{"id":11697,"date":"2023-12-12T13:30:12","date_gmt":"2023-12-12T08:00:12","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=11697"},"modified":"2023-12-13T15:57:59","modified_gmt":"2023-12-13T10:27:59","slug":"envision-math-common-core-grade-4-answer-key-topic-10","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-4-answer-key-topic-10\/","title":{"rendered":"enVision Math Common Core Grade 4 Answer Key Topic 10 Extend Multiplication Concepts to Fractions"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 4 Answer Key<\/a>\u00a0Topic 10 Extend Multiplication Concepts to Fractions<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 4th Grade Answers Key Topic 10 Extend Multiplication Concepts to Fractions<\/h2>\n

Essential Questions:<\/strong>
\nHow can you describe a fraction using a unit fraction? How can you multiply a fraction by a whole number?
\nAnswer:
\nA fraction can be converted into a unit fraction as explained below:
\nPut the whole number over 1 to turn it into a fraction.
\nEx:
\nThe whole number is: 5
\nThe conversion of 5 into a unit fraction is: \\(\\frac{1}{5}\\)
\nA fraction can be multiplied by a whole number as explained below:
\nStep 1:
\nMultiply across the top number by top number (numerator) and bottom number by bottom number (denominator).
\nStep 2:
\nSimplify your answer by dividing both numerator and denominator by the same number, when applicable.\"Envision<\/p>\n

enVision STEM Project: Light and Multiplication<\/strong>
\nDo Research<\/strong>
\nUse the Internet or other sources to research the words transparent, translucent, and opaque? Write a definition for each word.
\nAnswer:
\nTransparent:
\nIf any material allows all light to pass through it, then it is called “Transparent”
\nTranslucent:
\nIf any material allows some light to pass through it, then it is called “Translucent”
\nOpaque:
\nWhen any material allows no light to pass through it, then it is called “Opaque”<\/p>\n

Journal<\/strong>: Write a Report<\/strong>
\nInclude what you found. Also in your report:
\nPART A:
\nList 1 example of each of the items that are transparent, translucent, or opaque.
\nAnswer:
\nExamples of Transparent items are:
\na. Clean glass
\nb. Water
\nc. Air
\nExamples of Translucent items are:
\na. Frosted glass
\nb. Wax paper
\nc. Smoke
\nd Butter paper
\nExamples of Opaque items are:
\na. Stone
\nb. Metal
\nc. Wood<\/p>\n

PART B:
\nSuppose one-third of each of 5 same-sized posters is covered with opaque paper. What fraction of the posters are not covered by opaque paper? Explain how to use multiplication to find what parts of the posters are not covered by opaque paper?
\nAnswer:
\nIt is given that
\nOne-third of each of 5 same-sized posters is covered with opaque paper
\nNow,
\nThe representation of the 5 same-sized posters with opaque paper is:
\n\"\"
\nNow,
\nFrom the given figure,
\nWe can observe that
\nThe total number of parts are: 5
\nThe number of parts covered with opaque paper is: 3
\nThe number of parts that are not covered with opaque paper is: 2
\nNow,
\nThe fraction of the posters that are covered by the opaque paper = \\(\\frac{The number of parts that are covered with opaque paper}{The total number of parts}\\)
\n= \\(\\frac{3}{5}\\)
\nSo,
\nThe fraction of the posters that are not covered by the opaque paper = \\(\\frac{The number of parts that\u00a0 are not covered with opaque paper}{The total number of parts}\\)
\n= \\(\\frac{2}{5}\\)
\nHence, from the above,
\nWe can conclude that
\nThe fraction of the posters that are not covered by the opaque paper is: \\(\\frac{2}{5}\\)<\/p>\n

\"Extend<\/p>\n

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

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

    \n
  • equivalent fractions<\/li>\n
  • mixed number<\/li>\n
  • fraction<\/li>\n
  • whole number<\/li>\n<\/ul>\n

    Choose the best term from the box. Write it on the blank.
    \nQuestion 1.
    \nA _________ has a whole number and a fraction.
    \nAnswer:
    \nWe know that,
    \nA “Mixed number” has a whole number and a fraction.
    \nHence, from the above,
    \nWe can conclude that
    \nThe best term that is suitable for the given sentence is: Mixed number<\/p>\n

    Question 2.
    \nFractions that name the same region, part of a set or part of a segment are called __________
    \nAnswer:
    \nWe know that,
    \nFractions that name the same region, part of a set, or part of a segment are called “Equivalent fractions”
    \nHence, from the above,
    \nWe can conclude that
    \nThe best term that is suitable for the given sentence is: Equivalent fractions<\/p>\n

    Question 3.
    \nA _________ has a numerator and a denominator.
    \nAnswer:
    \nWe know that,
    \nA “Fraction” has a numerator and a denominator
    \nHence, from the above,
    \nWe can conclude that
    \nThe best term that is suitable for the given sentence is: Fraction<\/p>\n

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

    Write the fraction shown by each model.
    \nQuestion 4.
    \n\"Envision
    \nAnswer:
    \nThe given model is:
    \n\"Envision
    \nNow,
    \nFrom the given model,
    \nThe total number of parts are: 4
    \nThe shaded part is: 1
    \nSo,
    \nThe fraction represented by the given model = \\(\\frac{The shaded part}{The total number of parts}\\)
    \n= \\(\\frac{1}{4}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe fraction represented by the given model is: \\(\\frac{1}{4}\\)<\/p>\n

    Question 5.
    \n\"Envision
    \nAnswer:
    \nThe given model is:
    \n\"Envision
    \nNow,
    \nFrom the given model,
    \nThe total number of parts are: 3
    \nThe shaded part is: 2
    \nSo,
    \nThe fraction represented by the given model = \\(\\frac{The shaded part}{The total number of parts}\\)
    \n= \\(\\frac{2}{3}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe fraction represented by the given model is: \\(\\frac{2}{3}\\)<\/p>\n

    Question 6.
    \n\"Envision
    \nAnswer:
    \nThe given model is:
    \n\"Envision
    \nNow,
    \nFrom the given model,
    \nThe total number of parts are: 8
    \nThe shaded part is: 5
    \nSo,
    \nThe fraction represented by the given model = \\(\\frac{The shaded part}{The total number of parts}\\)
    \n= \\(\\frac{5}{8}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe fraction represented by the given model is: \\(\\frac{5}{8}\\)<\/p>\n

    \"Extend<\/p>\n

    Question 7.
    \n\"Envision
    \nAnswer:
    \nThe given model is:
    \n\"Envision
    \nNow,
    \nFrom the given model,
    \nThe total number of parts are: 5
    \nThe shaded part is: 1
    \nSo,
    \nThe fraction represented by the given model = \\(\\frac{The shaded part}{The total number of parts}\\)
    \n= \\(\\frac{1}{5}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe fraction represented by the given model is: \\(\\frac{1}{5}\\)<\/p>\n

    Question 8.
    \n\"Envision
    \nAnswer:
    \nThe given model is:
    \n\"Envision
    \nNow,
    \nFrom the given model,
    \nThe total number of parts are: 10
    \nThe shaded part is: 5
    \nSo,
    \nThe fraction represented by the given model = \\(\\frac{The shaded part}{The total number of parts}\\)
    \n= \\(\\frac{5}{10}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe fraction represented by the given model is: \\(\\frac{5}{10}\\)<\/p>\n

    Question 9.
    \n\"Envision
    \nAnswer:
    \nThe given model is:
    \n\"Envision
    \nNow,
    \nFrom the given model,
    \nThe total number of parts are: 2
    \nThe shaded part is: 1
    \nSo,
    \nThe fraction represented by the given model = \\(\\frac{The shaded part}{The total number of parts}\\)
    \n= \\(\\frac{1}{2}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe fraction represented by the given model is: \\(\\frac{1}{2}\\)<\/p>\n

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

    Write a fraction for each statement.
    \nQuestion 10.
    \n3 copies of \\(\\frac{1}{6}\\) is _______.
    \nAnswer:
    \nThe given statement is:
    \n3 copies of \\(\\frac{1}{6}\\)
    \nSo,
    \nThe representation of the given statement is: 3 \u00d7 \\(\\frac{1}{6}\\)
    \nSo,
    \n3 \u00d7 \\(\\frac{1}{6}\\)
    \n= \\(\\frac{3}{6}\\)
    \nHence, from the above,
    \nWe can conclude that the fraction for the given statement is: \\(\\frac{3}{6}\\)<\/p>\n

    Question 11.
    \n9 copies of \\(\\frac{1}{12}\\) is _________
    \nAnswer:
    \nThe given statement is:
    \n9 copies of \\(\\frac{1}{12}\\)
    \nSo,
    \nThe representation of the given statement is: 9 \u00d7 \\(\\frac{1}{12}\\)
    \nSo,
    \n9 \u00d7 \\(\\frac{1}{12}\\)
    \n= \\(\\frac{9}{12}\\)
    \nHence, from the above,
    \nWe can conclude that the fraction for the given statement is: \\(\\frac{9}{12}\\)<\/p>\n

    Question 12.
    \n5 copies of \\(\\frac{1}{5}\\) is ___________
    \nAnswer:
    \nThe given statement is:
    \n5 copies of \\(\\frac{1}{5}\\)
    \nSo,
    \nThe representation of the given statement is: 5 \u00d7 \\(\\frac{1}{5}\\)
    \nSo,
    \n5 \u00d7 \\(\\frac{1}{5}\\)
    \n= \\(\\frac{5}{5}\\)
    \nHence, from the above,
    \nWe can conclude that the fraction for the given statement is: \\(\\frac{5}{5}\\)<\/p>\n

    Question 13.
    \n3 copies of \\(\\frac{1}{10}\\) is _________.
    \nAnswer:
    \nThe given statement is:
    \n3 copies of \\(\\frac{1}{10}\\)
    \nSo,
    \nThe representation of the given statement is: 3 \u00d7 \\(\\frac{1}{10}\\)
    \nSo,
    \n3 \u00d7 \\(\\frac{1}{10}\\)
    \n= \\(\\frac{3}{10}\\)
    \nHence, from the above,
    \nWe can conclude that the fraction for the given statement is: \\(\\frac{3}{10}\\)<\/p>\n

    Question 14.
    \n6 copies of \\(\\frac{1}{8}\\) is _________.
    \nAnswer:
    \nThe given statement is:
    \n6 copies of \\(\\frac{1}{8}\\)
    \nSo,
    \nThe representation of the given statement is: 6 \u00d7 \\(\\frac{1}{8}\\)
    \nSo,
    \n6 \u00d7 \\(\\frac{1}{8}\\)
    \n= \\(\\frac{6}{8}\\)
    \nHence, from the above,
    \nWe can conclude that the fraction for the given statement is: \\(\\frac{6}{8}\\)<\/p>\n

    \"Extend<\/p>\n

    Question 15.
    \n7 copies of \\(\\frac{1}{10}\\) is _________.
    \nAnswer:
    \nThe given statement is:
    \n7 copies of \\(\\frac{1}{10}\\)
    \nSo,
    \nThe representation of the given statement is: 7 \u00d7 \\(\\frac{1}{10}\\)
    \nSo,
    \n7 \u00d7 \\(\\frac{1}{10}\\)
    \n= \\(\\frac{7}{10}\\)
    \nHence, from the above,
    \nWe can conclude that the fraction for the given statement is: \\(\\frac{7}{10}\\)<\/p>\n

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

    Question 16.
    \nDraw a rectangle that shows 8 equal parts. Shade more than \\(\\frac{3}{8}\\) of the rectangle but less than \\(\\frac{5}{8}\\). What fraction did you model? Use multiplication or division to write two equivalent fractions for your model.
    \nAnswer:
    \nIt is given that
    \nDraw a rectangle that shows 8 equal parts. Shade more than \\(\\frac{3}{8}\\) of the rectangle but less than \\(\\frac{5}{8}\\)
    \nNow,
    \nThe representation of the rectangle with the total number of parts and shaded parts is:
    \n\"\"
    \nNow,
    \nFrom the given figure,
    \nWe can observe that
    \nThe total number of parts are: 8
    \nThe number of shaded parts is: 4
    \nThe number of non-shaded parts is: 4
    \nNow,
    \nThe fraction of the shaded part from the model = \\(\\frac{The number of shaded parts}{The total number of parts}\\)
    \n= \\(\\frac{4}{8}\\)
    \n= \\(\\frac{1}{2}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe equivalent fractions of the shaded part for your model are:
    \na. \\(\\frac{4}{8}\\)
    \nb. \\(\\frac{1}{2}\\)<\/p>\n

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

    PROJECT 10A
    \nWould you like to work with tiles?
    \nProject: Design with Tiles
    \n\"Envision<\/p>\n

    PROJECT 10B
    \nWhat cause would you donate your time or money to?
    \nProject: Set Up a Charity Event
    \n\"Envision<\/p>\n

    PROJECT 10C
    \nHow fast can a jet aircraft travel?
    \nProject: Write and Perform a Skit
    \n\"Envision<\/p>\n

    PROJECT 10D
    \nHow would you like to run a marathon?
    \nProject: Make a Game about Marathon Winners
    \n\"Envision<\/p>\n

