{"id":12600,"date":"2023-12-20T12:04:17","date_gmt":"2023-12-20T06:34:17","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=12600"},"modified":"2023-12-21T10:25:45","modified_gmt":"2023-12-21T04:55:45","slug":"envision-math-common-core-grade-4-answer-key-topic-8","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-4-answer-key-topic-8\/","title":{"rendered":"enVision Math Common Core Grade 4 Answer Key Topic 8 Extend Understanding of Fraction Equivalence and Ordering"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 4 Answer Key<\/a>\u00a0Topic 8 Extend Understanding of Fraction Equivalence and Ordering<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 4th Grade Answers Key Topic 8 Extend Understanding of Fraction Equivalence and Ordering<\/h2>\n

Essential Questions:<\/strong>
\nWhat are some ways to name the same part of a whole?
\nHow can you compare fractions with unlike numerators and denominators?
\n\"Envision<\/p>\n

Answer:
\nFraction,
\nTo compare fractions with unlike numerators and denominators we
\nmultiply the numerator and denominator of one fraction by the same number,
\nso both fractions will have the same denominator then if denominators
\nof both are same we compare numerators,<\/p>\n

Explanation:
\nA part\u00a0or\u00a0parts of a whole is called fraction,
\nA number that names part\u00a0of a\u00a0whole\u00a0or\u00a0part of a group is called fraction.
\nFractions represent equal parts of a whole or a collection.<\/p>\n

If two fractions have different numerators and denominators
\nit is difficult to determine which fraction is larger. So we multiply
\nthe numerator and denominator of one fraction by the same number,
\nso both fractions will have the same denominator.
\nFor example, if 5\/12 and 1\/3 are being compared,
\n1\/3 should be multiplied by 4\/4. It does not change the value of
\n1\/3 to be multiplied by 4\/4 (which is equal to 1) because any number
\nmultiplied by 1 is still the same number.
\nAfter the multiplication (1\/3 * 4\/4 = 4\/12),
\nthe comparison can be made between 5\/12 and 4\/12.
\nWe may have to multiply both fractions by different numbers
\nto produce the same denominator for both fractions.
\nFor example if 2\/3 and 3\/4 are compared, we need to
\nmultiply 2\/3 by 4\/4 to give 8\/12 and multiply 3\/4 by 3\/3 to give 9\/12.
\nThe fraction 3\/4 which is equal to 9\/12 is larger than 2\/3 which is equal to 8\/12.
\nThe fraction with the larger numerator is the larger fraction if the
\ndenominators are the same.
\n
\nEnvision STEM Project: Senses<\/strong>
\nDo Research Use the Internet or other resources to find information
\nabout how animals use special senses, such as echolocation,
\nelectricity, or magnetism. Include information about where the
\nanimal lives and how the special sense is used.
\nJournal: Write a Report Include what you found. Also in your report:<\/p>\n

    \n
  • Some spiders rely on sight to receive information about food.
    \nMost spiders have 8 eyes. Draw a picture of a spider with many eyes,
    \nusing some shaded circles as eyes and some empty circles as eyes.<\/li>\n
  • Write a fraction that names shaded spider eyes to total spider eyes.
    \nWrite three equivalent fractions.<\/li>\n<\/ul>\n

    Answer:
    \nSenses also allow animals to see, feel, hear, taste, and smell,
    \nEcholocation : Using reflected sound animals hunt, Ex: Bats,<\/p>\n

    Explanation:
    \nSenses also allow animals to see, feel, hear, taste, and smell,
    \nInformation from these senses is transferred to the brain,
    \nallowing reaction and interpretation of external stimuli.<\/p>\n

    Echolocation is a technique used by bats, dolphins and
    \nother animals to determine the location of objects using
    \nreflected sound. This allows the animals to move around
    \nin pitch darkness, so they can navigate, hunt, identify friends and
    \nenemies, and avoid obstacles.<\/p>\n

    Saltwater creatures, such as sharks, rays, and even one
    \nspecies of dolphin also rely on special sensory organs to
    \nhunt underwater. Though less common, land animals such as
    \nthe bumblebee, platypus and echidna harness electricity to
    \nforage and communicate.<\/p>\n

    \"Extend
    \n
    \nReview What You Know<\/strong><\/p>\n

    Vocabulary<\/strong><\/p>\n

    Choose the best term from the box. Write it on the blank.<\/p>\n

      \n
    • denominator<\/li>\n
    • fraction<\/li>\n
    • numerator<\/li>\n
    • unit fraction<\/li>\n<\/ul>\n

      Question 1.
      \nA symbol, such as \\(\\frac{2}{3}\\) or \\(\\frac{1}{2}\\),
      \nused to name part of a whole, part of a set, or a
      \nlocation on a number line is called a __fraction_______.
      \nAnswer:
      \nFraction
      \nExplanation:
      \nA numerical quantity that is not a whole number.<\/p>\n

      Question 2.
      \nThe number above the fraction bar in a fraction is called the ___numerator______.
      \nAnswer:
      \nNumerator
      \nExplanation:
      \nThe number above the line in a fraction showing how many of the parts
      \nindicated by the denominator are taken or the term of a fraction,
      \nusually above the line, that indicates the number of equal parts that are to
      \nbe added together; the dividend placed over a divisor is called numerator.
      \n<\/span><\/p>\n

      Question 3.
      \nA fraction with a numerator of 1 is called a ____Unit Fraction__<\/strong><\/em>____
      \nAnswer:
      \nUnit Fraction
      \nExplanation:
      \nA unit fraction is any fraction with 1 as its numerator and whole number as its denominator.<\/p>\n

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

      Write a fraction for each statement.
      \nQuestion 4.
      \n2 copies of \\(\\frac{1}{6}\\) is ___1\/3_____.
      \nAnswer:
      \n1\/3 or \\(\\frac{1}{3}\\)<\/p>\n

      Explanation:
      \n\"Envision<\/p>\n

      Question 5.
      \n3 copies of \\(\\frac{1}{3}\\) is _______
      \nAnswer:
      \n1
      \nExplanation:
      \n\"Envision<\/p>\n

      Question 6.
      \n4 copies of \\(\\frac{1}{5}\\) is __4\/5______.
      \nAnswer:
      \n4\/5 or \\(\\frac{4}{5}\\)<\/p>\n

      Explanation:
      \n\"Envision<\/p>\n

      Question 7.
      \n2 copies of \\(\\frac{1}{10}\\) to is ___1\/5______.
      \nAnswer:
      \n1\/5 or \\(\\frac{1}{5}\\)<\/p>\n

      Explanation:
      \n\"Envision
      \nQuestion 8.
      \n7 copies of \\(\\frac{1}{12}\\) is ____7\/12______
      \nAnswer:
      \n7\/12 or \\(\\frac{7}{12}\\)<\/p>\n

      Explanation:
      \n\"Envision<\/p>\n

      Question 9.
      \n3 copies of \\(\\frac{1}{8}\\) is ____3\/8_______
      \nAnswer:
      \n3\/8 or \\(\\frac{3}{8}\\)<\/p>\n

      Explanation:
      \n\"Envision<\/p>\n

      Fraction Concepts<\/strong><\/p>\n

      Write the fraction shown by each figure.
      \nQuestion 10.
      \n\"Envision
      \nAnswer:
      \n\\(\\frac{1}{2}\\)
      \n\"Envision<\/p>\n

      Explanation:
      \nIn the given circle the whole is equally divided into 2 halves and one part is shaded.
      \nSo fraction is 1\/2 or \\(\\frac{1}{2}\\)<\/p>\n

      Question 11.
      \n\"Envision
      \nAnswer:
      \n\\(\\frac{3}{8}\\)
      \n\"Envision<\/p>\n

      Explanation:
      \nIn given picture the whole is equally divided into 8 parts and 3 parts are shaded.
      \nSo the fraction is 3\/8 or\u00a0 \\(\\frac{3}{8}\\)<\/p>\n

      Question 12.
      \n\"Envision
      \nAnswer:
      \n1 (Whole)<\/p>\n

      Explanation:
      \nThe whole is divided into 6 equal parts and no shaded parts.
      \nSo 6\/6 or \\(\\frac{6}{6}\\) = 1.<\/p>\n

      \"Extend<\/p>\n

      Question 13.
      \n\"Envision
      \nAnswer:
      \n\\(\\frac{1}{3}\\)
      \n\"Envision<\/p>\n

      Explanation:
      \nThe given whole is divided equally into 3 parts, among that one is shaded.
      \nSo, the fraction is 1\/3 or \\(\\frac{1}{3}\\)<\/p>\n

      Question 14.
      \n\"Envision
      \nAnswer:
      \n\\(\\frac{5}{10}\\) or \\(\\frac{1}{2}\\)
      \n\"Envision<\/p>\n

      Explanation:
      \nThe given whole is equally divided into 10 parts,
      \namong that 5 parts are shaded.
      \nSo the fraction is \\(\\frac{5}{10}\\) or \\(\\frac{1}{2}\\) (as both goes in 5).<\/p>\n

      Question 15.
      \n\"Envision
      \nAnswer:
      \n\\(\\frac{2}{4}\\) or \\(\\frac{1}{2}\\)<\/p>\n

      \"Envision<\/p>\n

      Explanation:
      \nThe given whole is equally divided into 4 parts, out of that 2 parts are shaded.
      \nSo the fraction is \\(\\frac{2}{4}\\) or \\(\\frac{1}{2}\\)
      \n
      \nParts of Wholes<\/strong><\/p>\n

      Question 16.
      \nConstruct Arguments is \\(\\frac{1}{4}\\) of the figure below green? Explain.
      \n\"Envision
      \nAnswer:
      \nArgument:
      \n\\(\\frac{1}{4}\\) is not the figure shown it is \\(\\frac{1}{5}\\)<\/p>\n

      \"Envision<\/p>\n

      Explanation:
      \nIt is not\u00a0\\(\\frac{1}{4}\\), there are five parts and one part shaded green,
      \nit will be written as 1\/5 or \\(\\frac{1}{5}\\).<\/p>\n

      Question 17.
      \nThis picture shows a square. Shade in \\(\\frac{3}{4}\\) of the square.
      \n\"Envision
      \nAnswer:
      \n\\(\\frac{3}{4}\\)
      \n\"Envision<\/p>\n

      Explanation:
      \n<\/strong>The given square is equally divided into 4 parts, out of that 3 parts are shaded.
      \nSo the fraction is \\(\\frac{3}{4}\\) is as shown above.
      \n
      \nPick a Project<\/strong><\/p>\n

      PROJECT 8A
      \nHow much do you know about the Indianapolis Motor Speedway?
      \nProject: Create a Fraction Game
      \n\"Envision<\/p>\n

      Answer:
      \nThe Indianapolis Motor Speedway is the largest sports venue in the world.
      \nIt is located on the corner of 16th Street and Georgetown Road,
      \napproximately six miles (10 km) west of Downtown Indianapolis.
      \nConstructed in 1909, it is the second purpose-built,
      \nbanked oval racing circuit after Brook lands and the first to be called a ‘speedway’.<\/p>\n

      A Fraction Game
      \n<\/strong>The objective of the game is to get all of the markers to the right side of the game board, using as few cards as possible.<\/p>\n

      How to Play<\/h3>\n

      Click on the pile to turn over one card. This is your target fraction. Move the markers so that the sum of your moves is a fraction that is less than or equal to the target fraction.
      \nFor example, if the first card turned over is 4\/5,
      \nYou could move the fifths marker to 3\/5 and the tenths marker to 2\/1,
      \nbecause\u00a0\"\\frac{3}{5}\u00a0.
      \nThese moves are shown below.<\/p>\n

      \"Envision<\/p>\n

      In addition, any of the following moves would also be acceptable:<\/p>\n

      The fifths marker to\u00a0\"\\frac{4}{5}\"\u00a0.<\/p>\n

      The tenths marker to\u00a0\"\\frac{8}{{10}}\"\u00a0, because\u00a0\"\\frac{8}{{10}}\u00a0.<\/p>\n

      The thirds marker to\u00a0\"\\frac{2}{3}\"\u00a0, because\u00a0\"\\frac{2}{3}\u00a0.<\/p>\n

      The fifths marker to\u00a0\u00a0\"\\frac{1}{5}\"\u00a0and the tenths marker to\u00a0\"\\frac{6}{{10}}\"\u00a0, because\u00a0\"\\frac{1}{5}\u00a0.<\/p>\n

      The halves marker to\u00a0\"\\frac{1}{2}\"\u00a0, the sixths marker to\u00a0\"\\frac{1}{6}\"\u00a0, and the eighths marker to\u00a0\"\\frac{1}{8}\"\u00a0, because\u00a0\"\\frac{1}{2}\u00a0.<\/p>\n

      There are many other moves that would also be acceptable, as long as the sum of the moves is less than or equal to 4\/5.<\/p>\n

      PROJECT 8B
      \nWho does all the stage work for a play or musical?
      \nProject: Build a Model
      \n\"Envision<\/p>\n

      \n
      \n
      Answer:
      \nThe stage is usually indicated by the playwright,
      \nbut the degree of detail and specificity of this rendering vary
      \nfrom one playwright to another and from one literary period to another.<\/span><\/span><\/span><\/span><\/p>\n
      Most Common Required things for Music:<\/b><\/div>\n
      \n
        \n
      • Record Producer. We’ve all heard of the title record producer.<\/li>\n
      • Audio Technician.
        \nRecording Studio Manager.<\/li>\n
      • Sound Designer.<\/li>\n
      • Instrument Tech.<\/li>\n
      • Sound Mixer.<\/li>\n
      • Radio Broadcast Engineer.<\/li>\n
      • Digital Audio Editor.
        \nPROJECT:
        \n\"Envision<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n
        \n
        \n

        PROJECT 8C<\/span><\/p>\n<\/div>\n<\/div>\n

        What is your favorite pie?
        \nProject: Write and Perform a Skit
        \n\"Envision<\/p>\n

        Answer:
        \nPUMPKIN PIE,<\/p>\n

        \"Extend<\/p>\n

        PROJECT
        \nPUMPKIN PRINCESS<\/strong><\/p>\n

        Halloween was over and Jessica was wondering what to do with leftover
        \npumpkin she was not ready to throw them away because they were all in
        \ngood condition. She got an idea to prepare a Pie with that and
        \nshe gathered all the ingredients needed to make her pie,
        \nshe rolled out the dough mashed up the pumpkin and
        \nmade sure all the seeds were taken out, than she added
        \nsome Cinnamon and nutmeg and then she put the Pie in oven.
        \nWow! said mom when she came into the kitchen.
        \nThat’s your sure smells Yummy. I can’t wait for the Pie to finish and
        \nshe said to invite all her friends for the party. Jessica was proud of her
        \nPie and her mother crowned her with PUMPKIN PRINCESS
        \n\"Envision<\/p>\n

        PROJECT 8D
        \nHow do you make clothes that could fit anyone?
        \nProject: Create a Game
        \n\"Envision<\/p>\n

        Lesson 8.1 Equivalent Fractions: Area Models<\/h3>\n

        Solve & Share<\/strong>
        \nLena has yellow tile on \\(\\frac{1}{4}\\) of her kitchen floor.
        \nWrite another fraction equivalent to \\(\\frac{1}{4}\\).
        \nSolve this problem any way you choose.
        \nI can … recognize and generate equivalent fractions.
        \n\"Envision<\/p>\n

        Look Back! How do you know your fraction is equivalent to \\(\\frac{1}{4}\\)?<\/p>\n

        Answer:
        \nEquivalent fraction for \\(\\frac{1}{4}\\) can be \\(\\frac{2}{8}\\),<\/p>\n

        Explanation:
        \nEquivalent fractions can be defined as\u00a0fractions that may have
        \ndifferent numerators and denominators but they represent the same value.
        \nSo given \\(\\frac{1}{4}\\) if multiply numerator and denominator by 2
        \nthe value will not differ so \\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\).<\/p>\n

        Essential Question<\/strong>
        \nWhat Are Some Ways to Name the Same Part of a Whole?
        \nAnswer:
        \nThe following are some ways to name the same part of a whole.
        \nA part\u00a0or\u00a0parts of a whole is called fraction,
        \nA number that names part\u00a0of a\u00a0whole\u00a0or\u00a0part of a group is called fraction.
        \nFractions represent equal parts of a whole or a collection.<\/p>\n

        Visual Learning Bridge
        \nJames ate part of the pizza shown in the picture at the right.
        \nHe said \\(\\frac{5}{6}\\) of the pizza is left.
        \nCardell said \\(\\frac{10}{12}\\) of the pizza is left. Who is correct?
        \n\"Envision
        \nEquivalent fractions name the same part of the same whole.
        \nAnswer:
        \nBoth James and Cardell are correct,<\/p>\n

        Explanation:
        \nGiven James ate part of the pizza shown in the picture at the right.
        \nHe said \\(\\frac{5}{6}\\) of the pizza is left.
        \nCardell said \\(\\frac{10}{12}\\) of the pizza is left as
        \n\\(\\frac{10}{12}\\) can be further simplified as both goes
        \nby 2 it becomes \\(\\frac{5}{6}\\) which is equivalent to
        \nagain \\(\\frac{5}{6}\\) ,Both James and Cardell are correct because
        \n\\(\\frac{5}{6}\\) = \\(\\frac{10}{12}\\).<\/p>\n

