{"id":16431,"date":"2023-12-27T13:53:52","date_gmt":"2023-12-27T08:23:52","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=16431"},"modified":"2023-12-28T12:54:36","modified_gmt":"2023-12-28T07:24:36","slug":"envision-math-common-core-grade-6-answer-key-topic-5","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-6-answer-key-topic-5\/","title":{"rendered":"enVision Math Common Core Grade 6 Answer Key Topic 5 Understand And Use Ratio And Rate"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 6 Answer Key<\/a>\u00a0Topic 5 Understand And Use Ratio And Rate<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 6th Grade Answers Key Topic 5 Understand And Use Ratio And<\/h2>\n

Rate<\/h2>\n

Topic 5 Essential Question<\/h3>\n

What are ratios and rates? How can you use ratios and rates to describe quantities and solve problems?<\/p>\n

3-ACT MATH<\/strong><\/p>\n

\"Envision<\/p>\n

Get in Line
\nIt is hard to call it a freeway when you are stuck in the middle of a traffic jam. To keep vehicles moving on the freeway, some on-ramps have traffic signals. Controlling when cars enter the freeway is not only about reducing delays. It can decrease air pollution and collisions.
\nThese ramp meters typically have alternating green and red lights. The time for one cycle depends on the time of day and the amount of traffic on the freeway. Think about this during the 3-Act Mathematical Modeling lesson.
\n\"Envision<\/p>\n

Topic 5 enVision STEM Project<\/h3>\n

\"Envision<\/p>\n

Your Task: Get into Gear
\nCyclists strive to achieve efficiency during continuous riding. But, which pairing of gears is the best or most efficient? And does the answer change depending on the terrain? You and your classmates will explore gear ratios and how they can affect pedaling and riding speeds.
\n\"Envision<\/p>\n

Topic 5 Get Ready!<\/h3>\n

Review What You Know!<\/strong><\/p>\n

Vocabulary<\/strong>
\nChoose the best term from the box to complete each definition.<\/p>\n

    \n
  • common factor<\/li>\n
  • common multiple<\/li>\n
  • equivalent fractions<\/li>\n
  • fraction<\/li>\n<\/ul>\n

    Question 1.
    \nFractions that name the same amount are called ___________<\/p>\n

    Answer:
    \nFractions that name the same amount are called equivalent fractions.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfractions that name the same amount are called equivalent fractions.
    \nfor example:
    \n1\/2 = 2\/4.
    \n2 x 1 = 2.
    \n2 x 2 = 4.<\/p>\n

    \"Understand<\/p>\n

    Question 2.
    \nThe number 3 is a ___________ of 9 and 12.<\/p>\n

    Answer:
    \nThe number 3 is a factor of 9 and 12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number 3 is a factor of 9 and 12.
    \nfor example:
    \nG.C.F of 9 and 12 = 3.
    \nH.C.F of 9 and 12 = 3.<\/p>\n

    Question 3.
    \nA number that can be used to describe a part of a set or a part of a whole is a(n) ___________<\/p>\n

    Answer:
    \nA number that can be used to describe a part of a set or a part of a whole is a(n) common factor.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA number that can be used to describe a part of a set or a part of a whole is a(n) common factor.
    \nfor example:
    \nG.C.F of 9 and 12 = 3.
    \nH.C.F of 9 and 12 = 3.<\/p>\n

    Equivalent Fractions<\/strong><\/p>\n

    Write two fractions equivalent to the given fraction.
    \nQuestion 4.
    \n\\(\\frac{3}{4}\\)<\/p>\n

    Answer:
    \nThe two fractions are equivalent to the 3\/4 = 9\/12 and 27\/36.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe fraction is 3\/4.
    \nthe two fractions are equivalent to 3\/4 is:
    \n27\/36 = 3\/4.
    \n9\/12 = 3\/4.<\/p>\n

    Question 5.
    \n\\(\\frac{7}{8}\\)<\/p>\n

    Answer:
    \nThe two fractions are equivalent to the 7\/8 = 14\/16 and 21\/24.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe fraction is 7\/8.
    \nthe two fractions are equivalent to 7\/8 is:
    \n14\/16 = 7\/8.
    \n21\/24 = 7\/8.<\/p>\n

    Question 6.
    \n\\(\\frac{12}{5}\\)<\/p>\n

    Answer:
    \nThe two fractions are equivalent to the 12\/5 = 24\/10 and 84\/60.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe fraction is 12\/5.
    \nthe two fractions are equivalent to 12\/5 is:
    \n24\/10 = 12\/5.
    \n84\/60 = 12\/5.<\/p>\n

    \"Understand<\/p>\n

    Question 7.
    \n\\(\\frac{1}{2}\\)<\/p>\n

    Answer:
    \nThe two fractions are equivalent to the 1\/2 = 2\/4 and 3\/6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe fraction is 1\/2.
    \nthe two fractions are equivalent to 1\/2 is:
    \n2\/4 = 1\/2.
    \n3\/6 = 1\/2.<\/p>\n

    Question 8.
    \n\\(\\frac{8}{9}\\)<\/p>\n

    Answer:
    \nThe two fractions are equivalent to the 8\/9 = 16\/18 and 24\/27.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe fraction is 8\/9.
    \nthe two fractions are equivalent to 8\/9 is:
    \n16\/18 = 8\/9.
    \n24\/27 = 8\/9.<\/p>\n

    Question 9.
    \n\\(\\frac{2}{3}\\)<\/p>\n

    Answer:
    \nThe two fractions are equivalent to the 2\/3 = 4\/6 and 12\/9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe fraction is 2\/3.
    \nthe two fractions are equivalent to 2\/3 is:
    \n4\/6 = 2\/3.
    \n12\/9 = 2\/3.<\/p>\n

    Equation<\/strong><\/p>\n

    Write an equation that represents the pattern in each table.
    \nQuestion 10.
    \n\"Envision<\/p>\n

    Answer:
    \nThe equation is y = 8x.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nx contains numbers 2, 3, 4, 5, and 6.
    \ny : 16, 24, 32, 40, and 48.
    \ny = 8x.
    \n16 = 8 x 2.
    \n24 = 8 x 3.
    \n32 = 8 x 4.
    \n40 = 8 x 5.
    \n48 = 8 x 6.<\/p>\n

    Question 11.
    \n\"Envision<\/p>\n

    Answer:
    \nThe equation is y = 2x + 1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nx : 2, 4, 6, 8, and 10.
    \ny : 5, 7, 9, 11, and 13.
    \ny = 2x + 1.
    \n5 = 2(2) + 1.
    \n7 = 2(4) – 1.
    \n9 = 2(6) – 3.<\/p>\n

    \"Understand<\/p>\n

    Units of Measure.<\/strong><\/p>\n

    Choose the best unit of measure by writing inch, foot, yard, ounce, pound, ton, cup, quart, or gallon.
    \nQuestion 12.
    \nserving of trail mix<\/p>\n

    Answer:
    \nThe serving of a trail mix can be measured in cups.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nServing of a trail mix.
    \nfor example:
    \nnutrition facts are also measured in cups.<\/p>\n

    Question 13.
    \nheight of a person<\/p>\n

    Answer:
    \nThe height of a person can be measured in feet.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe height of a person can be measured in feet.
    \nfor example:
    \nthe height of the short girl is 5 feet.
    \nthe height of the tall girl is 5.6 feet.<\/p>\n

    Question 14.
    \nweight of a newborn kitten<\/p>\n

    Answer:
    \nThe weight of a newborn kitten can be measured in ounces.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe weight of a newborn kitten can be measured in ounces.
    \nfor example:
    \nnewborn kittens usually weigh about 3.5 ounces.
    \na healthy kitten should gain at least 10 grams per day.<\/p>\n

    Question 15.
    \ngasoline<\/p>\n

    Answer:
    \nGasoline can be measured in cubic feet.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nGasoline can be measured in cubic feet.
    \nfor example:
    \ngas is sometimes measured in cubic feet at a temperature of 60 degrees Fahrenheit and an atmospheric pressure of 14.7 pounds per square inch.<\/p>\n

    Measurement Conversions<\/strong><\/p>\n

    Question 16.
    \nMichael is 4 feet tall. Explain how Michael could find his height in inches. Then explain how he could find his height in yards.<\/p>\n

    Answer:
    \nThe height in inches = 48.
    \nthe height in yards = 12 yards.
    \nExplanation:
    \nIn the above-given question,
    \ngiven that,
    \nMichael is 4 feet tall.
    \n1 feet = 12 inches.
    \n12 x 4 = 48 inches.
    \n1 yard = 3 feets.
    \n3 x 4 = 12 feets.<\/p>\n

    Language Development<\/strong><\/p>\n

    A bag contains the following marbles:
    \n\"Envision<\/p>\n

    Complete each math statement.
    \nThe following ratio statement reads, for every 1 red marble, there are ___2_____ yellow marbles.
    \nA ratio that compares the yellow marbles to the green marbles is ___6_____ to ____4____.
    \n3 : 4 is the ratio of red marbles to____green____ marbles.
    \nThe following ratio statement reads, for every 1 blue marble, there are 2 ___yellow_____ marbles.
    \n\\(\\frac{3}{2}\\) represents the ____ratio____ of red marbles to blue marbles.
    \n4 to 15 is the ratio of green marbles to the ___total_____ number of marbles.
    \nIn the ratio of yellow marbles to blue marbles, 6:2, the quantities 6 and 2 are called __ratio______
    \nA __ratio______ compares one ___quantity_____ to another ___quantity_____.<\/p>\n

    Pick A Project<\/strong><\/p>\n

    PROJECT 5A
    \nWhat animal would you most like to have as a pet?
    \nPROJECT: COMPARE COSTS OF PET FOODS
    \n\"Envision<\/p>\n

    Answer:
    \nThe animal I would most like to have as a pet is the dog.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe animal I would most like to have as a pet is the dog.
    \nfor example:
    \nthe cost of the lams is $1.07.
    \nthe cost of the Victor is $1.44.<\/p>\n

    \"Understand<\/p>\n

    PROJECT 5B
    \nHow fast do you think you can throw a baseball?
    \nPROJECT: ANALYZE A SPORT STATISTIC
    \n\"Envision<\/p>\n

    PROJECT 5C
    \nWhat color would you want to paint a room?
    \nPROJECT: EXPERIMENT WITH COMBINATIONS OF COLORS
    \n\"Envision<\/p>\n

    Answer:
    \nThe color I would like to paint a room is cream color.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe color I would like to paint a room is cream color.
    \nfor example:
    \nthere are many different colors.
    \nthey are cream, red, pink, blue, and orange.<\/p>\n

    PROJECT 5D
    \nIf you could visit any U.S. National Park, which would it be?
    \nPROJECT: PLAN A TOUR
    \n\"Envision<\/p>\n

    Answer:
    \nI could visit the Yellowstone National Park.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe Yellowstone national park wilderness and recreation area with active geysers like old faithful, plus canyons, rivers, and lakes.
    \nso I could visit the Yellowstone national park.
    \nthe area of Yellowstone national park is 8,991 sq km.<\/p>\n

    Lesson 5.1 Understand Ratios<\/h3>\n

    Explore It!<\/strong>
    \nA band just released an album that contains both pop songs and R&B (rhythm and blues) songs.<\/p>\n

    I can… use a ratio to describe the relationship between two quantities.
    \n\"Envision<\/p>\n

    A. How can you describe the relationship between the number of pop songs and the number of R&B songs on the album?<\/p>\n

    Answer:
    \nThe relationship between the number of pop songs and the number of R&B songs is 3: 6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 9 pop songs.
    \nthere are 6 R&B songs.
    \nthe relationship between the number of pop songs and the number of R&B songs is 9 and 6.
    \n9 : 6 = 3 : 6.
    \n3 x 3 = 9.
    \n3 x 2 = 6.
    \nso the relationship between the number of pop songs and the number of R&B songs is 3: 6.<\/p>\n

    B. How does the bar diagram represent the relationship between the number of pop songs and the number of R&B songs?
    \n\"Envision<\/p>\n

    Answer:
    \nThe bar diagram represents the relationship between the number of pop songs and the number of R&B songs is 3: 6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 9 pop songs.
    \nthere are 6 R&B songs.
    \nthe relationship between the number of pop songs and the number of R&B songs is 9 and 6.
    \n9 : 6 = 3 : 6.
    \n3 x 3 = 9.
    \n3 x 2 = 6.
    \nso the relationship between the number of pop songs and the number of R&B songs is 3: 6.<\/p>\n

    Focus on math practices
    \nReasoning Another album has 2 pop songs and 10 R&B songs. Draw a bar diagram that you could use to represent the relationship between the number of pop songs and the number of R&B songs.<\/p>\n

    Answer:
    \nThe relationship between the number of pop songs and the number of R&B songs = 1: 5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAnother album has 2 pop songs and 10 R&B songs.
    \n2 : 10 = 1 : 5.
    \nso the relationship between the number of pop songs and the number of R&B songs = 1: 5.<\/p>\n

    \"Understand<\/p>\n

    Essential Question<\/strong>
    \nWhat is a mathematical way to compare quantities?<\/p>\n

    Try It!<\/strong><\/p>\n

    What are three ways to write the ratio of the number of dogs to the total number of pets?<\/p>\n

    Answer:
    \nThe ratio of the number of dogs to the total number of pets = 3: 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio of a number of dogs to the total number of pets is same.
    \nfor example:
    \n3 : 3.
    \n1: 1.<\/p>\n

    Convince Me! Is the ratio of dogs to cats the same as the ratio of cats to dogs? Explain.<\/p>\n

    Try It!<\/strong><\/p>\n

    Chen’s friend Alisa can ride her bike 2 miles in 7 minutes. Use a bar diagram or a double number line diagram to find how long it would take Alisa to ride 10 miles if she rides at the same rate.<\/p>\n

    Answer:
    \nThe longer it would take Alisa to ride 10 miles = 70 minutes.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nChen’s friend Alisa can ride her bike for 2 miles in 7 minutes.
    \n2 x 7 = 14 minutes.
    \n10 x 7 = 70 minutes.
    \nso the longer it would take Alisa to ride 10 miles = 70 minutes.<\/p>\n

    KEY CONCEPT<\/strong>
    \nA ratio compares two quantities. A ratio can be written 3 ways: x to y, x:y, or Ratios can be represented using bar diagrams and double number line diagrams.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> What is a mathematical way to compare quantities?<\/p>\n

    Answer:
    \nA ratio compares two quantities.
    \nA ratio can be written in 3 ways: x to y, x: y, and x and y.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA ratio compares two quantities.
    \na ratio can be written in 3 ways are x to y.
    \nx: y, and x\/y.
    \nso ratio compares two quantities.<\/p>\n

    Question 2.
    \nReasoning<\/strong> What are two different types of comparisons that a ratio can be used to make?<\/p>\n

    Answer:
    \nThe two different types of comparisons that a ratio can be used to make are x:y and x\/y.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is x: y.
    \nx to y.
    \nx\/y.
    \nso the two different types of comparisons that a ratio can be used to make are x: y and x \/ y.<\/p>\n

    Question 3.
    \nA science classroom has 5 turtles and 7 frogs. What is the ratio of frogs to total animals?
    \n\"Envision<\/p>\n

    Answer:
    \nThe ratio of frogs to total animals is 7: 12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA science classroom has 5 turtles and 7 frogs.
    \nthere are 7 frogs in the science classroom.
    \ntotally there are 12 animals.
    \nfrogs: animals.
    \n7: 12.
    \nso the ratio of frogs to total animals is 7: 12.<\/p>\n

    \"Understand<\/p>\n

    Question 4.
    \nTye is making trail mix with 3 cups of nuts for every 4 cups of granola. If Tye has 6 cups of nuts, how many cups of granola should he use?<\/p>\n

    Answer:
    \nThe number of cups of granola should use = 2: 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTye is making trail mix with 3 cups of nuts for every 4 cups of granola.
    \n6 : 3 = 2 : 3.
    \nso the number of cups of granola should use = 2: 3.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 5-7, use three different ways to write a ratio for each comparison.<\/p>\n

    A sixth-grade basketball team has 3 centers, 5 forwards, and 6 guards.
    \nQuestion 5.
    \nForwards to guards<\/p>\n

    Answer:
    \nForwards to guards = 5: 6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA sixth-grade basketball team has 3 centers, 5 forwards, and 6 guards.
    \nForwards to guards:
    \n5: 6.<\/p>\n

    Question 6.
    \nCenters to total players<\/p>\n

    Answer:
    \nCenters to total players= 3: 14.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCenters to total players.
    \nthe total number of players = 14.
    \ncenters to total players = 3: 14.<\/p>\n

    Question 7.
    \nGuards to centers<\/p>\n

    Answer:
    \nGuards to centers = 6 : 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 6 Guards and 3 Guards.
    \n6 : 3 = 2 : 3.
    \nso Guards to centers = 6 : 3.<\/p>\n

    Question 8.
    \nThe ratio of blue cards to green cards is 2 to 5. There are 8 blue cards. Complete the diagram and explain how you can find the number of green cards.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of blue cards to the number of green cards = 8: 11.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe ratio of blue cards to green cards is 2 to 5.
    \nThere are 8 blue cards.
    \nthe number of green cards is 11.
    \nso the number of blue cards to the number of green cards = 8: 11.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 9-14, use the data to write a ratio for each comparison in three different ways.<\/p>\n

    A person’s blood type is denoted with the letters A, B, and O, and the symbols + and -. The blood type A+ is read as A positive. The blood type B- is read as B negative.
    \n\"Envision<\/p>\n

    Question 9.
    \nO+ donors to A+ donors<\/p>\n

    Answer:
    \nO+ donors to A+ donors = 2 : 1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA person’s blood type is denoted with the letters A, B, and O, and the symbols + and -.
    \nO+ donors to A+ donors.
    \nthere are 90 O+ donors.
    \nthere are 45 A+ donors.
    \n90 : 45 = 2 : 1.<\/p>\n

    Question 10.
    \nAB-donors to AB+ donors<\/p>\n

    Answer:
    \nAB- donors to AB+ donors = 2 : 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA person’s blood type is denoted with the letters A, B, and O, and the symbols+ and -.
    \nAB- donors to AB+ donors.
    \nthere are 4 AB- donors.
    \nthere are 6 AB+ donors.
    \n4 : 6 = 2 : 3.
    \nso AB- donors to AB+ donors = 2 : 3.<\/p>\n

    Question 11.
    \nB+ donors to total donors<\/p>\n

    Answer:
    \nB+ donors to total donors = 20 : 195.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \ntotally there are 195 donors.
    \nB+ donors to total donors.
    \n20: 195.<\/p>\n

    Question 12.
    \nO- donors to A-donors<\/p>\n

    Answer:
    \nO- donors to A- donors = 9 : 21.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nO- donors to A- donors.
    \nthere are 9 O- donors.
    \nthere are 21 A- donors.
    \nO- donors to A- donors = 9 : 21.<\/p>\n

    Question 13.
    \nA+ and B+ donors to AB+ donors<\/p>\n

    Answer:
    \nA+ and B+ donors to AB+ donors = 6 : 65.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA+ and B+ donors to AB+ donors.
    \nthere are A+ and B+ donors who are 65.
    \nthere are\u00a0 6 AB+ donors.
    \nA+ and B+ donors to AB+ donors = 6 : 65.<\/p>\n

    Question 14.
    \nA- and B-donors to AB- donors<\/p>\n

    Answer:
    \nA- and B- donors to AB- donors = 21: 4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 21 A- donors.
    \nthere are 0 B- donors.
    \nthere are 4 AB- donors.
    \nso A- and B- donors to AB- donors = 21: 4.<\/p>\n

    Question 15.
    \nWhich comparison does the ratio \\(\\frac{90}{9}\\) represent?<\/p>\n

    Answer:
    \nThe ratio 90\/9 represent = 10 : 1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio 90\/9 represents.
    \n90 : 9 = 10: 1.
    \nso the ratio represent = 10 : 1.<\/p>\n

    Question 16.
    \nWhich comparison does the ratio 20:21 represent?<\/p>\n

    Answer:
    \nThe comparison does the ratio 20:21 represent = B+ and A-.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 20 B+ donors.
    \nthere are 21 A- donors.
    \nso the ratio 20:21 represent = B+ and A+.<\/p>\n