    Lesson 10.1 Fractions as Multiples of Unit Fractions<\/h3>\n

    Solve & Share<\/strong>
    \nKalil and Mara were working on their math homework. Mara wrote \\(\\frac{4}{5}\\) as \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\). Kalil looked at Mara’s work and said, \u201cI think you could use multiplication to rewrite your equation.\u201d Is Kalil’s observation correct? Explain.
    \nI can … use fraction strips or number lines to understand a fraction as a multiple of a unit fraction.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nKalil and Mara were working on their math homework. Mara wrote \\(\\frac{4}{5}\\) as \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\). Kalil looked at Mara’s work and said, \u201cI think you could use multiplication to rewrite your equation.\u201d
    \nNow,
    \nWe know that,
    \n“Repeated addition” is also known as “Multiplication”. If the same number is repeated then in short we can write that in the form of multiplication
    \nEx:
    \n2 is repeated 5 times so in short, we can write this addition as 2 x 5.
    \nSo,
    \nAccording to Kalil, Mara’s work can also be represented in the form of multiplication
    \nSo,
    \n\\(\\frac{4}{5}\\) can also be written as:
    \n\\(\\frac{4}{5}\\) = 4 \u00d7 \\(\\frac{1}{5}\\)
    \nHence, from the above,
    \nWe can conclude that Kalil’s observation is correct<\/p>\n

    Look Back!<\/strong> Model with Math<\/strong>
    \nWrite an equation to show the relationship between Mara’s work and Kalil’s observation.
    \nAnswer:
    \nAccording to Mara,
    \n\\(\\frac{4}{5}\\) = \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\) + \\(\\frac{1}{5}\\)
    \nNow,
    \nWe know that,
    \n“Repeated addition” is also known as “Multiplication”. If the same number is repeated then in short we can write that in the form of multiplication
    \nSo,
    \nAccording to Kalil,
    \nMara’s work can also be represented as:
    \n\\(\\frac{4}{5}\\) = 4 \u00d7 \\(\\frac{1}{5}\\)
    \nNow,
    \nThe relationship between Mara’s work and Kalil’s observation is:
    \n\\(\\frac{4}{5}\\) = 4 \u00d7 \\(\\frac{1}{5}\\)
    \nSo,
    \n\\(\\frac{1}{5}\\)\u00a0 is repeated 4 times
    \nSo,
    \nIn short, we can write this addition as 4 x \\(\\frac{1}{5}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe relationship between Mara’s work and Kalil’s observation is:
    \n\\(\\frac{1}{5}\\)\u00a0 is repeated 4 times
    \nSo,
    \nIn short, we can write this addition as 4 x \\(\\frac{1}{5}\\)<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Describe a Fraction Using a Unit Fraction?
    \nAnswer:
    \nA fraction can be converted into a unit fraction as explained below:
    \nPut the whole number over 1 to turn it into a fraction.
    \nEx:
    \nThe whole number is: 5
    \nThe conversion of 5 into a unit fraction is: \\(\\frac{1}{5}\\)<\/p>\n

    Visual Learning Bridge
    \nCourtney ran \\(\\frac{3}{4}\\) of the way to school. Describe \\(\\frac{3}{4}\\) using unit fractions.
    \n\"Envision
    \nA unit fraction is a fraction that describes one part of the whole. Unit fractions always contain the numerator 1.<\/p>\n

    When a whole is divided into four equal parts, each part is described as the unit fraction \\(\\frac{1}{4}\\).
    \nDecompose \\(\\frac{3}{4}\\) into unit fractions.
    \n\"Envision<\/p>\n

    Repeated addition can be represented as multiplication.
    \n\"Envision<\/p>\n

    Convince Me!<\/strong> Reasoning<\/strong>
    \nThe number \\(\\frac{5}{8}\\) is a multiple of what unit fraction? Explain.
    \nAnswer:
    \nThe given fraction is: \\(\\frac{5}{8}\\)
    \nIn the given fraction,
    \nThe numerator represents the shaded parts
    \nThe denominator represents the total number of parts
    \nNow,
    \nThe representation of \\(\\frac{5}{8}\\) is:
    \n\"\"
    \nNow,
    \nFrom the given model,
    \nWe will add \\(\\frac{1}{8}\\) 5 times
    \nSo,
    \n5 \u00d7 \\(\\frac{1}{8}\\) = \\(\\frac{5}{8}\\)
    \nHence, from the above,
    \nWe can conclude that
    \n\\(\\frac{5}{8}\\) is a multiple of \\(\\frac{1}{8}\\)<\/p>\n

    Another Example!<\/strong>
    \nDescribe \\(\\frac{5}{4}\\) as a multiple of a unit fraction.
    \n\"Envision<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nDraw a picture to explain why \\(\\frac{3}{5}\\) = 3 \u00d7 \\(\\frac{1}{5}\\).
    \nAnswer:
    \nThe given fraction is: \\(\\frac{3}{5}\\)
    \nIn the given fraction,
    \nThe numerator represents the shaded parts
    \nThe denominator represents the total number of parts
    \nNow,
    \nThe representation of the given fraction in the form of unit fractions is:
    \n\"\"
    \nNow,
    \nFrom the given model,
    \nWe will add \\(\\frac{1}{5}\\) 3 times
    \nSo,
    \n3 \u00d7 \\(\\frac{1}{5}\\) = \\(\\frac{3}{5}\\)
    \nHence, from the above,
    \nWe can conclude that
    \n\\(\\frac{3}{5}\\) = 3 \u00d7 \\(\\frac{1}{5}\\)<\/p>\n

    Question 2.
    \nWrite a multiplication equation to show each part of the following story. Mark’s family ate \\(\\frac{7}{4}\\) chicken pot pies for dinner. There are 7 people in Mark’s family. Each family member ate \\(\\frac{1}{4}\\) of a pie.
    \nAnswer:
    \nIt is given that
    \nMark’s family ate \\(\\frac{7}{4}\\) chicken pot pies for dinner. There are 7 people in Mark’s family. Each family member ate \\(\\frac{1}{4}\\) of a pie.
    \nSo,
    \nThe representation of the given information in the form of a bar diagram is:
    \n\"\"
    \nSo,
    \nThe equation that shows the given information is:
    \n(The total number of people present in Mark’s family) \u00d7 (The fraction of pie eaten by each family member of Mark) = (The total amount of chicken pot pies eaten by Mark’s family for dinner)
    \n7 \u00d7 \\(\\frac{1}{4}\\) = \\(\\frac{7}{4}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe multiplication equation to show the given information is:
    \n(The total number of people present in Mark’s family) \u00d7 (The fraction of pie eaten by each family member of Mark) = (The total amount of chicken pot pies eaten by Mark’s family for dinner)<\/p>\n

    Do You Know How?<\/strong>
    \nFor 3-6, write each fraction as a multiple of a unit fraction. Use a tool as needed.
    \nQuestion 3.
    \n\\(\\frac{2}{3}\\) = ______ \u00d7 \\(\\frac{1}{3}\\)
    \nAnswer:
    \nThe given fraction is: \\(\\frac{2}{3}\\)
    \nNow,
    \nIn the given fraction,
    \nThe numerator represents the shaded part
    \nThe denominator represents the total number of parts
    \nNow,
    \nThe representation of the given fraction as a multiple of a unit fraction is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \n\\(\\frac{2}{3}\\) = 2 \u00d7 \\(\\frac{1}{3}\\)<\/p>\n

    Question 4.
    \n\\(\\frac{5}{6}\\) = 5 \u00d7 \\(\\frac{1}{}\\)
    \nAnswer:
    \nThe given fraction is: \\(\\frac{5}{6}\\)
    \nNow,
    \nIn the given fraction,
    \nThe numerator represents the shaded part
    \nThe denominator represents the total number of parts
    \nNow,
    \nThe representation of the given fraction as a multiple of a unit fraction is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \n\\(\\frac{5}{6}\\) = 5 \u00d7 \\(\\frac{1}{6}\\)<\/p>\n

    Question 5.
    \n\\(\\frac{4}{2}\\) = 4 \u00d7 \\(\\frac{1}{}\\)
    \nAnswer:
    \nThe given fraction is: \\(\\frac{4}{2}\\)
    \nNow,
    \nIn the given fraction,
    \nThe numerator represents the shaded part
    \nThe denominator represents the total number of parts
    \nNow,
    \nThe representation of the given fraction as a multiple of a unit fraction is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \n\\(\\frac{4}{2}\\) = 4 \u00d7 \\(\\frac{1}{2}\\)<\/p>\n

    Question 6.
    \n\\(\\frac{6}{5}\\) = 6 \u00d7 \\(\\frac{1}{}\\)
    \nAnswer:
    \nThe given fraction is: \\(\\frac{6}{5}\\)
    \nNow,
    \nIn the given fraction,
    \nThe numerator represents the shaded part
    \nThe denominator represents the total number of parts
    \nNow,
    \nThe representation of the given fraction as a multiple of a unit fraction is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \n\\(\\frac{6}{5}\\) = 6 \u00d7 \\(\\frac{1}{5}\\)<\/p>\n

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

    Leveled Practice For 7-12, write each fraction as a multiple of a unit fraction. Use a tool as needed.
    \nQuestion 7.
    \n\"Envision
    \nAnswer:
    \nThe given fraction is: \\(\\frac{7}{8}\\)
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nHence, from the above model,
    \nWe can conclude that
    \n\\(\\frac{7}{8}\\) = 7 \u00d7 \\(\\frac{1}{8}\\)<\/p>\n

    Question 8.
    \n\"Envision
    \nAnswer:
    \nThe given fraction is: \\(\\frac{3}{6}\\)
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nHence, from the above model,
    \nWe can conclude that
    \n\\(\\frac{3}{6}\\) = 3 \u00d7 \\(\\frac{1}{6}\\)<\/p>\n

    Question 9.
    \n\"Envision
    \nAnswer:
    \nThe given fraction is: \\(\\frac{2}{5}\\)
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nHence, from the above model,
    \nWe can conclude that
    \n\\(\\frac{2}{5}\\) = 2 \u00d7 \\(\\frac{1}{5}\\)<\/p>\n

    Question 10.
    \n\\(\\frac{6}{4}\\)
    \nAnswer:
    \nThe given fraction is: \\(\\frac{6}{4}\\)
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nHence, from the above model,
    \nWe can conclude that
    \n\\(\\frac{6}{4}\\) = 6 \u00d7 \\(\\frac{1}{4}\\)<\/p>\n

    Question 11.
    \n\\(\\frac{9}{6}\\)
    \nAnswer:
    \nThe given fraction is: \\(\\frac{9}{6}\\)
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nHence, from the above model,
    \nWe can conclude that
    \n\\(\\frac{9}{6}\\) = 9 \u00d7 \\(\\frac{1}{6}\\)<\/p>\n

    Question 12.
    \n\\(\\frac{8}{5}\\)
    \nAnswer:
    \nThe given fraction is: \\(\\frac{8}{5}\\)
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nHence, from the above model,
    \nWe can conclude that
    \n\\(\\frac{8}{5}\\) = 8 \u00d7 \\(\\frac{1}{5}\\)<\/p>\n

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

    Question 13.
    \nMark slices \\(\\frac{4}{6}\\) of a tomato. Each slice is of the tomato. How many slices does Mark have? Explain by writing \\(\\frac{4}{6}\\) as a multiple of \\(\\frac{1}{6}\\).
    \nAnswer:
    \nIt is given that
    \nMark slices \\(\\frac{4}{6}\\) of a tomato. Each slice is of the tomato
    \nNow,
    \nFrom the given fraction,
    \nWe can observe that
    \nThe number of shaded slices of tomato is: 4
    \nThe total number of slices of tomato are: 6
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nSo,
    \nThe representation of the given fraction as a multiple of \\(\\frac{1}{6}\\) is:
    \n\\(\\frac{4}{6}\\) = 4 \u00d7 \\(\\frac{1}{6}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of slices does Mark have is: 6 slices
    \nThe representation of the given fraction as a multiple of \\(\\frac{1}{6}\\) is:
    \n\\(\\frac{4}{6}\\) = 4 \u00d7 \\(\\frac{1}{6}\\)<\/p>\n

    Question 14.
    \nDelia flew 2,416 miles the first year on the job. She flew 3,719 miles the second year. Delia flew 2,076 more miles the third year than the first and second years combined. How many miles did Delia fly the third year?
    \nAnswer:
    \nIt is given that
    \nDelia flew 2,416 miles the first year on the job. She flew 3,719 miles the second year. Delia flew 2,076 more miles the third year than the first and second years combined
    \nSo,
    \nThe number of miles Deli flew the third year = 2,076 + (The number of miles Delia flew the first and the second years combined)
    \n= 2,076 + (2,416 + 3,719)
    \n= 2,076 + 6,135
    \n= 8,211 miles
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of miles did Delia fly the third year is: 8,211 miles<\/p>\n