        One Way<\/strong>
        \nUse an area model. Draw a rectangle and divide it into sixths.
        \nShade \\(\\frac{5}{6}\\). Then divide the rectangle into twelfths.
        \nAnswer:
        \n\"Envision
        \nExplanation:
        \nDrawn a rectangle and divided it into sixths.
        \nShaded \\(\\frac{5}{6}\\). Then divided the rectangle into twelfths
        \nas shown above.
        \nThe number and size of parts differ, but the shaded part
        \nof each rectangle is the same \\(\\frac{5}{6}\\) and \\(\\frac{10}{12}\\)
        \nare equivalent fractions.<\/p>\n

        Another Way<\/strong>
        \nUse a different area model. Draw a circle and divide it into sixths.
        \nShade \\(\\frac{5}{6}\\). Then divide the circle into twelfths.
        \nAnswer:
        \n\"Envision
        \nExplanation:
        \nDrawn a circle and divided it into sixths.
        \nShaded \\(\\frac{5}{6}\\). Then divide the
        \ncircle into twelfths as shown above, The number and size
        \nof parts differ, but the shaded part of each circle is the same.
        \n\\(\\frac{5}{6}\\) and \\(\\frac{10}{12}\\) are equivalent fractions.<\/p>\n

        Convince Me! Reasoning Mia ate \\(\\frac{1}{4}\\) of a pizza.
        \nMatt ate \\(\\frac{2}{8}\\) of another pizza.
        \nDid Mia and Matt eat the same amount of pizza? Explain.
        \nAnswer:
        \nYes, both ate same fraction of pizza,<\/p>\n

        Explanation:
        \nGiven Mia ate \\(\\frac{1}{4}\\) of a pizza and
        \nMatt ate \\(\\frac{2}{8}\\) of another pizza, as 2 and 8 goes
        \nby 2 we get \\(\\frac{1}{4}\\) and 1\/4 of a pizza is
        \nequivalent to 2\/8 of another pizza so both Mia and Matt ate
        \nsame amount of pizza.<\/p>\n

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

        Do You Understand?<\/strong>
        \nQuestion 1.
        \nUse the area model to explain why \\(\\frac{3}{4}\\) and
        \n\\(\\frac{9}{12}\\) are equivalent.
        \n\"Envision
        \nAnswer:
        \n\\(\\frac{3}{4}\\) and \\(\\frac{9}{12}\\) are equivalent fractions.<\/p>\n

        Explanation:
        \nBy using the given area model. Given rectangle is
        \ndivide into four parts. Shaded\u00a0\\(\\frac{3}{4}\\) parts.
        \nThen divide the rectangle into twelve parts.
        \nThe number and size of parts differ, but the shaded part of
        \neach rectangle is the same\u00a0\\(\\frac{3}{4}\\) and \\(\\frac{9}{12}\\) are equivalent fractions,
        \nas shown in below picture.
        \n\"Envision<\/p>\n

        Do You Know How?<\/strong>
        \nFor 2-3, use the area model to solve each problem.
        \nQuestion 2.
        \nFind the missing numerator.
        \n\"Envision
        \nAnswer:
        \nMissing number is 4,<\/p>\n

        Explanation:
        \nThe shaded part of each rectangle is the same \\(\\frac{2}{4}\\) and \\(\\frac{4}{8}\\)
        \nare equivalent fractions as shown in the above picture.
        \n\"Envision<\/p>\n

        Question 3.
        \nFind the missing numerator.
        \n\"Envision
        \nAnswer:
        \nMissing number is 2,<\/p>\n

        Explanation:
        \nThe shaded part of each rectangle is the same \\(\\frac{1}{3}\\) and \\(\\frac{2}{6}\\)
        \nare equivalent fractions as shown in the above picture.
        \n\"Envision<\/p>\n

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

        Question 4.
        \nWrite a fraction equivalent to \\(\\frac{1}{5}\\).
        \n\"Envision
        \nAnswer:
        \nEquivalent fraction is \\(\\frac{2}{10}\\).<\/p>\n

        Explanation:
        \nThe Equivalent fraction for \\(\\frac{1}{5}\\) is \\(\\frac{2}{10}\\)
        \nIf we multiply both numerator and denominator by 2 to \\(\\frac{1}{5}\\)
        \nwe get \\(\\frac{2}{10}\\) which is equivalent fraction to \\(\\frac{2}{10}\\).<\/p>\n

        \"Extend<\/p>\n

        Question 5.
        \nWrite two fractions equivalent to \\(\\frac{4}{12}\\).
        \n\"Envision
        \nAnswer:
        \nThe two equivalent fractions for \\(\\frac{4}{12}\\) are
        \n\\(\\frac{1}{3}\\) and \\(\\frac{2}{6}\\),<\/p>\n

        Explanation:
        \nGiven \\(\\frac{4}{12}\\) if we divide numerator and
        \ndenominator by\u00a0 4 we get \\(\\frac{1}{3}\\) and
        \nif we divide numerator and denominator by 2 we get \\(\\frac{2}{6}\\),
        \nSo two equivalent fractions for \\(\\frac{4}{12}\\) are
        \n\\(\\frac{1}{3}\\) and \\(\\frac{8}{24}\\).<\/p>\n

        Question 6.
        \nWrite a fraction equivalent to \\(\\frac{2}{6}\\).
        \n\"Envision
        \nAnswer:
        \nEquivalent fraction is \\(\\frac{1}{3}\\).<\/p>\n

        Explanation:
        \nThe Equivalent fraction for \\(\\frac{2}{6}\\) is \\(\\frac{1}{3}\\)
        \nIf we divide both numerator and denominator by 2
        \nwe get \\(\\frac{1}{3}\\) which is equivalent fraction to \\(\\frac{2}{6}\\).<\/p>\n

        Question 7.
        \nWrite two fractions equivalent to \\(\\frac{1}{2}\\).
        \n\"Envision
        \nAnswer:
        \nThe two equivalent fractions for \\(\\frac{1}{2}\\) are
        \n\\(\\frac{2}{4}\\) and \\(\\frac{3}{6}\\),<\/p>\n

        Explanation:
        \nGiven \\(\\frac{1}{2}\\) if we multiply numerator and
        \ndenominator by 2 we get \\(\\frac{2}{4}\\) and
        \nif we multiply numerator and denominator by 3 we get \\(\\frac{3}{6}\\),
        \nSo two equivalent fractions for \\(\\frac{1}{2}\\) are
        \n\\(\\frac{2}{4}\\) and \\(\\frac{3}{6}\\).<\/p>\n

        For 8-15, draw an area model or use fraction strips to solve each problem.
        \nQuestion 8.
        \n\\(\\frac{2}{8}=\\frac{}{4}\\)
        \nAnswer:
        \n\\(\\frac{2}{8}=\\frac{}{4}\\)
        \n\"Envision<\/p>\n

        Explanation:
        \nGiven \\(\\frac{2}{8} = \\frac{}{4}\\) other side denominator is 4
        \nmeans if we divided \\(\\frac{2}{8} both by 2 we get denominator as 4
        \nso we get numerator as 1, therefore
        \n[latex]\\frac{2}{8}\\) = \\(\\frac{1}{4}\\) as shown above.<\/p>\n

        Question 9.
        \n\\(\\frac{2}{4}=\\frac{ }{8}\\)
        \nAnswer:
        \n\\(\\frac{2}{4}=\\frac{ 4}{8}\\)<\/p>\n

        \"Envision<\/p>\n

        Explanation:
        \nGiven \\(\\frac{2}{4}=\\frac{}{8}\\) other side denominator is 8
        \nmeans if we multiply \\(\\frac{2}{4} both by 2 we get denominator as 8
        \nand we get numerator as 4,
        \ntherefore [latex]\\frac{2}{4}\\) = \\(\\frac{4}{8}\\) as shown above.<\/p>\n

        Question 10.
        \n\\(\\frac{1}{2}=\\frac{ }{6}\\)
        \nAnswer:
        \n\\(\\frac{1}{2}=\\frac{ 3}{6}\\)
        \n\"Envision<\/p>\n

        Explanation:
        \nGiven \\(\\frac{1}{2}=\\frac{}{6}\\) other side denominator is 6
        \nmeans if we multiply \\(\\frac{1}{2} both by 3 we get denominator as 6
        \nand we get numerator as 3,
        \ntherefore [latex]\\frac{1}{2}\\) = \\(\\frac{3}{6}\\) as shown above.<\/p>\n

        Question 11.
        \n\\(\\frac{3}{3}=\\frac{6}{}\\)
        \nAnswer:
        \n\\(\\frac{3}{3}=\\frac{6}{6}\\)<\/p>\n

        \"Envision<\/p>\n

        Explanation:
        \nGiven \\(\\frac{3}{3}=\\frac{6}{}\\) other side numerator is 6
        \nmeans if we multiply \\(\\frac{3}{3} both by 2 we get numerator as 6
        \nand we get denominator also as 6,
        \ntherefore [latex]\\frac{3}{3}\\) = \\(\\frac{6}{6}\\) as shown above.<\/p>\n

        Question 12.
        \n\\(\\frac{1}{5}=\\frac{ }{10}\\)
        \nAnswer:
        \n\\(\\frac{1}{5}=\\frac{2 }{10}\\)
        \n\"Envision<\/p>\n

        Explanation:
        \nGiven \\(\\frac{1}{5}=\\frac{}{10}\\) other side denominator is 10
        \nmeans if we multiply \\(\\frac{1}{5} both by 2 we get denominator as 10
        \nand we get numerator as 1 X 2 = 2,
        \ntherefore [latex]\\frac{1}{5}\\) = \\(\\frac{2}{5}\\) as shown above.<\/p>\n

        Question 13.
        \n\\(\\frac{5}{6}=\\frac{10}{}\\)
        \nAnswer:
        \n\\(\\frac{5}{6}=\\frac{10}{12}\\)
        \n\"Envision<\/p>\n

        Explanation:
        \nGiven \\(\\frac{5}{6}=\\frac{10}{}\\) other side numerator is 10
        \nmeans if we multiply \\(\\frac{5}{6} both by 2 we get numerator as 10
        \nand we get denominator as 12,
        \ntherefore [latex]\\frac{5}{6}\\) = \\(\\frac{10}{12}\\) as shown above.<\/p>\n

        Question 14.
        \n\\(\\frac{8}{12}=\\frac{2}{}\\)
        \nAnswer:
        \n\\(\\frac{8}{12}=\\frac{2}{3}\\)
        \n\"Envision<\/p>\n

        Explanation:
        \nGiven \\(\\frac{8}{12}=\\frac{2}{}\\) other side numerator is 2
        \nmeans if we divide \\(\\frac{8}{12} both by 4 we get numerator as 2
        \nand we get denominator as 3,
        \ntherefore [latex]\\frac{8}{12}\\) = \\(\\frac{2}{3}\\) as shown above.<\/p>\n

        Question 15.
        \n\\(\\frac{4}{5}=\\frac{8}{}\\)
        \nAnswer:
        \n\\(\\frac{4}{5}=\\frac{8}{10}\\)<\/p>\n

        \"Envision<\/p>\n

        Explanation:
        \nGiven \\(\\frac{4}{5}=\\frac{8}{}\\) other side numerator is 8
        \nmeans if we multiply \\(\\frac{4}{5} both by 2 we get numerator as 8
        \nand we get denominator as 10,
        \ntherefore [latex]\\frac{4}{5}\\) = \\(\\frac{8}{10}\\) as shown above.
        \n
        \nProblem Solving<\/strong><\/p>\n

        Question 16.
        \nEnvision\u00aeSTEM Monarch butterflies migrate when they sense
        \ndaylight hours are shorter and temperatures get colder.
        \nWrite two equivalent fractions for the part of the migration a monarch butterfly can complete in 1 week.
        \n\"Envision
        \nAnswer:
        \n\\(\\frac{7}{35} and \\frac{14}{70}\\),
        \nTwo equivalent fractions for the part of the migration a
        \nmonarch butterfly can complete in 1 week are
        \n\\(\\frac{7}{35} and \\frac{14}{70}\\),<\/p>\n

        Explanation:
        \nGiven Monarch butterflies travel \\(\\frac{1}{5}\\)
        \nthe total migration in 1 week,
        \nits equivalent fraction can be written by multiplying both numerator and
        \ndenominator by 7 we get
        \n\"\"
        \n\\(\\frac{1}{5}\\). = \\(\\frac{7}{35}\\) and if we multiply numerator and denominator by 2
        \nwe get another equivalent fraction as \\(\\frac{14}{35}\\).<\/p>\n

        Question 17.
        \nMake Sense and Persevere Garrett buys lunch for himself and his friend.
        \nHe buys 2 sandwiches, 2 fries, and 2 malts. How much did Garrett spend on lunch?
        \n\"Envision
        \nAnswer:
        \nGarrett spend $30 on lunch,<\/p>\n

        Explanation:
        \n2 X $8 + 2 X $3 + 2 X $4 = $16 + $6 + $8 = $30,
        \nTherefore Garrett spent total $30.<\/p>\n

        Question 18.
        \nConnor said, \u201cTo the nearest hundred, I’ve attended
        \nschool for 800 days of my life!” Write three numbers that
        \ncould be the actual number of days Connor has attended school.
        \nAnswer:
        \nThe numbers can be anything between 750 to 849,
        \ncan be 790, 812 and 801,<\/p>\n

        Explanation:
        \nGiven Connor said, \u201cTo the nearest hundred, I’ve attended
        \nschool for 800 days of my life!” Write three numbers that
        \ncould be the actual number of days Connor has attended school.
        \nSo nearest hundred to 800 can be any numbers between 750 to 849,
        \nso it can be 790, 812 and 801.<\/p>\n

        Question 19.
        \nHigher Order Thinking<\/strong> Josh, Lisa, and Vicki each ate \\(\\frac{1}{4}\\)
        \nof their own pizza. Each pizza was the same size,
        \nbut Josh ate 1 slice, Lisa ate 2 slices, and Vicki ate 3 slices. How is this possible?
        \nAnswer:
        \n\"Envision<\/p>\n

        Explanation:
        \nEach pizza was of the same size but the portion of slices are different
        \nJosh ate \\(\\frac{1}{4}\\), Lisa ate 2 slices means
        \n2 X \\(\\frac{1}{4}\\) = \\(\\frac{2}{8}\\) and
        \nVicki ate 3 slices means 3 X \\(\\frac{1}{4}\\) = \\(\\frac{3}{12}\\).<\/p>\n

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

        Question 20.
        \nSelect all the fractions that are equivalent to \\(\\frac{2}{3}\\).
        \nUse the area models to help.
        \n\"Envision
        \nAnswer:
        \n\"Envision<\/p>\n

        Explanation:
        \nAs \\(\\frac{8}{12}\\), \\(\\frac{4}{6}\\) are
        \nthe equivalent fractions of \\(\\frac{2}{3}\\) when
        \n\\(\\frac{8}{12}\\) if numerator and denominator is
        \ndivided by 4 we get \\(\\frac{2}{3}\\) and
        \n\\(\\frac{4}{6}\\) if numerator and denominator is
        \ndivided by 2 we get \\(\\frac{2}{3}\\), therefore \\(\\frac{8}{12}\\), \\(\\frac{4}{6}\\) are the equivalent fractions of \\(\\frac{2}{3}\\).<\/p>\n

        Question 21.
        \nSelect all the pairs that are equivalent fractions. Use the area models to help.
        \n\"Envision
        \nAnswer:
        \n\"\"<\/p>\n

        Explanation:
        \nAs \\(\\frac{1}{4}\\) if numerator and denominator is
        \nmultiplied by 2 we get the equivalent fractions of \\(\\frac{2}{8}\\) if
        \n\\(\\frac{3}{4}\\) if numerator and denominator is
        \nmultiplied by 2 we get the equivalent fractions of \\(\\frac{6}{8}\\) and
        \n\\(\\frac{8}{8}\\) we get 1 and\u00a0the equivalent fractions of
        \n\\(\\frac{4}{4}\\) we get 1 so selected all the pairs that are
        \nequivalent fractions as shown above.<\/p>\n

        Lesson 8.2 Equivalent Fractions: Number Lines
        \nSolve & Share<\/strong>
        \nSuppose you have a ruler showing fourths. Use your ruler to name a fraction that is equivalent to . Tell how you know the fraction is equivalent.
        \nI can … name the same point on a number line using equivalent fractions.
        \n\"Envision<\/p>\n

        Look Back! Model with Math Do you think there is more than one fraction equivalent to \\(\\frac{2}{4}\\)? Draw a picture to explain.
        \nAnswer:
        \n2\/4 Equivalent fraction is 1\/2
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Use a Number Line to Explain Why Fractions Are Equivalent?<\/p>\n

        \"\"
        \nAnswer:
        \nA part or parts of a whole is called fraction, A number that names part of a whole or part of a group is called fraction. the sum of all fractions is a whole.
        \nExplanation:
        \nSo Number Line can be used to explain the equivalent fractions.<\/p>\n