    Question 17.
    \nSam is packing gift boxes with fruit. For each apple, he packs 3 plums and 5 oranges. If he puts 3 apples in a box, how many plums and oranges will Sam put in the box? Draw a diagram to solve the problem.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of plums and oranges will Sam put in the box is 9:15.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSam is packing gift boxes with fruit.
    \nFor each apple, he packs 3 plums and 5 oranges.
    \n1:3, 2:6, and 3:9.
    \n1:5, 2:10, and 3:15.
    \nso the number of plums and oranges will Sam put in the box is 9:15.<\/p>\n

    Question 18.
    \nWrite a ratio that compares the number of teal squares to the total number of squares in the quilt.
    \n\"Envision<\/p>\n

    Answer:
    \nThe ratio that compares the number of teal squares to the total number of squares in the quilt = 1:3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 18 teal squares and 6 squares.
    \n6 : 18 = 1:3.
    \nso the ratio that compares the number of teal squares to the total number of squares in the quilt = 1:3.<\/p>\n

    Question 19.
    \nReasoning<\/strong> Rita’s class has 14 girls and 16 boys. How does the ratio 14:30 describe Rita’s class?<\/p>\n

    Answer:
    \nThe ratio 14:30 describes there are 7 girls and 15 boys.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nRita’s class has 14 girls and 16 boys.
    \nthere are 14 girls and 16 boys.
    \nthere are 14 girls and 30 boys.
    \n14: 30 = 7:15.
    \nso there are 7 girls and 15 boys.<\/p>\n

    Question 20.
    \nA math class surveyed students about their musical preferences and recorded the results in the table. Use the data to write a ratio for each comparison in three different ways.
    \n\"Envision
    \na. Students who prefer classical to students who prefer techno<\/p>\n

    Answer:
    \nThe students who prefer classical to students who prefer techno is 1:3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 4 classical students.
    \nthere are 12 techno students.
    \n4 : 12 = 1:3.
    \nso the students who prefer classical to students who prefer techno is 1:3.<\/p>\n

    b. Students who prefer hip-hop to total number of students surveyed<\/p>\n

    Answer:
    \nStudents who prefer hip-hop to the total number of students surveyed = 15:53.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthere are 15 hip-hop students.
    \nthe total number of students is 53.
    \nso the ratio is 15:53.<\/p>\n

    Question 21.
    \nConstruct Arguments<\/strong> Justin used blocks to model the following situation: A car dealership sells 7 cars for every 4 minivans it sells. How can Justin use his model to find the number of minivans the dealership sells if it sells 35 cars?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of minivans the dealership sells if it sells 35 cars = 20 minivans.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA car dealership sells 7 cars for every 4 minivans it sells.
    \n35\/7 = 5.
    \n4 x 5 = 20.
    \nso the number of minivans the sealership sells if it sells 35 cars = 20 minivans.<\/p>\n

    Question 22.
    \nMake Sense and Persevere The ratio of adult dogs to puppies at a dog beach in Florida on Monday was 3:2. There were 12 puppies there that day. On Tuesday, 15 adult dogs were at the dog beach. What is the difference between the number of adult dogs at the dog beach on Monday and Tuesday?<\/p>\n

    Answer:
    \nThe difference between the number of adult dogs at the dog beach on Monday and Tuesday = 1:3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe ratio of adult dogs to puppies at a dog beach in Florida on Monday was 3:2.
    \nThere were 12 puppies there that day.
    \nOn Tuesday, 15 adult dogs were at the dog beach.
    \n12:15 = 4:5.
    \n4:5 – 3:2 = 1:3.
    \nso the difference between the number of adult dogs at the dog beach on Monday and Tuesday = 1:3.<\/p>\n

    Question 23.
    \nHigher Order Thinking<\/strong> At 9:30 A.M., Sean started filling a swimming pool. At 11:30 A.M., he had filled 1,800 gallons. At what time will the pool be full?
    \n\"Envision<\/p>\n

    Answer:
    \nAt 2:30 P.M the pool will fill completely.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAt 9:30 A.M., Sean started filling a swimming pool.
    \nAt 11:30 A.M., he had filled 1,800 gallons.
    \nfor 2 hours it will fill 1800 gallons.
    \n1800 + 1800 = 3600.
    \n3600 + 900 = 4500.
    \nso at 2:30 P.M the pool will fill completely.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 24.
    \nThe diagram below represents the relationship between the number of students taking Spanish and the number of students taking French in a foreign language class.
    \n\"Envision
    \nWhat is the ratio of the number of students taking Spanish to the number of students taking French?
    \nA. 8 : 3
    \nB. 8 : 5
    \nC. 8 : 8
    \nD. 8 : 13<\/p>\n

    Answer:
    \nThe ratio of the number of students taking Spinach to the number of students taking French = 8: 5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of Spanish students is 8.
    \nthe number of French students is 5.
    \nthe ratio is 8:5.
    \nso the ratio of a number of students taking spinach to the number of students taking french = 8:5.<\/p>\n

    Lesson 5.2 Generate Equivalent Ratios<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nSally used all of the paint shown below to make a certain tint of orange paint. How many pints of red paint should be mixed with 24 pints of yellow paint to make the same tint of orange?
    \nI can… use multiplication and division to find equivalent ratios.
    \n\"Envision<\/p>\n

    Look for Relationships
    \nHow can you use the relationship between the number of pints of yellow paint and the number of pints of red paint to answer the question?<\/p>\n

    Answer:
    \nThe ratio of yellow paint to the red paint is 4:3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of yellow paint is 4.
    \nthe number of red paint is 3.
    \nthe relationship between the number of pints of yellow paint and the number of pints of red paint is 4:3.<\/p>\n

    Focus on math practices
    \nReasoning If Sally uses the same ratio of yellow paint to red paint, how many pints of yellow paint should she mix with 16 pints of red paint?<\/p>\n

    Essential Question<\/strong>
    \nHow can you find equivalent ratios?<\/p>\n

    Try It!<\/strong><\/p>\n

    If you extend the table above, how would you find the next ratio of basketball players to soccer players?
    \nAnswer:<\/p>\n

    Convince Me! What is the relationship between the number of basketball players and the number of soccer players in each column in the table?<\/p>\n

    Try It!<\/strong><\/p>\n

    Rashida uses 8 cups of tomatoes and 3 cups of onions to make salsa. How many cups of onions should Rashida use if she uses only 4 cups of tomatoes?<\/p>\n

    Answer:
    \nRashida use 1.5 cups of onions when she use 4 cups of tomatoes.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nRashida uses 8 cups of tomatoes and 3 cups of onions to make salsa.
    \nfor 1.5 cups of onions is used for 4 cups of tomatoes.
    \n4 : 1.5.
    \nso the ratio is 4:1.5.<\/p>\n

    Try It!<\/strong><\/p>\n

    Which of the following ratios are equivalent to 16:20?
    \n2:3, 4:5, 18:22, 20:25<\/p>\n

    Answer:
    \nThe ratio 4:5 equal to 16:20.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratios are 2:3, 4:5, 18:22, and 20:25.
    \n16: 20 = 4:5.
    \nso the ratio 4:5 equal to 16:20.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can multiply or divide both terms of a ratio by the same nonzero number to find equivalent ratios.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you find equivalent ratios?<\/p>\n

    Answer:
    \nWe can multiply or divide both terms of a ratio by the same nonzero number to find equivalent ratios.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nmultiply both terms by same non-zero number.
    \ndivide both terms by same non-zero number.
    \nfor example:
    \n30 x 2 = 60.
    \n40 x 2 = 80.<\/p>\n

    Question 2.
    \nCritique Reasoning Deshawn says that the ratios 3:5 and 5:7 are equivalent ratios because by adding 2 to both terms of 3:5 you get 5:7. Is Deshawn correct? Explain.<\/p>\n

    Answer:
    \nNo, he was not correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDeshawn says that the ratios 3:5 and 5:7 are equivalent ratios because by adding 2 to both terms of 3:5 you get 5:7.
    \n3:5 and 9:15.
    \nso he was not correct.<\/p>\n

    Question 3.
    \nWhat are two ways you can find an equivalent ratio for \\(\\frac{12}{16}\\)?<\/p>\n

    Answer:
    \nThe equivalent ratio for 12\/16 is 3:4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 12\/16.
    \n12: 16 = 3:4.
    \nso the ratio is 3:4.<\/p>\n

    Question 4.
    \nHow can you show that the ratios 10:4 and 15:6 are equivalent?<\/p>\n

    Answer:
    \nThe ratios are not equal.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratios are 10:4 and 15:6.
    \n10 : 4 = 15:6.
    \nso the ratios are not equal.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 5.
    \nComplete the table using multiplication to find ratios that are equivalent to 4:5.
    \n\"Envision<\/p>\n

    Answer:
    \nThe ratios are 8:10, 12:15, and 16:20.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 4:5.
    \n8 : 10 = 4:5.
    \n12:15 = 4:5.
    \n16:20 = 4:5.<\/p>\n

    Question 6.
    \nComplete the table using division to find ratios that are equivalent to 40:28.
    \n\"Envision<\/p>\n

    Answer:
    \nThe ratios that are equivalent to 40:28 = 20:14 and 10:7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe numbers are 40\/28.
    \n40\/28 = 20\/14.
    \n40\/28 = 10\/7.
    \nso the ratios that are equivalent to 40:28 = 20:14 and 10:7.<\/p>\n

    In 7-10, write an equivalent ratio for each given ratio.
    \nQuestion 7.
    \n\\(\\frac{12}{21}\\)<\/p>\n

    Answer:
    \nThe equivalent ratio is<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 12\/21.<\/p>\n

    Question 8.
    \n1:3<\/p>\n

    Answer:
    \nThe equivalent ratio is 3:9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 1:3.
    \n3:9 = 1:3.
    \n3 x 1 = 3.
    \n3 x 3 = 9.
    \nso the equialent ratio is 3:9.<\/p>\n

    Question 9.
    \n6 to 8<\/p>\n

    Answer:
    \nThe equivalent ratio is 3:4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 6 to 8.
    \n6\/8 = 3\/4.
    \nso the ratio is 3\/4.
    \n2 x 3 = 6.
    \n2 x 4 = 8.<\/p>\n

    Question 10.
    \nPi (st) can be approximated using decimals as the ratio 3.14:1. Find 3 ratios equivalent to the ratio 3.14:1.<\/p>\n

    Answer:
    \nThe equivalent ratio is 22\/7:1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 3.14:1.
    \n22\/7 = 3.14.
    \n22\/7:1 = 3.14:1.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Question 11.
    \nEva is making French toast. How many ounces of milk should Eva use with 10 eggs?
    \n\"Envision<\/p>\n

    Answer:
    \nThe recipe uses 10, 15, 20, 25, and 30.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfor 2 eggs the recipe uses 5 ounces of milk.
    \nfor 4 eggs the recipe uses 10 ounces of milk.
    \nfor 6 eggs the recipe uses 15 ounces of milk.
    \nfor 8 eggs the recipe uses 20 ounces of milk.
    \nfor 10 eggs the recipe uses 25 ounces of milk.<\/p>\n

    In 12-15, write three ratios that are equivalent to the given ratio.
    \nQuestion 12.
    \n\\(\\frac{6}{7}\\)<\/p>\n

    Answer:
    \nThe three ratios are 3\/14 and 18\/21.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 6\/7.
    \n3\/14 = 6\/7.
    \n18\/21 = 6\/7.
    \nso the three ratios are 3\/14 and 18\/21.<\/p>\n

    Question 13.
    \n\\(\\frac{9}{5}\\)<\/p>\n

    Answer:
    \nThe three ratios are 27\/15 and 18\/10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 9\/5.
    \n18\/10 = 9\/5.
    \n27\/15 = 9\/5.<\/p>\n

    Question 14.
    \n8:14<\/p>\n

    Answer:
    \nThe three ratios are 16\/28 and 24\/42.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 8\/14.
    \n16\/28 = 8\/14.
    \n24\/42 = 8\/14.
    \nso the three ratios are 16\/28 and 24\/42.<\/p>\n

    Question 15.
    \n7:9<\/p>\n

    Answer:
    \nThe three ratios are 6\/28 and 21\/27.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 7\/9.
    \n6\/28 = 7\/9.
    \n21\/27 = 7\/9.<\/p>\n

    Question 16.
    \nA teacher kept track of what students consumed at a school picnic. For three grades, the ratios of the amount of water consumed to the amount of fruit juice consumed were equivalent. Complete the table.
    \n\"Envision<\/p>\n

    Answer:
    \nThe juice contains 21 and 28 gallons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA teacher kept track of what students consumed at a school picnic.
    \nFor three grades, the ratios of the amount of water consumed to the amount of fruit juice consumed were equivalent.
    \nfor 6th grade 24 gallons of water contains the juice 28 gallons.
    \nfor 7th grade 18 gallons of water contains the juice 21 gallons.
    \nso the juice contains 21 and 28 gallons.<\/p>\n

    Question 17.
    \nThe attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot during a weekend. The ratios for the three days were equivalent. Complete the table.
    \n\"Envision<\/p>\n

    Answer:
    \nThe ratios for the three days were equivalent is 28 and 72.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe attendant at a parking lot compared the number of hybrid vehicles to the total number of vehicles in the lot during a weekend.
    \nthe ratios for the three days were equivalent.
    \n28 and 72 are the equivalent ratio.<\/p>\n

    Question 18.
    \nShiloh is sharing jellybeans. The jar of jellybeans has the ratio shown. If Shiloh keeps the ratio the same and gives his friend 7 pink jellybeans, how many green jellybeans should he also share?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of green jellybeans should he also share =<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nShiloh is sharing jellybeans.
    \nThe jar of jellybeans has the ratio shown.
    \nIf Shiloh keeps the ratio the same and gives his friend 7 pink jellybeans.<\/p>\n

    Question 19.
    \nUse Appropriate Tools Equivalent ratios can be found by extending pairs of rows or columns in a multiplication table. Write three ratios equivalent to \\(\\frac{2}{5}\\) using the multiplication table.
    \n\"Envision<\/p>\n

    Answer:
    \nThe three ratios equivalent to 2\/5 are 4\/10 and 6\/15.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 2\/5.
    \n4\/10 = 2\/5.
    \n6\/15 = 2\/5.
    \nso the three ratios equivalent to 4\/10 and 6\/15.<\/p>\n

    Question 20.
    \nIf 5 mi \u2248 8 km, about how many miles would be equal to 50 km? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of miles is equal to 31.069 miles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n5 miles \u2248 8 km.
    \n50 km is equal to 31.069 miles.
    \nso 31.069 miles is equal to 50 km.<\/p>\n

    Question 21.
    \nVocabulary<\/strong> How is the word term defined when used to describe a ratio relationship? How is the word term defined in the context of an expression?<\/p>\n

    Answer:
    \nThe term is one of the two numbers in the ratio a to b.
    \nwhere a is the first term and b is the second term.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe term is one of the two numbers in the ratio a to b.
    \nwhere a is the first term and b is the second term.
    \nit is also used to indicate each one of the 4 numbers in a proportion.
    \nif a = c.
    \nthen a,b,c, and d are the terms of the proportion.<\/p>\n

    Question 22.
    \nHigher Order Thinking<\/strong> Three sisters are saving for a special vacation in Orlando, Florida. The ratio of Ada’s savings to Ellie’s savings is 7:3, and the ratio of Ellie’s savings to Jasmine’s savings is 3:4. Together all three girls have saved $56. How much has each girl saved? Complete the table. Explain how the table can be used to solve the problem.
    \n\"Envision<\/p>\n

    Answer:
    \nThe Ada’s savings are $14 and $28.
    \nEllie’s savings are $3, $9, and $12.
    \nJasmine’s savings are $8 and $12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThree sisters are saving for a special vacation in Orlando, Florida.
    \nThe ratio of Ada’s savings to Ellie’s savings is 7:3, and the ratio of Ellie’s savings to Jasmine’s savings is 3:4.
    \nTogether all three girls have saved $56.
    \n7 x 2 = 14, 7 x 4 = 28.
    \n3 x 1 = 3, 3 x 3 = 9, and 3 x 4 = 12.
    \n4 x 2 = 8, 4 x 3 = 12, and 4 x 4 = 16.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 23.
    \nCorey is making key lime pies for the school fair. For every 3 egg yolks, he uses 2 tablespoons of key lime zest.
    \nPART A
    \nComplete the table to find equivalent ratios.
    \n\"Envision<\/p>\n

    Answer:
    \nThe egg yolks are 6, 9, and 12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCorey is making key lime pies for the school fair.
    \nFor every 3 egg yolks, he uses 2 tablespoons of key lime zest.
    \nthe equivalent ratios are 6, 9, and 12.
    \nso the egg yolks are 6, 9, and 12.<\/p>\n

    PART B
    \nHow can you use the table to find how many egg yolks are needed for 8 tablespoons of lime zest?<\/p>\n

    Answer:
    \nThe number of egg yolks are 12 needed for 8 tablespoons of lime zest.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCorey is making key lime pies for the school fair.
    \nFor every 3 egg yolks, he uses 2 tablespoons of key lime zest.
    \n3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9, and 3 x 4 =12.
    \nso the number of egg yolks are 12 needed for 8 tablespoons of lime zest.<\/p>\n

    Question 24.
    \nWhich ratios can be represented by Pi (t)? Select all that apply.
    \n\u2610 Diameter : Circumference
    \n\u2610 Circumference : Diameter
    \n\u2610 Circumference : Radius
    \n\u2610 Radius : Circumference
    \n\u2610 Circumference : Twice the radius<\/p>\n

    Answer:
    \nOptions A and B are correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \ndiameter and circumference are represented.
    \nso options A and B are correct.<\/p>\n

    Lesson 5.3 Compare Ratios<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nScott is making a snack mix using almonds and raisins. For every 2 cups of almonds in the snack mix, there are 3 cups of raisins. Ariel is making a snack mix that has 3 cups of almonds for every 5 cups of sunflower seeds. If Scott and Ariel each use 6 cups of almonds to make a batch of snack mix, who will make a larger batch?<\/p>\n

    I can… compare ratios to solve problems.
    \n\"Envision<\/p>\n

    Model with Math
    \nHow can you use ratio tables to represent Scott’s and Ariel’s snack mixes?<\/p>\n

    Focus on math practices
    \nLook for Relationships Scott and Ariel want to make as much snack mix as possible, but no more than 25 cups of mix. If they can use only full cups of ingredients, who can make more mix without going over?<\/p>\n

    Essential Question<\/strong>
    \nHow can you compare ratios to solve a problem?<\/p>\n

    Try It!<\/strong><\/p>\n

    Marlon had 6 hits in 15 at bats. How does Marlon’s hits to at bats ratio compare to Adrian’s?<\/p>\n

    Answer:
    \nThe ratio is 2:5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMarlon had 6 hits in 15 at bats.
    \n6 : 15 = 2:5.
    \nso the ratio is 2:5.<\/p>\n

    Convince Me! Based on their hits to at bats ratios, who would you expect to have more hits in a game, Marlon or Dustin? Explain.<\/p>\n

    Try It!<\/strong><\/p>\n

    Tank 3 has a ratio of 3 guppies for every 4 angelfish. Complete the ratio table to find the number of angelfish in Tank 3 with 12 guppies.
    \nUsing the information in Example 2 and the table at the right, which tank with guppies has more fish?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of Guppies is 6, 9, and 12.
    \nthe number of Angelfish is 8, 12, and 16.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTank 3 has a ratio of 3 guppies for every 4 angelfish.
    \n3 x 1 = 3.
    \n3 x 2 = 6.
    \n3 x 3 = 9.
    \n3 x 4 = 12.
    \n4 x 1 = 4.
    \n4 x 2 = 8.
    \n4 x 3 = 12.
    \n4 x 4 = 16.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use ratio tables to compare ratios when one of the corresponding terms is the same.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you compare ratios to solve a problem?<\/p>\n