    Question 15.
    \nThe model with Math<\/strong>
    \nThe picture below shows \\(\\frac{6}{2}\\) pears. Write \\(\\frac{6}{2}\\) as repeated addition and as a multiple of a unit fraction.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nThe picture below shows \\(\\frac{6}{2}\\) pears
    \nNow,
    \nThe given picture is:
    \n\"Envision
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nNow,
    \nThe representation of the given fraction as a repeated addition is:
    \n\\(\\frac{6}{2}\\) = \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\)
    \nNow,
    \nThe representation of the given fraction as a multiple of the unit fraction is:
    \n\\(\\frac{6}{2}\\) = 6 \u00d7 \\(\\frac{1}{2}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe representation of \\(\\frac{6}{2}\\) as a repeated addition and as a multiple of unit fraction respectively is:
    \na. \\(\\frac{6}{2}\\) = \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\)
    \nb. \\(\\frac{6}{2}\\) = 6 \u00d7 \\(\\frac{1}{2}\\)<\/p>\n

    Question 16.
    \nThe picture below shows \\(\\frac{7}{2}\\) apples. Write \\(\\frac{7}{2}\\) as repeated addition and as a multiple of a unit fraction.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nThe picture below shows \\(\\frac{7}{2}\\) apples
    \nNow,
    \nThe given picture is:
    \n\"Envision
    \nSo,
    \nThe representation of the given fraction as a unit fraction is:
    \n\"\"
    \nNow,
    \nThe representation of the given fraction as a repeated addition is:
    \n\\(\\frac{7}{2}\\) = \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\)
    \nNow,
    \nThe representation of the given fraction as a multiple of the unit fraction is:
    \n\\(\\frac{7}{2}\\) = 7 \u00d7 \\(\\frac{1}{2}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe representation of \\(\\frac{7}{2}\\) as repeated addition and as a multiple of unit fraction respectively is:
    \na. \\(\\frac{6}{2}\\) = \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\)
    \nb. \\(\\frac{7}{2}\\) = 7 \u00d7 \\(\\frac{1}{2}\\)<\/p>\n

    Question 17.
    \nenVision\u00ae STEM Light travels at a speed of about 186,000 miles per second. How far does light travel in 5 seconds?
    \nAnswer:
    \nIt is given that
    \nLight travels at a speed of about 186,000 miles per second
    \nSo,
    \nThe distance traveled by light in 5 seconds = 5 \u00d7 (The distance traveled by light in 1 second)
    \n= 5 \u00d7 186,000
    \n= 930,000 miles
    \nHence, from the above,
    \nWe can conclude that
    \nThe distance traveled by light in 5 seconds is: 930,000 miles<\/p>\n

    Question 18.
    \nHigher-Order Thinking<\/strong> Kobe drinks \\(\\frac{1}{3}\\) cup of juice each day. He has 2\\(\\frac{1}{3}\\) cups of juice left. For how many days will it last? Explain by writing 2\\(\\frac{1}{3}\\) as a fraction and then writing the fraction as a multiple of \\(\\frac{1}{3}\\).
    \nAnswer:
    \nIt is given that
    \nKobe drinks \\(\\frac{1}{3}\\) cup of juice each day. He has 2\\(\\frac{1}{3}\\) cups of juice left.
    \nSo,
    \nThe representation of 2\\(\\frac{1}{3}\\) as a fraction is:
    \n2\\(\\frac{1}{3}\\) = \\(\\frac{8}{3}\\)
    \nBut,
    \nIt is given that
    \nKobe drinks \\(\\frac{1}{3}\\) cup of juice each day
    \nSo,
    \nThe representation of \\(\\frac{8}{3}\\) as a multiple of the unit fraction is:
    \n\\(\\frac{8}{3}\\) = 8 \u00d7 \\(\\frac{1}{3}\\)
    \nSo,
    \nThe total number of cups of juice left = (The total number of days) \u00d7 (The number of cups Kobe drinks each day)
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of days that \\(\\frac{8}{3}\\) cups of juice will last is: 8 days<\/p>\n

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

    Question 19.
    \nWhich multiplication equation describes the fraction plotted on the number line?
    \n\"Envision
    \nAnswer:
    \nThe given number line is:
    \n\"\"
    \nNow,
    \nWe know that,
    \nWe will write any fraction in terms of a multiple of the unit fraction as:
    \n\\(\\frac{x}{y}\\) = x \u00d7 \\(\\frac{1}{y}\\)
    \nNow,
    \nFrom the given number line,
    \nWe can observe that,
    \nThe value of y is: 8
    \nSo,
    \nFrom the given options,
    \nWe have to check whether the given fraction is in the form of
    \n\\(\\frac{x}{8}\\) = x \u00d7 \\(\\frac{1}{8}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe multiplication equation that describes the fraction plotted on the number line is:
    \n\"\"<\/p>\n

    Question 20.
    \nWhich multiplication equation describes the picture below?
    \n\"Envision
    \nAnswer:
    \nThe given number line is:
    \n\"\"
    \nNow,
    \nWe know that,
    \nWe will write any fraction in terms of a multiple of the unit fraction as:
    \n\\(\\frac{x}{y}\\) = x \u00d7 \\(\\frac{1}{y}\\)
    \nNow,
    \nFrom the given number line,
    \nWe can observe that,
    \nThe value of y is: 2
    \nSo,
    \nFrom the given options,
    \nWe have to check whether the given fraction is in the form of
    \n\\(\\frac{x}{2}\\) = x \u00d7 \\(\\frac{1}{2}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe multiplication equation that describes the picture is:
    \n\"\"<\/p>\n

    Lesson 10.2 Multiply a Fraction by a Whole Number: Use Models<\/h3>\n

    Solve & Share<\/strong>
    \nHow much tomato juice is needed for a group of 4 people if each person gets \\(\\frac{1}{3}\\) cup of juice? How much tomato juice is needed if they each get \\(\\frac{2}{3}\\) cup of juice? Solve these problems any way you choose.
    \nI can… use drawings, area models, or number lines to multiply fractions by whole numbers.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nThere are 4 people and each person gets \\(\\frac{1}{3}\\) cup of juice and after some time gets \\(\\frac{2}{3}\\) cup of juice
    \nSo,
    \nThe amount of tomato juice needed for 4 people when each person gets \\(\\frac{1}{3}\\) of juice
    \n= (The number of people) \u00d7 (The amount of juice each person gets)
    \n= 4 \u00d7 \\(\\frac{1}{3}\\)
    \n= \\(\\frac{4}{3}\\) cups of tomato juice
    \nSo,
    \nThe amount of tomato juice needed for 4 people when each person gets \\(\\frac{2}{3}\\) cups of juice
    \n= (The number of people) \u00d7 (The amount of juice each person gets)
    \n= 4 \u00d7 \\(\\frac{2}{3}\\)
    \n= \\(\\frac{4 \u00d7 2}{3}\\)
    \n= \\(\\frac{8}{3}\\) cups of tomato juice
    \nHence, from the above,
    \nWe can conclude that
    \na. The amount of tomato juice needed for 4 people when each person gets \\(\\frac{1}{3}\\) cup of juice is: \\(\\frac{4}{3}\\) cups of tomato juice
    \nb. The amount of tomato juice needed for 4 people when each person gets \\(\\frac{2}{3}\\) cups of juice is: \\(\\frac{8}{3}\\) cups of tomato juice<\/p>\n

    Look Back!<\/strong> Use Structure<\/strong> How does finding the total juice for 4 people with \\(\\frac{2}{3}\\) cup servings compare to finding it for \\(\\frac{1}{3}\\) cup servings? Why?
    \nAnswer:
    \nFrom the above problem,
    \nWe can observe that
    \nThe amount of tomato juice needed for 4 people when each person gets \\(\\frac{1}{3}\\) cup of juice is: \\(\\frac{4}{3}\\) cups of tomato juice
    \nThe amount of tomato juice needed for 4 people when each person gets \\(\\frac{2}{3}\\) cups of juice is: \\(\\frac{8}{3}\\) cups of tomato juice
    \nSo,
    \nThe amount of tomato juice needed for 4 people when each person gets \\(\\frac{2}{3}\\) cups of juice = \\(\\frac{8}{3}\\) cups of tomato juice
    \n= 4 \u00d7 \\(\\frac{2}{3}\\)
    \n= 4 \u00d7 2 \u00d7 \\(\\frac{1}{3}\\)
    \n= 2 \u00d7 (The amount of tomato juice needed for 4 people when each person gets \\(\\frac{1}{3}\\) cups of juice)
    \nHence, from the above,
    \nWe can conclude that
    \nThe amount of tomato juice needed for 4 people when each person gets \\(\\frac{2}{3}\\) of juice is “2 Times” of the amount of tomato juice needed for 4 people when each person gets \\(\\frac{1}{3}\\) of juice<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Multiply a Fraction by a Whole Number?
    \nAnswer:
    \nA fraction can be multiplied by a whole number as explained below:
    \nStep 1:
    \nMultiply across the top number by top number (numerator) and bottom number by bottom number (denominator).
    \nStep 2:
    \nSimplify your answer by dividing both numerator and denominator by the same number, when applicable.<\/p>\n

    Visual Learning Bridge
    \nDori lives \\(\\frac{1}{4}\\) mile from school. If she walks to and from school each day, how far does Dori walk during a school week?
    \n\"Envision
    \nRemember, multiplication is repeated addition. So, you can use addition or multiplication to solve this problem.<\/p>\n

    One Way<\/strong>
    \nDraw a picture to show Dori walks \\(\\frac{1}{4}\\) mile, 10 times.
    \n\"Envision
    \nSince \\(\\frac{2}{4}\\) is equivalent to \\(\\frac{1}{2}\\), 2\\(\\frac{2}{4}\\) is equivalent to 2\\(\\frac{1}{2}\\). Dori walks 2\\(\\frac{1}{2}\\)miles to and from school each week.<\/p>\n

    Another Way<\/strong>
    \nDraw a number line to show Dori walks \\(\\frac{1}{4}\\) mile, 10 times
    \n\"Envision<\/p>\n

    Convince Me!<\/strong> Generalize<\/strong> Why can both addition and multiplication be used to represent the problem above? Write an equation to explain.
    \nAnswer:
    \nWe know that,
    \nThe addition is the process of combining a number of individual items together to form a new total. This means that in multiplication, groups are created to represent the numbers being multiplied, and then the groups are added together\u00a0to produce a total. Relating addition to multiplication is relatively simple.
    \nExample:
    \nWe can write \\(\\frac{10}{4}\\) as the repeated addition of \\(\\frac{2}{4}\\) and as a multiplication as a multiple of \\(\\frac{2}{4}\\)
    \nSo,
    \nIn the form of addition,
    \n\\(\\frac{10}{4}\\) = \\(\\frac{2}{4}\\) + \\(\\frac{2}{4}\\) + \\(\\frac{2}{4}\\) + \\(\\frac{2}{4}\\) + \\(\\frac{2}{4}\\)
    \nIn the form of multiplication,
    \n\\(\\frac{10}{4}\\) = 5 \u00d7 \\(\\frac{2}{4}\\)<\/p>\n

    Another Example!<\/strong>
    \nHow far did Jess bike to practice if he biked mile each day for 4 days?
    \n\"Envision
    \nUse addition
    \n\\(\\frac{3}{5}+\\frac{3}{5}+\\frac{3}{5}+\\frac{3}{5}=\\frac{12}{5}=\\frac{5}{5}+\\frac{5}{5}+\\frac{2}{5}=2 \\frac{2}{5}\\)
    \nJess bikes 2\\(\\frac{2}{5}\\) miles.<\/p>\n

    Use multiplication.
    \n\\(4 \\times \\frac{3}{5}=\\frac{12}{5}=\\frac{5}{5}+\\frac{5}{5}+\\frac{2}{5}=2 \\frac{2}{5}\\)
    \nJess bikes 2\\(\\frac{2}{5}\\) miles.<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nDraw a picture to explain how to find 3 \u00d7 \\(\\frac{2}{5}\\).
    \nAnswer:
    \nThe given fraction is:
    \n3 \u00d7 \\(\\frac{2}{5}\\)
    \nNow,
    \nIn the given fraction,
    \nThe numerator represents the shaded parts
    \nThe denominator represents the total number of parts
    \nSo,
    \nThe representation of the given fraction in the form of a bar diagram is:
    \n\"\"
    \nNow,
    \nFrom the given figure,
    \nWe can observe that
    \n3 \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{2}{5}\\) + \\(\\frac{2}{5}\\) + \\(\\frac{2}{5}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe representation of the given fraction is:
    \n3 \u00d7 \\(\\frac{2}{5}\\) = \\(\\frac{2}{5}\\) + \\(\\frac{2}{5}\\) + \\(\\frac{2}{5}\\)<\/p>\n