        Visual Learning Bridge
        \nSal rode his bike \\(\\frac{3}{4}\\) mile to school. Name two fractions that are equivalent to \\(\\frac{3}{4}\\).
        \nA number line is another appropriate tool for finding equivalent fractions.
        \n\"Envision<\/p>\n

        Show \\(\\frac{3}{4}\\) on the number line.<\/p>\n

        Divide each fourth into two equal parts to show eighths.
        \n\"Envision
        \nDivide each fourth into three equal parts to show twelfths.
        \n\\(\\frac{3}{4}, \\frac{6}{8}\\) and \\(\\frac{9}{12}\\) are at the same point on the number lines that are all the same length. \\(\\frac{6}{8}\\) and \\(\\frac{9}{12}\\) are equivalent to \\(\\frac{3}{4}\\).<\/p>\n

        Convince Me! The number and size of each part on two number lines are different. Can the number lines show equivalent fractions? Use the number lines above to explain.
        \nAnswer:
        \nYes, the number and size of each part on two number lines are different can also show equivalent fractions.
        \nExplanation:
        \n\\(\\frac{3}{6}\\) = \\(\\frac{6}{8}\\) = \\(\\frac{9}{12}\\)
        \n3 x 1 = 3
        \n3 x 2 = 6
        \n3 x 3 = 9
        \n2 x 3 = 6
        \n2 x 4 = 8
        \n2 x 6 = 12<\/p>\n

        Another Example!<\/strong>
        \nYou can use a number line to find equivalent fractions that are greater than or equal to 1.
        \n\"Envision<\/p>\n

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

        Do You Understand?<\/strong>
        \nQuestion 1.
        \nUse the number line above to write a fraction equivalent to \\(\\frac{9}{6}\\). Why are the fractions equivalent? Explain.
        \nAnswer:
        \n\\(\\frac{3}{2}\\) is equivalent fraction to \\(\\frac{9}{6}\\)
        \n\"\"
        \n\\(\\frac{9}{6}\\) = \\(\\frac{3}{2}\\)
        \n3 x 3 = 9
        \n3 x 2 = 6
        \nExplanation:
        \nIf the numerator and denominator of a fraction are equal, then the fraction is less then 1, greater then 1, equal to 1.
        \nThese fractions are actually the same because when we multiply or divide both the numerator and the denominator by the same number,\u00a0the value of the fraction actually doesn’t change. Therefore, equivalent fractions, when reduced to their simplified value, will all be the same.<\/span><\/p>\n

        Do You Know How?<\/strong>
        \nFor 2-3, use the number line below.
        \nQuestion 2.
        \nWrite an equivalent fraction for \\(\\frac{1}{3}\\).
        \nAnswer:
        \n\\(\\frac{2}{6}\\) is an equivalent fraction for \\(\\frac{1}{3}\\).
        \nExplanation:
        \n\"\"<\/p>\n

        Question 3.
        \nWrite an equivalent fraction for \\(\\frac{1}{2}\\).
        \n\"Envision
        \nAnswer:
        \n\\(\\frac{3}{6}\\) is an equivalent fraction for \\(\\frac{1}{2}\\).
        \nExplanation:
        \n\"\"<\/p>\n

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

        For 4-7, use the number line to find equivalent fractions. Circle the correct answers.
        \n\"Envision<\/p>\n

        Question 4.
        \nWhich of the following fractions is an equivalent fraction for point A?
        \n\\(\\begin{array}{lllll}
        \n\\frac{1}{4} & \\frac{1}{3} & \\frac{2}{3} & \\frac{1}{6} & \\frac{2}{6}
        \n\\end{array}\\)
        \nAnswer:
        \n\\(\\frac{1}{3}\\), \\(\\frac{2}{6}\\) are the equivalent fractions for point A.
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Question 5.
        \nWhich of the following fractions is an equivalent fraction for point B?
        \n\\(\\begin{array}{lllll}
        \n\\frac{11}{12} & \\frac{12}{12} & \\frac{13}{12} & \\frac{7}{6} & \\frac{6}{6}
        \n\\end{array}\\)
        \nAnswer:
        \n\\(\\frac{12}{12}\\) and \\(\\frac{6}{6}\\) are the equivalent fractions for point B.
        \nExplanation:
        \n\"\"<\/p>\n

        Question 6.
        \nWhich of the following fractions is an equivalent fraction for point C?
        \n\\(\\begin{array}{lllll}
        \n\\frac{8}{6} & \\frac{2}{3} & \\frac{1}{2} & \\frac{3}{2} & \\frac{6}{4}
        \n\\end{array}\\)
        \nAnswer:
        \n\\(\\frac{3}{2}\\)and \\(\\frac{6}{4}\\) are the equivalent fractions for point C.
        \nExplanation:
        \n\"\"<\/p>\n

         <\/p>\n

        Question 7.
        \nWhich of the following fractions is an equivalent fraction for point D?
        \n\\(\\begin{array}{lllll}
        \n\\frac{6}{5} & \\frac{10}{6} & \\frac{3}{2} & \\frac{6}{10} & \\frac{5}{3}
        \n\\end{array}\\)
        \nAnswer:
        \n\\(\\frac{10}{6}\\) and \\(\\frac{5}{3}\\) are the equivalent fractions for point D.
        \nExplanation:
        \n\"\"<\/p>\n

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

        Question 8.
        \nWhat equivalent fractions are shown by the two number lines?
        \n\"Envision
        \nAnswer:
        \n\\(\\frac{2}{4}\\) and \\(\\frac{3}{6}\\)
        \n\\(\\frac{4}{4}\\) and \\(\\frac{6}{6}\\)\u00a0 are equivalent fractions
        \nExplanation:
        \n\"\"<\/p>\n

        Question 9.
        \nMake Sense and Persevere Randy and Carla like to walk the path around their town park. The path is 2 miles long. Last month Randy walked the path 13 times, and Carla walked it 22 times. How many more miles did Carla walk than Randy last month?
        \nAnswer:
        \n18 miles more.
        \nExplanation:
        \nRandy walk 13 X 2 = 26 miles
        \nCarla walk\u00a0 22 X 2 = 44 miles
        \n44 – 26 = 18 miles<\/p>\n

        Question 10.
        \nHigher Order Thinking<\/strong> Jarred says these number lines show \\(\\frac{3}{4}\\) is equivalent to \\(\\frac{2}{3}\\). Is Jarred correct? Explain.
        \n\"Envision
        \nAnswer:
        \nNO, Jarred is not correct.
        \nExplanation:
        \n\"\"
        \nAs blue line is smaller then the red line in the bench mark number line picture3\/4 and 2\/3 are not correct, Jarred said wrong.<\/p>\n

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

        Question 11.
        \nKevin and Gabbie use a number line to find fractions that are equivalent to \\(\\frac{4}{10}\\).
        \nKevin says he can find an equivalent fraction with a denominator greater than 10. Gabbie says she can find an equivalent fraction with a denominator less than 10.
        \n\"Envision<\/p>\n

        Part A
        \nWrite to explain how Kevin can use the number line to find his equivalent fraction.
        \nAnswer:
        \n\\(\\frac{4}{10}\\) = \\(\\frac{4}{100}\\)
        \n\"\"
        \nExplanation:
        \n10 x 4 = 40
        \n10 x 10 = 100
        \nSo, \\(\\frac{4}{10}\\) = \\(\\frac{4}{100}\\)<\/p>\n

        Part B
        \nWrite to explain how Gabbie can use the number line to find her equivalent fraction.
        \nAnswer:
        \n\\(\\frac{4}{10}\\) = \\(\\frac{2}{5}\\)
        \n\"\"
        \nExplanation:
        \n2 x 2 = 4
        \n2 x 5 = 10
        \nSo, \\(\\frac{4}{10}\\) = \\(\\frac{2}{5}\\)<\/p>\n

        8.3 Generate Equivalent Fractions: Multiplication
        \nSolve & Share<\/strong>
        \nWayne bought a box of muffins. Four sixths of the muffins are blueberry. Write a fraction equivalent to solve this problem any way you choose.
        \nI can … use multiplication to find equivalent fractions.
        \n\"Envision<\/p>\n

        Look Back! How are the numerator and denominator of your fraction related to the numerator and denominator of \\(\\frac{4}{6}\\)?
        \nAnswer:
        \n\\(\\frac{2}{3}\\) related to\u00a0\\(\\frac{4}{6}\\).
        \nExplanation:
        \nBy multiplying the numerator and denominator of a fraction with 2 factor
        \n2 x2 = 4
        \n2 x 3 = 6
        \nSo,\u00a0\\(\\frac{4}{6}\\) = \u00a0\\(\\frac{2}{3}\\)<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Use Multiplication to Find Equivalent Fractions?
        \nAnswer:
        \nMultiplications can be used to find an equivalent fraction by multiplying the numerator and denominator by the same number.
        \nExplanation:
        \nIf you are given the fraction \\(\\frac{1}{2}\\).
        \nYou can multiply the numerator by 3 and the denominator by\u00a0 3.
        \n1 x 3 = 3
        \n2 x 3 = 6
        \nSo, \\(\\frac{1}{2}\\) = \u00a0\\(\\frac{3}{6}\\)<\/p>\n

        Visual Learning Bridge
        \nA librarian said \\(\\frac{1}{2}\\) of the books checked out yesterday were nonfiction. What are some fractions equivalent to \\(\\frac{1}{2}\\)?
        \n\"Envision
        \nTo find equivalent fractions, multiply by a fraction equal to one.<\/p>\n

        \"Envision<\/p>\n

        Convince Me! Critique Reasoning Kevin said, “In each of the examples above, all you are doing is multiplying by one. When you multiply by 1, the value doesn’t change.” Is Kevin correct? Explain.
        \nAnswer:
        \nYes, Kelvin is correct,<\/p>\n

        Explanation:
        \nMultiplying by one doesn’t change the value. So we call\u00a01<\/strong> the multiplicative identity.<\/p>\n

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

        Do You Understand?<\/strong>
        \nQuestion 1.
        \nUse an area model and multiplication to show why \\(\\frac{5}{6}\\) and \\(\\frac{10}{12}\\) are equivalent fractions.
        \n\"Envision
        \nAnswer:
        \nYes, \\(\\frac{5}{6}\\) and \\(\\frac{10}{12}\\) are Equivalent fractions.<\/p>\n

        Explanation:<\/p>\n

        \"\"<\/p>\n

        Question 2.
        \nUse multiplication to explain why \\(\\frac{3}{4}\\) and \\(\\frac{8}{12}\\) are NOT equivalent fractions.
        \nAnswer:
        \nNo, \\(\\frac{3}{4}\\) and \\(\\frac{8}{12}\\) are not equivalent fractions,<\/p>\n

        Explanation:
        \n\"\"
        \n\\(\\frac{8}{12}\\) = \u00a0\\(\\frac{2}{3}\\),
        \nSo \\(\\frac{3}{4}\\) = \u00a0\\(\\frac{2}{3}\\) are NOT Equivalent fractions<\/p>\n

        Do You Know How?<\/strong>
        \nFor 3-7, multiply to find equivalent fractions.
        \nQuestion 3.
        \n\"Envision
        \nAnswer:
        \n\\(\\frac{2}{4}\\)<\/p>\n

        Explanation:<\/p>\n

        \"\"<\/p>\n

        Question 4.
        \n\\(\\frac{3}{4}=\\frac{}{12}\\)
        \nAnswer:
        \n\\(\\frac{9}{12}\\)]
        \n\"\"<\/p>\n

        Explanation:
        \nTo find equivalent fractions, multiply by a fraction equal to one in both numerator and denominator.
        \nSo in the given fraction multiply with 3 in both numerator and denominator.<\/p>\n

        Question 5.
        \n\\(\\frac{5}{5}=\\frac{10}{}\\)
        \nAnswer:
        \n\\(\\frac{10}{10}\\)<\/p>\n

        Explanation:
        \n\"\"
        \nTo find equivalent fractions, multiply by a fraction equal to one in both numerator and denominator.
        \nSo in the given fraction multiply with 2 in both numerator and denominator.<\/p>\n

        Question 6.
        \n\\(\\frac{3}{2}=\\frac{6}{}\\)
        \nAnswer:
        \n\\(\\frac{6}{4}\\)
        \nExplanation:
        \nTotal 3 box, 2 are shaded
        \n\"\"
        \nTo find equivalent fractions, multiply by a fraction equal to one in both numerator and denominator.
        \nSo in the given fraction multiply with 2 in both numerator and denominator.<\/p>\n

        Question 7.
        \n\\(\\frac{1}{6}=\\frac{}{12}\\)
        \nAnswer:
        \n\\(\\frac{2}{12}\\)<\/p>\n

        Explanation:
        \nTotal six box, one box is shaded
        \n\"\"
        \nTo find equivalent fractions, multiply by a fraction equal to one in both numerator and denominator.
        \nSo in the given fraction multiply with 2 in both numerator and denominator.<\/p>\n

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

        Leveled Practice For 8-13, fill in the missing numbers to find equivalent fractions.
        \nQuestion 8.
        \n\"Envision
        \nAnswer:
        \n\\(\\frac{4}{6}\\)
        \nExplanation:
        \nWrite the product of numerator and denominator in the missing boxes.
        \n\"\"<\/p>\n

        Question 9.
        \n\"Envision
        \nAnswer:
        \n\\(\\frac{6}{12}\\) is missing.<\/p>\n

        Explanation:
        \nWrite the product of numerator and denominator in the missing boxes.
        \n\"\"<\/p>\n

        Question 10.
        \n\"Envision
        \nAnswer:
        \nMissing number is 2.<\/p>\n

        Explanation:
        \nWrite the product of numerator and denominator in the missing boxes.
        \n\"\"
        \nQuestion 11.
        \n\"Envision
        \nAnswer:
        \nMissing number is 25.<\/p>\n

        Explanation:
        \nWrite the product of numerator and denominator in the missing boxes.
        \n\"\"<\/p>\n

        Question 12.
        \n\"Envision
        \nAnswer:
        \nMissing number is 3.<\/p>\n

        Explanation:
        \nWrite the product of numerator and denominator in the missing boxes.
        \n\"\"<\/p>\n

        Question 13.
        \n\"Envision
        \nAnswer:
        \nMissing number is 3
        \nExplanation:
        \nWrite the product of numerator and denominator in the missing boxes.
        \n\"\"<\/p>\n

        For 14-21, write two equivalent fractions for each given fraction.
        \nQuestion 14.
        \n\\(\\frac{1}{10}\\)
        \nAnswer:
        \n\\(\\frac{2}{20}\\)
        \nExplanation:
        \nMultiply with 2 in numerator and denominator to get \\(\\frac{2}{20}\\)<\/p>\n

        \"\"<\/p>\n

        Question 15.
        \n\\(\\frac{4}{2}\\)
        \nAnswer:
        \n\\(\\frac{8}{4}\\)
        \nExplanation:
        \nMultiply with 2 in numerator and denominator to get \\(\\frac{8}{4}\\)
        \n\"\"<\/p>\n

        Question 16.
        \n\\(\\frac{5}{6}\\)
        \nAnswer:
        \n\\(\\frac{10}{2}\\)
        \nExplanation:
        \nMultiply with 2 in numerator and denominator to get \\(\\frac{10}{2}\\)
        \n\"\"<\/p>\n

        Question 17.
        \n\\(\\frac{1}{3}\\)
        \nAnswer:
        \n\\(\\frac{3}{9}\\)
        \nExplanation:
        \nMultiply with 3 in numerator and denominator to get \\(\\frac{3}{9}\\)
        \n\"\"<\/p>\n

        Question 18.
        \n\\(\\frac{2}{5}\\)
        \nAnswer:
        \n\\(\\frac{4}{10}\\)
        \nExplanation:
        \nMultiply with 2 in numerator and denominator to get \\(\\frac{4}{10}\\)
        \n\"\"<\/p>\n

        Question 19.
        \n\\(\\frac{3}{4}\\)
        \nAnswer:
        \n\\(\\frac{6}{8}\\)
        \nExplanation:
        \nMultiply with 2 in numerator and denominator to get \\(\\frac{6}{8}\\)
        \n\"\"<\/p>\n

        Question 20.
        \n\\(\\frac{9}{2}\\)
        \nAnswer:
        \n\\(\\frac{18}{4}\\)
        \nExplanation:
        \nMultiply with 2 in numerator and denominator to get \\(\\frac{18}{4}\\)
        \n\"\"<\/p>\n

        Question 21.
        \n\\(\\frac{7}{12}\\)
        \nAnswer:
        \n\\(\\frac{14}{21}\\)
        \nExplanation:
        \nMultiply with 2 in numerator and denominator to get \\(\\frac{14}{21}\\)
        \n\"\"<\/p>\n

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

        For 22-23, use the chart at the right.
        \n\"Envision<\/p>\n

        Question 22.
        \nWrite three equivalent fractions to describe the portion of .
        \nAnswer:
        \n\\(\\frac{1}{6}\\), \\(\\frac{2}{12}\\), \\(\\frac{3}{18}\\) are three equivalent fractions.
        \nExplanation:
        \nThree equivalent fractions of \\(\\frac{1}{6}\\)\u00a0 are…
        \n\"\"<\/p>\n