    Answer:
    \nWe can use ratio tables to compare ratios when one of the corresponding terms is the same.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nwe can use ratio tables to compare ratios when one of the corresponding terms is the same.
    \nfor example:
    \n5 x 2 = 10.
    \n5 x 3 = 15.
    \n5 x 4 = 20.<\/p>\n

    Question 2.
    \nIn Example 1, how many hits would Adrian have in 50 at bats? Explain.<\/p>\n

    Answer:<\/p>\n

    Question 3.
    \nReasoning During the first week of a summer camp, 2 out of 3 campers were boys. During the second week, 3 out of 5 campers were boys. There were 15 total campers each week. During which week were there more boy campers? Explain.<\/p>\n

    Answer:
    \nIn the second week, there are more boy campers.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDuring the first week of a summer camp, 2 out of 3 campers were boys.
    \nDuring the second week, 3 out of 5 campers were boys.
    \nThere were 15 total campers each week.
    \nso in the second week, there are more boy campers.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nTo make plaster, Kevin mixes 3 cups of water with 4 pounds of plaster powder. Complete the ratio table. How much water will Kevin mix with 20 pounds of powder?
    \n\"Envision<\/p>\n

    Answer:
    \nThe amount of Kevin mix with 20 pounds of powder = 15 cups of water.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTo make plaster, Kevin mixes 3 cups of water with 4 pounds of plaster powder.
    \n3 x 2 = 6.
    \n3 x 3 = 9.
    \n3 x 4 = 12.
    \n3 x 5 = 15.
    \nso the amount of Kevin mix with 20 pounds of powder = 15 cups of water.<\/p>\n

    Question 5.
    \nJenny makes plaster using a ratio of 4 cups of water to 5 pounds of plaster powder. Whose plaster recipe uses more water? Use the ratio table here and in Exercise 4 to compare.
    \n\"Envision<\/p>\n

    Answer:
    \n16 cups of water to 20 pounds of powder.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJenny makes plaster using a ratio of 4 cups of water to 5 pounds of plaster powder.
    \n8 cups of water to 10 pounds of powder.
    \n12 cups of water to 15 pounds of powder.
    \n16 cups of water to 20 pounds of powder.<\/p>\n

    Question 6.
    \nKevin and Jenny each use 12 cups of water to make plaster. Who will make more plaster? Explain.<\/p>\n

    Answer:
    \nKevin makes more plaster than Jenny.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKevin and Jenny each use 12 cups of water to make plaster.
    \nKevin uses 12 cups of water to make 20 pounds of plaster.
    \nJenny uses 12 cups of water to make 15 pounds of plaster.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 7-10, use the ratio table at the right.
    \n\"Envision
    \nQuestion 7.
    \nLocal radio station WMTH schedules 2 minutes of news for every 20 minutes of music. Complete the ratios shown in the table at the right.<\/p>\n

    Answer:
    \nThe ratios are 30\/3, 40\/4, 50\/5, and 60\/6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n20 minutes of music is equal to 2 minutes of news.
    \n20\/2 = 10.
    \n30\/3 = 10.
    \n40\/4 = 10.
    \n50\/5 = 10.
    \n60\/6 = 10.
    \nso the ratios are 30\/3, 40\/4, 50\/5, and 60\/6.<\/p>\n

    Question 8.
    \nWhat is the ratio of minutes of music to minutes of news?<\/p>\n

    Answer:
    \nThe ratio of minutes of music to minutes of news = 10:1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n20 minutes of music is equal to 2 minutes of news.
    \n20\/2 = 10.
    \n30\/3 = 10.
    \n40\/4 = 10.
    \n50\/5 = 10.
    \n60\/6 = 10.
    \nso the ratios are 30\/3, 40\/4, 50\/5, and 60\/6.<\/p>\n

    Question 9.
    \nRadio station WILM broadcasts 4 minutes of news for every 25 minutes of music. Which radio station broadcasts more news each hour?<\/p>\n

    Answer:
    \nThe radio station broadcasts more news each hour =<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nRadio station WILM broadcasts 4 minutes of news for every 25 minutes of music.<\/p>\n

    Question 10.
    \nWhich station will have to be on the air longer to broadcast 4 minutes of news? Explain.<\/p>\n

    Answer:
    \nThe station will have to be on the air longer to broadcast 4 minutes of news = 40 minutes of music.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n20 minutes of music is equal to 2 minutes of news.
    \n20\/2 = 10.
    \n30\/3 = 10.
    \n40\/4 = 10.
    \n50\/5 = 10.
    \n60\/6 = 10.
    \nso the station will have to be on the air longer to broadcast 4 minutes of news = 40 minutes of music.<\/p>\n

    Question 11.
    \nReasoning<\/strong> The ratio tables at the right show the comparison of books to games for sale at Bert’s Store and at Gloria’s Store. Complete the ratio tables. Which store has the greater ratio of books to games? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe ratio of Bert’s store is 5\/7, 6\/8, 7\/9, and 8\/10.
    \nThe ratio of Gloria’s store is 5\/8, 6\/9, 7\/12, 8\/15, and 9\/18.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe ratio tables at the right show the comparison of books to games for sale at Bert’s Store and at Gloria’s Store.
    \nthe ratios of Bert’s store are 5\/7, 6\/8, 7\/9, and 8\/10.
    \nthe ratio of Gloria’s store is 5\/8, 6\/9, 7\/12, 8\/15, and 9\/18.<\/p>\n

    Question 12.
    \nThe ratio of soy sauce to lime juice in a homemade salad dressing is 7:6. The ratio of soy sauce to lime juice in a store-bought dressing is 11:9. Which dressing has the greater ratio of soy sauce to lime juice?
    \n\"Envision<\/p>\n

    Answer:
    \nThe ratio of Soy sauce to Lime juice is 7:6, 8:7, 9:8, 10:9, and 11:10.
    \nthe ratio of Soy sauce to lime juice is 11:9, 12:10, 13:11, 14:12, and 15:13.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe ratio of soy sauce to lime juice in a homemade salad dressing is 7:6.
    \nThe ratio of soy sauce to lime juice in a store-bought dressing is 11:9.
    \nthe ratio of soy sauce to the Lime juice is 7:6, 8:7, 9:8, 10:9, and 11:10.
    \nthe ratio of soy sauce to lime juice is 11:9, 12:10, 13:11, 14:12, and 15:13.<\/p>\n

    Question 13.
    \nOne bouquet of flowers has 3 milkweeds for every 5 tickseeds. Another bouquet has 4 tickseeds for every 5 canna lilies. If both bouquets have 20 tickseeds, which bouquet has more flowers?
    \n\"Envision<\/p>\n

    Answer:
    \nBouquet 4 has more flowers.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOne bouquet of flowers has 3 milkweeds for every 5 tickseeds.
    \nAnother bouquet has 4 tickseeds for every 5 canna lilies.
    \n3 x 5 =15.
    \n4 x 6 = 24.
    \n5 x 7 = 35.
    \n6 x 8 = 48.
    \n7 x 9 = 63.
    \n4 x 5 = 20.
    \n5 x 6 = 30.
    \n6 x 7 = 42.
    \n7 x 8 = 56.
    \n8 x 9 = 72.<\/p>\n

    Question 14.
    \nHigher Order Thinking<\/strong> Lauren can drive her car 320 miles on 10 gallons of gasoline. Melissa can drive her car 280 miles on 8 gallons of gasoline. Who can drive farther on 40 gallons of gasoline? Complete the ratio tables to justify your solution.
    \n\"Envision<\/p>\n

    Answer:<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLauren can drive her car 320 miles on 10 gallons of gasoline.
    \nMelissa can drive her car 280 miles on 8 gallons of gasoline.
    \n320\/10 and 280\/8.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 15.
    \nFran buys Florida cone seashells in packages that contain 9 purple-dyed Florida cone seashells for every 3 pink-dyed Florida cone seashells. Mia buys Florida cone seashells in packages with a ratio of 2 pink-dyed Florida cone seashells to 4 purple-dyed Florida cone seashells.
    \nPART A
    \nComplete the tables using the ratios given.
    \n\"Envision<\/p>\n

     <\/p>\n

    Answer:
    \nThe missing ratios of Fran’s shell packages are 18\/6, 27\/9, and 36\/12.
    \nthe missing ratios of Mia’s shell packages are 8\/4, 12\/6, and 16\/8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nFran buys Florida cone seashells in packages that contain 9 purple-dyed Florida cone seashells for every 3 pink-dyed Florida cone seashells.
    \n6 x 3 = 18, 3 x 3 = 9, 9 x 3 = 27, and 12 x 3 = 36.
    \n2 x 2 = 4, 4 x 2 = 8, 6 x 2 = 12, and 8 x 2 = 16.<\/p>\n

    PART B
    \nIf the girls each buy packages that contain 6 pinkdyed Florida cone seashells, how many purple-dyed Florida cone seashells would each have? Explain.<\/p>\n

    Answer:
    \nThe number of purple-dyed Florida cone seashells would each have = 18.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIf the girls each buy packages that contain 6 pink dyed Florida cone seashells.
    \n6 x 3 = 18.
    \nso the number of purple-dyed Florida cona seashells would each have = 18.<\/p>\n

    Lesson 5.4 Represent and Graph Ratios<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nFor every 4 adults at the beach one afternoon, there were 3 children. How many children were at the beach if there were 8, 12, 16, or 20 adults at the beach?<\/p>\n

    I can… solve ratio problems by using tables and graphs to show equivalent ratios.
    \n\"Envision<\/p>\n

    Model with Math
    \nHow does the graph show the ratio?<\/p>\n

    Answer:
    \nThe graph shows the ratio y = x-1, y = x-2, y = x-4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nFor every 4 adults at the beach one afternoon, there were 3 children.
    \nif there were 8 adults there were 6 children.
    \nif there were 12 adults there were 9 children.
    \n4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12, and 4 x 4 = 16.
    \n3 x 1 = 3, 3 x 2 = 6, 3 x 3 = 9, and 3 x 4 = 12.<\/p>\n

    Focus on math practices
    \nCritique Reasoning There were 25 children and 15 adults at the beach. Emery said that there were 5 children for every 3 adults. Is he correct? Explain.<\/p>\n

    Answer:
    \nYes, Emery was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere were 25 children and 15 adults at the beach.
    \nEmery said that there were 5 children for every 3 adults.
    \n3 x 5 = 15.
    \nfor 15 adults there were 25 children.
    \nso Emery was correct.<\/p>\n

    Essential Question<\/strong>
    \nHow can you use tables and graphs to show equivalent ratios?<\/p>\n

    Try It!<\/strong><\/p>\n

    What are the coordinates of the point that represents the number of balloons you can buy for $6?<\/p>\n

    Answer:
    \nThe coordinates of the point that represents the number of balloons we can but for $6 is (6,0) and (0,6).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfor example:
    \nfor example:
    \nthe points are (6, 0) and (0,6).<\/p>\n

    Convince Me! How can you use the graph to find the cost of 15 balloons?<\/p>\n

    Try It!<\/strong><\/p>\n

    Can you draw an object with a diameter of 10 inches and a circumference of 50 inches? Explain.<\/p>\n

    Answer:
    \nYes, we can draw a diameter of 10 inches and a circumference of 50 inches.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nwe can draw a diameter of 10 inches and a circumference of 50 inches.
    \nthe circumference is the center of the circle.
    \nradius is half of the diameter.
    \ndiameter is 50\/2 = 25.
    \nso we can draw a diameter.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use ratio tables and graphs to show equivalent ratios. When ordered pairs representing equivalent ratios are graphed as points in the coordinate plane, they form a line.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you use tables and graphs to show equivalent ratios?<\/p>\n

    Answer:
    \nWhen ordered pairs representing equivalent ratios are graphed as points in the coordinate plane, they form a line.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfor example:
    \nfor every 3 tennis rackets sold, 4 tennis balls are sold.
    \nfor every 12 tennis rockets sold, 16 tennis balls are sold.
    \nso when ordered pairs representing equivalent ratios are graphed as points in the coordinate plane, they form a line.<\/p>\n

    Question 2.
    \nLook for Relationships In Example 2, how could you use the graph to find the number of apples needed for 30 celery sticks?<\/p>\n

    Answer:
    \nThe number of apples needed for 30 celery sticks = 40 apples.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nif there are 30 celery sticks, there would be 40 apples.
    \n3 x 10 = 30.
    \n4 x 10 = 40.
    \nso the number of apples needed for 30 celery sticks = 40 apples.<\/p>\n

    Question 3.
    \nHow could you use repeated addition to show ratios equivalent to 1:3 on a graph?<\/p>\n

    Answer:
    \nThe ratios forms a straight line.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfor example:
    \nfor every 3 tennis rackets sold, 4 tennis balls are sold.
    \nfor every 12 tennis rockets sold, 16 tennis balls are sold.
    \nso when ordered pairs representing equivalent ratios are graphed as points in the coordinate plane, they form a line.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nComplete the table to show equivalent ratios representing a cost of $8 for every 3 boxes. Then write the pairs of values as points to be plotted on a coordinate plane.
    \n\"Envision<\/p>\n

    Answer:
    \nThe points are (12, 32) and (15, 40).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12, and 3 x 5 = 15.
    \n8 x 2 = 16, 8 x 3 = 24, 8 x 4 = 32, and 8 x 5 = 40.
    \nso the coordinate points are (12, 32) and (15, 40).<\/p>\n

    Question 5.
    \nModel with Math Plot the equivalent ratios (3, 4), (6, 8), and (9, 12) on the graph. Use the graph to find the number of nonfiction books purchased if 10 fiction books are purchased.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of nonfiction books purchased if 10 fiction books are purchased = 14.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe equivalent ratios are (3, 4), (6, 8), (9, 12), and (10, 14).
    \nthe points form a straight line.
    \nso the number of nonfiction books purchased if 10 fiction books are purchased = 14.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice in 6 and 7, complete the table and graph the pairs of values.
    \nQuestion 6.
    \n\"Envision<\/p>\n

    Answer:
    \nThe points are (6, 9).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe points are (2,3) and (4,6).
    \n2 x 2 = 4, 2 x 3 = 6.
    \n3 x 2 = 6, 3 x 3 = 9.
    \nso the points are (6, 9).<\/p>\n

    Question 7.
    \n\"Envision<\/p>\n

    Answer:
    \nThe points are (50, 20).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe points are (5, 2) and (25, 10).
    \n5 x 5 = 25, 5 x 10 = 50.
    \n2 x 5 = 10, 2 x 10 = 20.
    \nso the points are (50, 20).<\/p>\n

    Question 8.
    \nA student runs 2 minutes for every 10 minutes she walks.
    \na. Complete the table. Graph the pairs of values.
    \n\"Envision<\/p>\n

    Answer:
    \nThe points are (6, 30).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe running minutes are 2, 4.
    \nthe walking minutes are 10, 20.
    \n2 x 2 = 4.
    \n2 x 3 = 6.
    \n10 x 2 = 20.
    \n10 x 3 = 30.
    \nso the points are (6, 30).<\/p>\n

    b. For how long would the student walk if she runs for 7 minutes?<\/p>\n

    Answer:
    \nThe student walks if she runs for 7 minutes = 35.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe running minutes are 2, 4.
    \nthe walking minutes are 10, 20.
    \n2 x 2 = 4.
    \n2 x 3 = 6.
    \n10 x 2 = 20.
    \n10 x 3 = 30.
    \nso the student walks if she runs for 7 minutes = 35.<\/p>\n

    Question 9.
    \nA car magazine reports the number of miles driven for different amounts of gas for three cars. Which car travels the farthest on 1 gallon of gas? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nCar A can travels the farthest on 1 gallon of gas.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCar A can travels for 1 gallon of gas the number of miles driven is 50.
    \nCar B can travels for 1 gallon of gas the number of miles driven is 30.
    \nCar C can travels for 1 gallon of gas the number of miles driven is 25.
    \nSo car A can travels the farthest on 1 gallon of gas.<\/p>\n

    Question 10.
    \nModel with Math A bread recipe calls for 4 cups of white flour for every 5 cups of whole-wheat flour. Complete the table to show how many cups of whole-wheat flour are needed to mix with 16 cups of white flour. Then graph the pairs of values.
    \n\"Envision<\/p>\n

    Answer:
    \nThe points of whole-wheat flour are 4, 8, 12, and 16.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA bread recipe calls for 4 cups of white flour for every 5 cups of whole-wheat flour.
    \n4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12, and 4 x 4 = 16.
    \nso the points of whole-wheat flour is 4, 8, 12, and 16.<\/p>\n

    Question 11.
    \nThe graph shows the relationship between the number of cups of sugar and the number of cups of flour in a key-lime bread recipe. What point on the graph represents the number of cups of sugar that would be used with 8 cups of flour?
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of cups of sugar that would be used with 8 cups of flour is 2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe flour(c) is on the x-axis.
    \nthe sugar (c) is on the y-axis.
    \nthe points are (2, 0.5), (4, 1), (6, 1.5), (8, 2), (10, 2.5),\u00a0 (12, 3), and (14, 3.5).
    \nso the number of cups of sugar that would be used with 8 cups of flour is 2.<\/p>\n

    Question 12.
    \nHigher Order Thinking<\/strong> Ishwar can read 5 pages in 15 minutes. Anne can read 15 pages in 1 hour. Explain how you could use a table or graph to find how much longer it would take Anne to read a 300-page book than Ishwar.<\/p>\n

    Answer:
    \nThe much longer it would take Anne to read a 300-page book than Ishwar = 20 hours.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIshwar can read 5 pages in 15 minutes.
    \nAnne can read 15 pages in 1 hour.
    \n30 pages in 2 hours.
    \n60 in 4 hours.
    \n90 in 6 hours.
    \n90 + 90 = 180 pages in 12 hours.
    \n8 hours is 120 pages.
    \n12 + 8 = 20 hours.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 13.
    \nThe measurements of a circular object are given in the ratio table.
    \nPART A
    \nFind the missing dimensions of other circular objects by completing the ratio table.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing dimensions are 42 and 301.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe measurements of a circular object are given in the ratio table.
    \nthe missing dimensions are 42 and 301.<\/p>\n

    PART B
    \nGraph the pairs of values.
    \n\"Envision<\/p>\n

    Answer:
    \nThe points are (200, 200), (400, 400), (600, 600), and (800, 800).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe diameter is shown on the x-axis.
    \nthe circumference is shown on y-axis.
    \nso the points are (200, 200), (400, 400), (600, 600), and (800, 800).<\/p>\n

    Topic 5 Mid-Topic Checkpoint<\/h3>\n

    Question 1.
    \nVocabulary How can a ratio be used to compare quantities? Lesson 5-1
    \nAnswer:<\/p>\n

    Question 2.
    \nThe circumference of the outside of a ring is 66 mm, and it has an outer diameter of 21 mm. If the circumference of the inside of the ring is 50 mm, what is the inner diameter of the ring? Lesson 5-4<\/p>\n

    Answer:
    \nThe inner diameter of the ring = 50 mm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe circumference of the outside of a ring is 66 mm, and it has an outer diameter of 21 mm.
    \nIf the circumference of the inside of the ring is 50 mm.
    \nthe inner diameter of the ring = 50 mm.<\/p>\n

    Question 3.
    \nDuring the breakfast service, the D-Town Diner sells 12 cups of coffee for every 10 glasses of orange juice. How many cups of coffee would the diner have sold if 40 glasses of orange juice had been sold? Complete the table with equivalent ratios. Lesson 5-2
    \n\"Envision<\/p>\n

    Answer:
    \nThe ratios are (24, 20), (36, 30), and (48,40).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDuring the breakfast service, the D-Town Diner sells 12 cups of coffee for every 10 glasses of orange juice.
    \n2 x 5 = 10, and 2 x 6 = 12.
    \n3 x 10 = 30, and 3 x 12 = 36.
    \n4 x 10 = 40, and 4 x 12 = 48.
    \nso the ratios are (24, 20), (36, 30), and (48, 40).<\/p>\n

