 © Houghton Mifflin Harcourt Publishing Company Image Credits: (c) ©Andersen Ross/Getty Images ​ 2 ​and _ are equivalent ratios, __ The ratios 12 2 ​  ​ = ___ so ___ ​  ​. 12 48 So, the boat will use _ gallons of gas to travel 48 miles. What if the boat uses 14 gallons of gas? Explain how you can use equivalent ratios to find the number of miles the boat travels when it uses 14 gallons of gas. Go Online For more help Chapter 4 Lesson 3   183  Example Use equivalent ratios to find the unknown value. 3 A. ​ ​ ​ __​ = ___ 4 20 Use common denominators to write equivalent ratios. 3 __ ​  ​ ​ ​ = ___ _ is a multiple of 4, so _ is a common denominator. 4 20 Multiply the ___ and denominator by write the ratios using a common denominator. _ to ​ ×    ​ = ___ 3 _______ ​  ​ 4 ×    20 The ___ are the same, so the ___    are equal to each other. ​____​ = ___ ​  ​ 20 20 So, the unknown value is _, and 3_4​  ​= ​  ____ 20 ​. Check your answer by making a table of equivalent ratios. Original ratio ∙3 ∙3 ∙3 ∙3 3 6 4 8 ∙4 ∙4 ∙4 ∙4 56​ = __ B. ​ ___ ​  8 ​ 42 Write an equivalent ratio with 8 in the numerator. 56 ___ ​ 8​ ​ ​ = __ 42 Think: Divide 56 by _ to get 8. So, divide the denominator by _ as well. ​ ÷    ​ = __ 56 ________ 8​ ​  42 ÷    The ___ are the same, so the ___ ​  8 ​ = __ ___    ​ 8​ are equal to each other. So, the unknown value is _, and ​ 56 __ ​= ​  ____ 8 ​. Math Express regularity in 42 Talk MP repeated reasoning. Check your answer by making a table of equivalent ratios. Give an example of two © Houghton Mifflin Harcourt Publishing Company equivalent ratios. Explain how you know that they are Original ratio ∙8 ∙8 ∙8 ∙8 ∙8 ∙8 equivalent. 8 16 6 12 ∙6 ∙6 ∙6 ∙6 ∙6 ∙6 184 Go Math! Grade 6  Name Share and Show Math Board Use equivalent ratios to find the unknown value. 1. ​ ____ 4 ​ = __ ​ ​ 18 6 ____​ = __ 2. ​ ​  ​ 10 5 24 4 18 ÷    ​ __ 6 ​ × = ​ ____________ ​  ​ ​ ____​ = ________​ 10 5 × 24 ÷    6 ​ __ 6 ​ =    ​ ____ _____ ​ ​    ​ _____ ​  ​ = 10 10 So, the unknown value is _. So, the unknown value is _. 3 _​ = 15 3. ​ __ ​ ​ ​  8 ​ __​ = __ 4. ​ ​ ​ 5. ​7_​ = __ 6. ​10 __​= 40 __ ​ ​ 6 5 10 4 12 12 __ __ __ __ Math Construct arguments and Talk MP critique reasoning of others. Explain whether you can always find an equivalent ratio by subtracting the same number On Your Own from the numerator and denominator. Give an example to support your answer. Use equivalent ratios to find the unknown value. 2 ​ ​ _​= __ 7. ​ 6 5 ​= ___ 8. ​ __ ​  55 ​ ​  9 ​ 3_​ = __ 9. ​ 10. ​ __​= 16 __ ​ ​ 30 110 9 6 24 __ __ __ __ 12. The ratio of appetizers to entrees served in a 11. Mavis walks 3 miles in 45 minutes. How many restaurant is 3 to 8. There are 32 entrees served. minutes will it take Mavis to walk 9 miles? How many plates are served in all? © Houghton Mifflin Harcourt Publishing Company 13. MP ​the same as the unknown value in ​  3_ ​= ​  18 Is the unknown value in ​  2_3 ​= ​  __ __ ​? Explain. 18 2 Chapter 4 Lesson 3   185  Problem Solving · Applications Real World Solve by finding an equivalent ratio. 14. It takes 8 minutes for Suriani to make 2 laps around the go-kart track. How many laps can Suriani complete in 24 minutes? 15. The width of Adonis’s original photo is 8 inches. The length of the original photo is 10 inches. He prints a smaller version that has an equivalent ratio of width to length. The width of the smaller version is 4 inches less than the width of the original. What is the length of the smaller version? 16. Ariel bought 3 raffle tickets for $5. How many tickets could Ariel buy for $15? 17. Esad used the steps shown to find the unknown value. Describe his error, and give the correct solution. on the Spot © Houghton Mifflin Harcourt Publishing Company Image Credits: (t) ©Darryl Leniuk/Corbis ©Crystal Home/Shutterstock      ​2_​ = 12 __ ​  ​ 6 2 + 6​ = __ ​_____ ​  ​ 6+6 12    ​ __ 8 ​ = __ ​  ​ 12 12 The unknown value is 8. 18. Jelani bought 3 maps for $10. Use the table of equivalent ratios to find how many maps Jelani can buy for $30. 3 6 10 20 30 186 Go Math! Grade 6  LESSON 4.3 Name Practice and Homework Use Equivalent Ratios Go Online Interactive Examples Use equivalent ratios to find the unknown value. 