        Question 23.
        \nReasoning<\/strong> Which vegetable takes up the same amount of the garden as the tomatoes? Explain.
        \nAnswer:
        \nBeans = \\(\\frac{3}{12}\\)\u00a0\u00a0 and Tomatoes = \\(\\frac{1}{4}\\)
        \nBeans take up the same amount of the garden as the tomatoes
        \nExplanation:
        \n\"\"<\/p>\n

        Question 24.
        \nJeena has 5 packets of seeds. Each packet has 12 seeds. Jeena wants to divide the seeds evenly among 10 flower pots. How many seeds can she plant in each flower pot?
        \nAnswer:
        \n6 seeds in one flower pot<\/p>\n

        Explanation:
        \n5 packets X 12 Seeds = 60 Seeds\u00a0 total
        \n60 seeds,10 flower pots
        \n\\(\\frac{60}{10}\\)\u00a0 = 6<\/p>\n

        Question 25.
        \nHigher Order Thinking<\/strong> Jen says, “I can use this equation to find equivalent fractions but n cannot be zero.”
        \n\\(\\frac{a}{b}=\\frac{(n \\times a)}{(n \\times b)}\\)
        \nDo you agree with Jen? Explain. Give examples to support your reasoning.
        \nAnswer:
        \nYES, I agree with Jen.
        \nExplanation:
        \n\"\"
        \nBy multiplying the numerator and denominator with the same number, we get equivalent fractions, n should not be zero.<\/p>\n

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

        Question 26.
        \nSelect the equivalent fraction.
        \n\"Envision
        \nAnswer:
        \n\"\"
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Question 27.
        \nNia found a fraction that is equivalent to \\(\\frac{1}{2}\\). Is Nia’s fraction work, shown below, correct? Explain.
        \n\\(\\frac{3 \\times 4}{8 \\times 3}=\\frac{12}{24}\\)
        \nAnswer:
        \nYES,\u00a0 Nia’s fraction work is Correct.
        \nExplanation:
        \n\"\"
        \nThe equivalent fraction is \\(\\frac{1}{2}\\)\u00a0 for both the fraction Nai found<\/p>\n

        Lesson 8.4 Generate Equivalent Fractions: Division<\/h3>\n

        Solve & Share<\/strong>
        \nSara bought a piece of ribbon. The length of the ribbon is given in tenths. Write the length as two other equivalent fractions. Solve this problem any way you choose.
        \nI can … use division to find equivalent fractions.
        \n\"Envision<\/p>\n

        Look Back! Sara wrote the following equivalent fractions: \\(\\frac{6}{10}=\\frac{3}{5}\\). What two operations could Sara have used to find her equivalent fractions? Explain.
        \nAnswer:
        \nSara could use common factorization, cross multiplication operations.
        \nExplanation:
        \nTo find equivalent fractions, divide the numerator and the denominator by a common factor.
        \nA common factor is a factor two or more numbers have in common.<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Use Division to Find Equivalent Fractions?
        \nAnswer:
        \nYou can multiply or divide to find an equivalent fraction.
        \nAdding or subtracting does not work for finding an equivalent fraction.
        \nIf you multiply or divide by the top of the fraction, you must do the same to the bottom.
        \nUse cross multiplication to determine if two fractions are equivalent.<\/p>\n

        Visual Learning Bridge
        \nIn early May, Fairbanks, Alaska, has daylight for \\(\\frac{18}{24}\\) of the day. What are some fractions equivalent to \\(\\frac{18}{24}\\)?
        \nAnswer:
        \n\\(\\frac{3}{4}\\)
        \nExplanation:
        \nHere 18 and 24 can be divided by 6
        \n18 can be divided by 6 in 3 times so 18 \u00f7 6 = 3
        \n24 can be divided by 6 in 4 times so 24\u00f7 6 = 4
        \nso we get
        \n\\(\\frac{18}{24}\\) = \\(\\frac{3}{4}\\)
        \n\"Envision<\/p>\n

        Two common factors of 18 and 24 are 2 and 3.
        \n\"Envision<\/p>\n

        Convince Me! Model with Math Draw a number line and label it with equivalent fractions to show \\(\\frac{18}{24}=\\frac{9}{12}=\\frac{6}{8}=\\frac{3}{4}\\).<\/p>\n

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

        Do You Understand?<\/strong>
        \nQuestion 1.
        \nUse division to show \\(\\frac{9}{12}\\) and \\(\\frac{3}{4}\\) are equivalent fractions.
        \nAnswer:
        \nyes, these are equivalent fractions.
        \n\\(\\frac{9}{12}\\) and \\(\\frac{3}{4}\\) are equivalent fractions.
        \nExplanation:
        \nHere 9 and 12 can be divided by 3
        \n9 can be divided by 3 in 3 times so 9 \u00f7 3 = 3
        \n12 can be divided by 3 in 4 times so 12 \u00f7 3 = 4
        \nso we get
        \n\\(\\frac{9}{12}\\) = \\(\\frac{3}{4}\\)<\/p>\n

        Question 2.
        \nIs there a fraction with a smaller numerator and denominator that is equivalent to \\(\\frac{4}{12}\\)? Explain.
        \nAnswer:
        \nYes, a fraction with a smaller numerator and denominator that is equivalent to 4\/12 is 1\/3
        \nExplanation:
        \nHere 4 and 12 can be divided by 4
        \n4 can be divided by 4 in 1 time so 4 \u00f7 4 = 1
        \n12 can be divided by 4 in 3 times so 12 \u00f7 4 = 3
        \nso we get
        \n\\(\\frac{4}{12}\\) = \\(\\frac{1}{3}\\)<\/p>\n

        Do You Know How?<\/strong>
        \nFor 3-8, divide to find equivalent fractions.
        \nQuestion 3.
        \n\\(\\frac{6}{10}=\\frac{}{}\\)
        \nAnswer:
        \n\\(\\frac{3}{5}\\)
        \nExplanation:
        \nHere 6 and 10 can be divided by 2
        \n6 can be divided by 2 in 3 times so 6 \u00f7 2 = 3
        \n10 can be divided by 2 in 5 times so 10 \u00f7 2 = 5
        \nso we get
        \n\\(\\frac{6}{10}\\) = \\(\\frac{3}{5}\\)<\/p>\n

        Question 4.
        \n\\(\\frac{8}{12}=\\frac{ }{ }\\)
        \nAnswer:
        \n\\(\\frac{2}{3}\\)
        \nExplanation:
        \nHere 8 and 12 can be divided by 4
        \n8 can be divided by 4 in 2 times so 8 \u00f7 4 = 2
        \n12 can be divided by 4 in 3 times so 12 \u00f7 4 = 3
        \nso we get
        \n\\(\\frac{8}{12}\\) = \\(\\frac{2}{3}\\)<\/p>\n

        Question 5.
        \n\\(\\frac{8}{12}=\\frac{ }{3}\\)
        \nAnswer:
        \n\\(\\frac{2}{3}\\)
        \nExplanation:
        \nHere 8 and 12 can be divided by 4
        \n8 can be divided by 4 in 2 times so 8 \u00f7 4 = 2
        \n12 can be divided by 4 in 3 times so 12 \u00f7 4 = 3
        \nso we get
        \n\\(\\frac{8}{12}\\) = \\(\\frac{2}{3}\\)<\/p>\n

        Question 6.
        \n\\(\\frac{10}{12}=\\frac{5}{}\\)
        \nAnswer:
        \n\\(\\frac{5}{6}\\)
        \nExplanation:
        \nHere 10 and 12 can be divided by 2
        \n10 can be divided by 2 in 5 times so 10 \u00f7 2 = 5
        \n12 can be divided by 2 in 6 times so 12 \u00f7 2 = 6
        \nso we get
        \n\\(\\frac{10}{12}\\) = \\(\\frac{5}{6}\\)<\/p>\n

        Question 7.
        \n\\(\\frac{2}{10}=\\frac{ }{5}\\)
        \nAnswer:
        \n\\(\\frac{1}{5}\\)
        \nExplanation:
        \nHere 2 and 10 can be divided by 2
        \n2 can be divided by 2 in 1 time so 2 \u00f7 2 = 1
        \n10 can be divided by 2 in 5 times so 10 \u00f7 2 = 5
        \nso we get
        \n\\(\\frac{2}{10}\\) = \\(\\frac{1}{5}\\)<\/p>\n

        Question 8.
        \n\\(\\frac{10}{100}=\\frac{ }{10}\\)
        \nAnswer:
        \n\\(\\frac{1}{10}\\)
        \nExplanation:
        \nHere 10 and 100 can be divided by 10
        \n10 can be divided by 10 in 1 time so 10 \u00f7 10 = 1
        \n100 can be divided by 10 in 10 times so 100 \u00f7 10 = 10
        \nso we get
        \n\\(\\frac{10}{100}\\) = \\(\\frac{1}{10}\\)<\/p>\n

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

        Leveled Practice For 9-16, fill in the missing numbers to find equivalent fractions.
        \nQuestion 9.
        \n\\(\\frac{6 \\div 6}{12 \\div 6}=\\)
        \nAnswer:
        \nMissing number is \\(\\frac{1}{2}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 10.
        \n\\(\\frac{70 \\div 5}{10 \\div 5}=\\)
        \nAnswer:
        \nMissing number is \\(\\frac{35}{2}\\)
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Question 11.
        \n\\(\\frac{2 \\div 2}{6 \\div 2}=\\)
        \nAnswer:
        \nMissing number is \\(\\frac{1}{3}\\)
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Question 12.
        \n\\(\\frac{50 \\div 10}{100 \\div 10}=\\)
        \nAnswer:
        \nMissing number is \\(\\frac{1}{2}\\)
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

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

        \"\"
        \nExplanation:
        \nDividing \\(\\frac{9}{6}\\)\u00a0 with 3 on both the sides we get \\(\\frac{3}{2}\\)<\/p>\n

        Question 14.
        \n\"Envision
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nDividing 10\/4 with 2 on both the sides we get \\(\\frac{5}{2}\\)<\/p>\n

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

        \"\"<\/p>\n

        Explanation:
        \nDividing \\(\\frac{4}{12}\\)\u00a0 with 2 on both the sides we get \\(\\frac{2}{6}\\)<\/p>\n

        Question 16.
        \n\"Envision
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \nDividing \\(\\frac{2}{8}\\) with 2 on both the sides we get \\(\\frac{1}{4}\\)<\/p>\n

        For 17-24, divide to find two equivalent fractions.
        \nQuestion 17.
        \n\\(\\frac{20}{100}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \n\\(\\frac{20}{10}\\)\u00a0 = 2
        \n\\(\\frac{100}{10}\\)\u00a0 = 10
        \nSo,
        \n\\(\\frac{2}{10}\\)\u00a0 =\\(\\frac{1}{5}\\)<\/p>\n

        Question 18.
        \n\\(\\frac{40}{10}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \n10 x 1 = 10
        \n10 x 4 = 40
        \nSo \\(\\frac{40}{10}\\)\u00a0 = \\(\\frac{4}{1}\\)\u00a0 are equivalent fractions.<\/p>\n

        Question 19.
        \n\\(\\frac{16}{12}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \n4 x 4 = 16
        \n4 x 3 = 12
        \nSo \\(\\frac{16}{12}\\)\u00a0 = \\(\\frac{4}{3}\\) are equivalent fractions.<\/p>\n

        Question 20.
        \n\\(\\frac{12}{8}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \n4 x 3 = 12
        \n4 x 2 = 8
        \nSo, \\(\\frac{12}{8}\\) = \\(\\frac{3}{2}\\)\u00a0 are equivalent fractions.<\/p>\n

        Question 21.
        \n\\(\\frac{24}{12}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \n12 x 2 = 24
        \n12 x 1 = 12
        \nSo, \\(\\frac{24}{12}\\) = \\(\\frac{2}{1}\\) are equivalent fractions.<\/p>\n

        Question 22.
        \n\\(\\frac{10}{100}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \n10 x 1 = 10
        \n10 x 10 =100
        \nSo, \\(\\frac{10}{100}\\)\u00a0 = \\(\\frac{1}{10}\\)\u00a0 are equivalent fractions.<\/p>\n

        Question 23.
        \n\\(\\frac{90}{10}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \n10 x 1 = 10
        \n10 x 9 = 90
        \nSo, \\(\\frac{90}{10}\\)\u00a0 = \\(\\frac{9}{1}\\)\u00a0 are equivalent fractions.<\/p>\n

        Question 24.
        \n\\(\\frac{80}{100}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \n10 x 8 = 80
        \n10 x 10 = 100
        \n2 x 4 = 8
        \n2 x 5 = 10
        \nSo, \\(\\frac{80}{100}\\) = \\(\\frac{4}{5}\\)<\/p>\n

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

        For 25-27, use the table at the right.
        \n\"Envision<\/p>\n

        Question 25.
        \nComplete the table at the right by writing the fraction of the day each animal sleeps and an equivalent fraction. Remember, there are 24 hours in a day.
        \nAnswer:
        \n\"\"<\/p>\n

        Explanation:
        \n\\(\\frac{12}{24}\\) divide both numerator and denominator with 2 to get equivalent fraction \\(\\frac{1}{2}\\)
        \n\\(\\frac{4}{24}\\) divide both numerator and denominator with 4 to get equivalent fraction \\(\\frac{1}{6}\\)\\(\\frac{15}{24}\\) divide both numerator and denominator with 3 to get equivalent fraction \\(\\frac{5}{8}\\)
        \n\\(\\frac{16}{24}\\)divide both numerator and denominator with 8 to get equivalent fraction \\(\\frac{2}{3}\\)
        \nQuestion 26.
        \nSuppose the cow slept 4 more hours. What fraction of the day would the cow spend sleeping?
        \nAnswer:
        \nThe Cow spend\u00a0\\(\\frac{1}{3}\\) of sleeping hours.
        \nExplanation:
        \n\"\"<\/p>\n

        Question 27.
        \nHow many hours does a tiger sleep in 7 days?
        \nAnswer:
        \nTiger sleeps 112 hours in 7 days.
        \nExplanation:
        \n\"\"<\/p>\n

        Question 28.
        \nUse Structure Ethan ate \\(\\frac{4}{8}\\) of his sandwich. Andy ate \\(\\frac{1}{2}\\) of his sandwich. The sandwiches were the same size.
        \na. Whose sandwich had more equal parts?
        \nAnswer:
        \nEthan sandwich had more equal parts.
        \nExplanation:
        \n\"\"
        \nb. Whose sandwich had larger equal parts?
        \nAnswer:
        \nAndy had larger equal parts.
        \nExplanation:
        \n\"\"<\/p>\n

        c. Who ate more? Explain.
        \nAnswer:
        \nBoth of them ate same,
        \nAs, the sandwiches were of the same size.
        \nExplanation:
        \n\"\"
        \nQuestion 29.
        \nHigher Order Thinking<\/strong> If the numerator and denominator of a fraction are both odd numbers, can you write an equivalent fraction with a smaller numerator and denominator? Give an example to explain.
        \nAnswer:
        \nThe numerator and denominator of a fraction are both odd numbers,
        \nAs shown in the bench mark number line 1\/3 and 3\/9 are the odd numbers fraction and they are equivalent fractions.
        \nExplanation:
        \nExample,
        \n\"\"<\/p>\n

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

        Question 30.
        \nSelect all the equations that are correct.
        \n\u2610 \\(\\frac{12 \\div 3}{3 \\div 3}=\\frac{3}{1}\\)
        \n\u2610 \\(\\frac{4 \\div 2}{8 \\div 2}=\\frac{2}{4}\\)<\/strong>
        \n\u2610 \\(\\frac{5 \\div 5}{10 \\div 5}=\\frac{1}{5}\\)
        \n\u2610 \\(\\frac{10 \\div 2}{4 \\div 2}=\\frac{5}{2}\\)<\/strong>
        \n\u2610 \\(\\frac{12 \\div 4}{8 \\div 4}=\\frac{3}{2}\\)
        \n<\/strong>
        \nAnswer:
        \n\"\"
        \nExplanation:
        \nIn the above equation 4\/8 divide both numerator and denominator with 2 to get equivalent fraction 2\/4.
        \nIn the above equation10\/4 divide both numerator and denominator with 2 to get equivalent fraction 5\/2.
        \nIn the above equation 12\/8 divide both numerator and denominator with 4 to get equivalent fraction 1\/2.<\/p>\n

        Question 31.
        \nThere are 12 students in DeLynn’s class. Eight students own pets. Which pair of fractions show the fraction of the class that owns pets?
        \nA. \\(\\frac{8}{12}, \\frac{2}{3}\\)
        \nB. \\(\\frac{1}{2}, \\frac{2}{3}\\)
        \nC. \\(\\frac{6}{4}, \\frac{3}{2}\\)
        \nD. \\(\\frac{12}{8}, \\frac{3}{2}\\)<\/p>\n