    Question 4.
    \nThe ratio of cows to chickens at Old McDonald’s Farm is 2:7. Select all the farms that have a greater ratio of cows to chickens than Old McDonald’s Farm. Lessons 5-3
    \n\u2610 Red’s Farm: 3 cows for every 5 chickens
    \n\u2610 Pasture Farm: 2 cows for every 9 chickens
    \n\u2610 Cluck & Moo Farm: 1 cow for every 5 chickens
    \n\u2610 C & C Farm: 3 cows for every 8 chickens
    \n\u2610 T Family Farm: 1 cow for every 3 chickens<\/p>\n

    Answer:<\/p>\n

    Question 5.
    \nA package of 3 notebooks costs $5. Complete the ratio table and graph the pairs of values. How much will 18 notebooks cost? Lesson 5-4
    \n\"Envision<\/p>\n

    Answer:
    \nThe cost of 18 notebooks is $30.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA package of 3 notebooks costs $5.
    \n3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12, 3 x 5 =15, 3 x 6 = 18.
    \n5 x 2 = 10, 5 x 3 = 15, 5 x 4 = 20, 5 x 5 = 25, 5 x 6 = 30.
    \nso the cost of 18 notebook is $30.<\/p>\n

    Topic 5 Mid-Topic Performance Task<\/h3>\n

    Hillsdale Orchard grows Fuji apples and Gala apples. There are 160 Fuji apple trees and 120 Gala apple trees in the orchard.<\/p>\n

    PART A
    \nHillsdale Orchard’s owners decide to plant 30 new Gala apple trees. Complete the ratio table to find the number of new Fuji apple trees the owners should plant if they want to maintain the same ratio of Fuji apple trees to Gala apple trees.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of Fuji Apple trees to the Gala Apple trees is (40,30), (80, 60), and (160,120).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHillsdale Orchard’s owners decide to plant 30 new Gala apple trees.
    \n30 x 2 = 60.
    \n60 x 2 = 120.
    \n40 x 2 = 80.
    \n80 x 2 = 160.
    \nso the number of Fuji Apple trees to the Gala Apple trees is (40,30), (80, 60), and (160, 120).<\/p>\n

    PART B
    \nUse the ratio table to complete a graph that shows the relationship between the number of Fuji apple trees and Gala apple trees at Hillsdale Orchard.
    \n\"Envision<\/p>\n

    Answer:
    \nFuji Apple trees on the x-axis.
    \nGala Apple trees on the y-axis.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nFuji Apple trees on the x-axis.
    \nGala Apple trees on the y-axis.
    \nthe points are (80, 60), (160, 120), and (240, 180).<\/p>\n

    PART C
    \nBy the end of the next season, the owners of Hillsdale Orchard plan to have 240 Fuji apple trees. Explain how you could use the graph to find the total number of Fuji and Gala apple trees that Hillsdale Orchard will have if the owners achieve their goal.<\/p>\n

    Answer:
    \nThe total number of Fuji and Gala apple trees that Hillsdale Orchard is (240, 180).<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe owners of Hillsdale Orchard plan to have 240 Fuji apple trees.
    \nthe points are (80, 60), (160, 120), and (240, 180).
    \nso the total number of Fuji and Gala apple trees that Hillsdale Orchard is (240, 180).<\/p>\n

    Lesson 5.5 Understand Rates and Unit Rates<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nWhat is the cost of 10 bottles of fruit juice?<\/p>\n

    I can… solve problems involving rates.
    \n\"Envision<\/p>\n

    Make Sense and Persevere
    \nHow can you use tables or diagrams to make sense of the quantities in the problem?<\/p>\n

    Focus on math practices
    \nCritique Reasoning Monica says, “If 4 bottles cost $10, then 2 bottles cost $5, and 8 bottles cost $20. So 10 bottles cost $5 + $20.” Is Monica correct? Explain.<\/p>\n

    Answer:
    \nNo Monica was not correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIf 4 bottles cost $10, then 2 bottles cost $5, and 8 bottles cost $20.
    \n4 bottles cost $10.
    \n8 bottles cost $20.
    \n10 bottles cost $30.
    \nso Monica was not correct.<\/p>\n

    Essential Question<\/strong>
    \nWhat are rates and unit rates?<\/p>\n

    Try It!<\/strong><\/p>\n

    At the same rate, how long would it take the car to travel 60 kilometers?
    \n\"Envision
    \nIt will take the car _______ minutes to travel ________ kilometers.<\/p>\n

    Answer:
    \nIt will take the car 6 minutes to travel 60 kilometers.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n10 x 6 = 60.
    \n3 x 6 = 18.
    \nit will take the car 6 minutes to travel 60 kilometers.<\/p>\n

    Convince Me! Sal draws the double number line diagram at the right. He says it shows that at this rate the race car will travel 35 kilometers in 10.5 minutes. Critique Sal’s reasoning. Is he correct? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nYes, he was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSal draws the double number line diagram at the right.
    \nHe says it shows that at this rate the race car will travel 35 kilometers in 10.5 minutes.
    \nthe points are (3, 10), (6, 20), (9, 30), (10.5, 35), and (12, 40).
    \nso he was correct.<\/p>\n

    Try It!<\/strong><\/p>\n

    A recipe for scrambled eggs uses 2 tablespoons of milk for every 3 eggs. What are two unit rates that could represent the recipe?<\/p>\n

    Answer:
    \nThe two-unit rates that could represent the recipe = 2\/3, 4\/6, and 6\/9.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA recipe for scrambled eggs uses 2 tablespoons of milk for every 3 eggs.
    \n2 x 2 = 4, 2 x 3 = 6, 2 x 4 = 8.
    \n3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12.
    \nso the two-unit rates that could represent the recipe = 2\/3, 4\/6, and 6\/9.<\/p>\n

    Try It!<\/strong><\/p>\n

    A canoeing club travels 78 miles in 3 days. How far could they travel in 5 days if they maintain the same speed?<\/p>\n

    Answer:
    \nThey can travel 130 miles in 5 days.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA canoeing club travels 78 miles in 3 days.
    \n78 miles in 3 days.
    \n78\/3 = 26.
    \n26 + 26 = 52.
    \n78 + 52 = 130.
    \nso they can travel 130 miles in 5 days.<\/p>\n

    KEY CONCEPT<\/strong>
    \nA rate compares quantities with unlike units of measure.
    \n\\(\\frac{\\$ 3.50}{7 \\text { oranges }}\\)
    \nA unit rate compares a quantity to 1 unit of another quantity.
    \n\\(\\frac{\\$ 3.50}{7 \\text { oranges }}=\\frac{\\$ 0.50}{1 \\text { orange }}\\)<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> What are rates and unit rates?<\/p>\n

    Answer:
    \nA rate compares quantities with unlike units of measure.
    \nA unit rate compares a quantity to 1 unit of another quantity.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA rate compares quantities with unlike units of measure.
    \nA unit rate compares a quantity to 1 unit of another quantity.
    \nfor example:
    \n3.50\/7 = 0.5.<\/p>\n

    Question 2.
    \nBe Precise Use what you know about ratios to describe a rate.<\/p>\n

    Answer:
    \nA rate compares quantities with unlike units of measure.
    \nA unit rate compares a quantity to 1 unit of another quantity.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA rate compares quantities with unlike units of measure.
    \nA unit rate compares a quantity to 1 unit of another quantity.
    \nfor example:
    \n3.50\/7 = 0.5.<\/p>\n

    Question 3.
    \nReasoning<\/strong> A bathroom shower streams 5 gallons of water in 2 minutes.
    \na. Find the unit rate for gallons per minute and describe it in words.<\/p>\n

    Answer:
    \nThe unit rate for gallons per minute is 2.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA bathroom shower streams 5 gallons of water in 2 minutes.
    \n5\/2 = 2.5.
    \nso the unit rate for gallons per minute.<\/p>\n

    b. Find the unit rate for minutes per gallon and describe it in words.
    \n\"Envision<\/p>\n

    Answer:
    \nThe unit rate for minutes per gallon = 2.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA bathroom shower streams 5 gallons of water in 2 minutes.
    \n5\/2 = 2.5.
    \nso the unit rate for gallons per minute.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 4 and 5, find the value of n.
    \nQuestion 4.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of hours for n = 12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of hours is 4 for the number of miles = 45.
    \n45 + 45 + 45 = 135.
    \n4 + 4 + 4 = 12.
    \nso for the n hours the number of miles = 12.<\/p>\n

    Question 5.
    \n\"Envision<\/p>\n

    Answer:
    \nThe value of n is 4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe cost in dollars are shown in the figure.
    \nthe pounds are also shown.
    \nfor 2 dollars the pounds count is 1.
    \nfor 3 dollars the pounds count is 2.
    \nfor 4 dollars the pounds count is 3.
    \nfor 5 dollars the pounds count is 4.
    \nso the value of n is 4.<\/p>\n

    Question 6.
    \nJenny packaged 108 eggs in 9 cartons. Write this statement as a rate.<\/p>\n

    Answer:
    \nJenny packaged 108 eggs in 2 cartons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJenny packaged 18 eggs in 9 cartons.
    \n18\/9 = 2.
    \nso the Jenny packaged 108 eggs in 9 cartons is 2.<\/p>\n

    Question 7.
    \nAnna Maria read 40 pages in 60 minutes. What is her unit rate in pages per minute?<\/p>\n

    Answer:
    \nThe unit rate in pages per minute = 0.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAnna Maria read 40 pages in 60 minutes.
    \n40\/60 = 4\/6.
    \n2\/3 = 0.6.
    \nso the unit rate in pages per minute = 0.6.<\/p>\n

    In 8 and 9, use the unit rates that you found in Exercise 3.
    \nQuestion 8.
    \nHow many gallons of water does the shower stream in 6 minutes?<\/p>\n

    Answer:
    \nThe number of gallons of water does the shower stream in 6 minutes = 6.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n40\/6 = 20\/3.
    \n20\/3 = 6.6.
    \nso the number of gallons of water does the shower stream in 6 minutes = 6.6.<\/p>\n

    Question 9.
    \nHow long can someone shower to use only 10 gallons of water?<\/p>\n

    Answer:
    \nThe shower to use only 10 gallons of water = 0.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe long can someone shower to use only 10 gallons of water.
    \n10\/20 = 1\/2 = 0.5.
    \nso the length can someone shower to use only 10 gallons of water = 0.5.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 10 and 11, write each statement as a rate.
    \nQuestion 10.
    \nJan saw 9 full moons in 252 days.<\/p>\n

    Answer:
    \nThe rate is 0.03.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJaw saw 9 full moons in 252 days.
    \n9\/252 = 0.03.
    \nso the rate is 0.03.<\/p>\n

    Question 11.
    \nIt took Hannah 38 minutes to run 8 laps.
    \n\"Envision<\/p>\n

    Answer:
    \nThe rate is 4.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIt took Hannah 38 minutes to run 8 laps.
    \n38\/8 = 4.75.
    \nso the rate is 4.75.<\/p>\n

    In 12 and 13, find the value of x.
    \nQuestion 12.
    \n\"Envision<\/p>\n

    Answer:
    \nThe value of x is 8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of bowls is 2.
    \nthe number of fish in 2 bowls is 16.
    \nthe number of bowls is 6.
    \nthe number of fish in 6 bowls is 48.
    \n48\/6 = 8.
    \nso the value of x is 8.<\/p>\n

    Question 13.
    \n\"Envision<\/p>\n

    Answer:
    \nThe value of x is 46.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of miles and the number of hours are given.
    \nthe number of miles for 4 is 46.
    \nthe number of miles for 8 is 92.
    \nthe number of miles for 12 is 138.
    \nthe number of miles for 16 is 184.<\/p>\n

    In 14 and 15, find the unit rate.
    \nQuestion 14.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of miles is 20.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n320 mi\/16 gal.
    \n320\/16 \/ 16\/16.
    \n20\/1 = 20.
    \nso the number of miles is 20.<\/p>\n

    Question 15.
    \n\"Envision<\/p>\n

    Answer:
    \nThe value of cm = 15.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n75 cm to 5 h.
    \n75\/5 \/ 5\/5.
    \n15 \/ 1 = 15.
    \nso the value of the cm = 15.<\/p>\n

    In 16-19, complete each table.
    \nQuestion 16.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing values are 2, 5, 5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe minutes on the number of pages are given.
    \n9 x 2 = 18.
    \n1 x 2 = 2.
    \n5 x 2 =10.
    \n5 x 3 = 15.<\/p>\n

    Question 17.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing values are 62, 434, and 682.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n186\/3 = 62.
    \n62\/1 = 62.
    \n434\/7 = 62.
    \n682\/11 = 62.
    \nso the missing values are 62, 434, and 682.<\/p>\n

    Question 18.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing values are 12.3, 61.5, and 10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n12.3\/1 = 12.3.
    \n24.6\/2 = 12.3.
    \n61.5\/5 =12.3.
    \n123\/10 = 12.3.
    \nso the missing values are 12.3, 61.5, and 10.<\/p>\n

    Question 19.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing values are 1, 75, 300.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of gallons and miles are given.
    \n125\/5 = 25.
    \n25\/1 = 25.
    \n75\/3 = 25.
    \n300\/12 = 25.
    \nso the missing values are 1, 75, and 300.<\/p>\n

    Question 20.
    \nWhich runner set the fastest pace? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nAllison runs at the fastest pace.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe runner Martha did 20 laps in 32 min.
    \nthe runner Allison did 16 laps in 25 min.
    \nthe runner Rachel did 17 laps in 27.2 min.
    \nspeed = distance\/time.
    \nMartha = 20\/32.
    \nMartha = 0.625.
    \nAllison = 16\/25.
    \nAllison = 0.64.
    \nRachel = 17\/27.2.
    \nRachel = 0.625.
    \nAllison runs at the fastest pace.<\/p>\n

    Question 21.
    \nModel with Math Over the summer, Alexis read 15 books in 12 weeks. The diagram below can be used to track her progress. If Alexis read at the same rate each week, how many books had she read in 4 weeks? In 8 weeks? Complete the diagram.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing books are 5 and 10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nOver the summer, Alexis read 15 books in 12 weeks.
    \nAlexis read the 5 books in 4 weeks.
    \nthe number of books Alexis read in 8 weeks = 10.
    \n5 x 1 = 5.
    \n5 x 2 = 10.
    \n5 x 3 = 15.
    \nso the missing books are 5 and 10.<\/p>\n

    Question 22.
    \nAn elephant charges an object that is 0.35 kilometer away. How long will it take the elephant to reach the object?
    \n\"Envision<\/p>\n

    Answer:
    \nThe distance will it take the elephant to reach the object = 0.5 km.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn elephant charges an object that is 0.35 kilometers away.
    \nElephants can charge at speeds of 0.7 km per minute.
    \n0.35\/0.7 = 0.5.
    \n7 x 5 = 35.
    \nso the distance will it take the elephant to reach the object = 0.5 km.<\/p>\n

    Question 23.
    \nA machine takes 1 minute to fill 6 cartons of eggs. At this rate, how many minutes will it take to fill 420 cartons?<\/p>\n

    Answer:
    \nThe number of minutes will it take to fill 420 cartons = 70 min.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA machine takes 1 minute to fill 6 cartons of eggs.
    \n70 x 6 = 420.
    \n420\/6 = 70.
    \nso the number of minutes will it take to fill 420 cartons = 70 min.<\/p>\n

    Question 24.
    \nHigher Order Thinking<\/strong> How are the ratios \\(\\frac{24 \\text { laps }}{1 \\text { hour }}\\) and \\(\\frac{192 \\text { laps }}{8 \\text { hours }}\\) alike? How are they different?<\/p>\n

    Answer:
    \nThey are same.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratios 24, 192, and 8 are alike.
    \n8 x 1 = 8.
    \n8 x 3 = 24.
    \n24 x 8 = 192.
    \nso they are same.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 25.
    \nA bakery sells 12 gourmet orange-zest cupcakes for $36.00. Select all the statements that are true.
    \n\u2610 \\(\\frac{\\$ 3.00}{1 \\text { cupcake }}\\) is a unit rate for the cost per 1 cupcake cupcake.
    \n\u2610 \\(\\frac{36}{12}\\) represents the ratio of $36.00 for 12 cupcakes.
    \n\u2610 Using the same rate, the bakery can sell 6 cupcakes for $20.00.
    \n\u2610 Using the same rate, the bakery can sell 2 dozen cupcakes for $72.00.
    \n\u2610 Using the same rate, it would cost $24.50 for 8 cupcakes.<\/p>\n

    Answer:
    \nOption A is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA bakery sells 12 gourmet orange-zest cupcakes for $36.00.
    \n36\/12 = 3.
    \n12 x 3 = 36.
    \nso option A is correct.<\/p>\n

    Lesson 5.6 Compare Unit Rates<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nRick and Nikki own remote-control cars. They use a stopwatch to record the speed of each car. Whose car is faster?<\/p>\n

    I can… compare unit rates to solve problems.
    \n\"Envision<\/p>\n

    Be Precise
    \nUse precise numbers and units to describe and compare rates.<\/p>\n

    Focus on math practices
    \nMake Sense and Persevere If each car maintains its rate of speed, how long will it take Rick’s car to travel 300 feet? How long will it take Nikki’s car to travel the same distance? Explain.<\/p>\n

    Answer:
    \nThe long will it take Nikki’s car to travel the same distance = 60 sec.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nRick and Nikki own remote-control cars.
    \nthe distance in 30 sec is 150 feet.
    \nthe distance will it take 300 feet in 60 sec.
    \n300\/150 = 2.
    \n30 x 2 = 60.
    \nso the long will it take Nikki’s car to travel the same distance = 60 sec.<\/p>\n

    Essential Question<\/strong>
    \nHow can you use unit rates to make comparisons?<\/p>\n

    Try It!<\/strong><\/p>\n

    Ashley is Austin’s older sister. She trains in the same pool and can swim 9 laps in 6 minutes. Is Ashley a faster swimmer than Austin?
    \n\"Envision
    \nAshley swims 1.5 laps per minute. Because ________ 1.4, Ashley is a _______ swimmer than Austin.<\/p>\n

    Answer:
    \nAshley swims faster than Austin.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAshley is Austin’s older sister.
    \nShe trains in the same pool and can swim 9 laps in 6 minutes.
    \nAshley swims 1.5 laps per minute.
    \n9\/1.5 = 6.
    \n6\/1.4 = 4.2.
    \nso Ashley swims faster than Austin.<\/p>\n

    Convince Me! How can you use the unit rate in minutes per lap to compare Ashley’s speed to Austin’s speed?<\/p>\n

    Try It!<\/strong><\/p>\n

    Explain how to decide which is the better value, 4 greeting cards for $10 or 6 greeting cards for $14.
    \n\"Envision<\/p>\n

    Answer:
    \nThe better value is 4 greeting cards for $10.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n4 greeting cards for $10.
    \n6 greeting cards for $14.
    \n10\/4 = 2.5.
    \n14\/6 = 2.3.
    \nso the better value is 4 greeting cards for $10.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use unit rates to make comparisons.
    \n$8.50 per hour > $8.00 per hour
    \n\\(\\frac{32 \\mathrm{~cm}}{1 \\mathrm{sec}}\\) < \\(\\frac{45 \\mathrm{~cm}}{1 \\mathrm{sec}}\\)<\/p>\n

    \\(\\frac{7 \\text { laps }}{1 \\mathrm{~min}}\\) < \\(\\frac{9 \\text { laps }}{1 \\mathrm{~min}}\\) 175 words per minute > 95 words per minute<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you use unit rates to make comparisons?<\/p>\n

    Answer:
    \nWe can use unit rates to make comparisons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nYou can use unit rates to make comparisons.
    \n$8.50 per hour > $8.00 per hour.
    \n175 words per minute > 95 words per minute.<\/p>\n

    Question 2.
    \nCritique Reasoning<\/strong> Paul says that a lower unit rate is a better value only if you can use all the items purchased to get the lower unit rate. Do you agree? Explain.<\/p>\n

    Answer:
    \nYes, i will agree.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPaul says that a lower unit rate is a better value only if you can use all the items purchased to get the lower unit rate.
    \nso I will agree.<\/p>\n

    Question 3.
    \nReasoning<\/strong> Car A travels 115 miles on 5 gallons of gas. Car B travels 126 miles on 6 gallons of gas. How can you find which car gets better gas mileage?<\/p>\n