    Do You Know How?<\/strong>
    \nFor 2-3, write and solve a multiplication equation.
    \nQuestion 2.
    \n\"Envision
    \nAnswer:
    \nThe given figures are:
    \n\"Envision
    \nNow,
    \nFrom the first figure,
    \nWe can observe that
    \nThe number of shaded parts is: 2
    \nThe total number of parts are: 6
    \nFrom the second figure,
    \nWe can observe that
    \nThe number of shaded parts is: 2
    \nThe total number of parts are: 6
    \nSo,
    \nThe representation of the given figures in the form of fractions are:
    \nFor the first figure,
    \nThe fraction of the shaded part = \\(\\frac{The number of shaded parts}{The total number of parts}\\)
    \n= \\(\\frac{2}{6}\\)
    \nFor the second figure,
    \nThe fraction of the shaded part = \\(\\frac{The number of shaded parts}{The total number of parts}\\)
    \n= \\(\\frac{2}{6}\\)
    \nSo,
    \nThe multiplication equation for the given figures is:
    \n\\(\\frac{2}{6}\\) + \\(\\frac{2}{6}\\) = 2 \u00d7 \\(\\frac{2}{6}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe multiplication equation for the given figures is:
    \n\\(\\frac{2}{6}\\) + \\(\\frac{2}{6}\\) = 2 \u00d7 \\(\\frac{2}{6}\\)<\/p>\n

    Question 3.
    \n\"Envision
    \nAnswer:
    \nThe given number line is:
    \n\"Envision
    \nNow,
    \nFrom the given number line,
    \nWe can observe that
    \nThe number line is showing the gap of 2 numbers
    \nNow,
    \nThe representation of the multiplication equation for the given number line is:
    \nn \u00d7 \\(\\frac{1}{3}\\)
    \nWhere,
    \nn = 2, 4, 6, 8
    \nHence, from the above,
    \nWe can conclude that
    \nThe representation of the multiplication equation for the given number line is:
    \nn \u00d7 \\(\\frac{1}{3}\\)
    \nWhere,
    \nn = 2, 4, 6, 8<\/p>\n

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

    For 4-7, write and solve a multiplication equation. Use drawings or number lines as needed.
    \nQuestion 4.
    \n\"Envision
    \nAnswer:
    \nThe given model is:
    \n\"Envision
    \nNow,
    \nFrom the given model,
    \nWe can observe that
    \n\\(\\frac{1}{8}\\) is repeated 5 times
    \nSo,
    \nThe multiplication equation for the given model is:
    \n\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) (or) 5 \u00d7 \\(\\frac{1}{8}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe multiplication equation for the given model is:
    \n\\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\)+ \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) + \\(\\frac{1}{8}\\) (or) 5 \u00d7 \\(\\frac{1}{8}\\)<\/p>\n

    Question 5.
    \n\"Envision
    \nAnswer:
    \nThe given model is:
    \n\"Envision
    \nNow,
    \nFrom the given model,
    \nWe can observe that
    \n\\(\\frac{2}{10}\\) is repeated 3 times
    \nSo,
    \nThe multiplication equation for the given model is:
    \n\\(\\frac{2}{10}\\) + \\(\\frac{2}{10}\\) + \\(\\frac{2}{10}\\) (or) 3 \u00d7 \\(\\frac{2}{10}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe multiplication equation for the given model is:
    \n\\(\\frac{2}{10}\\) + \\(\\frac{2}{10}\\) + \\(\\frac{2}{10}\\) (or) 3 \u00d7 \\(\\frac{2}{10}\\)<\/p>\n

    Question 6.
    \nCalculate the distance Margo rides her bike if she rides \\(\\frac{7}{8}\\) mile each day for 4 days.
    \nAnswer:
    \nIt is given that
    \nMargo rides her bike \\(\\frac{7}{8}\\) mile each day for 4 days
    \nSo,
    \nThe distance traveled by Margo for 4 days = 4 \u00d7 (The number of miles Margo rides each day)
    \n= 4 \u00d7 \\(\\frac{7}{8}\\)
    \n= \\(\\frac{4 \u00d7 7}{8}\\)
    \n= \\(\\frac{28}{8}\\) miles
    \nHence, from the above,
    \nWe can conclude that
    \nThe distance Margo rides her bike for 4 days is: \\(\\frac{28}{8}\\) miles<\/p>\n

    Question 7.
    \nCalculate the distance Tom rides his bike if he rides \\(\\frac{5}{6}\\) mile each day for 5 days.
    \nAnswer:
    \nIt is given that
    \nTom rides his bike \\(\\frac{5}{6}\\) miles each day
    \nSo,
    \nThe distance Tom rides his bike for 5 days = 5 \u00d7 (The number of miles Tom rides his bike each day)
    \n= 5 \u00d7 \\(\\frac{5}{6}\\)
    \n= \\(\\frac{5 \u00d7 5}{6}\\)
    \n= \\(\\frac{25}{6}\\) miles
    \nHence, from the above,
    \nWe can conclude that
    \nThe distance Tom rides his bike for 5 days is: \\(\\frac{25}{6}\\) miles<\/p>\n

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

    Question 8.
    \nKiona fills a measuring cup with \\(\\frac{3}{4}\\) cup of juice 3 times to make punch. Write and solve a multiplication equation with a whole number and a fraction to show the total amount of juice Kiona uses.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nKiona fills a measuring cup with \\(\\frac{3}{4}\\) cup of juice 3 times to make a punch
    \nSo,
    \nThe total amount of juice Kiona uses = (The number of times Kiona fills a measuring cup) \u00d7 (Each cup of juice that Kiona fills)
    \n= 3 \u00d7 \\(\\frac{3}{4}\\)
    \n= \\(\\frac{3 \u00d7 3}{4}\\)
    \n= \\(\\frac{9}{4}\\) cups of juice
    \nHence, from the above,
    \nWe can conclude that
    \nThe total amount of juice Kiona uses is: \\(\\frac{9}{4}\\) cups of juice<\/p>\n

    Question 9.
    \nEach lap around a track is \\(\\frac{3}{10}\\) kilometer. Eliot walked around the track 4 times. How far did Eliot walk?
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nEach lap around a track is \\(\\frac{3}{10}\\) kilometer. Eliot walked around the track 4 times.
    \nSo,
    \nThe distance that Eliot walked = (The number of times Eliot walked around the track) \u00d7 (Each lap Eliot walked around a track)
    \n= 4 \u00d7 \\(\\frac{3}{10}\\)
    \n= \\(\\frac{4 \u00d7 3}{10}\\)
    \n= \\(\\frac{12}{10}\\) Kilometers
    \nHence, from the above,
    \nWe can conclude that
    \nThe distance that Eliot walked is: \\(\\frac{12}{10}\\) Kilometers<\/p>\n

    Question 10.
    \nA chef serves \\(\\frac{5}{6}\\) of a pan of lasagna. Each piece is \\(\\frac{1}{6}\\) of the pan. How many pieces did the chef serve? Solve by writing \\(\\frac{5}{6}\\) as a multiple of \\(\\frac{1}{6}\\).
    \nAnswer:
    \nIt is given that
    \nA chef serves \\(\\frac{5}{6}\\) of a pan of lasagna. Each piece is \\(\\frac{1}{6}\\) of the pan.
    \nNow,
    \nLet the number of pieces did the chef serve be: x
    \nSo,
    \nThe amount of a pan of lasagna the chef serves = (The number of pieces did the chef serve) \u00d7 (Each piece of lasagna)
    \n\\(\\frac{5}{6}\\) = x \u00d7 \\(\\frac{1}{6}\\)
    \n5 \u00d7 \\(\\frac{1}{6}\\) = x \u00d7 \\(\\frac{1}{6}\\)
    \nx = 5 pieces
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of pieces did the chef serves is: 5 pieces<\/p>\n

    Question 11.
    \nModel with Math<\/strong>
    \nWendy uses \\(\\frac{2}{12}\\) of a loaf of bread to make one sandwich. Write and solve an equation to find b, how much of the loaf of bread she uses to make 4 sandwiches. Use a drawing, as needed.
    \nAnswer:
    \nIt is given that
    \nWendy uses \\(\\frac{2}{12}\\) of a loaf of bread to make one sandwich
    \nSo,
    \nThe amount of the loaf of bread Wendy uses to make 4 sandwiches = 4 \u00d7 (The loaf of a bread used by Wendy to make one sandwich)
    \n= 4 \u00d7 \\(\\frac{2}{12}\\)
    \n= \\(\\frac{4 \u00d7 2}{12}\\)
    \n= \\(\\frac{8}{12}\\) loaves of bread
    \nHence, from the above,
    \nWe can conclude that
    \nThe amount of loaf of bread used by Wendy to make 4 sandwiches is: \\(\\frac{8}{12}\\) loaves of bread<\/p>\n

    Question 12.
    \nHigher-Order Thinking<\/strong> A baker uses \\(\\frac{2}{3}\\) cup of rye flour in each loaf of bread. How many cups of rye flour will the baker use in 3 loaves? in 7 loaves? in 10 loaves?
    \nAnswer:
    \nIt is given that
    \nA baker uses \\(\\frac{2}{3}\\) cup of rye flour in each loaf of bread
    \nSo,
    \nThe number of cups of rye flour will the baker use in 3 loaves = 3 \u00d7 (The cup of rye flour used by the baker in each loaf of bread)
    \n= 3 \u00d7 \\(\\frac{2}{3}\\)
    \n= \\(\\frac{3 \u00d7 2}{3}\\)
    \n= \\(\\frac{6}{3}\\) cups of rye flour
    \nSo,
    \nThe number of cups of rye flour will the baker use in 7 loaves = 7 \u00d7 (The cup of rye flour used by the baker in each loaf of bread)
    \n= 7 \u00d7 \\(\\frac{2}{3}\\)
    \n= \\(\\frac{7 \u00d7 2}{3}\\)
    \n= \\(\\frac{14}{3}\\) cups of rye flour
    \nSo,
    \nThe number of cups of rye flour will the baker use in 10 loaves = 10 \u00d7 (The cup of rye flour used by the baker in each loaf of bread)
    \n= 10 \u00d7 \\(\\frac{2}{3}\\)
    \n= \\(\\frac{10 \u00d7 2}{3}\\)
    \n= \\(\\frac{20}{3}\\) cups of rye flour
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of cups of rye flour will the baker use in 3 loaves is: \\(\\frac{6}{3}\\) cups
    \nThe number of cups of rye flour will the baker use in 7 loaves is: \\(\\frac{14}{3}\\) cups
    \nThe number of cups of rye flour will the baker use in 10 loaves is: \\(\\frac{20}{3}\\) cups<\/p>\n

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

    Question 13.
    \nElaine jogged \\(\\frac{4}{5}\\) mile each day for 4 days. Select all the expressions that tell how far Elaine jogged in all. Use drawings or number lines as needed.
    \n\u2610 4 \u00d7 \\(\\frac{4}{5}\\)
    \n\u2610 \\(\\frac{16}{5}\\)
    \n\u2610 3 \\(\\frac{1}{5}\\)
    \n\u2610 4 \u00d7 \\(\\frac{1}{5}\\)
    \n\u2610 2\\(\\frac{1}{5}\\)
    \nAnswer:
    \nIt is given that
    \nElaine jogged \\(\\frac{4}{5}\\) mile each day for 4 days
    \nSo,
    \nThe number of miles Elaine jogged for 4 days = 4 \u00d7 (The number of miles Elaine jogged each day)
    \n= 4 \u00d7 \\(\\frac{4}{5}\\)
    \n= \\(\\frac{4 \u00d7 4}{5}\\)
    \n= \\(\\frac{16}{5}\\) miles
    \n= 3\\(\\frac{1}{5}\\) miles
    \nHence, from the above,
    \nWe can conclude that all the expressions that tell how far Elaine jogged are:
    \n\"\"<\/p>\n

    Question 14.
    \nFreddie skated \\(\\frac{1}{2}\\) mile each day for 6 days. Select all the equations that can be used to find s, the total distance Freddie skated.
    \n\u2610 s = \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\)
    \n\u2610 s = 6 \u00d7 \\(\\frac{1}{2}\\)
    \n\u2610 s = 6 + \\(\\frac{1}{2}\\)
    \n\u2610 s = 6 + 2 \u00d7 \\(\\frac{1}{2}\\)
    \n\u2610 s = 6 \u00d7 2
    \nAnswer:
    \nIt is given that
    \nFreddie skated \\(\\frac{1}{2}\\) mile each day for 6 days
    \nSo,
    \nThe number of miles (s) Freddie skated for 6 days = 6 \u00d7 (The number of miles Freddie skated each day)
    \n= 6 \u00d7 \\(\\frac{1}{2}\\)
    \n= \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\) + \\(\\frac{1}{2}\\)
    \n= \\(\\frac{6 \u00d7 1}{2}\\)
    \n= \\(\\frac{6}{2}\\) miles
    \nHence, from the above,
    \nWe can conclude that all the equations that can be used to find s, the total distance Freddie skated are:
    \n\"\"<\/p>\n

    Lesson 10.3 Multiply a Fraction by a Whole Number: Use Symbols<\/h3>\n

    Solve & Share<\/strong>
    \nA recipe for 1 gallon of fruit punch calls for \\(\\frac{3}{4}\\) cup of orange juice. How many cups of orange juice are needed to make 8 gallons of fruit punch? Solve this problem any way you choose.
    \nI can… use properties and equations to multiply a fraction by a whole number.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nA recipe for 1 gallon of fruit punch calls for \\(\\frac{3}{4}\\) cup of orange juice
    \nSo,
    \nThe number of cups of orange juice needed to make 8 gallons of fruit punch = 8 \u00d7 (The number of cups of orange juice needed to make 1 gallon of fruit punch)
    \n= 8 \u00d7 \\(\\frac{3}{4}\\)
    \n= \\(\\frac{8 \u00d7 3}{4}\\)
    \n= \\(\\frac{24}{4}\\)
    \n= 6 cups of orange juice
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of cups of orange juice needed to make 8 gallons of fruit punch is: 6 cups of orange juice<\/p>\n