10 40 ​  ​ 4 ​ = ___ 1. ​ ___ 3 ​ = ___ 2. ​ ___ 24 33 ​ ​ ​ 7 = ___ 3. ​ __ 27 21 ​ ​ 12 __ ​ = ___ 4. ​ 9 54 ​ ​   4 × 4​ = __ ​  ______ ​  ​ 10 × 4 40 ​ 16 ​ = __ __ ​  ​ 40 40 = 16 __ __ __ 3​ = ___ __ 5. ​ 2 12 ​ ​ 6. ​ 5 40 ​  ​ 4​ = ___ __ 45 __ ​ = ___ 7. ​ 2 30 ​ ​ 45 ​ 5​ ​ ___ = __ 8. ​ 6 __ __ __ __ Problem Solving Real World 9. Honeybees consume about 7 pounds of honey 10. A 3-ounce serving of tuna provides for every 1 pound of beeswax they produce. 21 grams of protein. Use equivalent ratios Use equivalent ratios to find how many pounds to find how many grams of protein are in of honey are consumed when 25 pounds of 9 ounces of tuna. beeswax are produced. 11. Write Math Explain how using equivalent ratios is like adding fractions with unlike denominators. © Houghton Mifflin Harcourt Publishing Company Chapter 4 Lesson 3   187 Lesson Check 12. Jaron paid $2.70 for 8 juice boxes. How much 13. A certain shade of orange paint is made by should Jaron expect to pay for 24 juice boxes? mixing 3 quarts of red paint with 2 quarts of yellow paint. To make more paint of the same shade, how many quarts of yellow paint should be mixed with 6 quarts of red paint? Spiral Review 14. What is the quotient 2 ​__4​÷ 1​__1​? 2​ ​? 15. What is the absolute value of ​ ​–​2__ 5 3 3 16. On a map, a clothing store is located at (–2, –3). 17. Marisol plans to make 9 mini-sandwiches for A seafood restaurant is located 6 units to every 2 people attending her party. Write a ratio the right of the clothing store. What are the that is equivalent to Marisol’s ratio. coordinates of the restaurant? © Houghton Mifflin Harcourt Publishing Company 188  Go Math! Grade 6  CHAPTER 4 Name Lesson 4 Find Unit Rates I Can use unit rates to make comparisons. UNLOCK the Problem Real World The star fruit, or carambola, is the fruit of a tree that U  nderline the sentence that tells you what you is native to Indonesia, India, and Sri Lanka. Slices are trying to find. of the fruit are in the shape of a five-pointed star. C  ircle the numbers you need to use to solve Lara paid $9.60 for 16 ounces of star fruit. Find the the problem. price of 1 ounce of star fruit. Recall that a unit rate makes a comparison to 1 unit. You can find a unit rate by dividing the numerator and denominator by the number in the denominator. Write the unit rate for the price of star fruit. Write a ratio that compares __ price _____ $      _______ ​  ​ ​        ​ to __. weight oz Divide the numerator and denominator by $9.60 ÷      ___________ ​ ​ the number in the ___. 16 oz ÷      $       ​_______​ 1 oz Math So, the unit rate is __. The price is __ Talk MP Attend to precision. per ounce. What is the difference between a ratio and a rate? 1. MP Explain why the unit rate is equivalent to the original rate. © Houghton Mifflin Harcourt Publishing Company 2. MP Explain a way to convince others that you found the unit rate correctly. Go Online For more help Chapter 4 Lesson 4   189  Example A. During migration, a hummingbird can fly 210 miles in 7 hours, and a goose can fly 165 miles in 3 hours. Which bird flies at a faster rate? Write the rate for each bird.      miles​ Hummingbird: ​_________ ​  165 miles ​ Goose: _________ 7 hours     hours Write the unit rates. 210 mi ÷    ​ __________ 165 mi ÷     ​ ​__________ ​ 3 hr ÷       7 hr ÷        mi ______ ​ ​ ​    mi​ ______ 1 hr 1 hr Compare the unit rates. _ miles per hour is faster than _ miles per hour. So, the __ flies at a faster rate. B. A 64-ounce bottle of apple juice costs $3.84. A 15-ounce bottle of apple juice costs $1.80. Which item costs less per ounce? Write the rate for ​        ​ 64-ounce bottle: ________ ​       ​ 15-ounce bottle: _________      each bottle. 64 ounces ounces Write the unit rates.       ÷     ​ ____________ $1.80 ÷      ___________ ​       ​      ÷     ​   64 oz ÷      oz ​        _______​         _______ ​ ​ 1 oz 1 oz Compare the unit rates. _ per ounce is less expensive than _ per ounce. So, the _ -ounce bottle costs less per ounce. Try This! At one grocery store, a dozen eggs cost $2.28. At another store, 1​  1_2 ​dozen eggs cost $3.24. Which is the better buy? © Houghton Mifflin Harcourt Publishing Company Store 1: Store 2: The unit price is lower at Store _ , so 1​1_​dozen eggs for __ is the 2 better buy. 190 Go Math! Grade 6  Name Share and Show Math