    Answer:
    \nThe Car A gets better gas mileage.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCar A travels 115 miles on 5 gallons of gas.
    \nCar B travels 126 miles on 6 gallons of gas.
    \n115\/5 = 23.
    \n126\/6 = 21.
    \nso car A gets better gas mileage.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 4.
    \nHakim’s car travels 600 feet in 20 seconds. Andre’s motorcycle travels 300 feet in 12 seconds. Which is faster, the car or the motorcycle? Explain.
    \n\"Envision
    \na. Find the unit rates.<\/p>\n

    Answer:
    \nThe car is faster.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHakim’s car travels 600 feet in 20 seconds.
    \nAndre’s motorcycle travels 300 feet in 12 seconds.
    \n300\/12 = 25.
    \n600\/20 = 30.
    \nso the car is faster.<\/p>\n

    b. Compare the unit rates.
    \nAnswer:<\/p>\n

    In 5 and 6, find each unit price.
    \nQuestion 5.
    \n7 movie tickets for $56<\/p>\n

    Answer:
    \nEach ticket cost $8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n7 movie tickets for $56.
    \n$56\/7 = 8.
    \nso each ticket cost $8.<\/p>\n

    Question 6.
    \n12 fluid ounces of shampoo for $2.76<\/p>\n

    Answer:
    \n12 fluid ounces of shampoo for $2.76.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n12 fluid ounces of shampoo for $2.76.
    \n12\/2.76 = 4.34.
    \nso 12 fluid ounces of shampoo for $2.76.<\/p>\n

    Question 7.
    \nWhich is the better value, 2 books for $15 or 6 books for $45? Explain.<\/p>\n

    Answer:
    \nBoth of them have better value.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2 books for $15.
    \n6 books for $45.
    \n15 + 15 + 15 = 45.
    \nso both of them have the better value.<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 8 and 9, find each unit price.
    \nQuestion 8.
    \n9 pens for $3.60
    \n\\(\\frac{\\$ 3.60 \\div 9}{9 \\div 9}=\\frac{ }{1}\\)<\/p>\n

    Answer:
    \n9 pens for $3.60 = $2.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n9 pens for $3.60.
    \n9\/3.60 = 2.5.
    \nso 9 pens for $3.60 = $2.5.<\/p>\n

    Question 9.
    \n15 ounces of canned beans for $2.25
    \n\\(\\frac{\\$ 2.25 \\div}{15 \\div}=\\frac{}{}\\)<\/p>\n

    Answer:
    \n15 ounces of canned beans for $2.25 = 6.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n15 ounces of canned beans for $2.25.
    \n15\/2.25 = 6.6.
    \nso 15 ounces of canned beans for $2.25 = 6.6.<\/p>\n

    In 10 and 11, determine which is the better value.
    \nQuestion 10.
    \n3 kilograms of charcoal for $7.95 or 5 kilograms of charcoal for $12.50<\/p>\n

    Answer:
    \n7.95\/3 = 2.65 and 12.50\/5 = 2.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3 kilograms of charcoal for $7.95.
    \n5 kilograms of charcoal for $12.50.
    \n7.95\/3 = 2.65.
    \n12.50\/5 = 2.5.<\/p>\n

    Question 11.
    \n50 envelopes for $2.49 or 90 envelopes for $5.50<\/p>\n

    Answer:
    \n50 envelopes for $2.49 or 90 envelopes for $5.50 is 16.36.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n50 envelopes for $2.49 or 90 envelopes for $5.50.
    \n50\/2.49 = 20.08.
    \n90\/5.50 = 16.36.<\/p>\n

    In 12-15, compare the rates to find which is greater.
    \nQuestion 12.
    \n35 points in 20 minutes or 49 points in 35 minutes<\/p>\n

    Answer:
    \n35 points in 20 minutes or 49 points in 35 minutes are 1.75 and 1.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n35 points in 20 minutes or 49 points in 35 minutes.
    \n35\/20 = 1.75.
    \n49\/35 = 1.4.<\/p>\n

    Question 13.
    \n12 laps in 8 minutes or 16 laps in 10 minutes<\/p>\n

    Answer:
    \n16 laps in 10 minutes.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n12 laps in 8 minutes or 16 laps in 10 minutes.
    \n12\/8 = 1.5.
    \n16\/10 = 1.6.
    \nso 16 laps in 10 minutes.<\/p>\n

    Question 14.
    \n45 strikeouts in 36 innings or 96 strikeouts in 80 innings<\/p>\n

    Answer:
    \n45 strikeouts in 36 innings or 96 strikeouts in 80 innings = 1.2.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n45 strikeouts in 36 innings or 96 strikeouts in 80 innings.
    \n45\/36 = 1.25.
    \n96\/80 = 1.2.<\/p>\n

    Question 15.
    \n480 stickers on 6 sheets or 120 stickers on 2 sheets<\/p>\n

    Answer:
    \n120 stickers on 2 sheets is 60.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n480 stickers on 6 sheets or 120 stickers on 2 sheets.
    \n480\/6 = 80.
    \n120\/2 = 60.
    \nso 120 stickers on 2 sheets is 60.<\/p>\n

    In 16-18, compare the rates to find which is the better value.
    \n\"Envision
    \nQuestion 16.
    \n$27 for 4 large pizzas or $32 for 5 large pizzas<\/p>\n

    Answer:
    \nThe both values are same.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n$27 for 4 large pizzas or $32 for 5 large pizzas.
    \n$27\/4 = $6.75.
    \n$32\/5 = $6.4.
    \nso both values are same.<\/p>\n

    Question 17.
    \n$30 for 100 flyers or $65 for 250 flyers<\/p>\n

    Answer:
    \n$30 for 100 flyers = 3.3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n$30 for 100 flyers.
    \n$65 for 250 flyers.
    \n100\/30 = 3.3.
    \n250\/100 = 2.5.<\/p>\n

    Question 18.
    \n36 pictures for $8 or 24 pictures for $5<\/p>\n

    Answer:
    \n24 pictures for $5 = 4.8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n36 pictures for $8 or 24 pictures for $5.
    \n36\/8 = 4.5.
    \n24\/5 = 4.8.
    \nso 24 pictures for $5 = 4.8.<\/p>\n

    Question 19.
    \nModel with Math Katrina and Becca exchanged 270 text messages in 45 minutes. An equal number of texts was sent each minute. The girls can send 90 more text messages before they are charged additional fees. Complete the double number line diagram. At this rate, for how many more minutes can the girls exchange texts before they are charged extra?
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing values are 90\/6, 180\/6, and 360\/6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nKatrina and Becca exchanged 270 text messages in 45 minutes.
    \nAn equal number of texts was sent each minute.
    \nThe girls can send 90 more text messages before they are charged additional fees.
    \n90\/6 = 15.
    \n180\/6 = 30.
    \n360\/6 = 60.
    \nso the missing values are 90\/6, 180\/6, and 360\/6.<\/p>\n

    Question 20.
    \nReasoning<\/strong> Which container of milk would you buy? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nI will buy 1\/2 gallon of milk for $2.29.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1\/2 gallon of milk for $2.29.
    \n1 gallon of milk for $3.99.
    \n$2.29\/0.5 = 4.58.
    \n$3.99\/1 = 3.99.
    \nI will buy 1\/2 gallon of milk for $2.29.<\/p>\n

    Question 21.
    \nHigher Order Thinking<\/strong> Amil and Abe rode in a bike-a-thon. Abe rode for 77 minutes at a faster rate per mile than Amil. Find Amil’s unit rate. Then explain how you could use it to find a possible unit rate for Abe.
    \n\"Envision<\/p>\n

    Answer:
    \nAbe’s rate is 4.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAmil and Abe rode in a bike-a-thon.
    \nAbe rode for 77 minutes at a faster rate per mile than Amil.
    \n77\/17 = 4.5.
    \nso Abe’s rate was 4.5.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 22.
    \nA food warehouse sells cans of soup in boxes. Bargain shoppers have four options.
    \nPART A
    \nComplete the table to find the unit price for each option.
    \n\"Envision<\/p>\n

    Answer:
    \nThe unit price is 1.13, 1.17, 1.16, and 1.12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA food warehouse sells cans of soup inboxes.
    \n12 cans for $10.56 = 1.13.
    \n16 cans for $13.60 = 1.17.
    \n20 cans for $17.20 = 1.16.
    \n24 cans for $21.36 = 1.12.<\/p>\n

    PART B
    \nCompare the unit rates found in Part A and identify the best value.<\/p>\n

    Answer:
    \nThe best value is 1.17.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA food warehouse sells cans of soup inboxes.
    \n12 cans for $10.56 = 1.13.
    \n16 cans for $13.60 = 1.17.
    \n20 cans for $17.20 = 1.16.
    \n24 cans for $21.36 = 1.12.<\/p>\n

    Lesson 5.7 Solve Unit Rate Problems<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nSuppose you are traveling by train to visit a friend who lives 275 miles away. How long will the trip take? Moving at a constant speed, how long would it take the train to travel 385 miles?<\/p>\n

    I can… use unit rates to solve problems.
    \n\"Envision<\/p>\n

    Model with Math
    \nHow can you use what you know about unit rates to model and solve this problem?<\/p>\n

    Focus on math practices
    \nReasoning Suppose the train was traveling at a constant speed that is twice as fast as 55 miles per hour. How long would it take the train to go 275 miles? Explain.<\/p>\n

    Answer:
    \nThe long would it take the train to go 275 miles = 5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSuppose you are traveling by train to visit a friend who lives 275 miles away.
    \nthe train travels at a constant speed of 55 miles per hour.
    \n275\/55 = 5.
    \nso the long would it take the train to go 275 miles = 5.<\/p>\n

    Essential Question<\/strong>
    \nHow can you use unit rates to solve problems?<\/p>\n

    Try It!<\/strong><\/p>\n

    At the same rate, how far would the jet fly in 75 minutes?
    \n\"Envision
    \nThe jet would fly ________ miles.<\/p>\n

    Answer:
    \nThe jet would fly 1 mile.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n15 x 5 = 75.
    \n1 minute x 75 = 75.
    \n75 miles\/75 minutes = 1.<\/p>\n

    Convince Me! How could you use the table from Example 1 to find how far the jet would fly in 75 minutes? Explain.<\/p>\n

    Try It!<\/strong><\/p>\n

    Jarod paid $13.80 for 5 tickets to the game. At the same rate, how much would 3 tickets cost?<\/p>\n

    Answer:
    \nThe 3 tickets cost is $8.28.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJarod paid $13.80 for 5 tickets to the game.
    \n$13.80\/5 = $2.76.
    \n$2.76 + $2.76 + $2.76 = $8.28.
    \nso the 3 tickets cost is $8.28.<\/p>\n

    Try It!<\/strong><\/p>\n

    A submarine travels 19 miles in \\(\\frac{1}{2}\\) hour. Write an equation to find out how long it would take the submarine to travel 57 miles at the same rate. Then find the time.<\/p>\n

    Answer:
    \nThe submarine to travel 57 miles at the same rate = 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA submarine travels 19 miles in \\(\\frac{1}{2}\\) hour.
    \n19 miles in 0.5 hours.
    \n19 x 3 = 57.
    \n57\/19 = 3.
    \nso the submarine to travel 57 miles at the same rate = 3.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use ratio tables or unit rates to solve rate problems, including constant speed problems.
    \n\"Envision<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you use unit rates to solve problems?<\/p>\n

    Answer:
    \nWe can use ratio tables to solve rate problems including constant speed problems.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nwe can use ratio tables to solve rate problems including constant speed problems.
    \nAnt traveled 6 cm in 1.5 sec.
    \nant traveled 3 cm in 12 sec.
    \nant traveled 4.5 cm in 18 sec.<\/p>\n

    Question 2.
    \nConstruct Arguments<\/strong> An ostrich runs 6 miles in 12 minutes at a constant speed. Explain how you can use a unit rate to find how far the ostrich could run in 40 minutes.<\/p>\n

    Answer:
    \nThe far ostrich could run in 40 minutes = 8 miles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAn ostrich runs 6 miles in 12 minutes at a constant speed.
    \n40\/6 = 8.
    \nso the far ostrich could run in 40 minutes = 8 miles.<\/p>\n

    Question 3.
    \nBananas sell for $0.58 per pound. How could you write an equation to show the relationship between the total cost, c, and the number of pounds of bananas, p?<\/p>\n

    Answer:
    \nC = $0.58p.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nBananas sell for $0.58 per pound.
    \nthe total cost is written as c.
    \nthe number of pounds is written as p.
    \nc = $0.58p.<\/p>\n

    Do You Know How?<\/strong>
    \nIn 4 and 5, use unit rates to solve.
    \nQuestion 4.
    \nA football player runs 80 yards in 25 seconds. If he maintains the same rate of speed, how far could he run in 60 seconds?<\/p>\n

    Answer:
    \nThe far could he run in 60 seconds = 1.3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA football player runs 80 yards in 25 seconds.
    \n80\/25 = 3.2.
    \n80\/60 = 1.3.
    \nso the far could he run in 60 seconds = 1.3.<\/p>\n

    Question 5.
    \nOn a family vacation, Amy’s dad drove the car at a constant speed and traveled 585 miles in 13 hours. At this rate, how long would it have taken the family to travel 810 miles? What was the car’s rate of speed?<\/p>\n

    Answer:
    \nThe rate of the car’s speed = 45 hours.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAmy’s dad drove the car at a constant speed and traveled 585 miles in 13 hours.
    \n585\/13 = 45.
    \n45 x 13 = 585.
    \nso the rate of the car’s speed = 45 hours.<\/p>\n

    Question 6.
    \nLook at Exercise 5. Write an equation to find the total distance, d, that Amy’s family traveled after t hours.
    \nAnswer:<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 7-9, solve the rate problems.
    \nQuestion 7.
    \nA horse named Northern Dancer won the Kentucky Derby with a time of exactly 2 minutes. At this constant rate, how long would it take Northern Dancer to run the Belmont Stakes?
    \n\"Envision
    \nIt would take Northern Dancer ______ minutes to run the Belmont Stakes.<\/p>\n

    Answer:
    \nIt would take Northern dancer 2 minutes to run the Belmont stakes.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA horse named Northern Dancer won the Kentucky Derby with a time of exactly 2 minutes.
    \n1.25\/ 1.25\/1 = 1 mile\/1 minute.
    \nthe equivalent rate is 1.5\/2.
    \nso it would take Northern dancer 2 minutes to run the Belmont stakes.<\/p>\n

    Question 8.
    \nIf a cyclist rides at a constant rate of 24 miles per hour, how long would it take the cyclist to ride 156 miles?<\/p>\n

    Answer:
    \nThe long would it take the cyclist to ride 156 miles = 6.5 hours.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIf a cyclist rides at a constant rate of 24 miles per hour.
    \n156\/24 = 6.5.
    \nso the long would it take the cyclist to ride 156 miles = 6.5 hours.<\/p>\n

    Question 9.
    \nThe price of an 8-minute phone call is $1.20. What is the price of a 17-minute phone call?<\/p>\n

    Answer:
    \nThe price of a 17-minute phone call = 0.07.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe price of an 8-minute phone call is $1.20.
    \n$1.20\/8 = 0.15.
    \n$1.20\/17 = 0.07.
    \nso the price of a 17-minute phone call = 0.07.<\/p>\n

    In 10 and 11, use the map at the right.
    \n\"Envision
    \nThe Garcia family is driving from Sacramento, California, to Key West, Florida. In 5 days, they have traveled 2,045 miles. At this rate, how long will it take them to travel from Sacramento to Key West?
    \nQuestion 10.
    \nHow can you use rate reasoning to solve this problem? Explain.<\/p>\n

    Answer:
    \nThe rate will it take them to travel from Sacramento to Key West = 409.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe Garcia family is driving from Sacramento, California, to Key West, Florida.
    \nIn 5 days, they have traveled 2,045 miles.
    \n2045\/5 = 409.
    \nso the rate will it take them to travel from Sacramento to Key West = 409.<\/p>\n

    Question 11.
    \nBe Precise Show how to use numbers, units, and symbols precisely to solve the problem.
    \nAnswer:<\/p>\n

    Question 12.
    \nVik wrote the equation 470 \u2022 h = 3,008, where h is the number of hours it took a plane flying at a constant speed of 470 miles per hour to travel 3,008 miles. Solve for h.<\/p>\n

    Answer:
    \nThe number of miles per hour to travel 3008 miles = 6.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nVik wrote the equation 470 \u2022 h = 3,008,
    \n470. h = 3008.
    \nh = 3008\/470.
    \nh = 6.4.
    \nso the number of miles per hour to travel 3008 miles = 6.4.<\/p>\n

    Question 13.
    \nA nursery owner buys 7 panes of glass to fix some damage to his greenhouse. The 7 panes cost $15.05. Unfortunately, he breaks 2 more panes while repairing the damage. What is the cost of another 2 panes of glass?
    \n\"Envision<\/p>\n

    Answer:
    \nThe cost of another 2 panes of glass = $7.5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA nursery owner buys 7 panes of glass to fix some damage to his greenhouse.
    \nthe 7 panes cost $15.05.
    \n$15.05 \/ 7 = $2.15.
    \n$15.05 \/ 2 = 7.525.
    \nso the cost of another 2 panes of glass = $7.5.<\/p>\n

    Question 14.
    \nCheyenne drew a circle with diameter 1 meter. She measured the circumference to estimate the value of Pi. Complete the table, and then write an equation to find the circumference, C, for a circle with diameter d.
    \n\"Envision<\/p>\n

    Answer:
    \nThe circumference, C, for a circle with diameter d is 6.28, 9.42, and 12.56.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCheyenne drew a circle with a diameter of 1 meter.
    \nShe measured the circumference to estimate the value of Pi.
    \n3.14 x 1 = 3.14.
    \n3.14 x 2 = 6.28.
    \n3.14 x 3 = 9.42.
    \n3.14 x 4 = 12.56.
    \nso the circumference, c, for a circle with diameter d is 6.28, 9.42, and 12.56.<\/p>\n

    Question 15.
    \nJayden bought 70 feet of speaker wire for $18.20. He needs 30 more feet. If the unit price is the same, how much will Jayden pay for the extra 30 feet of wire? Explain.<\/p>\n

    Answer:
    \nThe much will Jayden pay for the extra 30 feet of wire = 0.60.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJayden bought 70 feet of speaker wire for $18.20.
    \nHe needs 30 more feet.
    \n$18.20\/70 = 0.26.
    \n$18.20\/30 = 0.60.
    \nso the much will Jayden pay for the extra 30 feet of wire = 0.60.<\/p>\n

    Question 16.
    \nHigher Order Thinking<\/strong> Sasha runs at a constant speed of 3.8 meters per second for \\(\\frac{1}{2}\\) hour. Then she walks at a constant rate of 1.5 meters per second for \\(\\frac{1}{2}\\) hour. How far did Sasha run and walk in 60 minutes?<\/p>\n

    Answer:
    \nThe far did Sasha run and walk in 60 minutes = 30.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSasha runs at a constant speed of 3.8 meters per second for \\(\\frac{1}{2}\\) hour.
    \nThen she walks at a constant rate of 1.5 meters per second for \\(\\frac{1}{2}\\) hour.
    \n3.8\/ 0.5 = 7.6.
    \n1.5 \/ 0.5 = 30.
    \nso the far did Sasha run and walk in 60 minutes = 30.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 17.
    \nSuppose that a leatherback turtle swam 7.5 kilometers in 3 hours at a constant speed.
    \nPART A
    \nHow many kilometers per hour did the turtle swim?<\/p>\n

    Answer:
    \nThe turtle swim per hour = 2.5 miles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nleatherback turtle swam 7.5 kilometers in 3 hours.
    \n7.5\/3 = 2.5.
    \nso the turtle swim per hour = 2.5 miles.<\/p>\n

    PART B
    \nAt this rate, how long would it take the turtle to swim 10 kilometers?<\/p>\n

    Answer:
    \nThe long would it take the turtle to swim 10 kilometers = 0.75.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe long would it take the turtle to swim 10 kilometers.
    \n7.5\/10 = 0.75.
    \nso the long would it take the turtle to swim 10 kilometers = 0.75.<\/p>\n