        Answer:
        \nOption A
        \nExplanation:
        \nIn 8\/12 fraction divide both numerator and denominator with 4 to get equivalent fraction 2\/3.<\/p>\n

        \"\"<\/p>\n

        Lesson 8.5 Use Benchmarks to Compare Fractions<\/h3>\n

        Solve & Share<\/strong>
        \nColor a part of each strip of paper below. Estimate what fraction of each strip is colored. Explain how you made your estimate. Solve this problem any way you choose.
        \nI can … use benchmarks, area models, and number lines to compare fractions.
        \n\"Envision<\/p>\n

        Look Back! Generalize How could you tell if a fraction is greater than, less than, or equal \\(\\frac{1}{2}\\) to just by looking at the numerator and the denominator?
        \nAnswer:
        \nFractions greater than 1 have numerators larger than their denominators; those that are less than 1 have numerators smaller than their denominators; the rest are equal to 1..<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Use Benchmarks to Compare Fractions?
        \nAnswer:
        \nCompare fractions with different denominators by finding the least common denominators and converting the fractions to it so the numerators can be compared.
        \nExplanation:
        \nFor example,
        \nDetermine whether\u00a0\\(\\frac{8}{15}\\) is less than or equal to \\(\\frac{4}{5}\\)
        \nNote that because 5 is a multiple of 15, the least common denominator is 15.
        \nConvert the fractions:\u00a0\\(\\frac{8}{15}\\) remains the same and\u00a0\\(\\frac{4}{5}\\) becomes \\(\\frac{12}{15}\\)
        \nWrite that \\(\\frac{8}{15}\\) is less than\u00a0\\(\\frac{4}{5}\\) since the 8 is smaller than the 12.<\/p>\n

        Visual Learning Bridge
        \nRobert needs \\(\\frac{3}{8}\\) stick of butter to make muffins and stick of butter to make cookies. Which recipe uses more butter?
        \n\"Envision<\/p>\n

        Compare \\(\\frac{3}{8}\\) to the benchmark fraction \\(\\frac{1}{2}\\).
        \n\"Envision
        \nYou can compare these fractions because they refer to the same whole, a stick of butter.<\/p>\n

        Compare \\(\\frac{2}{3}\\) to the benchmark fraction \\(\\frac{1}{2}\\)?
        \nAnswer:<\/p>\n

        \"Envision
        \nThe cookie recipe uses more butter.
        \nExplanation:
        \n\"\"<\/p>\n

        Convince Me! Critique Reasoning Ernesto said, “I know \\(\\frac{3}{8}\\) is less than \\(\\frac{2}{3}\\) because \\(\\frac{3}{8}\\) is closer to 0 than it is to 1 and \\(\\frac{2}{3}\\) is closer to 1 than it is to 0.” Does Ernesto’s reasoning make sense? Draw two number lines to support your answer.<\/p>\n

        Answer:
        \ni) we can use benchmarks to compare fractions
        \nii) A benchmark is a known size or amount that helps us understand a different size or amount.
        \niii) we can use models or benchmarks on a number line to compare fractions.
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Another Example!<\/strong>
        \nCompare \\(\\frac{9}{10}\\) and \\(\\frac{7}{6}\\). Use 1 whole as a benchmark.
        \n\\(\\frac{9}{10}\\) < 1 and \\(\\frac{7}{6}\\) > 1, so \\(\\frac{9}{10}\\) < \\(\\frac{7}{6}\\).
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

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

        Do You Understand?<\/strong>
        \nQuestion 1.
        \nCarl found \\(\\frac{4}{8}\\) is equal to \\(\\frac{1}{2}\\), and \\(\\frac{1}{3}\\) is less than \\(\\frac{1}{2}\\). How can Carl compare \\(\\frac{4}{8}\\) to \\(\\frac{1}{3}\\).
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \ncarl – by comparing the blue line with the red line in the above number line picture, it shown that\u00a0\\(\\frac{1}{3}\\) is less then \\(\\frac{4}{8}\\)
        \n\\(\\frac{4}{8}\\) and\u00a0\\(\\frac{1}{2}\\) are equal.<\/p>\n

        Question 2.
        \nWrite a fraction that is closer to 0 than to 1. Write another fraction that is closer to 1 than to 0. Use your fractions to complete the comparison.
        \n\\(\\frac{}{}\\) < \\(\\frac{}{}\\)
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nLets take example\u00a0\\(\\frac{1}{8}\\) and \\(\\frac{7}{8}\\) are the two fractions
        \nBy applying division rule
        \n\\(\\frac{1}{8}\\) = 0.1
        \nSo,\u00a0\\(\\frac{1}{8}\\) is closer to the 0
        \n\\(\\frac{7}{8}\\) = 0.8
        \nSo, \\(\\frac{7}{8}\\)is closer to the 1<\/p>\n

        Do You Know How?<\/strong>
        \nFor 3-4, compare. Write <, >, or =.
        \nQuestion 3.
        \n\\(\\frac{2}{6}\\) \"Envision \\(\\frac{4}{5}\\)
        \nAnswer:
        \n\"\"
        \nExplanation:
        \nBy applying division rule
        \n\\(\\frac{2}{6}\\) = 0.3 and \\(\\frac{4}{5}\\) = 0.8
        \nSo, \\(\\frac{2}{6}\\) is less than \\(\\frac{4}{5}\\)<\/p>\n

        Question 4.
        \n\\(\\frac{11}{12}\\) \"Envision \\(\\frac{9}{8}\\)
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nBy applying division rule
        \n\\(\\frac{11}{12}\\) = 0.9 and\u00a0\\(\\frac{9}{8}\\) = 1.1
        \nSo,\u00a0\\(\\frac{11}{12}\\) smaller then\u00a0\\(\\frac{9}{8}\\)<\/p>\n

        Question 5.
        \nCircle the fractions that are less than \\(\\frac{1}{2}\\).
        \n\\(\\begin{array}{llllll}
        \n\\frac{5}{4} & \\frac{1}{4} & \\frac{1}{5} & \\frac{2}{3} & \\frac{2}{12} & \\frac{51}{100}
        \n\\end{array}\\)
        \nAnswer:
        \n\"\"
        \nExplanation:
        \nBy applying division rule
        \n\\(\\frac{5}{4}\\) = 1.2
        \n\\(\\frac{1}{4}\\) = 0.2
        \n\\(\\frac{1}{5}\\) = 0.2
        \n\\(\\frac{2}{3}\\) = 0.3
        \n\\(\\frac{2}{12}\\) =0.2
        \n\\(\\frac{51}{100}\\) = 0.4
        \nSo, Fractions \\(\\frac{1}{4}\\), \\(\\frac{1}{5}\\) and \\(\\frac{2}{12}\\) are less then \\(\\frac{1}{2}\\)<\/p>\n

        Question 6.
        \nCircle the fractions that are greater than 1.
        \n\\(\\begin{array}{llllll}
        \n\\frac{99}{100} & \\frac{6}{5} & \\frac{7}{8} & \\frac{14}{8} & \\frac{11}{10} & \\frac{11}{12}
        \n\\end{array}\\)
        \nAnswer:
        \n\"\"<\/p>\n

        Explanation:
        \nBy applying division rule
        \n\\(\\frac{99}{100}\\) = 0.9
        \n\\(\\frac{6}{5}\\) = 1.2
        \n\\(\\frac{7}{8}\\) = 0.8
        \n\\(\\frac{14}{8}\\) = 1.7
        \n\\(\\frac{11}{10}\\) = 1.1
        \n\\(\\frac{11}{12}\\) = 0.9
        \nSo, Fractions \\(\\frac{6}{5}\\), \\(\\frac{14}{8}\\) and \\(\\frac{11}{10}\\) are greater then 1<\/p>\n

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

        For 7-10, circle all the fractions that match each statement.
        \nQuestion 7.
        \nFractions less than \\(\\frac{1}{2}\\)
        \n\\(\\begin{array}{llllll}
        \n\\frac{3}{4} & \\frac{1}{6} & \\frac{6}{12} & \\frac{4}{10} & \\frac{5}{8} & \\frac{5}{2}
        \n\\end{array}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \nPerform the divisions:
        \n\\(\\frac{1}{6}\\) = 0.15 (rounded) and \\(\\frac{4}{10}\\) = 0.8 (rounded).
        \n\\(\\frac{1}{6}\\) and \\(\\frac{4}{10}\\) are the fractions less than \\(\\frac{1}{2}\\)
        \n\\(\\frac{3}{4}\\); \\(\\frac{6}{12}\\); \\(\\frac{5}{8}\\); \\(\\frac{5}{2}\\) are the fractions less than \\(\\frac{1}{2}\\)<\/p>\n

        Question 8.
        \nFractions greater than \\(\\frac{1}{2}\\)
        \n\\(\\begin{array}{llllll}
        \n\\frac{5}{8} & \\frac{1}{4} & \\frac{6}{3} & \\frac{7}{10} & \\frac{5}{12} & \\frac{6}{12}
        \n\\end{array}\\)
        \nAnswer:
        \n\"\"
        \nExplanation;
        \nPerform the divisions
        \n\\(\\frac{5}{8}\\) = 0.62 ; \\(\\frac{6}{3}\\) = 2.0; \\(\\frac{7}{10}\\) = 0.7
        \nSo, \\(\\frac{5}{8}\\); \\(\\frac{6}{3}\\); \\(\\frac{7}{10}\\) are the fractions greater than \\(\\frac{1}{2}\\)
        \nwhere as \\(\\frac{1}{4}\\); \\(\\frac{5}{12}\\); \\(\\frac{6}{12}\\) are the fractions less than \\(\\frac{1}{2}\\)<\/p>\n

        Question 9.
        \nFractions greater than \\(\\frac{1}{2}\\)
        \n\\(\\begin{array}{llllll}
        \n\\frac{5}{4} & \\frac{2}{3} & \\frac{6}{6} & \\frac{1}{10} & \\frac{15}{12} & \\frac{7}{8}
        \n\\end{array}\\)
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nwhen we perform the divisions
        \n\\(\\frac{5}{4}\\) = 1.24
        \n\\(\\frac{15}{12}\\) = 1.3
        \nSo, \\(\\frac{5}{4}\\)and \\(\\frac{15}{12}\\) fractions are greater than \\(\\frac{1}{2}\\)<\/p>\n

        Question 10.
        \nFractions closer to 0 than to 1
        \n\\(\\begin{array}{llllll}
        \n\\frac{3}{4} & \\frac{1}{8} & \\frac{1}{4} & \\frac{7}{5} & \\frac{2}{4} & \\frac{3}{10}
        \n\\end{array}\\)
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nwhen we perform the divisions
        \n\\(\\frac{3}{4}\\) = 0.7
        \n\\(\\frac{1}{8}\\) = 0.1
        \n\\(\\frac{1}{4}\\) = 0.2
        \n\\(\\frac{3}{10}\\) = 0.3
        \nSo, \\(\\frac{3}{4}\\); \\(\\frac{1}{8}\\); \\(\\frac{1}{4}\\)and \\(\\frac{3}{10}\\) fractions are closer to 0 than 1.<\/p>\n

        For 11-18, compare using benchmark fractions or 1. Then write >,<, or =.
        \nQuestion 11.
        \n\\(\\frac{1}{3}\\) \"Envision \\(\\frac{4}{6}\\)
        \nAnswer:
        \n\"\"<\/p>\n

        Explanation:
        \nPerform the divisions:
        \n\\(\\frac{1}{3}\\) = 0.33 (rounded) and \\(\\frac{4}{6}\\) = 0.58
        \nThe decimal form of \\(\\frac{1}{3}\\) is less than \\(\\frac{4}{6}\\)<\/p>\n

        Question 12.
        \n\\(\\frac{4}{8}[\/latex] <\/span>\"Envision [latex]\\frac{2}{4}\\)<\/span><\/p>\n

        Answer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \nBy applying division rule
        \n\\(\\frac{4}{8}\\) = 0.5
        \n\\(\\frac{2}{4}\\) = 0.5
        \nso, \\(\\frac{4}{8}\\) and \\(\\frac{2}{4}\\) are equivalent fractions.<\/p>\n

        Question 13.
        \n\\(\\frac{7}{5}\\) \"Envision \\(\\frac{7}{8}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \nPerform the divisions:
        \n\\(\\frac{7}{5}\\)= 1.4 (rounded) and \\(\\frac{7}{8}\\)= 0.87
        \nThe decimal form of \\(\\frac{7}{5}\\) is greater than \\(\\frac{7}{8}\\)<\/p>\n

        Question 14.
        \n\\(\\frac{6}{12}\\) \"Envision \\(\\frac{4}{5}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \nPerform the divisions:
        \n\\(\\frac{6}{12}\\) = 0.5 (rounded) and \\(\\frac{4}{5}\\) = 0.8
        \nThe decimal form of \\(\\frac{6}{12}\\) is less than \\(\\frac{4}{5}\\)<\/p>\n

        Question 15.
        \n\\(\\frac{4}{5}\\) \"Envision \\(\\frac{2}{5}\\)
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nPerform the divisions:
        \n\\(\\frac{4}{5}\\) = 0.8 (rounded) and \\(\\frac{2}{5}\\) = 0.4
        \nThe decimal form of \\(\\frac{4}{5}\\) is greater than \\(\\frac{2}{5}\\)<\/p>\n

        Question 16.
        \n\\(\\frac{6}{6}\\) \"Envision \\(\\frac{13}{12}\\)
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nPerform the divisions:
        \n\\(\\frac{6}{6}\\) = 1 and \\(\\frac{13}{12}\\) = 1.08
        \nThe decimal form of \\(\\frac{6}{6}\\) is less than \\(\\frac{13}{12}\\)<\/p>\n

        Question 17.
        \n\\(\\frac{8}{10}\\) \"Envision \\(\\frac{1}{8}\\)
        \nAnswer:<\/p>\n

        \"\"<\/p>\n

        Explanation:
        \nPerform the divisions:
        \n\\(\\frac{8}{10}\\) = 0.8 (rounded) and \\(\\frac{1}{8}\\) = 0.12
        \nThe decimal form of \\(\\frac{8}{10}\\) is greater than \\(\\frac{1}{8}\\)<\/p>\n

        Question 18.
        \n\\(\\frac{4}{4}\\) \"Envision \\(\\frac{10}{10}\\)
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nPerform the divisions:
        \n\\(\\frac{4}{4}\\) = 1 and \\(\\frac{10}{10}\\) = 1
        \nSo, The decimal form of \\(\\frac{4}{4}\\) is equal to \\(\\frac{10}{10}\\)<\/p>\n

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

        Question 19.
        \nReasoning<\/strong> Jordan has \\(\\frac{5}{8}\\) can of green paint and \\(\\frac{3}{6}\\) can of blue paint. If the cans are the same size, does Jordan have more green paint or blue paint? Explain.
        \nAnswer:<\/p>\n

        \"\"
        \nExplanation:
        \nBy applying division rule
        \n\\(\\frac{5}{8}\\) = 0.6
        \n\\(\\frac{4}{8}\\) = 0.5
        \n\\(\\frac{3}{6}\\) = 0.5
        \nSo, \\(\\frac{5}{8}\\) is greater than \\(\\frac{4}{8}\\) and \\(\\frac{3}{6}\\)
        \nSo, Jordan has more green paints rather than blue paints.<\/p>\n

        Question 20.
        \nVocabulary<\/strong> Write two examples of a benchmark fraction.
        \nAnswer:
        \nBenchmark fractions are fractions that are easy to picture mentally, like \\(\\frac{1}{4}\\), \\(\\frac{1}{2}\\), or \\(\\frac{3}{4}\\)
        \nFor example, the fraction \\(\\frac{1}{2}\\) is a very well-known fraction that means 1 of 2 equal parts, or exactly a half of a whole.
        \nBenchmark fractions can be used on number line to compare fractions.
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Question 21.
        \nFour neighbors each have gardens that are the same size.
        \n\"Envision
        \n\"\"
        \na. Which neighbors planted vegetables in less than half of their gardens?
        \nAnswer:
        \nJames and Claudia planted vegetables in less than half of their gardens
        \nExplanation:
        \nBy Multiple fraction method
        \nJames \\(\\frac{5}{12}\\) fraction is written as
        \n5 x 5 = 25
        \n12 x 5 = 60
        \nSo, \\(\\frac{5}{12}\\) = \\(\\frac{25}{60}\\) < \\(\\frac{1}{2}\\)
        \nClaudia fraction \\(\\frac{1}{6}\\) is written as
        \n10 x 1 = 10
        \n10 x 6 = 60
        \nSo, \\(\\frac{1}{6}\\) = \\(\\frac{10}{60}\\) < \\(\\frac{1}{2}\\)<\/p>\n

        b. Who has a larger section of vegetables in their garden, Margaret or Wayne?
        \nAnswer:
        \nWayne has a larger section of vegetables.
        \nExplanation:
        \nMargaret planted \\(\\frac{1}{2}\\) vegetables of their gardens,
        \n\\(\\frac{5}{10}\\) = \\(\\frac{30}{60}\\)
        \n6 x 5 = 30
        \n6 x 10 = 60
        \nWayne more then half planted vegetables of their gardens
        \n\\(\\frac{2}{3}\\) = \\(\\frac{40}{60}\\)
        \n20 x 2 = 40
        \n20 x 3 = 60<\/p>\n