    Look Back!<\/strong> Be Precise<\/strong> Look back at your solution. What units should you use to label your answer?
    \nAnswer:
    \nFrom the above problem,
    \nWe can observe that
    \nThe solution for the above problem is: 6 cups of orange juice (Which is the number of cups)
    \nHence, from the above,
    \nWe can conclude that
    \nThere are no units you should use to label your answer<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Use Symbols to Multiply a Fraction by a Whole Number?
    \nAnswer:
    \nA fraction can be multiplied by a whole number as explained below:
    \nStep 1:
    \nMultiply across the top number by top number (numerator) and bottom number by bottom number (denominator).
    \nStep 2:
    \nSimplify your answer by dividing both numerator and denominator by the same number, when applicable.<\/p>\n

    Visual Learning Bridge
    \nStanley makes ice cream sundaes. Today Stanley made 2 ice cream sundaes. How much ice cream did Stanley use? Find 2 \u00d7 \\(\\frac{3}{4}\\).
    \n\"Envision
    \nYou can use structure when multiplying a fraction and a whole number.<\/p>\n

    \"Envision<\/p>\n

    Convince Me! Use Structure<\/strong> Use properties of operations to calculate 3 \u00d7 \\(\\frac{3}{6}\\). Show your work.
    \nAnswer:
    \nThe given fraction is: 3 \u00d7 \\(\\frac{3}{6}\\)
    \nNow,
    \nBy using the unit fractions,
    \n3 \u00d7 \\(\\frac{3}{6}\\)
    \n= 3 \u00d7 3 \u00d7 \\(\\frac{1}{6}\\)
    \nBy using he Associative Property of Multiplication,
    \n= (3 \u00d7 3) \u00d7 \\(\\frac{1}{6}\\)
    \n= 9 \u00d7 \\(\\frac{1}{6}\\)
    \n= \\(\\frac{9 \u00d7 1}{6}\\)
    \n= \\(\\frac{9}{6}\\)
    \n= \\(\\frac{3}{2}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of 3 \u00d7 \\(\\frac{3}{6}\\) is: \\(\\frac{3}{2}\\)<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nSarah has \\(\\frac{1}{2}\\) of a granola bar. Her friend has 5 times as many granola bars. How many granola bars does Sarah’s friend have?
    \nAnswer:
    \nIt is given that
    \nSarah has \\(\\frac{1}{2}\\) of a granola bar. Her friend has 5 times as many granola bars
    \nSo,
    \nThe number of granola bars does Sarah’s friend have = (The number of times Sarah’s friend has as many granola bars) \u00d7 (The number of pieces of each granola bar)
    \n= 5 \u00d7 \\(\\frac{1}{2}\\)
    \n= \\(\\frac{5}{2}\\) granola bars
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of granola bars does Sarah’s friend have is: \\(\\frac{5}{2}\\) granola bars<\/p>\n

    Question 2.
    \nSue needs a \\(\\frac{5}{6}\\) cup of cocoa to make one batch of chocolate pudding. She wants to make 4 batches of pudding to take to a party. Write and solve an equation to find how many cups of cocoa, c, Sue will need for all 4 batches of pudding.
    \nAnswer:
    \nIt is given that
    \nSue needs a \\(\\frac{5}{6}\\) cup of cocoa to make one batch of chocolate pudding. She wants to make 4 batches of pudding to take to a party
    \nSo,
    \nThe number of cups of cocoa Sue will need for 4 batches of pudding (c) = 4 \u00d7 (The amount of cocoa needed to make one batch of chocolate pudding)
    \n= 4 \u00d7 \\(\\frac{5}{6}\\)
    \n= \\(\\frac{4 \u00d7 5}{6}\\)
    \n= \\(\\frac{20}{6}\\)
    \n= \\(\\frac{10}{3}\\) cups of cocoa
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of cups of cocoa Sue will need for 4 batches of pudding is: \\(\\frac{10}{3}\\) cups of pudding<\/p>\n

    Do You Know How?<\/strong>
    \nFor 3-4, multiply.
    \nQuestion 3.
    \n8 \u00d7 \\(\\frac{1}{2}\\)
    \nAnswer:
    \nThe given fraction is: 8 \u00d7 \\(\\frac{1}{2}\\)
    \nSo,
    \n8 \u00d7 \\(\\frac{1}{2}\\)
    \n= \\(\\frac{8 \u00d7 1}{2}\\)
    \n= \\(\\frac{8}{2}\\)
    \n= 4
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: 4<\/p>\n

    Question 4.
    \n3 \u00d7 \\(\\frac{3}{4}\\)
    \nAnswer:
    \nThe given fraction is: 3 \u00d7 \\(\\frac{3}{4}\\)
    \nSo,
    \n3 \u00d7 \\(\\frac{3}{4}\\)
    \n= \\(\\frac{3 \u00d7 3}{4}\\)
    \n= \\(\\frac{9}{4}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{9}{4}\\)<\/p>\n

    For 5-6, write and solve a multiplication equation.
    \nQuestion 5.
    \nCalculate the amount of medicine taken in 5 days if the dose is \\(\\frac{3}{4}\\) fluid ounce per day.
    \nAnswer:
    \nIt is given that
    \nThe dose is \\(\\frac{3}{4}\\) fluid ounce per day
    \nSo,
    \nThe amount of medicine taken in 5 days = 5 \u00d7 (The amount of dose taken per day)
    \n= 5 \u00d7 \\(\\frac{3}{4}\\)
    \n= \\(\\frac{5 \u00d7 3}{4}\\)
    \n= \\(\\frac{15}{4}\\) fluid ounces
    \nHence, from the above,
    \nWe can conclude that
    \nThe amount of medicine taken in 5 days is: \\(\\frac{15}{4}\\) fluid ounces<\/p>\n

    Question 6.
    \nCalculate the total length needed to decorate 9 boxes if each box uses \\(\\frac{2}{3}\\) yard of ribbon.
    \nAnswer:
    \nIt is given that
    \nEach box uses \\(\\frac{2}{3}\\) yard of ribbon
    \nSo,
    \nThe total length of ribbon needed to decorate 9 boxes = 9 \u00d7 (The length of ribbon used for each box)
    \n= 9 \u00d7 \\(\\frac{2}{3}\\)
    \n= \\(\\frac{9 \u00d7 2}{3}\\)
    \n= \\(\\frac{18}{3}\\)
    \n= 6 yards of ribbon
    \nHence, from the above,
    \nWe can conclude that
    \nThe total length of the ribbon needed to decorate 9 boxes is: 6 yards of ribbon<\/p>\n

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

    For 7-15, multiply.
    \nQuestion 7.
    \n4 \u00d7 \\(\\frac{1}{3}\\)
    \nAnswer:
    \nThe given fraction is: 4 \u00d7 \\(\\frac{1}{3}\\)
    \nSo,
    \n4 \u00d7 \\(\\frac{1}{3}\\)
    \n= \\(\\frac{4 \u00d7 1}{3}\\)
    \n= \\(\\frac{4}{3}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{4}{3}\\)<\/p>\n

    Question 8.
    \n6 \u00d7 \\(\\frac{3}{8}\\)
    \nAnswer:
    \nThe given fraction is: 6 \u00d7 \\(\\frac{3}{8}\\)
    \nSo,
    \n6 \u00d7 \\(\\frac{3}{8}\\)
    \n= \\(\\frac{3 \u00d7 6}{8}\\)
    \n= \\(\\frac{18}{8}\\)
    \n= \\(\\frac{9}{4}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{9}{4}\\)<\/p>\n

    Question 9.
    \n8 \u00d7 \\(\\frac{2}{5}\\)
    \nAnswer:
    \nThe given fraction is: 8 \u00d7 \\(\\frac{2}{5}\\)
    \nSo,
    \n8 \u00d7 \\(\\frac{2}{5}\\)
    \n= \\(\\frac{8 \u00d7 2}{5}\\)
    \n= \\(\\frac{16}{5}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{16}{5}\\)<\/p>\n

    Question 10.
    \n2 \u00d7 \\(\\frac{5}{6}\\)
    \nAnswer:
    \nThe given fraction is: 2 \u00d7 \\(\\frac{5}{6}\\)
    \nSo,
    \n2 \u00d7 \\(\\frac{5}{6}\\)
    \n= \\(\\frac{2 \u00d7 5}{6}\\)
    \n= \\(\\frac{10}{6}\\)
    \n= \\(\\frac{5}{3}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{5}{3}\\)<\/p>\n

    Question 11.
    \n4 \u00d7 \\(\\frac{2}{3}\\)
    \nAnswer:
    \nThe given fraction is: 4 \u00d7 \\(\\frac{2}{3}\\)
    \nSo,
    \n4 \u00d7 \\(\\frac{2}{3}\\)
    \n= \\(\\frac{4 \u00d7 2}{3}\\)
    \n= \\(\\frac{8}{3}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{8}{3}\\)<\/p>\n

    Question 12.
    \n5 \u00d7 \\(\\frac{7}{8}\\)
    \nAnswer:
    \nThe given fraction is: 5 \u00d7 \\(\\frac{7}{8}\\)
    \nSo,
    \n5 \u00d7 \\(\\frac{7}{8}\\)
    \n= \\(\\frac{5 \u00d7 7}{8}\\)
    \n= \\(\\frac{35}{8}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{35}{8}\\)<\/p>\n

    Question 13.
    \n7 \u00d7 \\(\\frac{3}{4}\\)
    \nAnswer:
    \nThe given fraction is: 7 \u00d7 \\(\\frac{3}{4}\\)
    \nSo,
    \n7 \u00d7 \\(\\frac{3}{4}\\)
    \n= \\(\\frac{7 \u00d7 3}{4}\\)
    \n= \\(\\frac{21}{4}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{21}{4}\\)<\/p>\n

    Question 14.
    \n9 \u00d7 \\(\\frac{3}{4}\\)
    \nAnswer:
    \nThe given fraction is: 9 \u00d7 \\(\\frac{3}{4}\\)
    \nSo,
    \n9 \u00d7 \\(\\frac{3}{4}\\)
    \n= \\(\\frac{9 \u00d7 3}{4}\\)
    \n= \\(\\frac{27}{4}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{27}{4}\\)<\/p>\n

    Question 15.
    \n4 \u00d7 \\(\\frac{5}{8}\\)
    \nAnswer:
    \nThe given fraction is: 4 \u00d7 \\(\\frac{5}{8}\\)
    \nSo,
    \n4 \u00d7 \\(\\frac{5}{8}\\)
    \n= \\(\\frac{4 \u00d7 5}{8}\\)
    \n= \\(\\frac{20}{8}\\)
    \n= \\(\\frac{5}{2}\\)
    \nHence, from the above,
    \nWe can conclude that
    \nThe value of the given fraction is: \\(\\frac{5}{2}\\)<\/p>\n

    For 16-17, write and solve a multiplication equation.
    \nQuestion 16.
    \nCalculate the total distance Mary runs in one week if she runs a \\(\\frac{7}{8}\\) mile each day.
    \nAnswer:
    \nIt is given that
    \nMary runs \\(\\frac{7}{8}\\) miles each day
    \nNow,
    \nWe know that,
    \n1 week = 7 days
    \nSo,
    \nThe total distance Mary runs in 1 week = 7 \u00d7 (The number of miles Mary runs each day)
    \n= 7 \u00d7 \\(\\frac{7}{8}\\)
    \n= \\(\\frac{7 \u00d7 7}{8}\\)
    \n= \\(\\frac{49}{8}\\) miles
    \nHence, from the above,
    \nWe can conclude that
    \nThe total distance Mary runs in 1 week is: \\(\\frac{49}{8}\\) miles<\/p>\n

    Question 17.
    \nCalculate the length of 5 pieces of ribbon laid end to end if each piece is \\(\\frac{2}{3}\\) yard long.
    \nAnswer:
    \nIt is given that
    \nEach piece is \\(\\frac{2}{3}\\) yard long
    \nSo,
    \nThe length of 5 pieces of ribbon laid end to end = 5 \u00d7 (The length of each piece)
    \n= 5 \u00d7 \\(\\frac{2}{3}\\)
    \n= \\(\\frac{5 \u00d7 2}{3}\\)
    \n= \\(\\frac{10}{3}\\) yards
    \nHence, from the above,
    \nWe can conclude that
    \nThe length of 5 pieces of ribbon laid end to end is: \\(\\frac{10}{3}\\) yards<\/p>\n

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

    Question 18.
    \nA baseball team bought 8 boxes of baseballs. If the team spent a total of $1,696, what was the cost of 1 box of baseballs?
    \nAnswer:
    \nA baseball team bought 8 boxes of baseballs and the team spent a total of $1,696
    \nNow,
    \nLet the cost of 1 box of baseballs be $x
    \nSo,
    \nThe total cost team spent = (The number of baseballs) \u00d7 (The cost of 1 box of baseballs)
    \n$1,696 = 8 \u00d7 x
    \nx = \\(\\frac{1,696}{8}\\)
    \nx = $212
    \nHence, from the above,
    \nWe can conclude that
    \nThe cost of 1 box of baseballs is: $212<\/p>\n