    3-ACT MATH<\/strong><\/p>\n

    3-Act Mathematical Modeling: Get in Line
    \n\"Envision<\/p>\n

    ACT 1<\/strong>
    \nQuestion 1.
    \nAfter watching the video, what is the first question that comes to mind?
    \nAnswer:<\/p>\n

    Question 2.
    \nWrite the Main Question you will answer.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 3.
    \nConstruct Arguments Predict an answer to this Main Question. Explain your prediction.
    \nAnswer:<\/p>\n

    Question 4.
    \nOn the number line below, write a number that is too small to be the answer. Write a number that is too large.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 5.
    \nPlot your prediction on the same number line.
    \nAnswer:<\/p>\n

    ACT 2<\/strong>
    \nQuestion 6.
    \nWhat information in this situation would be helpful to know? How would you use that information?
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 7.
    \nUse Appropriate Tools What tools can you use to solve the problem? Explain how you would use them strategically.
    \nAnswer:<\/p>\n

    Question 8.
    \nModel with Math Represent the situation using mathematics. Use your representation to answer the Main Question.
    \nAnswer:<\/p>\n

    Question 9.
    \nWhat is your answer to the Main Question? Is it higher or lower than your prediction? Explain why.
    \n\"Envision
    \nAnswer:<\/p>\n

    ACT 3<\/strong>
    \nQuestion 10.
    \nWrite the answer you saw in the video.
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 11.
    \nReasoning<\/strong> Does your answer match the answer in the video? If not, what are some reasons that would explain the difference?
    \nAnswer:<\/p>\n

    Question 12.
    \nMake Sense and Persevere Would you change your model now that you know the answer? Explain.
    \n\"Envision
    \nAnswer:<\/p>\n

    Reflect<\/strong>
    \nQuestion 13.
    \nModel with Math Explain how you used a mathematical model to represent the situation. How did the model help you answer the Main Question?
    \n\"Envision
    \nAnswer:<\/p>\n

    Question 14.
    \nGeneralize Will your model work on other lights? Explain your reasoning.
    \nAnswer:<\/p>\n

    SEQUEL<\/strong>
    \nQuestion 15.
    \nUse Structure Later that week, it took between 20 and 21 minutes to get through the same light. How many cars were in line?
    \nAnswer:<\/p>\n

    Lesson 5.8 Ratio Reasoning: Convert Customary Units<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nIf 6.5 feet of snow were to fall in a 24-hour period, would the 1921 record be broken? There are 12 inches in 1 foot.
    \nI can… use ratio reasoning to convert customary measurements.
    \n\"Envision<\/p>\n

    Reasoning<\/strong>
    \nUse the relationship between inches and feet to solve the problem.<\/p>\n

    Focus on math practices
    \nMake Sense and Persevere How many feet of snow would need to fall in Silver Lake, Colorado, to break the 1921 24-hour snowfall record from 1921?<\/p>\n

    Answer:
    \nThe record from 1921 is 3.15.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of feet of snow would need to fall in Silver Lake, Colorado, to break the 1921 24-hour snowfall record from 1921.
    \n75.8 inches in 24 hours.
    \n75.8\/24 = 3.15.
    \nso the record from 1921 is 3.15.<\/p>\n

    Essential Question
    \n<\/strong> How can you use ratios to convert customary units of measure?<\/p>\n

    Try It!<\/strong><\/p>\n

    According to city regulations, how many feet wide is the maximum sidewalk width? Explain.
    \nAnswer:<\/p>\n

    Convince Me! What conversion factor would you use when converting 66 inches to feet? Explain.<\/p>\n

    Try It!<\/strong><\/p>\n

    Brandon is making bread. His recipe says to use 21 tablespoons of sugar. How many teaspoons of sugar should he use?<\/p>\n

    Answer:
    \nThe number of teaspoons of sugar should be used = 21 tablespoons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nBrandon is making bread.
    \nHis recipe says to use 21 tablespoons of sugar.
    \nso the number of teaspoons of sugar should be used = 21 tablespoons.<\/p>\n

    Try It!<\/strong><\/p>\n

    How many pounds does the elephant weigh?
    \n\"Envision<\/p>\n

    Answer:
    \nThe elephant weigh about 3.3 tons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nstella weighs approximately 3.3 tons.
    \nso the weight of the elephant is 3.3 tons.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can convert customary measures by finding an equivalent rate or by using dimensional analysis.
    \n\"Envision
    \nUse an equivalent rate.
    \n1 mi = 5,280 ft
    \n\\(\\frac{5,280 \\mathrm{ft} \\times 4.25}{1 \\mathrm{mi} \\times 4.25}=\\frac{22,440 \\mathrm{ft}}{4.25 \\mathrm{mi}}\\)<\/p>\n

    Use dimensional analysis.
    \n4.25 m1 \u00d7 \\(\\frac{5,280 \\mathrm{ft}}{1 \\mathrm{~m}}\\)
    \n= 4.25 \u00d7 5,280 ft
    \n= 22,440 ft<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you use ratios to convert customary units of measure?<\/p>\n

    Answer:
    \nWe can find an equivalent rate by using dimensional analysis.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nYou can convert customary measures by finding an equivalent rate or by using dimensional analysis.
    \n1 feet = 12 inches.
    \n1 yard = 36 inches.
    \n1 yard = 3 feet.
    \n1 mile = 5280 feet.
    \n1 mile = 1760 yards.
    \n5280 – 1760 = 3520.
    \nso we can find an equivalent rate by using dimensional analysis.<\/p>\n

    Question 2.
    \nWhat is a conversion factor that relates miles to yards?<\/p>\n

    Answer:
    \nThe conversion factor that relates miles to yards is 5280 feet.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfor example:
    \n1 mile = 5280 feet.
    \n1 mile = 1760 yards.
    \n5280 – 1760 = 3520.
    \nso the conversion factor that relates miles to yards is 5280 feet.<\/p>\n

    Question 3.
    \nConstruct Arguments Jenna used the conversion factor \\(\\frac{1 \\mathrm{~T}}{2,000 \\mathrm{lb}}\\) to convert 50 tons to pounds. Did she use the correct conversion factor? Explain.<\/p>\n

    Answer:
    \nYes, she uses the correct conversion factor.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJenna used the conversion factor \\(\\frac{1 \\mathrm{~T}}{2,000 \\mathrm{lb}}\\) to convert 50 tons to pounds.
    \n2000\/50 = 40.
    \nso she use the correct conversion factor.<\/p>\n

    Question 4.
    \nHow can you use the conversion rates of fluid ounces to cups, and cups to pints, to find the number of fluid ounces in a pint?
    \nAnswer:<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 5.
    \nConvert 27 inches to yards by finding an equivalent rate.<\/p>\n

    Answer:
    \nThe equivalent rate is 0.729.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 inch = 0.027 yards.
    \n27 x 0.027 = 0.729.
    \nthe equivalent rate is 0.729.<\/p>\n

    Question 6.
    \nUse dimensional analysis to convert 1.8 pounds to ounces.<\/p>\n

    Answer:
    \n1.8 pounds to ounces = 28.8 ounces.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 pound = 16 ounces.
    \n1.8 x 16 = 28.8 ounces.
    \nso 1.8 pounds to ounces = 28.8 ounces.<\/p>\n

    Question 7.
    \nCritique Reasoning<\/strong> Sam is tripling a recipe for an organic cleaning solution. The new recipe calls for 15 tsp of orange oil. To find how many tbsp this is, Sam converted this way:
    \nConversion factor: \\(\\frac{3 \\text { tsp }}{1 \\text { tbsp }}\\)
    \n\\(15 t s p \\times \\frac{3 t s p}{1 \\text { tbsp }}=\\frac{45}{1} \\text { tbsp }=45 \\text { tbsp }\\)
    \nWhat error did Sam make?
    \nAnswer:<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 8-13, complete each conversion.
    \nQuestion 8.
    \n5 pt = _______c<\/p>\n

    Answer:
    \n5 pt = 10 cups.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n5 us liquid cups = 10 us cups.
    \n5 pt = 10 us cups.<\/p>\n

    Question 9.
    \n2\\(\\frac{1}{2}\\)gal = _________ qt<\/p>\n

    Answer:
    \n2\\(\\frac{1}{2}\\)gal = 10 qt.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \na half of a gallon equal to 2 quarts.
    \n2 + 2 + 2 + 2 + 2 = 10.
    \n2\\(\\frac{1}{2}\\)gal = 10 qt.<\/p>\n

    Question 10.
    \n2,640 yd = ________ mi<\/p>\n

    Answer:
    \n2640 yd = 1.5 miles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 yard = 0.000568 miles.
    \n2640 yards = 1.5 miles.
    \nso 2640 yds = 1.5 miles.<\/p>\n

    Question 11.
    \nConvert 16 yards to feet. Use the conversion rate 3 feet = 1 yard.<\/p>\n

    Answer:
    \n16 yards = 48 feet.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3 feet = 1 yard.
    \n16 yards = 48 feet.
    \n16 x 3 = 48.<\/p>\n

    Question 12.
    \nConvert 10 pints to quarts. Use the conversion rate 1 quart = 2 pints.<\/p>\n

    Answer:
    \n10 pints = 5 quarts.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 quart = 2 pints.
    \n10 us liquid pints = 5 us liquid quarts.
    \n10 pints = 5 quarts.<\/p>\n

    Question 13.
    \nConvert 12 ounces to pounds. Use the conversion rate 16 ounces = 1 pound.<\/p>\n

    Answer:
    \n12 ounces = 0.75 pounds.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n16 ounces = 1 pound.
    \n12 ounces = 0.75 pounds.
    \nso 12 ounces = 0.75 pounds.<\/p>\n

    Question 14.
    \nTwo neighbors in a rural area want to know the distance between their homes in miles. What should the neighbors use as a conversion factor to convert this distance to miles?
    \n\"Envision<\/p>\n

    Answer:
    \nThe distance to miles is 0.8 miles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTwo neighbors in a rural area want to know the distance between their homes in miles.
    \n4224 x 2 = 0.8 miles.
    \n1 feet = 12 inches.
    \nso the distance to miles is 0.8 miles.<\/p>\n

    Question 15.
    \nA school custodian discovered a leak in a water pipe. The custodian found that 1,920 fluid ounces of water had leaked out. How many gallons of water is this? Use the conversion factor \\(\\frac{1 \\text { gallon }}{128 \\text { fluid ounces }}\\).<\/p>\n

    Answer:
    \nThe conversion factor is 15 gallons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA school custodian discovered a leak in a water pipe.
    \nThe custodian found that 1,920 fluid ounces of water had leaked out.
    \n1920\/128 = 15.
    \n1920 us fluid ounces = 15 us liquid gallons.<\/p>\n

    Question 16.
    \nCritique Reasoning<\/strong> Two students, Stella and Vladimir, complete the conversion statement 12 feet 8 inches = __________ inches.
    \nStella stated that 12 feet 8 inches = 152 inches. Vladimir stated that 12 feet 8 inches = 9 inches.
    \nWhich student is incorrect? Explain.<\/p>\n

    Answer:
    \nVladimir is incorrect.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n12 feet 8 inches = 152 inches.
    \nVladimir is incorrect.
    \nStella is correct.<\/p>\n

    Question 17.
    \nThe hole for a support post needs to be 6 feet deep. It is currently 1 foot 8 inches deep. How much deeper must the hole be? Use the conversion factor \\(\\)
    \n\"Envision<\/p>\n

    Answer:
    \n1 ft 8 in is 50.8 cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe hole for a support post needs to be 6 feet deep.
    \nIt is currently 1 foot 8 inches deep.
    \n1 ft 8 in is 50.8 cm.<\/p>\n

    In 18 and 19, use the recipe card.
    \n\"Envision
    \nQuestion 18.
    \nLook for Relationships Cheryl has measured 3 cups of water. Is this enough water for Cheryl to make a double recipe of green slime for a class project? Explain.<\/p>\n

    Answer:<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nCheryl has measured 3 cups of water.<\/p>\n

    Question 19.
    \nThere are 16 tablespoons in 1 cup. How many tablespoons of cornstarch would Cheryl need to make the green slime recipe 15 times?<\/p>\n

    Answer:
    \nThe tablespoons of cornstarch would Cheryl need to make = 92 cups.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 16 tablespoons in 1 cup.
    \ntablespoons = 1 cup.
    \nso the tablespoons of cornstarch would Cheryl need to make = 92 cups.<\/p>\n

    Question 20.
    \nMake Sense and Persevere Len plans to run at least 3 miles each day to get ready for a cross-country race. One lap of the school track is 440 yards. If Len runs 10 laps each day, will he cover at least 3 miles? Explain.<\/p>\n

    Answer:
    \nThe Len runs 10 laps each day, will he cover at least 3 miles = 146.6.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLen plans to run at least 3 miles each day to get ready for a cross-country race.
    \nOne lap of the school track is 440 yards.
    \n440\/3 = 146.6.
    \nso len runs 10 laps each day, will he cover at least 3 miles = 146.6.<\/p>\n

    Question 21.
    \nHigher Order Thinking<\/strong> Hunter is splitting a quart of ice cream with 7 members of his family. If the quart is split evenly, how many cups will each family member get? Explain.<\/p>\n

    Answer:<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nHunter is splitting a quart of ice cream with 7 members of his family.<\/p>\n

    Question 22.
    \nA fully loaded and fueled space shuttle can weigh close to 4.5 million pounds at liftoff. What is this weight expressed in tons?
    \n\"Envision
    \nAnswer:
    \nThe weight expressed in tons = 2250 us tons.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA fully loaded and fueled space shuttle can weigh close to 4.5 million pounds at liftoff.
    \nweighs almost 4.5 million pounds.
    \nthe weight expressed in tons = 2250 us tons.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 23.
    \nSelect all the conversions that are true.
    \n\"Envision
    \n\u2610 18 ft = 6 yd
    \n\u2610 18 yd = 6 ft
    \n\u2610 0.5 mi = 10,560 ft
    \n\u2610 0.5 mi = 2,640 ft
    \n\u2610 \\(\\frac{1}{2}\\) mi = 880 yd<\/p>\n

    Answer:
    \n18 ft = 6 yd.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 ft = 12in.
    \n1yd = 36 in.
    \n6yd = 18 ft.
    \nso 18 ft = 6 yd.<\/p>\n

    Lesson 5.9 Ratio Reasoning: Convert Metric Units<\/h3>\n

    Solve & Discuss It!<\/strong>
    \nSam needs to fill a 5-liter water jug for his team. If Sam uses the water bottle to fill the jug, how many times does he
    \nneed to fill the water bottle to fill the jug?<\/p>\n

    I can… use unit rates to convert metric measurements.
    \n\"Envision<\/p>\n

    Reasoning<\/strong>
    \nHow many milliliters are in 5 liters?<\/p>\n

    Metric Units of Capacity
    \n1,000 milliliters (ml) = 1 liter (L)
    \n100 centiliters (CL) = 1 liter
    \n10 deciliters (dL) = 1 liter
    \n1 dekaliter (dal) = 10 liters
    \n1 hectoliter (hL) = 100 liters
    \n1 kiloliter (KL) = 1,000 liters<\/p>\n

    Focus on math practices
    \nBe Precise How many liters of water does Sam’s water bottle hold when full?<\/p>\n

    Essential Question<\/strong>
    \nHow can you use ratios to convert metric units of measure?<\/p>\n

    Try It!<\/strong><\/p>\n

    The middle of the skate ramp is 2.5 meters wide. Emelia and her father want to use a board that is 23.5 decimeters long. Is this board wide enough for them to use? Convert the decimeters to meters to explain.<\/p>\n

    Answer:
    \nYes, it is board-wide enough for them to use.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe middle of the skate ramp is 2.5 meters wide.
    \nEmelia and her father want to use a board that is 23.5 decimeters long.
    \n23.5 = 2.35 meters.
    \nso it is board-wide enough for them to use.<\/p>\n

    Convince Me! How can you convert 2.5 meters to decimeters to determine whether the board is wide enough?<\/p>\n

    Try It!<\/strong><\/p>\n

    To make violet paint, Iris mixes 0.25 liter of red paint, 0.25 liter of blue paint, and 4.5 centiliters of white paint. How many centiliters of paint are in the mixture?<\/p>\n

    Answer:
    \nThe number of centiliters of paint are in the mixture = 0.545 liters.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIris mixes 0.25 liter of red paint, 0.25 liter of blue paint, and 4.5 centiliters of white paint.
    \n4.5 centiliters = 0.045 litre.
    \n0.045 + 0.25 + 0.25 = 0.545.
    \nso the number of centiliters of paint are in the mixture = 0.545 liters.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can convert metric measures by finding an equivalent rate or by using dimensional analysis.
    \n\"Envision
    \nUse an equivalent rate.
    \n1 kg = 1,000 g
    \n\\(\\frac{1 \\mathrm{~kg} \\times 1.4}{1,000 \\mathrm{~g} \\times 1.4}=\\frac{1.4 \\mathrm{~kg}}{1,400 \\mathrm{~g}}\\)<\/p>\n

    Use dimensional analysis.
    \n1.4 kg is equivalent to 1,400 g.
    \n\\(1.4 \\mathrm{~kg} \\times \\frac{1,000 \\mathrm{~g}}{1 \\mathrm{~kg}}\\)
    \n= 1.4 \u00d7 1,000 g
    \n= 1,400 g<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you use ratios to convert metric units of measure?<\/p>\n

    Answer:
    \nWe can convert metric measures by finding an equivalent rate or by using dimensional analysis.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 kg = 1000 g.
    \n1.4 kilogram is equivalent to 1400 g.
    \n1.4 x 1000 = 1400 g.<\/p>\n

    Question 2.
    \nBe Precise<\/strong> How are the metric units kilometer and kilogram the same? How are they different?<\/p>\n

    Answer:
    \nThe metrics units kilometers and kilogram are the same.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 kg = 1000 g.
    \n1.4 kilogram is equivalent to 1400 g.
    \n1.4 x 1000 = 1400 g.<\/p>\n

    Question 3.
    \nReasoning<\/strong> Which is greater, 250 m or 0.25 km? Justify your reasoning.<\/p>\n

    Answer:
    \nBoth 250m or 0.25 km are the same.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n250 meters = 0.25 kilometers.
    \ndivide the length value by 1000.
    \nso both 250m or 0.25 km are the same.<\/p>\n

    Question 4.
    \nHow can you find the conversion rate for milliliters to kiloliters?<\/p>\n

    Answer:
    \nThe conversion rate for milliliters to kiloliters by 1000.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nfor example:
    \nwe can divide the length value by 1000.
    \n1 ml = 1000 l.<\/p>\n

    Do You Know How?<\/strong>
    \nQuestion 5.
    \nWhat is the conversion factor when converting from liters to milliliters?
    \nAnswer:<\/p>\n

    Question 6.
    \nUse an equivalent rate to convert 35 centimeters to meters.<\/p>\n

    Answer:
    \nThe equivalent rate to convert 35 centimeters to meters = 3500.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 meter = 100 cm.
    \n35 x 100 = 3500.
    \nso the equivalent rate to convert 35 centimeters to meters = 3500.<\/p>\n

    Question 7.
    \nCritique Reasoning<\/strong> Maddy wants to know how many centigrams are in 0.75 gram. She converted 0.75 gram to its equivalent in centigrams as shown. Is her work correct? Explain.
    \n\\(\\frac{10 \\mathrm{cg} \\times 0.75}{1 \\mathrm{~g} \\times 0.75}=\\frac{7.5 \\mathrm{cg}}{0.75 \\mathrm{~g}}\\)
    \nAnswer:<\/p>\n

    Question 8.
    \nLook at Exercise 7. Use dimensional analysis to convert 0.75 gram to centigrams.
    \nAnswer:<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    Leveled Practice In 9 and 10, complete each conversion using an equivalent rate.
    \nQuestion 9.
    \n\"Envision<\/p>\n

    Answer:
    \n4m = 400 cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n4m = 400 cm.
    \n100 cm x 4\/1m x 4m.
    \n400cm\/4m.<\/p>\n