        Question 22.
        \nGavin bought 3 pizzas for a party. Each pizza had 8 slices. There were 8 other people at the party. Everyone ate the same number of slices. How many slices did each person eat? How many slices were left over?
        \nAnswer:
        \nEach person ate 2 slices
        \n6 slices were left
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Question 23.
        \nHigher Order Thinking<\/strong> How can you tell just by looking at the numerator and denominator of a fraction if it is closer to O or to 1? Give some examples in your explanation.
        \nAnswer:
        \n\"\"
        \nIf the numerators are with smaller number and denominators are with greater number, we can conclude that the fraction is closer to 0 or to 1.
        \nExamples:<\/p>\n

        \"\"
        \nExplanation:
        \nPerform division rule
        \n\\(\\frac{3}{4}\\) = 0.7;
        \n\\(\\frac{1}{8}\\) = 0.1
        \n\\(\\frac{1}{4}\\) = 0.2
        \n\\(\\frac{3}{10}\\) = 0.3
        \nSo,\u00a0 \\(\\frac{3}{4}\\); \\(\\frac{1}{8}\\); \\(\\frac{1}{4}\\)and \\(\\frac{3}{10}\\) fractions are closer to 0 than 1.<\/p>\n

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

        Question 24.
        \nDonna ate \\(\\frac{7}{12}\\) box of popcorn. Jack ate \\(\\frac{4}{10}\\) box of popcorn. The boxes of popcorn are the same size. Write to explain how to use a benchmark fraction to determine who ate more popcorn.
        \nAnswer:
        \nDonna ate more
        \n\\(\\frac{7}{12}\\) > \\(\\frac{4}{10}\\)<\/p>\n

        Explanation
        \n\"\"<\/p>\n

        Lesson 8.6 Compare Fractions<\/h3>\n

        Solve & Share<\/strong>
        \nJuan read for \\(\\frac{5}{6}\\) of an hour. Larissa read for \\(\\frac{10}{12}\\) of an hour. Who read for a longer period of time? Explain. Solve this problem any way you choose.
        \n\"\"
        \nI can … use equivalent fractions to compare fractions.
        \n\"Envision<\/p>\n

        Look Back! Carlos read for \\(\\frac{8}{12}\\) of an hour. Did Carlos read for more or less time than Juan? Write your answer as a number sentence using >, <, or =.
        \nAnswer:
        \n\\(\\frac{5}{6}\\)> \\(\\frac{8}{12}\\)
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Compare Fractions with Unlike Denominators?
        \nAnswer:
        \nWe can compare fractions with unlike denominators by finding the least common denominator, or the smallest multiple the denominators share. Then we make equivalent fractions, or fractions that represent the same part of the whole.
        \nExplanation:
        \n\"\"
        \n\\(\\frac{3}{5}\\) > \\(\\frac{5}{10}\\)<\/p>\n

        Visual Learning Bridge
        \nIsabella’s father is building a model dinosaur with small pieces of wood. Compare the lengths of the pieces of wood. Compare \\(\\frac{1}{4}\\) inch and \\(\\frac{5}{6}\\) inch. Then, compare \\(\\frac{4}{5}\\) inch and \\(\\frac{4}{10}\\) inch.
        \n\"Envision
        \nYou can compare these fractions because they refer to the same whole, an inch.<\/p>\n

        Compare \\(\\frac{1}{4}\\) and \\(\\frac{5}{6}\\) by renaming each fraction so they both have the same denominator.
        \n\\(\\frac{1}{4}=\\frac{1 \\times 3}{4 \\times 3}=\\frac{3}{12} \\quad \\frac{5}{6}=\\frac{5 \\times 2}{6 \\times 2}=\\frac{10}{12}\\)
        \nCompare the numerators of the renamed fractions.
        \n\\(\\frac{1}{2}\\) < \\(\\frac{1}{2}\\)
        \nSo, \\(\\frac{1}{2}\\) < \\(\\frac{1}{2}\\).<\/p>\n

        Compare \\(\\frac{4}{5}\\) and \\(\\frac{4}{10}\\) on a number line.
        \n\"Envision<\/p>\n

        Convince Me! Critique Reasoning The fractions on the right refer to the same whole. Kelly said, \u201cThese are easy to compare. I just think about \\(\\frac{1}{8}\\) and \\(\\frac{1}{6}\\).” Circle the greater fraction. Explain what Kelly was thinking.
        \n\\(\\frac{5}{8}\\)
        \n\\(\\frac{5}{6}\\)<\/p>\n

        Another Example!<\/strong>
        \nCompare \\(\\frac{3}{4}\\) and \\(\\frac{6}{10}\\).
        \nCreate an equivalent fraction for either \\(\\frac{3}{4}\\) or \\(\\frac{6}{10}\\)
        \nso that the numerators are the same.
        \n\\(\\frac{6 \\div 2}{10 \\div 2}=\\frac{3}{5}\\)
        \n\\(\\frac{3}{4}>\\frac{3}{5}\\) When you divide a whole into 4 equal parts, each part is larger than when you divide it into 5 equal parts.
        \n\"Envision<\/p>\n

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

        Do You Understand?<\/strong>
        \nQuestion 1.
        \nMary says \\(\\frac{1}{8}\\) is greater than \\(\\frac{1}{4}\\), because 8 is greater than 4. Is Mary’s reasoning correct? Explain.
        \nAnswer:
        \nNO, Mary’s reasoning is wrong
        \nExplanation:
        \n\"\"<\/p>\n

        Do You Know How?<\/strong>
        \nFor 2-5, write >, <, or =. Use number lines, fraction strips, benchmark or equivalent fractions.
        \nQuestion 2.
        \n\\(\\frac{3}{4}\\) \"Envision \\(\\frac{6}{8}\\)
        \nAnswer:
        \n\\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\)
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Question 3.
        \n\\(\\frac{1}{4}\\) \"Envision \\(\\frac{1}{10}\\)
        \nAnswer:
        \n\\(\\frac{1}{4}\\) > \\(\\frac{1}{10}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 4.
        \n\\(\\frac{3}{5}\\) \"Envision \\(\\frac{5}{10}\\)
        \nAnswer:
        \n\\(\\frac{3}{5}\\) > \\(\\frac{5}{10}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 5.
        \n\\(\\frac{1}{2}\\) \"Envision \\(\\frac{4}{5}\\)
        \nAnswer:
        \n\\(\\frac{1}{2}\\) < \\(\\frac{4}{5}\\)
        \nExplanation:
        \n\"\"<\/p>\n

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

        Leveled Practice For 6-15, find equivalent fractions to compare. Then, write >, <, or =.
        \nQuestion 6.
        \n\"Envision
        \nAnswer:
        \n7\/8 > 6\/8
        \nExplanation:
        \n\"\"<\/p>\n

        Question 7.
        \n\\(\\frac{5}{6}\\) \"Envision \\(\\frac{10}{12}\\)<\/p>\n

        Answer:
        \n\\(\\frac{5}{6}\\) = \\(\\frac{10}{12}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 8.
        \n\\(\\frac{7}{10}\\) \"Envision \\(\\frac{4}{5}\\)
        \nAnswer:
        \n\\(\\frac{7}{10}\\) < \\(\\frac{4}{5}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 9.
        \n\\(\\frac{7}{12}\\) \"Envision \\(\\frac{1}{3}\\)
        \nAnswer:
        \n\\(\\frac{7}{12}\\) > \\(\\frac{1}{3}\\)
        \nExplanation:<\/p>\n

        \"\"<\/p>\n

        Question 10.
        \n\\(\\frac{5}{12}\\) \"Envision \\(\\frac{4}{5}\\)
        \nAnswer:
        \n\\(\\frac{5}{12}\\) <\u00a0\\(\\frac{4}{5}\\)5\/12 < 4\/5
        \nExplanation:
        \n\"\"<\/p>\n

        Question 11.
        \n\\(\\frac{2}{6}\\) \"Envision \\(\\frac{3}{12}\\)
        \nAnswer:
        \n\\(\\frac{2}{6}\\) > \\(\\frac{3}{12}\\)
        \n\"\"<\/p>\n

        Question 12.
        \n\\(\\frac{6}{8}\\) \"Envision \\(\\frac{3}{4}\\)
        \nAnswer:
        \n\\(\\frac{6}{8}\\) = \\(\\frac{3}{4}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 13.
        \n\\(\\frac{6}{10}\\) \"Envision \\(\\frac{3}{6}\\)
        \nAnswer:
        \n\\(\\frac{6}{10}\\) >\u00a0\\(\\frac{3}{6}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 14.
        \n\\(\\frac{2}{10}\\) \"Envision \\(\\frac{1}{6}\\)
        \nAnswer:
        \n\\(\\frac{2}{10}\\) >\u00a0\\(\\frac{1}{6}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 15.
        \n\\(\\frac{5}{6}\\) \"Envision \\(\\frac{2}{3}\\)
        \nAnswer:
        \n\\(\\frac{5}{6}\\) > \\(\\frac{2}{3}\\)<\/p>\n

        Explanation:
        \n\"\"<\/p>\n

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

        Question 16.
        \nFelicia drew the pictures at the right to show \\(\\frac{3}{8}\\) is greater than \\(\\frac{3}{4}\\). What was Felicia’s mistake?
        \n\"Envision
        \nAnswer:
        \nYES, Felicia mistake
        \n\\(\\frac{3}{8}\\) < \\(\\frac{3}{4}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 17.
        \nCritique Reasoning<\/strong> Jake said you can compare two fractions with the same denominator by only comparing the numerators. Is Jake correct? Explain.
        \nAnswer:
        \nYes, Jake is correct.
        \nExplanation:
        \nJack said correct
        \nOnly compare numerators of two fractions, with same denominator, if different denominators are there, either by multiplying or dividing the fraction to make the denominator same for comparing the fractions.
        \nExample : \\(\\frac{A}{D}\\) < \\(\\frac{B}{D}\\)
        \nA and B are numerators are compared (A<B), D denominator is same for both the fractions.<\/p>\n

        Question 18.
        \nTina completed \\(\\frac{2}{3}\\) of her homework. George completed \\(\\frac{8}{9}\\) of his homework. Tina and George have the same amount of homework. Who completed a greater fraction of homework?
        \nAnswer:
        \n\\(\\frac{2}{3}\\) < \\(\\frac{8}{9}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 19.
        \nIf 34 \u00d7 2 = 68 then what does 34 \u00d7 20 equal?
        \nAnswer:
        \n680
        \nExplanation:
        \n34 X 2 = 68
        \n34 X 20 =680<\/p>\n

        Question 20.
        \nWhat can you conclude about \\(\\frac{3}{5}\\) and \\(\\frac{60}{100}\\) if you know \\(\\frac{3}{5}\\) is equivalent to \\(\\frac{6}{10}\\) and \\(\\frac{6}{100}\\) is equivalent to \\(\\frac{60}{100}\\)?
        \nAnswer:
        \nEquivalent fractions.
        \n\\(\\frac{6}{100}\\)\u00a0 Not Equal to\u00a0 \\(\\frac{60}{100}\\)<\/p>\n

        \\(\\frac{3}{5}\\) = \\(\\frac{6}{10}\\)\u00a0 \u00a0 and\u00a0 \\(\\frac{6}{10}\\) = \\(\\frac{60}{100}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 21.
        \nJackson played a video game for \\(\\frac{1}{6}\\) hour. Hailey played a video game for \\(\\frac{1}{3}\\) hour. Who played the video game for a greater amount of time? Explain.
        \nAnswer:
        \nHailey played greater amount of time.
        \n\\(\\frac{1}{6}\\) < \\(\\frac{1}{3}\\)
        \nExplanation:
        \n\"\"<\/p>\n

        Question 22.
        \nHigher Order Thinking<\/strong> Write a fraction that is greater than \\(\\frac{3}{12}\\), is less than \\(\\frac{75}{100}\\) and has 6 as a denominator.
        \nAnswer:
        \n\\(\\frac{5}{6}\\)<\/p>\n

        Explanation:
        \n(\\(\\frac{75}100}]\\) = \\(\\frac{3}{4}\\) or \\(\\frac{9}{12}\\) are equivalent fractions)<\/p>\n

        \\(\\frac{3}{12}\\) < \\(\\frac{75}{100}\\) < \\(\\frac{X}{6}\\) X \\(\\frac{2}{2}\\)<\/p>\n

        \\(\\frac{3}{12}\\) < \\(\\frac{3}{4}\\) X \\(\\frac{3}{3}\\)< \\(\\frac{10}{12}\\)<\/p>\n

        \\(\\frac{3}{12}\\) < \\(\\frac{9}{12}\\)< \\(\\frac{10}{12}\\)<\/p>\n

        \\(\\frac{3}{12}\\) < \\(\\frac{75}{100}\\) < \\(\\frac{5}{6}\\)<\/p>\n

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

        Question 23.
        \nSelect all fractions that would make the comparison true.
        \n\\(\\frac{3}{4}\\) = ________
        \n\u2610 \\(\\frac{5}{12}\\)
        \n\u2610 \\(\\frac{75}{100}\\)
        \n\u2610 \\(\\frac{9}{12}\\)
        \n\u2610 \\(\\frac{7}{10}\\)
        \n\u2610 \\(\\frac{6}{8}\\)
        \nAnswer:
        \n\"\"<\/p>\n

        Question 24.
        \nSelect all answer choices that show a correct comparison
        \n\u2610 \\(\\frac{5}{6}\\) > \\(\\frac{7}{12}\\)
        \n\u2610 \\(\\frac{1}{2}\\) > \\(\\frac{10}{10}\\)
        \n\u2610 \\(\\frac{4}{10}\\) > \\(\\frac{2}{6}\\)
        \n\u2610 \\(\\frac{1}{5}\\) < \\(\\frac{2}{3}\\)
        \n\u2610 \\(\\frac{2}{3}\\) > \\(\\frac{9}{12}\\)
        \nAnswer:
        \n\"\"<\/p>\n

        Lesson 8.7 Problem Solving<\/h3>\n

        Construct Arguments<\/strong>
        \nSolve & Share<\/strong>
        \nSherry and Karl both started their hike with a small bottle filled with water. Tia started her hike with a larger bottle that was \\(\\frac{1}{2}\\) full. At the end of the hike, Sherry and Tia’s bottles were each half filled with water. Karl’s bottle was \\(\\frac{1}{3}\\) filled with water. Who has the most water left? Construct a math argument to support your answer.
        \nI can … construct math arguments using what I know about fractions.
        \n\"Envision<\/p>\n

        Thinking Habits
        \nBe a good thinker! These questions can help you.<\/p>\n

          \n
        • How can I use numbers, objects, drawings, or actions to justify my argument?<\/li>\n
        • Am I using numbers and symbols correctly?<\/li>\n
        • Is my explanation clear and complete?<\/li>\n<\/ul>\n

          Look Back! Construct Arguments if Tia’s bottle was filled with water at the end of the hike, would you be able to decide who had the most water left? Construct an argument to support your answer.
          \nAnswer:
          \nTia left with most water
          \nExplanation:
          \nSherry and Karl starter with say \\(\\frac{6}{12}\\) and left with \\(\\frac{3}{12}\\)
          \n\"\"
          \nSherry and Karl both started small bottle filled with water.
          \nTia started larger bottle \\(\\frac{1}{2}\\) filled.
          \nAs the sizes of the bottles are different, a common denominator to be find to compare these three fractions.
          \nLet 12 be the common denominator for these three fractions.
          \nSherry and Karl both started small bottle filled with water \\(\\frac{6}{12}\\) = \\(\\frac{1}{2}\\) of water compared to larger bottle.
          \nAfter hike Tia is with \\(\\frac{1}{3}\\) of water in her larger water bottle = \\(\\frac{4}{12}\\) of water left.<\/p>\n

          Essential Question<\/strong>
          \nHow Can You Construct Arguments?
          \nAnswer:
          \nI can<\/p>\n

            \n
          • use numbers, objects, drawings, or models to justify my arguments.<\/li>\n
          • use a counterexample in my argument.<\/li>\n
          • give an explanation of my argument that is clear and complete.<\/li>\n<\/ul>\n

            Visual Learning Bridge
            \nErin said \\(\\frac{1}{2}\\) is the same amount as \\(\\frac{2}{4}\\).
            \nMatt said \\(\\frac{1}{2}\\) and \\(\\frac{2}{4}\\) can be different amounts.
            \nWhich student is correct?<\/p>\n

            A good math argument is correct, simple, complete, and easy to understand.<\/p>\n

            What do you need to do to solve this problem?
            \nI need to construct an argument with what I know about fraction models and ways to show \\(\\frac{1}{2}\\) and \\(\\frac{2}{4}\\).<\/p>\n

            How can I construct an argument?
            \nI can<\/p>\n

              \n
            • use numbers, objects, drawings, or models to justify my arguments.<\/li>\n
            • use a counterexample in my argument.<\/li>\n
            • give an explanation of my argument that is clear and complete.<\/li>\n<\/ul>\n