    Question 19.
    \nOscar wants to make 4 chicken pot pies. The recipe requires \\(\\frac{2}{3}\\) pound of potatoes for each pot pie. How many pounds of potatoes will Oscar need?
    \nAnswer:
    \nIt is given that
    \nOscar wants to make 4 chicken pot pies. The recipe requires \\(\\frac{2}{3}\\) pound of potatoes for each pot pie
    \nSo,
    \nThe number of pounds of potatoes oscar will need = (The number of chicken pot pies) \u00d7 (The number of pounds of potatoes for each pot pie)
    \n= 4 \u00d7 \\(\\frac{2}{3}\\)
    \n= \\(\\frac{4 \u00d7 2}{3}\\)
    \n= \\(\\frac{8}{3}\\) pounds of potatoes
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of pounds of potatoes Oscar will need is: \\(\\frac{8}{3}\\) pounds of potatoes<\/p>\n

    Question 20.
    \nIt takes Mario \\(\\frac{1}{4}\\) hour to mow Mr. Harris’s lawn. It takes him 3 times as long to mow Mrs. Carter’s lawn. How long does it take Mario to mow Mrs. Carter’s lawn? Write your answer as a fraction of an hour, then as minutes.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nIt takes Mario \\(\\frac{1}{4}\\) hour to mow Mr. Harris’s lawn. It takes him 3 times as long to mow Mrs. Carter’s lawn
    \nSo,
    \nThe time taken for Mario to mow Mrs. harris’s lawn = 3 \u00d7 (The time taken for Mario to mow Mr.Harris’s lawn)
    \n= 3 \u00d7 \\(\\frac{1}{4}\\)
    \n= \\(\\frac{3 \u00d7 1}{4}\\)
    \n= \\(\\frac{3}{4}\\) hours
    \nNow,
    \nIt is given that
    \n\\(\\frac{1}{4}\\) hour = 15 minutes
    \nSo,
    \nThe time is taken for Mario to mow Mrsharris’s lawn = 3 \u00d7 15
    \n= 45 minutes
    \nHence, from the above,
    \nWe can conclude that
    \nThe time taken for Mario to mow MrsHarris’s lawn is: \\(\\frac{3}{4}\\) hours (or) 45 minutes<\/p>\n

    Question 21.
    \nVocabulary<\/strong> Use numerator, denominator, and whole number.
    \nWhen you multiply a fraction by a whole number, the __________ in the product is the same as the denominator of the fraction. The ___________ in the product is the product of the and the numerator of the fraction.
    \nAnswer:
    \nWhen you multiply a fraction by a whole number, the “Denominator” in the product is the same as the denominator of the fraction. The “Numerator” in the product is the product of the “Whole number” and the numerator of the fraction.<\/p>\n

    Question 22.
    \nModel with Math<\/strong>
    \nMalik swims \\(\\frac{9}{10}\\) mile each day. Write and solve an equation to find n, how many miles Malik swims in 4 days.
    \nAnswer:
    \nIt is given that
    \nMalik swims \\(\\frac{9}{10}\\) mile each day
    \nSo,
    \nThe number of miles Malik swims in 4 days = 4 \u00d7 (The number of miles Malik swims each day)
    \n= 4 \u00d7 \\(\\frac{9}{10}\\)
    \n= \\(\\frac{4 \u00d7 9}{10}\\)
    \n= \\(\\frac{36}{10}\\)
    \n= \\(\\frac{18}{5}\\) miles
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of miles Malik swims in 4 days is: \\(\\frac{18}{5}\\) miles<\/p>\n

    Question 23.
    \nHigher-Order Thinking<\/strong> Sam is making 7 fruit tarts. Each tart needs \\(\\frac{3}{4}\\) cup of strawberries and \\(\\frac{1}{4}\\) cup of blueberries. What is the total amount of fruit that Sam needs for his tarts? Use properties of operations to solve.
    \nAnswer:
    \nIt is given that
    \nSam is making 7 fruit tarts. Each tart needs \\(\\frac{3}{4}\\) cup of strawberries and \\(\\frac{1}{4}\\) cup of blueberries
    \nSo,
    \nThe total cups of fruit Sam needs for each tart = (The number of cups of strawberries needed for 1 fruit tart) + (The number of cups of blueberries needed for 1 fruit tart)
    \n= \\(\\frac{3}{4}\\) + \\(\\frac{1}{4}\\)
    \n= \\(\\frac{3 + 1}{4}\\)
    \n= \\(\\frac{4}{4}\\)
    \n= 1 cup
    \nSo,
    \nThe total amount of fruit Sam needs for his tarts = (The total number of fruit tarts) \u00d7 (The numebr of cups of fruit Sam needs for each tart)
    \n= 7 \u00d7 1
    \n= 7 cups
    \nHence, from the above,
    \nWe can conclude that
    \nThe total amount of fruit Sam needs from his tarts is: 7 cups of strawberry and blueberries<\/p>\n

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

    Question 24.
    \nSean is making picture frames. Each frame uses \\(\\frac{4}{5}\\) yard of wood. What is the total length of wood Sean will need to make 2 frames? Complete the equation.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nSean is making picture frames. Each frame uses \\(\\frac{4}{5}\\) yard of wood.
    \nSo,
    \nThe total length of the wood Sean will need to make 2 frames = (The total number of frames) \u00d7 (The length of wood needed to make each frame)
    \n= \"\"
    \nHence, from the above,
    \nWe can conclude that
    \nThe total length of the wood Sean will need to make 2 frames is: \\(\\frac{8}{5}\\) yards<\/p>\n

    Question 25.
    \nEllen is making plant boxes. Each box uses \\(\\frac{3}{6}\\) yard of wood. What is the total length of wood Ellen will need to make 7 plant boxes? Complete the equation.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nEllen is making plant boxes. Each box uses \\(\\frac{3}{6}\\) yard of wood
    \nSo,
    \nThe total length of wood Ellen need to make 7 plant boxes = 7 \u00d7 (The length of wood used by Ellen for each box)
    \n= \"\"
    \nHence, from the above,
    \nWe can conclude that
    \nThe total length of wood Ellen need to make 7 plant boxes is: \\(\\frac{21}{6}\\) yards<\/p>\n

    Lesson 10.4 Solve Time Problems<\/h3>\n

    Solve & Share<\/strong>
    \nThe Big Sur International Marathon is run on the California coast each spring. Sean’s mother was the women’s overall winner. How much faster was Sean’s mother than the women’s winner in the Ages 65-69 group? Tell me how you decided. Solve this problem any way you choose.
    \nI can… use addition, subtraction, multiplication, or division to solve problems involving time.
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nThe Big Sur International Marathon is run on the California coast each spring. Sean’s mother was the women’s overall winner
    \nNow,
    \nThe given table is:
    \n\"\"
    \nNow,
    \nFrom the given table,
    \nWe can observe that
    \nThe time is taken by Sean’s mother to complete the marathon = 2 hours 50 minutes
    \nThe time is taken by Women’s Age group 65 – 69 to complete the marathon = 3 hours 58 minutes
    \nSo,
    \nThe time difference between Sean’s mother and women’s Age group 65 – 69 to complete the marathon = 3 hours 58 minutes – 2 hours 50 minutes
    \n= 1 hour 8 minutes
    \nHence, from the above,
    \nWe can conclude that
    \nSean’s mother was faster by 1 hour 8 minutes than the women’s winner in the Ages 65-69 group<\/p>\n

    Look Back!<\/strong> The men’s winner in the Ages 70-74 group took 4\\(\\frac{1}{3}\\) hours. Sean’s grandfather, who is only 68, took 3\\(\\frac{2}{3}\\) hours. How can you find the difference in these times?
    \nAnswer:
    \nIt is given that
    \nThe men’s winner in the Ages 70-74 group took 4\\(\\frac{1}{3}\\) hours. Sean’s grandfather, who is only 68, took 3\\(\\frac{2}{3}\\) hours.
    \nNow,
    \nThe given table is:
    \n\"\"
    \nNow,
    \nFrom the given table,
    \nWe can observe that
    \nThe time taken by Men’s winner Ages 70 – 74 group = 4 hours 20 minutes
    \nNow,
    \nWe know that,
    \n1 hour = 60 minutes
    \nSo,
    \n4 hours 20 minutes = 4 + \\(\\frac{20}{60}\\)
    \n= 4\\(\\frac{1}{3}\\) hours
    \nNow,
    \nThe time is taken by Sean’s grandfather who is only 68 = 3 hours 34 minutes
    \n\u2248 3 hours 40 minutes
    \n= 3 + \\(\\frac{40}{60}\\)
    \n= 3\\(\\frac{2}{3}\\) hours
    \nSo,
    \nThe difference of time taken between men’s winner Ages 70 – 74 group and Sean’s grandfather
    \n= 4\\(\\frac{1}{3}\\) – 3\\(\\frac{2}{3}\\)
    \n= \\(\\frac{13}{3}\\) – \\(\\frac{11}{3}\\)
    \n= \\(\\frac{13 – 11}{3}\\)
    \n= \\(\\frac{2}{3}\\) hours
    \nHence, from the above,
    \nWe can conclude that
    \nThe difference of time taken between men’s winner Ages 70 – 74 group and Sean’s grandfather is about \\(\\frac{2}{3}\\) hours<\/p>\n

    Essential Question<\/strong>
    \nHow Can You Solve Problems Involving Time?
    \nAnswer:
    \nWe know that,
    \nWhen we want to find the total time,
    \nWe will add the given times
    \nWhen we want to find the difference between time,
    \nWe will subtract the given times
    \nNow,
    \nWe know that,
    \n1 hour = 60 minutes
    \n1 minute = \\(\\frac{1}{60}\\) hours<\/p>\n

    Visual Learning Bridge
    \nKrystal is training for a race. She trains every day for 8 days. How many hours does Krystal train?<\/p>\n

    Krystal spends an equal amount of time sprinting, walking, and jogging. How many minutes does Krystal spend on each activity during her 8 days of training?
    \n\"Envision
    \nYou can use what you know about time to help solve these problems.<\/p>\n

    Find how many hours Krystal trains.
    \nFind 8 \u00d7 \\(\\frac{3}{4}\\)
    \n\"Envision<\/p>\n

    Find how many minutes Krystal spends on each activity during her training.
    \n1 hour = 60 minutes
    \n6 \u00d7 60 minutes = 360 minutes of training
    \nIn 8 days, Krystal spends 360 minutes sprinting, walking, and jogging.
    \nDivide to find how many minutes Krystal spends on each activity. Find 360 \u00f7 3.
    \n\"Envision
    \nIn 8 days, Krystal spends 120 minutes, or 2 hours, training on each activity.<\/p>\n

    Convince Me! Construct Arguments<\/strong> Why do you multiply to convert 6 hours to minutes?
    \nAnswer:
    \nFrom the previous example,
    \nWe can observe that
    \nThe amount of time taken by Krystal to train for 8 days is: 6 hours
    \nBut,
    \nIt is given that we have to find the amount of time in minutes
    \nNow,
    \nWe know that,
    \n1 hour = 60 minutes
    \nSo,
    \n6 hours = 6 \u00d7 60 minutes
    \n= 360 minutes
    \nHence, from the above,
    \nWe can conclude that
    \nWe will convert 6 hours into minutes because it has been asked to find the amount of time taken in minutes<\/p>\n

    Another Example!<\/strong>
    \n\"Envision<\/p>\n

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

    Do You Understand?<\/strong>
    \nQuestion 1.
    \nHow are adding and subtracting measures of time like adding and subtracting whole numbers?
    \nAnswer:
    \nThe adding and subtracting measures of time is the same as adding and subtracting whole numbers when the measures of time are also whole numbers
    \nBut,
    \nWhen the measures of time are the decimal numbers, we will borrow 60 minutes when the borrowing number is less than the second number<\/p>\n

    Do You Know How?<\/strong>
    \nFor 2-3, solve. Remember there are 60 minutes in 1 hour and 7 days in 1 week.
    \nQuestion 2.
    \nHow many minutes are in a school day of 7 hours 25 minutes?
    \nAnswer:
    \nIt is given that
    \n1 hour = 60 minutes
    \n1 week = 7 days
    \nSo,
    \n7 hours 25 minutes = (7 \u00d7 60) + 25
    \n= 420 + 25
    \n= 445 minutes
    \nHence, from the above,
    \nWe can conclude that
    \nThe number of minutes present in a school day of 7 hours 25 minutes is: 445 minutes<\/p>\n

    Question 3.
    \nHow much is 3\\(\\frac{2}{4}\\) weeks + 2\\(\\frac{3}{4}\\) weeks?
    \nAnswer:
    \nThe given fraction is:
    \n3\\(\\frac{2}{4}\\) weeks + 2\\(\\frac{3}{4}\\) weeks
    \nSo,
    \n3\\(\\frac{2}{4}\\) weeks + 2\\(\\frac{3}{4}\\) weeks
    \n= \\(\\frac{14}{4}\\) weeks + \\(\\frac{11}{4}\\) weeks
    \n= \\(\\frac{14 + 11}{4}\\) weeks
    \n= \\(\\frac{25}{4}\\) weeks
    \nHence, from the above,
    \nWe can conclude that the value of 3\\(\\frac{2}{4}\\) weeks + 2\\(\\frac{3}{4}\\) weeks is:
    \n\\(\\frac{25}{4}\\) weeks<\/p>\n