    Question 10.
    \n\"Envision<\/p>\n

    Answer:
    \n800 ml = 0.8 l.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n800 ml = 0.8 liter.
    \n(1000 ml\/ 8)\/ (1l\/ 1000).
    \n800 ml\/ 1000l.
    \n0.8 l.<\/p>\n

    Leveled Practice In 11 and 12, complete each conversion using dimensional analysis.
    \nQuestion 11.
    \n\"Envision<\/p>\n

    Answer:
    \n200 cl = 2 liters.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n200 cl = 2 liters.
    \n200 cl x 20000\/100cl.
    \n200\/100 l.
    \n2 l.<\/p>\n

    Question 12.
    \n\"Envision<\/p>\n

    Answer:
    \n2.5 kg = 2500 grams.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2.5 kg x 1000g\/1 kg.
    \n250000\/100 = 2500.
    \n2.5 kg = 2500 grams.<\/p>\n

    In 13 and 14, complete each conversion.
    \nQuestion 13.
    \n80 cm = _______ m<\/p>\n

    Answer:
    \n80 cm = 0.8m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1m = 100 cm.
    \n0.8m = 80 cm.
    \n8 = 800 cm.<\/p>\n

    Question 14.
    \n2.1 g = ________ mg<\/p>\n

    Answer:
    \n2.1 g = 2100 mg.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2.1 g = 2100 milligrams.
    \n1 kg = 1000 g.
    \n2.1 g = 2100 mg.<\/p>\n

    In 15-17, use the table showing the amount of liquid that Whitney drinks each day.
    \n\"Envision
    \nQuestion 15.
    \nHow many liters of water does Whitney drink each day?<\/p>\n

    Answer:
    \nThe number of liters of water does Whitney drinks each day = 1.5 l.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe amount of juice = 250 ml.
    \nthe amount of milk = 400 ml.
    \nthe amount of water = 1500 ml.
    \n1 l = 1000 ml.
    \nso the number of liters of water does Whitney drinks each day = 1.5 L.<\/p>\n

    Question 16.
    \nWhat is the total amount of liquid, in liters, that Whitney drinks each day?<\/p>\n

    Answer:
    \nThe total amount of liquid in liters that Whitney drinks each day = 0.25 l.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe amount of juice = 250 ml.
    \nthe amount of milk = 400 ml.
    \nthe amount of water = 1500 ml.
    \n1 l = 1000 ml.
    \nso the total amount of liquid in liters that Whitney drinks each day = 0.25 L.<\/p>\n

    Question 17.
    \nTroy drinks 1.8 L of water each day. How many more milliliters of water does Troy drink each day than Whitney?<\/p>\n

    Answer:
    \nThe more milliliters of water does Troy drink each day than Whitney = 300 ml.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTroy drinks 1.8 L of water each day.
    \n1800 – 1500 = 300.
    \nso the number of milliliters does Troy drink each day = 300 ml.<\/p>\n

    Question 18.
    \nThere are 10 millimeters in 1 centimeter, so about how many millimeters long is this dinosaur bone? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nThe number of milliliters long is the dinosaur bone = 220 ml.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThere are 10 millimeters in 1 centimeter.
    \n22 x 10 = 220 ml.
    \nso the number of milliliters long is the dinosaur bone = 220 ml.<\/p>\n

    Question 19.
    \nCritique Reasoning<\/strong> Savannah says that 1 kilogram is equivalent to 1,000,000 milligrams. Is Savannah correct? Explain.<\/p>\n

    Answer:
    \nYes, Savannah was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSavannah says that 1 kilogram is equivalent to 1,000,000 milligrams.
    \n1 kg = 1000 g.
    \n1 g = 1000 mg.
    \n1000 x 1000 = 1000000 mg.
    \nso Savannah was correct.<\/p>\n

    Question 20.
    \nModel with Math Lucas hiked 14,300 meters through the Everglades in the morning. After lunch, he continued hiking. When he finished the hike, he had covered 31.5 kilometers in all. Write an equation that can be used to find how far Lucas hiked after lunch.<\/p>\n

    Answer:
    \nLucas hiked after lunch = 453.96.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLucas hiked 14,300 meters through the Everglades in the morning.
    \nAfter lunch, he continued hiking.
    \nWhen he finished the hike, he had covered 31.5 kilometers in all.
    \n14300\/31.5 = 453.96.
    \nso Lucas hiked after lunch = 453.96.<\/p>\n

    Question 21.
    \nTariq has a collection of 35 quarters that he wants to send to his cousin. What is the total weight of the quarters in kilograms?
    \n\"Envision<\/p>\n

    Answer:
    \nThe total weight of the quarters in kilograms = 6.17.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nTariq has a collection of 35 quarters that he wants to send to his cousin.
    \nOne quarter weighs 5.67 grams.
    \n35\/5.67 = 6.17.
    \nso the total weight of the quarters in kilograms = 6.17.<\/p>\n

    Question 22.
    \nHigher Order Thinking<\/strong> Louis has a bag of 25 pen shells. Each pen shell is 18 centimeters long. What is the combined length of the pen shells in meters?<\/p>\n

    Answer:
    \nThe combined length of the pen shells in meters = 450.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLouis has a bag of 25 pen shells.
    \nEach pen shell is 18 centimeters long.
    \n25 x 18 = 450.
    \nso the combined length of the pen shells in meters = 450.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 23.
    \nSelect all the conversions that are equivalent to the capacity of a 5.5-liter pitcher of lemonade.
    \n\u2610 0.0055 kL
    \n\u2610 55 mL
    \n\u2610 0.055 kL
    \n\u2610 550 mL
    \n\u2610 5,500 ml<\/p>\n

    Answer:
    \nOption A is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n5.5 liter = 5.5 x 1000.
    \n0.0055.
    \nso option A is correct.<\/p>\n

    Question 24.
    \nSelect all the conversions that are equivalent to the mass of a 425-gram football.
    \n\u2610 42,000 mg
    \n\u2610 42,500 cg
    \n\u2610 450 dg
    \n\u2610 4.25 hg
    \n\u2610 00.425 kg<\/p>\n

    Answer:<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n425 grams.<\/p>\n

    Lesson 5.10 Relate Customary and Metric Units<\/h3>\n

    Explain It!<\/strong>
    \nGianna and her friends are in a relay race. They have a pail that holds 1 liter of water. They need to fill the 1-liter pail, run 50 yards, and dump the water into the large bucket until it overflows. Gianna says that as long as they do not spill any of the water, they will need 7 trips with the 1-liter pail before the large bucket overflows.<\/p>\n

    I can… convert between customary and metric units.
    \n\"Envision<\/p>\n

    A. Which conversion factor could you use to determine whether Gianna is correct? Explain.<\/p>\n

    Answer:
    \n1 gal = 4 qt.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nGianna and her friends are in a relay race.
    \nThey have a pail that holds 1 liter of water.
    \n1 gal is equal to 4 qt.
    \nThey need to fill the 1-liter pail, run 50 yards, and dump the water into the large bucket until it overflows.
    \n1 gal = 4 qt.<\/p>\n

    B. Critique Reasoning<\/strong> Gianna’s friend Linus says that you cannot be certain how many trips it will take because the conversion is approximate. Is Linus’s reasoning appropriate? Explain.<\/p>\n

    Answer:
    \nYes, Gianna’s was correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nGianna and her friends are in a relay race.
    \nThey have a pail that holds 1 liter of water.
    \n1 gal is equal to 4 qt.
    \nThey need to fill the 1-liter pail, run 50 yards, and dump the water into the large bucket until it overflows.
    \n1 gal = 4 qt.<\/p>\n

    C. Construct Arguments<\/strong> Is Gianna correct that 7 trips are needed before the bucket overflows? If not, how many trips will it take? Use the table to justify your answer.
    \nAnswer:<\/p>\n

    Focus on math practices<\/p>\n

    Construct Arguments Morgan says that 4 liters is less than 1 gallon. Construct an argument to show that Morgan is incorrect.<\/p>\n

    Essential Question<\/strong>
    \nHow can you use ratios to convert customary and metric units of measure?<\/p>\n

    Try It!<\/strong><\/p>\n

    Jacob is building a robot named T3-X that is 75 inches tall. To the nearest tenth, how many centimeters tall is T3-X?
    \n\"Envision<\/p>\n

    Answer:
    \nT3-x is 75 cm tall.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJacob is building a robot named T3-X that is 75 inches tall.
    \n1 in = 12 cm.
    \n75in ( 1 cm\/1 in).
    \n75 x 1 cm = 75 cm.
    \nT3-x is 75 cm tall.<\/p>\n

    Convince Me! If you want to find the height of T3-X in meters, will you get the same answer if you convert inches to centimeters, and then centimeters to meters, as you would if you convert inches to feet, and then feet to meters? Explain.<\/p>\n

    Try It!<\/strong><\/p>\n

    Find the length of a 100-yard football field in meters. Use 1 yard = 3 feet and 1 meter \u2248 3.28 feet. Round to the nearest tenth.<\/p>\n

    Answer:
    \n1 yard = 3 feet.
    \n1 meter = 3.28 feet.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe length of a 100-yard football field meters.
    \n1 yard = 3 feet.
    \n1 meter = 3.28 feet.<\/p>\n

    KEY CONCEPT<\/strong>
    \nYou can use what you know about converting within one measurement system to relate customary and metric units. You can convert measures with customary and metric units by finding an equivalent rate or using dimensional analysis.
    \nUse an equivalent rate.
    \n1 kg \u2248 2.20 lb
    \n\\(\\frac{1 \\mathrm{~kg} \\times 5}{2.20 \\mathrm{lb} \\times 5}=\\frac{5 \\mathrm{~kg}}{11 \\mathrm{lb}}\\)
    \n5 kg \u2248 11 lb<\/p>\n

    Use dimensional analysis.
    \n\\(5 \\mathrm{~kg} \\times \\frac{2.20 \\mathrm{lb}}{1 \\mathrm{~kg}}\\)
    \n5 \u00d7 2.20 = 11 lb
    \n5 kg \u2248 11 lb<\/p>\n

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nEssential Question<\/strong> How can you use ratios to convert customary and metric units of measure?
    \nAnswer:<\/p>\n

    Question 2.
    \nReasoning<\/strong> When converting centimeters to inches, do you multiply or divide by 2.54? Explain.
    \nAnswer:<\/p>\n

    Question 3.
    \nUse Structure How can you find the approximate number of liters in 1 pint?
    \nRemember: 1 quart = 2 pints
    \nAnswer:<\/p>\n

    Question 4.
    \nHow is the conversion from inches to centimeters different from other conversions between customary and metric units?
    \nAnswer:<\/p>\n

    Do You Know How?<\/strong>
    \nIn 5-8, find the equivalent measure. Round to the nearest tenth.
    \nQuestion 5.
    \n5 in. = _______ cm<\/p>\n

    Answer:
    \n5 in = 12.7 cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 ft = 12 in.
    \n5 in = 12.7 cm.<\/p>\n

    Question 6.
    \n2 mi \u2248 _______ km<\/p>\n

    Answer:
    \n2 mi = 3.219 km.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2 mi is equal to 3.129 km.
    \n1 mi = 1.5645 km.
    \nso 2 miles = 3.219 km.<\/p>\n

    Question 7.
    \n113 g \u2248 _______ oz<\/p>\n

    Answer:
    \n113 g = 4 oz.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n113 g is equal to 3.986 ounces.<\/p>\n

    Question 8.
    \n14 kg \u2248 ______ lb<\/p>\n

    Answer:
    \n14 kg = 30 lb.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n14 kg = 30.865 pounds.
    \npounds is equal to lb.
    \nso 14 kg = 30 lb.<\/p>\n

    Question 9.
    \nConvert 30 gallons to liters by finding an equivalent rate.
    \nAnswer:<\/p>\n

    Question 10.
    \nApproximately how many ounces are equivalent to 1 kilogram?
    \nAnswer:<\/p>\n

    Practice & Problem Solving<\/strong><\/p>\n

    In 11-18, find the equivalent measure. Round to the nearest tenth.
    \nQuestion 11.
    \n9qt \u2248 _______ L<\/p>\n

    Answer:
    \n9 qt = 8.52 l.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 l = 1.06 qt.
    \n9 qt = 8.52 l.<\/p>\n

    Question 12.
    \n2 gal \u2248 _______ L<\/p>\n

    Answer:
    \n2 gal = 7.571 liters.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 l = 0.264 gal.
    \n2 gal = 7.571 liters.<\/p>\n

    Question 13.
    \n2 in. \u2248 _______ cm<\/p>\n

    Answer:
    \n2 in = 5.08 cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3 in = 7.62 cm.
    \n2 in = 5.08 cm.<\/p>\n

    Question 14.
    \n5 km \u2248 _______ mi<\/p>\n

    Answer:
    \n5 km = 3.1 miles.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n2 miles = 3.129 km.
    \n5 km = 3.1 miles.<\/p>\n

    Question 14.
    \n5 km \u2248 ______ mi<\/p>\n

    Answer:
    \n5 km = 3.1 mi.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n5 km = 3.1 mi.<\/p>\n

    Question 15.
    \n10 L \u2248 ______ qt<\/p>\n

    Answer:
    \n10 L = 10.567 q.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n10 L = 10.567 q.
    \n10.567 q = 10 L.<\/p>\n

    Question 16.
    \n5.5 t \u2248 ______ T<\/p>\n

    Answer:
    \n5.5 t = 5.401 T.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n5.5 t = 5.401.
    \n1 tone = 0.982.
    \n5.5 t = 5.401 T.<\/p>\n

    Question 17.
    \n50 lb \u2248 ______ kg<\/p>\n

    Answer:
    \n50 lb = 23 kg.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nlb is equal to pounds.
    \n50 pounds = 22.68 kg.
    \n50 lb = 23 kg.<\/p>\n

    Question 18.
    \n10 oz \u2248 ______ g<\/p>\n

    Answer:
    \n10 oz = 283.495.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n10 oz = 283.495 g.
    \n283.495 g = 10 oz.<\/p>\n

    Question 19.
    \nA chef at a restaurant uses 12 pounds of butter each day. About how many grams of butter does the chef use each day? Use the conversion factors \\(\\frac{16 \\text { ounces }}{1 \\text { pound }}\\) and \\(\\frac{28.35 \\text { grams }}{1 \\text { ounce }}\\)
    \nAnswer:<\/p>\n

    Question 20.
    \nReasoning<\/strong> Simone wants to know whether a new chest of drawers will fit next to her bed. The chest she would like to buy is 73 centimeters wide. She knows that her room is 86 inches wide. The bed is 76 inches wide. Will the chest fit next to her bed? Explain.
    \n\"Envision<\/p>\n

    Answer:
    \nYes, the chest fit next to her bed.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nSimone wants to know whether a new chest of drawers will fit next to her bed.
    \nThe chest she would like to buy is 73 centimeters wide.
    \nShe knows that her room is 86 inches wide.
    \nThe bed is 76 inches wide.
    \nso the chest fit next to her bed.<\/p>\n

    Question 21.
    \nBe Precise<\/strong> Denali is the highest mountain in the United States. What is its height in meters? Round to the nearest whole number.
    \n\"Envision<\/p>\n

    Answer:<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDenali is the highest mountain in the United States.
    \nDenali is approximately 20,320 ft high.<\/p>\n

    Question 22.
    \nConstruct Arguments<\/strong> Francesca wants to convert 1 foot to centimeters. Use what you know about customary units to explain how she can do this.
    \nAnswer:<\/p>\n

    Question 23.
    \nHigher Order Thinking<\/strong> At the state fair, a person must be at least 138 centimeters tall to ride the roller coaster. Billy wants to ride the coaster. He is 4 feet 7 inches tall. Is Billy tall enough to ride the coaster? Explain.
    \nAnswer:<\/p>\n

    Question 24.
    \nPaul’s car holds a maximum of 19 gallons of gas. About how many liters of gas does Paul need to fill his gas tank?
    \n\"Envision
    \nAnswer:
    \nThe number of liters of gas does Paul need to fill his gas tank = 10 liters.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nPaul’s car holds a maximum of 19 gallons of gas.
    \n9 gallons is remaining as shown.
    \n19 – 9 = 10.
    \nso the number of liters of gas does paul need to fill his gas tank = 10 liters.<\/p>\n

    Assessment Practice<\/strong><\/p>\n

    Question 25.
    \nThe posted speed limit is 65 miles per hour. Select all the metric measures that are faster than 65 miles per hour.
    \n\u2610 65 km per hour
    \n\u2610 97.5 km per hour
    \n\u2610 104 km per hour
    \n\u2610 105.7 km per hour
    \n\u2610 120.3 km per hour<\/p>\n

    Answer:
    \nOption A is correct.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe posted speed limit is 65 miles per hour.
    \n65 km per hour.
    \nso option A is correct.<\/p>\n

    Question 26.
    \nBoys competing in the long jump event must jump at least 15 feet to qualify for the state track and field meet. Select all the metric measures that are less than 15 feet.
    \n\u2610 6.5 m
    \n\u2610 5.0 m
    \n\u2610 4.5 m
    \n\u2610 3.92 m
    \n\u2610 3.5 m<\/p>\n

    Answer:<\/p>\n

    Topic 5 Review<\/h3>\n

    Essential Question<\/strong>
    \nWhat are ratios and rates? How can you use ratios and rates to describe quantities and solve problems?<\/p>\n

    Vocabulary Review
    \nComplete each definition and then provide an example of each vocabulary word.
    \n\"Envision<\/p>\n

    Use Vocabulary in Writing
    \nExplain how you can convert 52 ounces to pounds. Use vocabulary words in your explanation.<\/p>\n

    Concepts and Skills Review<\/strong><\/p>\n

    Lesson 5.1 Understand Ratios<\/strong><\/p>\n

    Quick Review<\/strong>
    \nA ratio is a relationship in which for every x units of one quantity there are y units of another quantity. A ratio can be written using the word “to,” a colon, or a fraction bar to separate the two terms.<\/p>\n

    Example<\/strong>
    \nThe ratio of men to women at a small wedding is 6:4. If there are 16 women at the wedding, how many men are at the wedding?
    \nDraw a diagram to represent the ratio. Because 4 boxes represent 16 women, each box represents 4 women.
    \n\"Envision
    \nThere are 24 men at the wedding.<\/p>\n

    Practice<\/strong>
    \nA florist uses 5 red roses for every 2 white roses in her bouquets.
    \nQuestion 1.
    \nWrite the ratio of white roses to red roses in three different ways.<\/p>\n

    Answer:
    \nThe ratio of white roses to red roses is 2:5.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA florist uses 5 red roses for every 2 white roses in her bouquets.
    \nthe ratio of white roses to red roses is 2:5.
    \nso the ratio is 2:5.<\/p>\n

    Question 2.
    \nWrite the ratio of red roses to the total number of flowers in three different ways.<\/p>\n

    Answer:
    \nThe ratio of red roses to the total number of flowers is 5:7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA florist uses 5 red roses for every 2 white roses in her bouquets.
    \nthe ratio of red roses to the total number of flowers is 5:7.
    \nso the ratio is 5:7.<\/p>\n

    Question 3.
    \nIf the florist uses 10 red roses in a bouquet, how many white roses does she use?<\/p>\n

    Answer:
    \nThe ratio is 10:4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA florist uses 5 red roses for every 2 white roses in her bouquets.
    \nif the florist uses 10 red roses in a bouquet.
    \nhe can use 4 white roses.
    \n10: 4.
    \n5:2.
    \nso the ratio is 10:4.<\/p>\n

    Question 4.
    \nIf the florist uses 10 white roses in an arrangement, how many red roses does she use?<\/p>\n

    Answer:
    \nThe ratio is 25:10<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nA florist uses 5 red roses for every 2 white roses in her bouquets.
    \nif the florist uses 10 white roses in an arrangement.
    \nhe can use 25 red roses.
    \n25:10.
    \n5:2.
    \nso the ratio is 25:10.<\/p>\n

    Lesson 5.2 Generate Equivalent Ratios<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou can multiply or divide both terms of a ratio by the same nonzero number to find equivalent ratios.<\/p>\n