              Here’s my thinking.<\/p>\n

              I will use drawings to show which student is correct.
              \nBoth wholes are the same size. The \\(\\frac{1}{2}\\) and \\(\\frac{2}{4}\\) represent the same part of the whole.
              \n\"Envision
              \nThese wholes are not the same size. So, \\(\\frac{2}{4}\\) of the larger circle represents more than \\(\\frac{1}{2}\\) of the smaller circle.<\/p>\n

              Both students are correct. \\(\\frac{1}{2}\\) and \\(\\frac{2}{4}\\) of the same-size whole are the same amount. \\(\\frac{1}{2}\\) and \\(\\frac{2}{4}\\) of different-size wholes are different amounts.<\/p>\n

              Convince Me! Critique Reasoning Erin also said \\(\\frac{3}{6}\\) and \\(\\frac{5}{10}\\) are NOT the same size because the denominators are not factors of each other. Is Erin’s argument correct? Explain.
              \nAnswer:
              \nNo, Erin’s argument is not correct.
              \nAs both fractions are same even though there denominators are different.
              \n\\(\\frac{3}{6}\\) and \\(\\frac{5}{10}\\)
              \nExplanation:
              \nWith reference to benchmark reference,
              \n\\(\\frac{3}{6}\\) \u00f7 \\(\\frac{3}{3}\\) = \\(\\frac{1}{2}\\)
              \n\\(\\frac{5}{10}\\) \u00f7 \\(\\frac{5}{5}\\) = \\(\\frac{1}{2}\\)<\/p>\n

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

              Construct Arguments<\/strong> Margie and Parker ordered the same-size burritos. Margie ate of her burrito. Parker ate of his burrito. Margie concluded she ate more than Parker because the fraction of the burrito she ate has a greater denominator.
              \nQuestion 1.
              \nWhat is Margie’s argument? How does she support her argument?
              \nAnswer:
              \nSame – size of burrito
              \nBurrito made 2 slices or 4 slices
              \nParker ate 2 slices and Margei ate 4 slice
              \n\\(\\frac{2}{2}\\) = \\(\\frac{4}{4}\\)<\/p>\n

              Question 2.
              \nDoes Margie’s conclusion make sense?
              \nAnswer:
              \nNo, Margies conclusion does not make sense,
              \nBecause both ate same quantity of burrito.<\/p>\n

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

              Construct Arguments<\/strong> In the after-school club, Dena, Shawn, and Amanda knit scarves that are all the same size with yellow, white, and blue yarn. Dena’s scarf is \\(\\frac{3}{5}\\) yellow, Shawn’s scarf is \\(\\frac{2}{5}\\) yellow, and Amanda’s scarf is \\(\\frac{3}{4}\\) yellow. The rest of each scarf has an equal amount of white and blue.
              \n\"Envision<\/p>\n

              \"\"
              \nQuestion 3.
              \nDescribe how Amanda could make the argument that her scarf has the most yellow.
              \nAnswer:
              \nAs per the above mathematical calculations
              \n\\(\\frac{15}{40}\\) > \\(\\frac{5}{40}\\) white and \\( \\frac{5}{40} blue \\)
              \nAmanda argument is correct, her scarf has the most yellow<\/p>\n

              Question 4.
              \nHow much of Dena’s scarf is blue?
              \nAnswer:
              \nDena’s scarf is \\(\\frac{2}{5}\\)\u00a0 or \\(\\frac{16}{40}\\) blue.<\/p>\n

              Question 5.
              \nDena has a scarf at home that is the same size as the scarf she made in the club. The scarf at home is \\(\\frac{6}{8}\\) yellow. Dena said the scarf at home has more yellow. Is she correct? Explain. Include an explanation of how you make the comparison.
              \nAnswer:
              \nYES, Dena is correct.
              \nExplanation:
              \nThe denominators are made common by multiplying with same number, as shown below
              \n\"\"<\/p>\n

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

              Performance Task<\/strong>
              \nSnail Race Mr. Aydin’s science class had a snail race to see which snail would crawl the farthest from a starting line in two minutes. The table shows the distances the snails crawled.
              \n\"Envision<\/p>\n

              Question 6.
              \nUse Appropriate Tools Curly and Stylo traveled the same distance. Justify this conjecture using a number line or fraction strips.
              \nAnswer:
              \nYes, Curly and Stylo traveled the same distance.<\/p>\n

              \\(\\frac{12}{60}\\) = \\(\\frac{12}{60}\\)
              \n\\(\\frac{1}{5}\\) = \\(\\frac{2}{10}\\)
              \n\"\"<\/p>\n

              Question 7.
              \nConstruct Arguments<\/strong> who traveled farther, Slimy or Slinky? Change the fractions to have the same denominator.
              \n\"Envision
              \nAnswer:
              \nSlimy traveled farther
              \n\\(\\frac{15}{60}\\) > \\(\\frac{10}{60}\\)<\/p>\n

              Question 8.
              \nReasoning<\/strong> Who traveled farther, Creeper or Slimy? Change the fractions to have the same numerator.
              \nAnswer:
              \nCreeper travelled farther.
              \n\\(\\frac{20}{60}\\) > \\(\\frac{15}{60}\\)<\/p>\n

              Question 9.
              \nMake Sense and Persevere Who won the race?
              \nAnswer:
              \nCreeper won the race.<\/p>\n

              Topic 8 Fluency Practice Activity<\/h3>\n

              Point & Tally<\/strong>
              \nFind a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue.<\/p>\n

              Partner 1 and Partner 2 each point to a black number at the same time. Each partner subtracts the two numbers.<\/p>\n

              If the answer is on your color, you get a tally mark. Work until one partner has twelve tally marks.
              \nI can … subtract multi-digit whole numbers.
              \n\"Envision<\/p>\n

              Answer:
              \nLet partner one choose light blue,
              \nLet partner two choose dark blue.
              \nNow partner one and partner two choose a black number from the columns at the same time.
              \nNow subtract the chosen numbers.
              \n\"\"<\/p>\n

              \"\"<\/h3>\n

              Topic 8 Vocabulary Review<\/h3>\n

              Understand Vocabulary
              \nWord List<\/p>\n

                \n
              • benchmark fraction<\/li>\n
              • common factor<\/li>\n
              • denominator<\/li>\n
              • equivalent fractions<\/li>\n
              • fraction<\/li>\n
              • numerator<\/li>\n<\/ul>\n

                Choose the best term from the box. Write it on the blank.
                \nQuestion 1.
                \nA number that names part of a whole, part of a set, or a location on a number line is a(n) ___________
                \nAnswer:
                \nFraction.<\/p>\n

                Question 2.
                \nA commonly used fraction that helps you understand a different size or amount is called a(n) ___________
                \nAnswer:
                \nBenchmark Fraction.<\/p>\n

                Question 3.
                \nThe number below the fraction bar in a fraction that shows the total number of equal parts is the ___________
                \nAnswer:
                \nDenominator.<\/p>\n

                Question 4.
                \nFractions that name the same part of a whole or the same location on a number line are called ____________
                \nAnswer:
                \nEquivalent Fractions.<\/p>\n

                Question 5.
                \nThe number above the fraction bar that represents part of the whole is called a(n) ____________
                \nAnswer:
                \nNumerator.<\/p>\n

                For each of these terms, give an example and a non-example.
                \n\"Envision
                \nAnswer:
                \n\"\"<\/p>\n

                Use Vocabulary in Writing<\/strong>
                \nQuestion 9.
                \nExplain how to compare \\(\\frac{5}{8}\\) and \\(\\frac{3}{8}\\). Use at least 3 terms from the Word List in your explanation.
                \nAnswer:
                \n\\(\\frac{5}{8}\\) and \\(\\frac{3}{8}\\)
                \nExplanation:
                \nFirst the denominators are compared, both the fraction must be of same denominator then numerators are compared.
                \nhere in the given fractions, numerator 5 is greater then the 3.
                \n\\(\\frac{5}{8}\\) > \\(\\frac{3}{8}\\)<\/p>\n

                Topic 8 Reteaching<\/h3>\n

                Set A pages 293-300<\/strong><\/p>\n

                Use an area model to write an equivalent fraction for \\(\\frac{1}{2}\\).
                \n\"Envision
                \n\\(\\frac{1}{2}\\) and \\(\\frac{3}{6}\\)name the same part of the whole.
                \n\\(\\frac{1}{2}\\) and \\(\\frac{3}{6}\\) are equivalent fractions.
                \nUse a number line to write an equivalent fraction for \\(\\frac{1}{3}\\).
                \n\"Envision
                \n\\(\\frac{1}{3}\\) and \\(\\frac{2}{6}\\) name the same part of the whole.
                \n\\(\\frac{1}{3}\\) and \\(\\frac{2}{6}\\) are equivalent fractions.<\/p>\n

                Remember<\/strong> that equivalent fractions name the same part of a whole.<\/p>\n

                Write an equivalent fraction for each fraction given.
                \nQuestion 1.
                \n\\(\\frac{2}{8}\\)
                \nAnswer:
                \n\\(\\frac{1}{4}\\)
                \nExplanation:
                \nBy dividing the fraction with the common factor [2] we get:
                \n2 \u00f7 2 = 1
                \n8 \u00f7 2 = 4
                \nso we get an equivalent fraction \\(\\frac{1}{4}\\)<\/p>\n

                Question 2.
                \n\\(\\frac{2}{3}\\)
                \nAnswer:
                \n\\(\\frac{4}{6}\\)<\/p>\n

                Explanation:
                \nBy multiplying the fraction with the common factor [2] we get:
                \n2 X 2 = 4
                \n2 X 3 = 6
                \nso we get an equivalent fraction \\(\\frac{4}{6}\\)<\/p>\n

                Question 3.
                \n\\(\\frac{1}{4}\\)
                \nAnswer:
                \n\\(\\frac{2}{8}\\)
                \nExplanation:
                \nBy dividing the fraction with the common factor [2] we get:
                \n2\u00f7 2 = 1
                \n8\u00f7 2 = 4
                \nso we get an equivalent fraction \\(\\frac{2}{8}\\)<\/p>\n

                Question 4.
                \n\\(\\frac{3}{4}\\)
                \nAnswer:
                \n\\(\\frac{9}{12}\\)<\/p>\n

                Draw a number line to shown each fraction and an equivalent fraction.
                \nQuestion 5.
                \n\\(\\frac{4}{6}\\)
                \nAnswer:
                \n\\(\\frac{2}{3}\\)
                \nExplanation:
                \n\"\"<\/p>\n

                Question 6.
                \n\\(\\frac{4}{10}\\)
                \nAnswer:
                \n\\(\\frac{2}{5}\\)
                \nExplanation:
                \n\"\"<\/p>\n

                Set B pages 301-308<\/strong><\/p>\n

                Find two equivalent fractions for \\(\\frac{1}{2}\\).
                \n\\(\\frac{1}{2} \\times \\frac{2}{2}=\\frac{2}{4} \\quad \\frac{1}{2} \\times \\frac{3}{3}=\\frac{3}{6}\\)
                \n\\(\\frac{1}{2}, \\frac{2}{4}\\), and \\(\\frac{3}{6}\\) are equivalent fractions.
                \nFind two equivalent fractions for \\(\\frac{8}{12}\\).
                \n\\(\\frac{8}{12} \\div \\frac{2}{2}=\\frac{4}{6} \\quad \\frac{8}{12} \\div \\frac{4}{4}=\\frac{2}{3}\\)
                \n\\(\\frac{8}{12}, \\frac{4}{6}\\), and \\(\\frac{2}{3}\\) are equivalent fractions.<\/p>\n

                Remember<\/strong> that you can multiply or divide to find equivalent fractions.<\/p>\n

                Multiply or divide to find equivalent fractions.
                \nQuestion 1.
                \n\\(\\frac{2}{3}=\\frac{8}{}\\)
                \nAnswer:
                \n\\(\\frac{8}{12}\\)
                \nExplanation:
                \nMultiply the given fraction with common factor 4, then
                \n\\(\\frac{2}{3}\u00d7\\frac{4}{4}=\\frac{8}{12}\\)<\/p>\n

                Question 2.
                \n\\(\\frac{1}{4}=\\frac{}{8}\\)
                \nAnswer:
                \n\\(\\frac{2}{8}\\)
                \nExplanation:
                \nMultiply numerattor and denominator with common factor 2, then
                \n\\(\\frac{1}{4}\u00d7\\frac{2}{2}=\\frac{2}{8}\\)<\/p>\n

                Question 3.
                \n\\(\\frac{1}{6}=\\frac{2}{}\\)
                \nAnswer:
                \n\\(\\frac{2}{12}\\)
                \nExplanation:
                \nMultiply numerator and denominator with common factor in numerator and denominator then,
                \n\\(\\frac{1}{6}\u00d7\\frac{2}{2}=\\frac{2}{12}\\)<\/p>\n

                Question 4.
                \n\\(\\frac{3}{5}=\\frac{}{10}\\)
                \nAnswer:
                \n\\(\\frac{6}{10}\\)
                \nExplanation:
                \nMultiply numerator and denominator with common factor 2 then,
                \n\\(\\frac{3}{5}\u00d7\\frac{2}{2}=\\frac{6}{10}\\)<\/p>\n

                Question 5.
                \n\\(\\frac{10}{12}=\\frac{5}{}\\)
                \nAnswer:
                \n\\(\\frac{5}{6}\\)
                \nExplanation:
                \nDivide numerator and denominator with common factor 2, then
                \n\\(\\frac{10}{12}\u00f7\\frac{2}{2}=\\frac{5}{6}\\)<\/p>\n

                Question 6.
                \n\\(\\frac{4}{10}=\\frac{}{5}\\)
                \nAnswer:
                \n\\(\\frac{2}{5}\\)
                \nExplanation:
                \nDivide numerator and denominator with common factor 2, then
                \n\\(\\frac{4}{10}\u00f7\\frac{2}{2}=\\frac{2}{5}\\)<\/p>\n

                Question 7.
                \n\\(\\frac{2}{6}=\\frac{1}{}\\)
                \nAnswer:
                \n\\(\\frac{1}{3}\\)
                \nExplanation:
                \nDivide numerator and denominator with common factor 2, then
                \n\\(\\frac{2}{6}\u00f7\\frac{2}{2}=\\frac{1}{3}\\)<\/p>\n

                Question 8.
                \n\\(\\frac{6}{10}=\\frac{}{5}\\)
                \nAnswer:
                \n\\(\\frac{3}{5}\\)
                \nExplanation:
                \nDivide numerator and denominator with common factor 2, then
                \n\\(\\frac{6}{10}\u00f7\\frac{2}{2}=\\frac{3}{5}\\)<\/p>\n

                Set C pages 309-316<\/strong><\/p>\n

                Compare \\(\\frac{5}{8}\\) and \\(\\frac{4}{10}\\). Use benchmark fractions.
                \n\"Envision<\/p>\n

                Remember<\/strong> when the numerators of two fractions are the same, the fraction with the lesser denominator is greater.<\/p>\n

                Use benchmark fractions to compare. Write >, <, or = for each \"Envision.
                \nQuestion 1.
                \n\\(\\frac{5}{5}\\) \"Envision \\(\\frac{4}{6}\\)
                \nAnswer:
                \n\\(\\frac{5}{5}\\) >\u00a0\\(\\frac{4}{6}\\)
                \nExplanation:
                \nMultiply the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{5}{5}\\) \u00d7 \\(\\frac{6}{6}\\) = \\(\\frac{30}{30}\\)
                \n\\(\\frac{4}{6}\\) \u00d7\u00a0\\(\\frac{5}{5}\\) = \\(\\frac{20}{30}\\)<\/p>\n

                \\(\\frac{30}{30}\\) > \\(\\frac{20}{30}\\)
                \nSo, \\(\\frac{5}{5}\\) > \\(\\frac{4}{6}\\)<\/p>\n

                Question 2.
                \n\\(\\frac{4}{8}\\) \"Envision \\(\\frac{1}{2}\\)
                \nAnswer:
                \n\\(\\frac{4}{8}\\) = \\(\\frac{1}{2}\\)<\/p>\n

                Explanation:
                \nDivide the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{4}{8}\\) \u00f7 \\(\\frac{4}{4}\\) = \\(\\frac{1}{2}\\)
                \n\\(\\frac{1}{2}\\) \u00f7 \\(\\frac{1}{1}\\) = \\(\\frac{1}{2}\\)<\/p>\n

                So \\(\\frac{4}{8}\\) = \\(\\frac{1}{2}\\)<\/p>\n

                Question 3.
                \n\\(\\frac{5}{12}\\) \"Envision \\(\\frac{7}{8}\\)
                \nAnswer:<\/p>\n

                \\(\\frac{5}{12}\\) <\u00a0\\(\\frac{7}{8}\\)<\/p>\n

                Explanation:<\/p>\n

                Multiply the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{5}{12}\\) \u00d7 \\(\\frac{2}{2}\\) = \\(\\frac{10}{24}\\)
                \n\\(\\frac{7}{8}\\) \u00d7 \\(\\frac{3}{3}\\) = \\(\\frac{21}{24}\\)<\/p>\n