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

    For 4-7, add, subtract, multiply, or divide.
    \n\"Envision<\/p>\n

    Question 4.
    \n\"Envision
    \nAnswer:
    \nWe know that,
    \n\"\"
    \nNow,
    \nWe know that,
    \nWhen the number of minutes is greater than 60,
    \nConvert 60 minutes into 1 hour and add that 1 hour to the number of hours we obtained in the result
    \nHence,
    \n\"\"<\/p>\n

    Question 5.
    \n\"Envision
    \nAnswer:
    \nWe know that,
    \n\"\"
    \nNow,
    \nWe know that,
    \nWhen the number of months is less than the second number of months,
    \nWe have to borrow and we will borrow 12 months and add that 12 months into the first number of months
    \nHence,
    \n\"\"<\/p>\n

    Question 6.
    \n\"Envision
    \nAnswer:
    \nWe know that,
    \n\"\"
    \nHence,
    \n\"\"<\/p>\n

    Question 7.
    \nHow long must each person work for 4 people to evenly share 48 hours of work?
    \n48 \u00f7 4 = \u2610 hours
    \nAnswer:
    \nWe know that,
    \n\"\"
    \nSo,
    \nThe amount of time each person work for 4 people to evenly share 48 hours of work is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \nThe amount of time each person work for 4 people to evenly share 48 hours of work is: 12 hours<\/p>\n

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

    For 8-9, use the table at the right.
    \n\"Envision
    \nQuestion 8.
    \nHow long do all of the activities at the reunion last?
    \nAnswer:
    \nThe given data is:
    \n\"\"
    \nSo,
    \nThe time that all of the activities at the reunion last = The total time is taken for all the activities to end
    \nSo,
    \nThe time that all of the activities at the reunion last = 4 hours 15 minutes + 55 minutes + 1 hour 30 minutes + 1 hour 35 minutes
    \n= 6 hours 135 minutes
    \n= 6 hours + 2 hours + 15 minutes
    \n= 8 hours 15 minutes
    \nHence, from the above,
    \nWe can conclude that
    \nThe time that all of the activities at the reunion last is: 8 hours 15 minutes<\/p>\n

    Question 9.
    \nThere are 55 minutes between the time dinner ends and the campfire begins. What is the elapsed time from the beginning of dinner to the beginning of the campfire?
    \nAnswer:
    \nIt is given that
    \nThere are 55 minutes between the time dinner ends and the campfire begins
    \nNow,
    \nThe given data is:
    \n\"\"
    \nSo,
    \nThe elapsed time from the beginning of dinner to the beginning of the campfire = (The end time of the slide show) – (The end time of Dinner)
    \n= 1 hour 30 minutes – 55 minutes [1 hour = 60 minutes]
    \n= 90 – 55
    \n= 35 minutes
    \nHence, from the above,
    \nWe can conclude that
    \nThe elapsed time from the beginning of dinner to the beginning of the campfire is: 35 minutes<\/p>\n

    Question 10.
    \nMake Sense and Persevere<\/strong> The band boosters spent $4,520 on airline tickets and $1,280 on hotel costs for the 8 members of the color guard. How much was spent for each member of the color guard?
    \nAnswer:
    \nIt is given that
    \nThe band boosters spent $4,520 on airline tickets and $1,280 on hotel costs for the 8 members of the color guard
    \nSo,
    \nThe total amount spent by the band boosters = (The amount spent by the band boosters on airline tickets) + (The amount spent by the band boosters on hotel costs)
    \n= $4,520 + $1,280
    \n= $5,800
    \nSo,
    \nThe amount spend for each member of the color guard = \\(\\frac{The total amount spent by the band boosters}{The total members present in the color guard}\\)
    \n= \\(\\frac{$5,800}{8}\\)
    \n= $725
    \nHence, from the above,
    \nWe can conclude that
    \nThe amount spend for each member of the color guard is: $725<\/p>\n

    Question 11.
    \nHigher-Order Thinking<\/strong> A boat ride at the lake lasts 2\\(\\frac{2}{4}\\) hours. A canoe trip down the river lasts 3\\(\\frac{1}{4}\\) hours. Show each time on the number line. How much longer is the canoe trip than the boat ride in hours? in minutes?
    \n\"Envision
    \nAnswer:
    \nIt is given that
    \nA boat ride at the lake lasts 2\\(\\frac{2}{4}\\) hours. A canoe trip down the river lasts 3\\(\\frac{1}{4}\\) hours
    \nSo,
    \nThe difference of time between the canoe trip and the boat ride in hours = 3\\(\\frac{1}{4}\\) – 2\\(\\frac{2}{4}\\)
    \n= \\(\\frac{13}{4}\\) – \\(\\frac{10}{4}\\)
    \n= \\(\\frac{13 – 10}{4}\\)
    \n= \\(\\frac{3}{4}\\) hours
    \nNow,
    \nThe difference of time between the canoe trip and the boat ride in minutes = \\(\\frac{3}{4}\\) \u00d7 60 minutes
    \n= \\(\\frac{3 \u00d7 60}{4}\\)
    \n= \\(\\frac{180}{4}\\)
    \n= 45 minutes
    \nNow,
    \nThe representation of the canoe time and the time taken for a boat ride in the number line is:
    \n\"\"
    \nHence, from the above,
    \nWe can conclude that
    \nThe difference of time between the canoe trip and the boat ride in hours is: \\(\\frac{3}{4}\\) hours
    \nThe difference of time between the canoe trip and the boat ride in minutes is: 45 minutes<\/p>\n

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

    Question 12.
    \nIt takes Krys and Glen \\(\\frac{1}{4}\\) hour to walk a mile. This week Krys walked 9 miles and Glen walked 3 miles. How much longer did Krys walk than Glen?
    \n________ hours
    \nAnswer:
    \nIt is given that
    \nIt takes Krys and Glen \\(\\frac{1}{4}\\) hours to walk a mile. This week Krys walked 9 miles and Glen walked 3 miles
    \nSo,
    \nThe difference between the number of miles walked by Krys ad Glen = 9 – 3
    \n= 6 miles
    \nSo,
    \nThe difference of time taken for Krys to walk faster than Glen = (The difference between the number of miles walked by Krys and Glen) \u00d7 (The time taken by Krys and Glan to walk a mile)
    \n= 6 \u00d7 \\(\\frac{1}{4}\\)
    \n= \\(\\frac{6 \u00d7 1}{4}\\)
    \n= \\(\\frac{6}{4}\\)
    \n= \\(\\frac{3}{2}\\)
    \n= 1.5 hours
    \nHence, from the above,
    \nWe can conclude that
    \nThe difference of time taken for Krys to walk faster than Glen is: 1.5 hours<\/p>\n

    Question 13.
    \nHenry’s first flight lasts 1 hour 12 minutes. The second flight lasts 2 hours 41 minutes. How much time did Henry spend on the flights?
    \n_______ hours _______ minutes
    \nAnswer:
    \nIt is given that
    \nHenry’s first flight lasts 1 hour 12 minutes. The second flight lasts 2 hours 41 minutes
    \nSo,
    \nThe total time spent by Henry on the flights = 1 hour 12 minutes + 2 hours 41 minutes
    \n= 3 hours 53 minutes
    \nHence, from the above,
    \nWe can conclude that
    \nThe total time spent by Henry on the flights is: 3 hours 53 minutes<\/p>\n

    Lesson 10.5 Problem Solving<\/h3>\n

    Model with Math<\/strong>
    \nSolve & Share<\/strong>
    \nPierre’s mother owns an ice cream shop. She puts \\(\\frac{3}{12}\\) cup of vanilla extract and \\(\\frac{1}{12}\\) cup of almond extract in each 10-gallon batch of ice cream. How much total extract is used to make 5 batches of ice cream? Use the bar diagrams to represent and solve this problem.
    \nI can …use various representations to solve problems.
    \n\"Envision<\/p>\n

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

      \n
    • How can I use the math I know to help solve this problem?<\/li>\n
    • How can I use pictures, objects, or an equation to represent the problem?<\/li>\n
    • How can I use numbers, words, and symbols to solve the problem?<\/li>\n<\/ul>\n

      Answer:
      \nIt is given that
      \nPierre’s mother owns an ice cream shop. She puts \\(\\frac{3}{12}\\) cup of vanilla extract and \\(\\frac{1}{12}\\) cup of almond extract in each 10-gallon batch of ice cream.
      \nSo,
      \nThe total amount of extract that is used to make 1 batch of icecream = (The amount of vanilla extract) + (The amount of almond extract)
      \n= \\(\\frac{3}{12}\\) + \\(\\frac{1}{12}\\)
      \n= \\(\\frac{3 + 1}{12}\\)
      \n= \\(\\frac{4}{12}\\)
      \n= \\(\\frac{1}{3}\\) cups
      \nSo,
      \nThe total extract present in 5 batches of icecream = 5 \u00d7 (The total extract present in 1 batch of icecream)
      \n= 5 \u00d7 \\(\\frac{1}{3}\\)
      \n= \\(\\frac{5 \u00d7 1}{3}\\)
      \n= \\(\\frac{5}{3}\\) cups
      \nNow,
      \nThe representation of the given information in the form of a bar diagram is:
      \n\"\"
      \n\"\"
      \nHence, from the above,
      \nWe can conclude that
      \nThe total amount of extract present in 5 batches of ice cream is: \\(\\frac{5}{3}\\) cups<\/p>\n

      Look Back!<\/strong> Model with Math<\/strong> What number sentences can you write to model the problem?
      \nAnswer:
      \nThe number of sentences that you can write to model the above problem is:
      \na.
      \nThe total amount of extract that is used to make 1 batch of icecream = (The amount of vanilla extract) + (The amount of almond extract)
      \nb.
      \nThe total extract present in 5 batches of icecream = 5 \u00d7 (The total extract present in 1 batch of icecream)<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Represent a Situation with a Math Model?
      \nAnswer:
      \nA “Math model” usually describes a system by a set of variables and a set of equations that establish relationships between the variables<\/p>\n

      Visual Learning Bridge
      \nMr. Finn gives the number of snacks shown to the baseball team’s coach every time the team wins a game. How many total pounds of snacks does Mr. Finn give the coach after the baseball team wins 3 games?
      \n\"Envision
      \nWhat hidden question do you need to find and solve first?
      \nHow many total pounds of snacks does Mr. Finn give the coach when the baseball team wins one game?<\/p>\n

      How can I model with math?
      \nI can<\/p>\n

        \n
      • use previously learned concepts and skills.<\/li>\n
      • find and answer any hidden questions.<\/li>\n
      • use bar diagrams and equations to represent and solve this problem.<\/li>\n<\/ul>\n

        Here’s my thinking.
        \nLet p = the pounds of snacks after one game.
        \n\"Envision
        \nMr. Finn gives the coach 2\\(\\frac{5}{8}\\) pounds of snacks after the team wins 3 games.<\/p>\n

        Convince Me!<\/strong> Reasoning Explain how to solve this problem another way.
        \nAnswer:
        \nIt is given that
        \nMr. Finn gives the number of snacks shown to the baseball team’s coach every time the team wins a game.
        \nNow,
        \nThe given figure is:
        \n\"Envision
        \nNow,
        \nFrom the given figure,
        \nWe can observe that
        \nThe total number of pounds of snacks Mr.Finn give the coach after the baseball team wins 1 game =
        \n(The number of pounds of red licorice) + (The number of pounds of peanuts)
        \n= \\(\\frac{3}{8}\\) + \\(\\frac{4}{8}\\)
        \n= \\(\\frac{3 + 4}{8}\\)
        \n= \\(\\frac{7}{8}\\) pounds of snacks
        \nNow,
        \nThe total number of pounds of snacks Mr.Finn give the coach after the baseball team wins 3 games =
        \n3 \u00d7 (The total number of pounds of snacks Mr.Finn give the coach after the baseball team wins 1 game)
        \n= 3 \u00d7 \\(\\frac{7}{8}\\)
        \n= \\(\\frac{3 \u00d7 7}{8}[\/altex]
        \n= [latex]\\frac{21}{8}\\) pounds of snacks
        \nHence, from the above,
        \nWe can conclude that
        \nThe total number of pounds of snacks Mr.Finn give the coach after the baseball team wins 3 games is: \\(\\frac{21}{8}\\) pounds<\/p>\n

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

        Model with Math<\/strong>
        \nColton and his classmates are making maps of the streets where they live. How much green and black felt does his teacher need to buy so 5 groups of students can each make a map?
        \n\"Envision
        \nQuestion 1.
        \nDraw the bar diagrams and write equations to find g, the amount of green, and b, the amount of black felt.
        \nAnswer:
        \nIt is given that
        \nColton and his classmates are making maps of the streets where they live
        \nNow,
        \nThe given information is:
        \n\"\"
        \nNow,
        \nFrom the given information,
        \nThe amount of green felt needed for each map (g) = \\(\\frac{4}{6}\\) sheet of green
        \nThe amount of black felt needed for each map (b) = \\(\\frac{5}{6}\\) sheet of black
        \nHence,
        \nThe representation of the given information in the form of a bar diagram is:
        \n\"\"<\/p>\n