    Example<\/strong>
    \nFind two ratios that are equivalent to \\(\\frac{21}{126}\\)
    \nOne Way
    \nMultiply.
    \n\\(\\frac{21 \\times 2}{126 \\times 2}=\\frac{42}{252}\\)<\/p>\n

    Another Way
    \nDivide.
    \n\\(\\frac{21 \\div 3}{126 \\div 3}=\\frac{7}{42}\\)<\/p>\n

    Practice<\/strong>
    \nIn 1-4, find two ratios equivalent to the given ratio.
    \nQuestion 1.
    \n\\(\\frac{5}{12}\\)<\/p>\n

    Answer:
    \nThe ratios are 10\/24 and 1\/2.4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 5\/12.
    \n5 x 2 = 10.
    \n12 x 2 = 24.
    \nthe ratio is 10\/24.
    \ndivide by 5.
    \n5\/5 = 1.
    \n12\/5 = 2.4.
    \nso the ratio is 1\/2.4<\/p>\n

    Question 2.
    \n14:32<\/p>\n

    Answer:
    \nThe ratios are 7\/16 and 5\/12.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 14\/32.
    \n7 x 2 = 14.
    \n16 x 2 = 32.
    \nthe ratio is 7\/16.
    \ndivide by 2.
    \n10\/2 = 5.
    \n24\/2 = 12.
    \nso the ratio is 5\/12.<\/p>\n

    Question 3.
    \n3 to 4<\/p>\n

    Answer:
    \nThe ratios are 6\/8 and 1\/1.3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 3\/4.
    \n3 x 2 = 6.
    \n4 x 2 = 8.
    \nthe ratio is 6\/8.
    \ndivide by 3.
    \n3\/3 = 1.
    \n4\/3 = 1.3.
    \nso the ratio is 1\/1.3.<\/p>\n

    Question 4.
    \n\\(\\frac{7}{8}\\)<\/p>\n

    Answer:
    \nThe ratios are 14\/16 and 1\/1.14.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe ratio is 7\/8.
    \n7 x 2 = 14.
    \n8 x 2 = 16.
    \nthe ratio is 14\/16.
    \ndivide by 7.
    \n7\/7 = 1.
    \n8\/7 = 1.14.
    \nso the ratio is 1\/1.14.<\/p>\n

    Question 5.
    \nFor every 4 bagels sold at a bakery, 7 muffins are sold. How many muffins are sold when the bakery sells 24 bagels? Complete the table.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing values are 14, 21, 28, 35, and 42.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nFor every 4 bagels sold at a bakery, 7 muffins are sold.
    \nthe ratio is 1:2.
    \n4 x 1 = 4, 4 x 2 = 8, 4 x 3 = 12, 4 x 4 = 16, 4 x 5 = 20, and 4 x 6 = 24.
    \n7 x 1 = 7, 7 x 2 = 14, 7 x 3 = 21, 7 x 4 = 28, 7 x 5 = 35, and 7 x 6 = 42.
    \nso the missing values are 14, 21, 28, 35, and 42.<\/p>\n

    Lesson 5.3 Compare Ratios<\/strong><\/p>\n

    Quick Review<\/strong>
    \nTo compare ratios, make a table to show each ratio and then find a value in which one of the terms is the same in both tables.<\/p>\n

    Example<\/strong>
    \n\"Envision
    \nErica can complete more facts than Klayton.<\/p>\n

    Answer:
    \nThe missing value is 4.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nthe number of days is 1, 2, 3, and 4.
    \nthe days of the sun are 2, 4, 6, and 8.
    \n2 x 1 = 2.
    \n2 x 2 = 4.
    \n2 x 3 = 6.
    \n2 x 4 = 8.
    \nso the missing value is 4.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nThe school soccer team buys 3 soccer balls for every 2 players. The school volleyball team buys 7 volleyballs for every 5 players. Which team buys more balls per player?<\/p>\n

    Answer:
    \nThe team buys more balls per player = 6:35.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe school soccer team buys 3 soccer balls for every 2 players.
    \nThe school volleyball team buys 7 volleyballs for every 5 players.
    \n3 x 2 = 6.
    \n7 x 5 = 35.
    \nso the team buys more balls per player = 6:35.<\/p>\n

    Question 2.
    \nJenna walks 12 miles in 5 days. Alex walks 7 miles in 3 days. Who walks more miles per day?<\/p>\n

    Answer:
    \nThe ratio is 60\/21.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nJenna walks 12 miles in 5 days. Alex walks 7 miles in 3 days.
    \n12 x 5 = 60.
    \n7 x 3 = 21.
    \nso the ratio is 60\/21.<\/p>\n

    Lesson 5.4 Represent and Graph Ratios<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou can solve some ratio problems by making a table of equivalent ratios and then graphing the pairs of values on a coordinate plane.<\/p>\n

    Example<\/strong>
    \n\"Envision
    \nThere will be 4 rainy days if there are 8 sunny days.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nIn gym class, the sixth graders walk 2 laps for every 3 laps they run. If the students run 12 laps, how many laps will they walk? Complete the table. Then plot the pairs of values on the coordinate plane.
    \n\"Envision<\/p>\n

    Answer:
    \nThe missing values are 4, 6, and 8.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nIn gym class, the sixth graders walk 2 laps for every 3 laps they run.
    \nthe run laps on the y-axis.
    \nthe walk laps on the x-axis.
    \n3 x 2 = 6, 3 x 3 = 9, 3 x 4 = 12.
    \n2 x 2 = 4, 2 x 3 = 6, 2 x 4 = 8.<\/p>\n

    Lesson 5.5 Understand Rates and Unit Rates<\/strong><\/p>\n

    Quick Review<\/strong>
    \nA rate is a ratio that relates two quantities with different units. A unit rate relates a quantity to 1 unit of another quantity. You can use what you know about dividing fractions to write a ratio of fractions as a unit rate.<\/p>\n

    Example<\/strong>
    \nWrite 20 meters in 4 minutes as a rate and as a unit rate.
    \n\"Envision<\/p>\n

    Practice<\/strong>
    \nWrite each statement as a unit rate.
    \nQuestion 1.
    \n78 miles on 3 gallons<\/p>\n

    Answer:
    \nThe unit rate is 26\/1.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n78 miles on 3 gallons.
    \nunit rate is 78\/3.
    \n3 x 1 = 3.
    \n3 x 26 = 78.
    \nso the unit rate is 26\/1.<\/p>\n

    Question 2.
    \n18 laps in 6 minutes<\/p>\n

    Answer:
    \nThe unit rate is 18.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n18 laps in 6 minutes
    \nunit rate is 18\/6.
    \n6 x 1 = 6.
    \n3 x 6 = 18.
    \nso the unit rate is 18\/1.<\/p>\n

    Question 3.
    \n48 sandwiches for 16 people<\/p>\n

    Answer:
    \nThe unit rate is 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n48 sandwiches for 16 people.
    \nunit rate is 48\/16.
    \n16 x 1 = 16.
    \n3 x 16 = 48.
    \nso the unit rate is 3.<\/p>\n

    Question 4.
    \n49 houses in 7 blocks<\/p>\n

    Answer:
    \nThe unit rate is 7.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n49 houses in 7 blocks.
    \nunit rate is 49\/7.
    \n7 x 1 = 7.
    \n7 x 7 = 49.
    \nso the unit rate is 7.<\/p>\n

    Question 5.
    \n6 desks in 2 rows<\/p>\n

    Answer:
    \nThe unit rate is 3.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n6 desks in 2 rows.
    \nunit rate is 6\/2.
    \n2 x 1 = 2.
    \n3 x 2 = 6.
    \nso the unit rate is 3.<\/p>\n

    Lesson 5.6 Compare Unit Rates<\/strong><\/p>\n

    Quick Review<\/strong>
    \nA unit rate compares a quantity to 1 unit of another quantity. To compare unit rates, compare the first terms.<\/p>\n

    Example<\/strong>
    \nOn Pet Day, Meg’s turtle crawled 30 feet in 6 minutes, and Pat’s turtle crawled 25 feet in 5 minutes. Whose turtle crawled at a faster rate?
    \nWrite each rate.
    \n\"Envision
    \nBoth turtles crawled at the same rate.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nWhich is the better value? Circle it.
    \n$5.00 for 4 mangoes
    \n$6.00 for 5 mangoes<\/p>\n

    Answer:
    \nBoth have the same value.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n$5.00 for 4 mangoes
    \n$6.00 for 5 mangoes
    \n$5\/4 = 1.25.
    \n$6\/5 = 1.2.
    \nso both of the values are the same.<\/p>\n

    Question 2.
    \nWho earned more each month? Circle it.
    \nAtif: $84 over 3 months
    \nJafar: $100 over 4 months<\/p>\n

    Answer:
    \nAtif earned more than Jafar.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nAtif: $84 over 3 months
    \nJafar: $100 over 4 months
    \n84\/3 = 28.
    \n100\/4 = 25.
    \nso Atif earned more.<\/p>\n

    Question 3.
    \nWhich is a faster rate? Circle it.
    \n3 laps in 5 minutes
    \n4 laps in 7 minutes<\/p>\n

    Answer:
    \n3 laps in 5 minutes is the faster rate.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3 laps in 5 minutes
    \n4 laps in 7 minutes
    \n3\/5 = 0.6.
    \n4\/7 = 0.5.
    \noption A is correct.<\/p>\n

    Question 4.
    \nWhich is the better value? Circle it.
    \n3 sandwiches for $15.00
    \n4 sandwiches for $21.00<\/p>\n

    Answer:
    \n3 sandwiches for $15.00.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n3 sandwiches for $15.00
    \n4 sandwiches for $21.00
    \n3\/15 = 1\/5.
    \n1\/5 = 0.2.
    \n4\/21 = 0.1.<\/p>\n

    Question 5.
    \nWhich is the greater rate? Circle it.
    \n6 points in 3 attempts
    \n15 points in 5 attempts<\/p>\n

    Answer:
    \n15 points in 5 attempts.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n6 points in 3 attempts
    \n15 points in 5 attempts
    \n6\/3 = 2.
    \n15\/5 = 3.
    \n15 points in 5 attempts.<\/p>\n

    Lesson 5.7 Solve Unit Rate Problems<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou can use a ratio table or a unit rate to solve problems involving ratios or rates.<\/p>\n

    Example<\/strong>
    \nA plane travels at a rate of 780 miles in 2 hours. At this rate, how far will it travel in 3.5 hours?
    \nFind the unit rate
    \n\\(\\frac{780 \\text { miles } \\div 2}{2 \\text { hours } \\div 2}=\\frac{390 \\text { miles }}{1 \\text { hour }}\\)<\/p>\n

    Find an equivalent rate.
    \n\\(\\frac{390 \\text { miles } \\times 3.5}{1 \\text { hour } \\times 3.5}=\\frac{1,365 \\text { miles }}{3.5 \\text { hours }}\\)
    \nThe plane will travel 1,365 miles in 3.5 hours.<\/p>\n

    Practice<\/strong>
    \nQuestion 1.
    \nDoug has 5 hours to make an on-time delivery 273 miles away. Doug drives at a constant speed of 55 miles per hour. Will Doug make the delivery by the deadline? Explain.<\/p>\n

    Answer:
    \nYes, Doug makes the delivery by the deadline.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nDoug has 5 hours to make an on-time delivery 273 miles away.
    \nDoug drives at a constant speed of 55 miles per hour.
    \n273\/5 = 54.6.
    \n54.6 x 55 = 3003.
    \nYes, Doug makes the delivery by the deadline.<\/p>\n

    Question 2.
    \nMarie has 8 hours to write a 45-page chapter for her book. Marie writes at a constant speed of 4 pages per hour. Will Marie complete the chapter in time? Explain.<\/p>\n

    Answer:
    \nMarie takes 90 hours to complete.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nMarie has 8 hours to write a 45-page chapter for her book.
    \nMarie writes at a constant speed of 4 pages per hour.
    \n45 x 8 = 360.
    \n360 \/4 = 90.<\/p>\n

    Lesson 5.8 Ratio Reasoning: Convert Customary Units<\/strong><\/p>\n

    Quick Review<\/strong>
    \nYou can convert customary measures by finding equivalent rates or by using dimensional analysis.<\/p>\n

    Example<\/strong>
    \nHow many pints are equivalent to 4 quarts?
    \nFind an equivalent rate:
    \n2 pints = 1 quart …….. Identify the conversion rate.
    \n\"Envision
    \nSo, 8 pints are equivalent to 4 quarts.<\/p>\n

    Practice<\/strong>
    \nIn 1-4, complete each conversion.
    \nQuestion 1.
    \n2 mi = _______ ft<\/p>\n

    Answer:
    \n2 miles = 10560 feet.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 mile = 63360 in.
    \n1 ft = 12 in.
    \n2 mi = 63360 x 2.
    \n126720\/2 = 10560.<\/p>\n

    Question 2.
    \n144 in. = _______ yd<\/p>\n

    Answer:
    \n144 in = 4.0032 yd.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 inch = 0.0278 yd.
    \n144 x 0.0278.
    \n4.0032.
    \n144 in = 4.0032 yd.<\/p>\n

    Question 3.
    \n4 oz = _______ lb<\/p>\n

    Answer:
    \n4 oz = 0.0625 lb.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 oz = 0.0625 lb.
    \n4 oz = 4 x 0.0625.
    \n0.25 lb.<\/p>\n

    Question 4.
    \n3 gal = _______ qt<\/p>\n

    Answer:
    \n3 gal = 12 qt.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 gal = 4 us qt.
    \n3 gal = 3 x 4.
    \n3 gal = 12 qt.<\/p>\n

    Question 5.
    \nThe hippo at the zoo weighs 1.5 tons. How many pounds does the hippo weigh?<\/p>\n

    Answer:
    \nThe weight of the hippo is 3000 pounds.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe hippo at the zoo weighs 1.5 tons.
    \n1 ton = 2000 pounds.
    \n1.5 tons = 1.5 x 2000.
    \n3000.
    \nThe weight of the hippo is 3000 pounds.<\/p>\n

    Lesson 5.9 Ratio Reasoning: Convert Metric Units<\/strong><\/p>\n

    Quick Review<\/strong>
    \nTo convert metric units, use the same methods used for converting customary units. Either use the conversion rate to find an equivalent rate or use dimensional analysis.<\/p>\n

    Example<\/strong>
    \nTariq rode his bike 15,100 meters. How many kilometers did he ride his bike?
    \nFind an equivalent rate:
    \n1,000 meters = 1 kilometer
    \n\\(\\frac{1,000 m \\times 15.1}{1 \\mathrm{~km} \\times 15.1}=\\frac{15,100 \\mathrm{~m}}{15.1 \\mathrm{~km}}\\)
    \nUse dimensional analysis:
    \n\\(15,100 \\mathrm{~m} \\times \\frac{1 \\mathrm{~km}}{1,000 \\mathrm{~m} }=\\frac{15,100}{1,000} \\mathrm{~km}=15.1 \\mathrm{~km}\\)
    \nTariq rode 15.1 kilometers.<\/p>\n

    Practice<\/strong>
    \nIn 1-4, complete each conversion.
    \nQuestion 1.
    \n3 m = _______ mm<\/p>\n

    Answer:
    \n3m = 3000 mm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 m = 1000 mm.
    \n3 m = 3 x 1000.
    \n3m = 3000 mm.<\/p>\n

    Question 2.
    \n3,520 mm = _______ cm<\/p>\n

    Answer:
    \n3520 mm = 352 cm.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1mm = 0.1 cm.
    \n3520 mm = 352 cm.<\/p>\n

    Question 3.
    \n4.2 kg = _______ g<\/p>\n

    Answer:
    \n4.2 kg = 4200 g.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 kg = 1000 g.
    \n4.2 kg = 4.2 x 1000.
    \n4.2 x 1000 = 4200 g.
    \n4.2 kg = 4200 g.<\/p>\n

    Question 4.
    \n300 mL = _______ L<\/p>\n

    Answer:
    \n300 ml = 0.3 l.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1ml = 0.001 l.
    \n300 ml = 300 x 0.001.
    \n300 x 0.001 = 0.3 l.
    \n300 ml = 0.3l.<\/p>\n

    Question 5.
    \nLi needs to buy 2 kilograms of apples. If she buys 9 apples that each weigh approximately 150 grams, will she have enough? Explain.<\/p>\n

    Answer:
    \nYes, she has enough.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nLi needs to buy 2 kilograms of apples.
    \nIf she buys 9 apples that each weigh approximately 150 grams.
    \n150 x 9 = 1350 g.
    \n2 kg = 2000 g.
    \nso she has enough space.<\/p>\n

    Lesson 5.10 Relate Customary and Metric Units<\/strong><\/p>\n

    Quick Review<\/strong>
    \nTo convert between metric and customary units, use the conversion rate and find an equivalent rate, or use dimensional analysis. Most conversions will be approximate because, except in the case of inches to centimeters, the conversion rates are approximate.<\/p>\n

    Example<\/strong>
    \nGwen has a cooler that holds 3 quarts. About how many liters does the cooler hold?
    \n1 qt \u2248 0.95 L
    \n3 qt \u00d7 \\(\\frac{0.95 \\mathrm{~L}}{1 \\mathrm{~qt}}\\) = (3 \u00d7 0.95) L = 2.85 L
    \nGwen’s cooler holds approximately 2.85 liters.<\/p>\n

    Practice<\/strong>
    \nIn 1-4, find the equivalent measure. Round to the nearest tenth.
    \nQuestion 1.
    \n100 g \u2248 ________ oz<\/p>\n

    Answer:
    \n100 g = 15372.2 oz.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 gal = 153.722 oz.
    \n100 g = 153.722 x 100.
    \n15372.2.<\/p>\n

    Question 2.
    \n6 ft \u2248 _______ m<\/p>\n

    Answer:
    \n6 ft = 1.83 m.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 ft = 0.305 m.
    \n6 ft = 6 x 0.305.
    \n6 x 0.305 = 1.83.
    \n6 ft = 1.83 m.<\/p>\n

    Question 3.
    \n57 gal \u2248 _______ L<\/p>\n

    Answer:
    \n57 gal = 256.5 l.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 gal = 4.5 l.
    \n57 gal = 57 x 4.5.
    \n57 x 4.5 = 256.5.
    \n57 gal = 256.5 l.<\/p>\n

    Question 4.
    \n27 km \u2248 _______ mi<\/p>\n

    Answer:
    \n27 km = 16.767 mi.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \n1 km = 0.621 mi.
    \n27 km = 27 x 0.621.
    \n27 x 0.621 = 16.767.
    \n27 km = 16.767 mi.<\/p>\n

    Question 5.
    \nThe science class is raising monarch caterpillars. One of the caterpillars weighs 2.3 ounces. About how many grams does the caterpillar weigh? Round to the nearest tenth.<\/p>\n

    Answer:
    \nThe caterpillar weighs 65.2 grams.<\/p>\n

    Explanation:
    \nIn the above-given question,
    \ngiven that,
    \nThe science class is raising monarch caterpillars.
    \nOne of the caterpillars weighs 2.3 ounces.
    \n1 ounce = 28.35 grams.
    \n2.3 x 28.35 = 65.205.
    \nso the caterpillar weighs 65.2 grams.<\/p>\n

    Topic 5 Fluency Practice<\/h3>\n

    Pathfinder<\/strong>
    \nShade a path from START to FINISH. Follow the sums and differences in which the digit in the ones place is greater than the digit in the tenths place. You can only move up, down, right, or left.
    \nI can… add and subtract multidigit decimals.
    \n\"Envision<\/p>\n","protected":false},"excerpt":{"rendered":"

    Go through the\u00a0enVision Math Common Core Grade 6 Answer Key\u00a0Topic 5 Understand And Use Ratio And Rate\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 6th Grade Answers Key Topic 5 Understand And Use Ratio And Rate Topic 5 Essential Question What are ratios and rates? How can you use ratios and …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/16431"}],"collection":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/comments?post=16431"}],"version-history":[{"count":5,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/16431\/revisions"}],"predecessor-version":[{"id":28107,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/16431\/revisions\/28107"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=16431"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=16431"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=16431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}