                \\(\\frac{10}{24}\\) < \\(\\frac{21}{24}\\)
                \nSo, \\(\\frac{5}{12}\\) < \\(\\frac{7}{8}\\)<\/p>\n

                Question 4.
                \n\\(\\frac{2}{3}\\) \"Envision \\(\\frac{4}{6}\\)
                \nAnswer:
                \n\\(\\frac{2}{3}\\) = \\(\\frac{4}{6}\\)<\/p>\n

                Explanation:<\/p>\n

                Divide the fractions on both sides with common number to get same denominator, then compare the numerator<\/p>\n

                \\(\\frac{2}{3}\\) \u00f7 \\(\\frac{1}{1}\\) = \\(\\frac{2}{3}\\)
                \n\\(\\frac{4}{6}\\) \u00f7 \\(\\frac{2}{2}\\) = \\(\\frac{2}{3}\\)
                \n\\(\\frac{2}{3}\\) = \\(\\frac{4}{6}\\)<\/p>\n

                Compare. Write >, <, or = for each \"Envision.
                \nQuestion 5.
                \n\\(\\frac{3}{4}\\) \"Envision \\(\\frac{5}{8}\\)
                \nAnswer:
                \n\\(\\frac{3}{4}\\) >\u00a0\\(\\frac{5}{8}\\)
                \nExplanation:
                \nMultiply\u00a0 the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{2}{2}\\) = \\(\\frac{6}{8}\\)
                \n\\(\\frac{5}{8}\\) \u00d7 \\(\\frac{1}{2}\\) = \\(\\frac{5}{8}\\)
                \n\\(\\frac{3}{4}\\) > \\(\\frac{8}{6}\\)<\/p>\n

                Question 6.
                \n\\(\\frac{1}{5}\\) \"Envision \\(\\frac{2}{10}\\)
                \nAnswer:
                \n\\(\\frac{1}{5}\\)\u00a0 = \\(\\frac{2}{10}\\)
                \nExplanation:
                \nMultiply the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{1}{5}\\) \u00d7 \\(\\frac{2}{2}\\) = \\(\\frac{2}{10}\\)
                \n\\(\\frac{2}{10}\\) \u00d7 \\(\\frac{1}{1}\\) = \\(\\frac{2}{10}\\)
                \n\\(\\frac{1}{5}\\) = \\(\\frac{2}{10}\\)<\/p>\n

                Question 7.
                \n\\(\\frac{2}{5}\\) \"Envision \\(\\frac{1}{4}\\)
                \nAnswer:
                \n\\(\\frac{2}{5}\\) >\u00a0\\(\\frac{1}{4}\\)
                \nExplanation:
                \nMultiply the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{2}{5}\\) \u00d7 \\(\\frac{4}{4}\\) = \\(\\frac{8}{20}\\)
                \n\\(\\frac{1}{4}\\) \u00d7 \\(\\frac{5}{5}\\) = \\(\\frac{5}{120}\\)
                \n\\(\\frac{2}{5}\\) = \\(\\frac{1}{4}\\)<\/p>\n

                Question 8.
                \n\\(\\frac{3}{6}\\) \"Envision \\(\\frac{3}{4}\\)
                \nAnswer:
                \n\\(\\frac{3}{6}\\) <\u00a0\\(\\frac{3}{4}\\)
                \nExplanation:
                \nMultiply the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{3}{6}\\) \u00d7 \\(\\frac{2}{2}\\) = \\(\\frac{6}{12}\\)
                \n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{3}{3}\\) = \\(\\frac{9}{12}\\)
                \n\\(\\frac{3}{6}\\) < \\(\\frac{3}{4}\\)<\/p>\n

                Question 9.
                \n\\(\\frac{2}{4}\\) \"Envision \\(\\frac{2}{3}\\)
                \nAnswer:
                \n\\(\\frac{2}{4}\\) <\u00a0\\(\\frac{2}{3}\\)
                \nExplanation:
                \nMultiply the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{2}{4}\\) \u00d7 \\(\\frac{3}{3}\\) = \\(\\frac{6}{12}\\)
                \n\\(\\frac{2}{3}\\) \u00d7 \\(\\frac{4}{4}\\) = \\(\\frac{8}{12}\\)
                \n\\(\\frac{2}{4}\\) < \\(\\frac{2}{3}\\)<\/p>\n

                Question 10.
                \n\\(\\frac{8}{10}\\) \"Envision \\(\\frac{4}{6}\\)
                \nAnswer:
                \n\\(\\frac{8}{10}\\) >\\(\\frac{4}{6}\\)
                \nExplanation:
                \nMultiply the fractions on both sides with common number to get same denominator, then compare the numerator
                \n\\(\\frac{8}{10}\\) \u00d7 \\(\\frac{6}{6}\\) = \\(\\frac{48}{60}\\)
                \n\\(\\frac{4}{6}\\) \u00d7 \\(\\frac{10}{10}\\) = \\(\\frac{40}{60}\\)
                \n\\(\\frac{8}{10}\\) > \\(\\frac{4}{6}\\)<\/p>\n

                Set D pages 317-320<\/strong><\/p>\n

                Think about these questions to help you construct arguments.
                \nThinking Habits<\/p>\n

                  \n
                • How can I use numbers, objects, drawings, or actions to justify my argument?<\/li>\n
                • Am I using numbers and symbols correctly?<\/li>\n
                • Is my explanation clear and complete?
                  \n\"Envision<\/li>\n<\/ul>\n

                  Remember<\/strong> you can use drawings and numbers to construct arguments.<\/p>\n

                  Peter says \\(\\frac{3}{4}\\) of a pizza is always the same as of a pizza. Nadia says while \\(\\frac{3}{4}\\) and \\(\\frac{6}{8}\\) are equivalent fractions, \\(\\frac{3}{4}\\) and \\(\\frac{6}{8}\\) of a pizza could represent different amounts.
                  \nQuestion 1.
                  \nWho is correct? Explain. Use a drawing to justify your argument.
                  \nAnswer:
                  \nNadia is correct
                  \n\\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\)
                  \nExplanation:
                  \n\"\"<\/p>\n

                  Question 2.
                  \nUse a counter example to explain who is correct.
                  \nAnswer:
                  \n\\(\\frac{1}{2}\\) = \\(\\frac{2}{4}\\)
                  \n\"\"<\/p>\n

                  Topic 8 Assessment Practice<\/h3>\n

                  Question 1.
                  \nDraw a model to show that \\(\\frac{3}{4}=\\frac{6}{8}\\).
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Question 2.
                  \nLeslie will use more than \\(\\frac{1}{2}\\) cup but less than 1 whole cup of flour for a recipe. What fraction of a cup might Leslie use? Explain.
                  \nAnswer:
                  \n\\(\\frac{3}{4}\\)
                  \n\\(\\frac{1}{2}\\) < \\(\\frac{3}{4}\\) < 1
                  \nExplanation:
                  \nLeslie use \\(\\frac{3}{4}\\) cup of flour
                  \n\"\"<\/p>\n

                  Question 3.
                  \nJared has mowed \\(\\frac{2}{5}\\) of the yard. Abby says that Jared has mowed \\(\\frac{4}{6}\\) of the yard. Is Abby correct? Explain.
                  \nAnswer:
                  \nNo, Abby is wrong.
                  \nExplanation:
                  \n\\(\\frac{2}{5}\\) and \\(\\frac{4}{6}\\) are not equivalent fractions
                  \n\"\"<\/p>\n

                  Question 4.
                  \nExplain how to use division to find an equivalent fraction for \\(\\frac{9}{12}\\).
                  \nAnswer:
                  \n\\(\\frac{3}{4}\\) is an equivalent fraction for \\(\\frac{9}{12}\\).
                  \nExplanation:
                  \nDivide both numerator and denominator with common factor 3, then
                  \n\\(\\frac{9}{12}\u00f7\\frac{3}{3}=\\frac{3}{4}\\)<\/p>\n

                  Question 5.
                  \nWrite two fractions that are equivalent to \\(\\frac{3}{6}\\). Describe how you can show they are equivalent.
                  \nAnswer:
                  \n\\(\\frac{1}{2}\\) and \\(\\frac{6}{12}\\) are two equivalent fractions of \\(\\frac{3}{6}\\)
                  \nExplanation
                  \n\"\"<\/p>\n

                  Question 6.
                  \nCompare the fractions to \\(\\frac{1}{2}\\). Write each fraction in the correct answer space.
                  \n\"Envision
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Question 7.
                  \nSarah and Cole both ordered large subs for lunch. Sarah had \\(\\frac{1}{2}\\) of a sub and Cole had \\(\\frac{2}{5}\\) of a sub. Who ate more? Explain.
                  \nA. The subs are different sizes, so it is impossible to compare the fractions and tell who ate more.
                  \nB. Sarah ate more than Cole, as \\(\\frac{2}{5}\\) < \\(\\frac{1}{2}\\).
                  \nC. Sarah’s sub was bigger than Cole’s, so Sarah ate more.
                  \nD. They ate the same amount because \\(\\frac{1}{2}\\) is the same as \\(\\frac{2}{4}\\).
                  \nAnswer:
                  \nOption B
                  \nExplanation:
                  \n\\(\\frac{2}{5}\u00d7\\frac{2}{2}\\) < \\(\\frac{1}{2}\u00d7\\frac{5}{5}\\)<\/p>\n

                  \\(\\frac{4}{10}\\) < \\(\\frac{5}{10}\\).<\/p>\n

                  \\(\\frac{2}{5}\\) < \\(\\frac{1}{2}\\) is correct<\/p>\n

                  Question 8.
                  \nThe Sahas were reading a best-selling novel as a family. After the first week, they checked in with each other to see how much of the book each had read.
                  \n\"Envision
                  \nA. Who read the greatest fraction of the book?
                  \nAnswer:
                  \nMaddie read the greatest fraction of the book
                  \nExplanation:
                  \nApply division rule
                  \n\\(\\frac{3}{4}\\) = 0.7
                  \nWhen compared with others Maddie read more.<\/p>\n

                  B. Name the two family members who read the same fraction of the book. Explain.
                  \nAnswer:
                  \nMr Saha and Mrs Saha read the same fraction of the book
                  \n\\(\\frac{2}{6}\\) = \\(\\frac{1}{3}\\)
                  \nExplanation:
                  \nApply division rule
                  \n\\(\\frac{3}{4}\\) = 0.7
                  \n\\(\\frac{1}{3}\\) = 0.3<\/p>\n

                  Question 9.
                  \nJohnny found a fraction equivalent to the one shown by the point on the number line. Which fraction could Johnny have found? Explain.
                  \n\"Envision
                  \nAnswer:
                  \nOption C
                  \nExplanation:
                  \n\\(\\frac{1}{2}\\) = \\(\\frac{4}{8}\\).
                  \n\"\"<\/p>\n

                  Question 10.
                  \nBill and Gina each ate \\(\\frac{1}{2}\\) of their own pizza. Bill ate more pizza than Gina. Draw a picture and explain how that is possible.
                  \nAnswer:
                  \nBill pizza is bigger in size
                  \n\"\"
                  \nExplanation:
                  \nAs the sizes of pizza are different.
                  \nSo, Bill ate more.<\/p>\n

                  Question 11.
                  \nOrder \\(\\frac{1}{2}\\), from least to greatest.
                  \nAnswer:<\/p>\n

                  Question 12.
                  \nOnly one of the comparisons below is correct. Which is correct? What benchmark was used to check your answer?
                  \nA. \\(\\frac{2}{3}\\) < \\(\\frac{1}{2}\\); I used \\(\\frac{1}{2}\\) as a benchmark.
                  \nB. \\(\\frac{1}{2}\\) = \\(\\frac{3}{5}\\); I used \\(\\frac{1}{4}\\) as a benchmark.
                  \nC. \\(\\frac{2}{3}\\) < \\(\\frac{9}{10}\\); I used \\(\\frac{3}{4}\\) as a benchmark.
                  \nD. \\(\\frac{3}{4}\\) < \\(\\frac{2}{3}\\); I used \\(\\frac{1}{2}\\) as a benchmark.
                  \nAnswer:
                  \nOption C
                  \n\\(\\frac{2}{3}\\) < \\(\\frac{9}{10}\\); I used \\(\\frac{3}{4}\\) as a benchmark.<\/p>\n

                  Question 13.
                  \nDraw a model to compare \\(\\frac{1}{3}\\) and \\(\\frac{3}{5}\\).
                  \nAnswer:
                  \n\"\"
                  \n\\(\\frac{1}{3}\u00d7\\frac{5}{5}\\)\u00a0 and\u00a0 \\(\\frac{3}{5}\u00d7\\frac{3}{3}\\)<\/p>\n

                  Explanation:
                  \nFrist the denominators are multiplied with common number to get same denominator for the both the fractions such that they can compare each other, as shown below
                  \n\\(\\frac{5}{15}\\)\u00a0 and\u00a0 \\(\\frac{9}{15}\\)<\/p>\n

                  Topic 8 Performance Task<\/h3>\n

                  Comparing Grasshoppers<\/strong>
                  \nMrs. Rakin’s class measured the lengths of some grasshoppers. The Grasshopper Lengths table shows the lengths they found.
                  \n\"Envision
                  \n\"\"
                  \nQuestion 1.
                  \nMrs. Rakin asked the students to choose two grasshoppers and compare their lengths.
                  \nPart A
                  \nHenry used benchmark fractions to compare the lengths of grasshoppers A and C. Which grasshopper is longer? Explain.
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Explanation:
                  \nBy using above benchmark number line. Grasshopper F is nearer to 0 and C too far to 0, that means F is smaller and C is bigger in size.
                  \n\\(\\frac{3}{8}\\) < \\(\\frac{14}{8}\\)<\/p>\n

                  Part B
                  \nRiley used a number line to compare the lengths of grasshoppers A and E. Which grasshopper is longer? Use the number line to show the comparison.
                  \n\"Envision
                  \nAnswer:
                  \n\"\"<\/p>\n

                  Part C
                  \nJack compared the lengths of grasshoppers D and E. He said grasshopper D is longer. Is Jack correct? Justify the comparison using fraction strips.
                  \nAnswer:
                  \nYES, Jack is correct.
                  \nGrasshopper D is longer
                  \n\\(\\frac{7}{8}\\) > \\(\\frac{6}{8}\\)
                  \nExplanation:
                  \nAs denominators are same numerators are compared to find the longer one.
                  \nSo, \\(\\frac{7}{8}\\) > \\(\\frac{6}{8}\\)<\/p>\n

                  Question 2.
                  \nOne group of students measured the lengths of grasshoppers in centimeters, instead of inches. The More Grasshopper Lengths table shows the lengths they found.
                  \n\"Envision
                  \nPart A
                  \nTommy compared the lengths of grasshoppers G and H. Which grasshopper is longer? Explain how to rename the fractions using multiplication so they have the same denominator to compare.
                  \nAnswer:
                  \nH is longer
                  \nI < G < H
                  \n\\(\\frac{6}{10} < \\frac{7}{10} < \\frac{8}{10}\\)
                  \nExplanation:
                  \nAs denominators are same numerators are compared to find the longer one.
                  \nSo, \\(\\frac{6}{10} < \\frac{7}{10} < \\frac{8}{10}\\)<\/p>\n

                  Part B
                  \nVenon compared the lengths of grasshoppers Hand I. Which grasshopper is longer? Explain how to rename the fractions using division so they have the same denominator to compare.
                  \nAnswer:
                  \nGrasshopper G is longer.
                  \n\\(\\frac{6}{10} < \\frac{7}{10} < \\frac{4}{5}\\)
                  \nExplanation:<\/p>\n\\(\\frac{6}{10}\u00f7\\frac{2}{2} < \\frac{7}{10} \u00f7\\frac{2}{2} < \\frac{4}{5}\\)\n

                   <\/p>\n\\(\\frac{30}{50} < \\frac{35}{50} < \\frac{40}{50}\\)\n

                  Part C
                  \nRina wants to determine if grasshopper D is longer or shorter than grasshopper G. Explain how Rina can compare the fractions.
                  \nAnswer:<\/p>\n

                  D = \\(\\frac{7}{8}\\)<\/p>\n

                  G = \\(\\frac{7}{10}\\)
                  \nExplanation:<\/p>\n

                  \\(\\frac{7}{8}\\) > \\(\\frac{7}{10}\\)<\/p>\n

                  \\(\\frac{7}{8}\u00d7\\frac{10}{10}\\) > \\(\\frac{7}{10}\u00d7\\frac{8}{8}\\)<\/p>\n

                  \\(\\frac{70}{80}\\) > \\(\\frac{56}{80}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"

                  Go through the\u00a0enVision Math Common Core Grade 4 Answer Key\u00a0Topic 8 Extend Understanding of Fraction Equivalence and Ordering\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 4th Grade Answers Key Topic 8 Extend Understanding of Fraction Equivalence and Ordering Essential Questions: What are some ways to name the same part of a …<\/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\/12600"}],"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=12600"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/12600\/revisions"}],"predecessor-version":[{"id":27980,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/12600\/revisions\/27980"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=12600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=12600"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=12600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}