        Question 2.
        \nWrite and solve an equation to find t, the amount of green and black felt the class will use.
        \nAnswer:
        \nFrom Question 1,
        \nWe can observe that
        \nThe amount of green felt needed for each map (g) = \\(\\frac{4}{6}\\) sheet of green
        \nThe amount of black felt needed for each map (b) = \\(\\frac{5}{6}\\) sheet of black
        \nSo,
        \nThe total amount of green and black felts needed for each map (t) = (The amount of green felt needed fro each map) + (The amount of black felt needed for each map)
        \n= \\(\\frac{4}{6}\\) + \\(\\frac{5}{6}\\)
        \n= \\(\\frac{4 + 5}{6}\\)
        \n= \\(\\frac{9}{6}\\)
        \n= \\(\\frac{3}{2}\\)
        \nSo,
        \nthe amount of green and black felt the class will use = 5 \u00d7 \\(\\frac{3}{2}\\)
        \n= [altex]\\frac{5 \u00d7 3}{2}[\/latex]
        \n= \\(\\frac{15}{2}\\)
        \nHence, from the above,
        \nWe can conclude that
        \nThe total amount of green and black felt the class will use is: \\(\\frac{15}{2}\\)<\/p>\n

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

        Model with Math<\/strong>
        \nMoira swims \\(\\frac{3}{6}\\) hour before school 5 days a week and \\(\\frac{5}{6}\\) hour after school 4 days a week. For how long does she swim each week? Use Exercises 3-5 to answer the question.
        \nQuestion 3.
        \nDraw a bar diagram and write an equation to find b, how many hours Moira swims before school each week.
        \nAnswer:
        \nIt is given that
        \nMoira swims \\(\\frac{3}{6}\\) hour before school 5 days a week and \\(\\frac{5}{6}\\) hour after school 4 days a week.
        \nSo,
        \nThe number of hours Moira swims before school a week (b) = (The number of days Moira swims before school in a week) \u00d7 (The number of hours Moira swims each day before school in\u00a0 a week)
        \n= 5 \u00d7 \\(\\frac{3}{6}\\)
        \n= \\(\\frac{5 \u00d7 3}{6}\\)
        \n= \\(\\frac{15}{6}\\)
        \n= \\(\\frac{5}{2}\\) hours
        \nHence,
        \nThe representation of the information about the number of hours Moira swims before school each week is:
        \n\"\"
        \nThe number of hours Moira swims before school a week is: \\(\\frac{5}{2}\\) hours<\/p>\n

        Question 4.
        \nDraw a bar diagram and write an equation to find a, how many hours she swims after school each week.
        \nAnswer:
        \nIt is given that
        \nMoira swims \\(\\frac{3}{6}\\) hour before school 5 days a week and \\(\\frac{5}{6}\\) hour after school 4 days a week.
        \nSo,
        \nThe number of hours Moira swims after school a week (a) = (The number of days Moira swims after school in a week) \u00d7 (The number of hours Moira swims each day after school in\u00a0 a week)
        \n= 4 \u00d7 \\(\\frac{5}{6}\\)
        \n= \\(\\frac{5 \u00d7 4}{6}\\)
        \n= \\(\\frac{20}{6}\\)
        \n= \\(\\frac{10}{3}\\) hours
        \nHence,
        \nThe representation of the information about the number of hours Moira swims after school each week is:
        \n\"\"
        \nThe number of hours Moira swims after school a week is: \\(\\frac{10}{3}\\) hours<\/p>\n

        Question 5.
        \nDraw a bar diagram and write an equation to find h, how many hours Moira swims each week.
        \nAnswer:
        \nFrom Questions 3 and 4,
        \nWe can observe that
        \nThe number of hours Moira swims before school a week (b) is: \\(\\frac{5}{2}\\) hours
        \nThe number of hours Moira swims after school a week (a) is: \\(\\frac{10}{3}\\) hours
        \nSo,
        \nThe total number of hours Moira swims each week (h) = b + a
        \n= \\(\\frac{5}{2}\\) + \\(\\frac{10}{3}\\)
        \n= \\(\\frac{15}{6}\\) + \\(\\frac{20}{6}\\)
        \n= \\(\\frac{15 + 20}{6}\\)
        \n= \\(\\frac{35}{6}\\) hours
        \nHence,
        \nThe representation of the bar diagram for the number of hours Moira swims each week is:
        \n\"\"
        \nThe number of hours Moira swims each week is: \\(\\frac{35}{6}\\) hours<\/p>\n

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

        Performance Task<\/strong><\/p>\n

        Seeing Orange<\/strong>
        \nPerry mixed \\(\\frac{5}{8}\\) gallon of red paint and \\(\\frac{3}{8}\\) gallon of yellow paint to make the right shade of orange paint. He needs 2 gallons of orange paint to paint the basement floor. How many gallons of red and yellow paint should Perry use to make enough orange paint to cover the floor?
        \nQuestion 6.
        \nReasoning<\/strong> What do you need to know to find how many gallons of each color Perry should use?
        \nAnswer:
        \nIt is given that
        \nPerry mixed \\(\\frac{5}{8}\\) gallon of red paint and \\(\\frac{3}{8}\\) gallon of yellow paint to make the right shade of orange paint. He needs 2 gallons of orange paint to paint the basement floor
        \nHence,
        \nTo find how many gallons of each color Perry should use, we have to answer:
        \nHow many gallons of red paint and yellow paint are needed to make the right side of orange paint?<\/p>\n

        Question 7.
        \nModel with Math<\/strong>
        \nDraw the bar diagrams and write equations to find g, how many gallons of paint are in a batch, and b, how many batches Perry needs to make.
        \n\"Envision
        \nAnswer:
        \nIt is given that
        \nPerry mixed \\(\\frac{5}{8}\\) gallon of red paint and \\(\\frac{3}{8}\\) gallon of yellow paint to make the right shade of orange paint. He needs 2 gallons of orange paint to paint the basement floor
        \nSo,
        \nThe total amount of paint needed to make the right side of orange paint = (The number of gallons of red paint) + (The number of gallons of yellow paint)
        \n= \\(\\frac{5}{8}\\) + \\(\\frac{3}{8}\\)
        \n= \\(\\frac{5 + 3}{8}\\)
        \n= \\(\\frac{8}{8}\\)
        \n= 1 gallon
        \nNow,
        \nThe number of gallons needed for Perry to paint the basement floor = (The number of gallons of orange paint needed to paint the basement floor) \u00d7 (The total amount of paint needed to make the right side of orange paint)
        \n= 2 \u00d7 1
        \n= 2 gallons
        \nHence,
        \nThe representation of the given information in the form of a bar diagram is:
        \n\"\"
        \nThe number of gallons needed for Perry to paint the basement floor is: 2 gallons<\/p>\n

        Question 8.
        \nModel with Math<\/strong>
        \nDraw the bar diagrams and write and solve equations to show how to find how many gallons of each color Perry should use. Tell what your variables represent.
        \nAnswer:
        \nIt is given that
        \nPerry mixed \\(\\frac{5}{8}\\) gallon of red paint and \\(\\frac{3}{8}\\) gallon of yellow paint to make the right shade of orange paint. He needs 2 gallons of orange paint to paint the basement floor
        \nSo,
        \nThe number of gallons of each color Perry should use = 2 \u00d7 (The number of gallons of red paint) + 2 \u00d7 (The number of gallons of yellow paint)
        \n= 2 \u00d7 \\(\\frac{5}{8}\\) + 2 \u00d7 \\(\\frac{3}{8}\\)
        \n= \\(\\frac{2 \u00d7 5}{8}\\) + \\(\\frac{2 \u00d7 3}{8}\\)
        \n= \\(\\frac{10}{8}\\) + \\(\\frac{6}{8}\\)
        \n= \\(\\frac{10 + 6}{8}\\)
        \n= \\(\\frac{16}{8}\\)
        \n= 2 gallons
        \nHence,
        \nThe representation of the given information in the form of a bar diagram is:
        \n\"\"
        \nThe number of gallons of red paint Perry should use is: \\(\\frac{10]{8}\\) gallons
        \nThe number of gallons of yellow paint Perry should use is: \\(\\frac{6]{8}\\) gallons<\/p>\n

        Topic 10 Fluency Practice Activity<\/h3>\n

        Pointe Tall<\/strong>
        \nFind a partner. Get paper and a pencil. Each partner chooses a different color: light blue or dark blue.
        \nPartner 1 and Partner 2 each point to a black number at the same time. Each partner adds the two numbers.
        \nIf the answer is on your color, you get a tally mark. Work until one partner has twelve tally marks.
        \nI can … add multi-digit whole numbers.
        \n\"Envision<\/p>\n

        Topic 10 Vocabulary Review<\/h3>\n

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

          \n
        • denominator<\/li>\n
        • equivalent fractions<\/li>\n
        • fraction<\/li>\n
        • mixed number<\/li>\n
        • multiple<\/li>\n
        • numerator<\/li>\n
        • unit fraction<\/li>\n<\/ul>\n

          Write T for true and F for false.
          \nQuestion 1.
          \n_______ The fraction \\(\\frac{3}{4}\\) is a multiple of \\(\\frac{1}{4}\\).
          \nAnswer:
          \nThe given statement is:
          \nThe fraction \\(\\frac{3}{4}\\) is a multiple of \\(\\frac{1}{4}\\)
          \nNow,
          \nWe know that,
          \nn \u00d7 \\(\\frac{1}{y}\\) is always a multiple of \\(\\frac{1}{y}\\)
          \nHence, from the above,
          \nWe can conclude that
          \nThe fraction \\(\\frac{3}{4}\\) is a multiple of \\(\\frac{1}{4}\\) is: True<\/p>\n

          Question 2.
          \n__________ Equivalent fractions are fractions where the numerator and the denominator have the same value.
          \nAnswer:
          \nThe given statement is:
          \nEquivalent fractions are fractions where the numerator and the denominator have the same value
          \nNow,
          \nWe know that,
          \nThe “Equivalent fractions” are the fractions that have different values of numerator and denominator
          \nHence, from the above,
          \nWe can conclude that
          \nEquivalent fractions are fractions where the numerator and the denominator have the same value is: False<\/p>\n

          Question 3.
          \n__________ The denominator of a fraction tells the number of equal parts in the whole.
          \nAnswer:
          \nThe given statement is:
          \nThe denominator of a fraction tells the number of equal parts in the whole.
          \nNow,
          \nWe know that,
          \nIn the fraction \\(\\frac{x}{y}\\),
          \nx represents the number of shaded parts
          \ny represents the total number of equal parts
          \nHence, from the above,
          \nWe can conclude that
          \nThe denominator of a fraction tells the number of equal parts in the whole is: True<\/p>\n

          Question 4.
          \n___________ A fraction names part of a whole, part of a set, or a location on a number line.
          \nAnswer:
          \nThe given statement is:
          \nA fraction names part of a whole, part of a set, or a location on a number line.
          \nNow,
          \nWe know that,
          \nA symbol used to name a part of a whole, a part of a set, or a location on a number line is called a “Fraction”
          \nHence, from the above,
          \nWe can conclude that
          \nA fraction names part of a whole, part of a set, or a location on a number line is: True<\/p>\n

          Question 5.
          \n________ The numerator is the number below the fraction bar in a fraction.
          \nAnswer:
          \nThe given statement is:
          \nThe numerator is the number below the fraction bar in a fraction.
          \nNow,
          \nWe know that,
          \nThe “Denominator” is the number below the fraction bar in a fraction
          \nHence, from the above,
          \nWe can conclude that
          \nThe numerator is the number below the fraction bar in a fraction is: False<\/p>\n

          Write always, sometimes, or never.
          \nQuestion 6.
          \nA unit fraction __________ has a numerator of 1.
          \nAnswer:
          \nThe given statement is:
          \nA unit fraction __________ has a numerator of 1.
          \nHence, from the above,
          \nWe can conclude that
          \nA unit fraction “always” has a numerator of 1.<\/p>\n

          Question 7.
          \nA numerator is _________ greater than its denominator.
          \nAnswer:
          \nThe given statement is:
          \nA numerator is _________ greater than its denominator.
          \nHence, from the above,
          \nWe can conclude that
          \nA numerator is “sometimes” greater than its denominator.<\/p>\n

          Question 8.
          \nA mixed number _________ has just a fraction part.
          \nAnswer:
          \nThe given statement is:
          \nA mixed number _________ has just a fraction part.
          \nHence, from the above,
          \nWe can conclude that
          \nA mixed number “never” has just a fraction part.<\/p>\n

          Use Vocabulary in Writing<\/strong>
          \nQuestion 9.
          \nSamatha wrote \\(\\frac{1}{2}\\). Use at least 3 terms from the Word List to describe Samantha’s fraction.
          \n\"Envision
          \nAnswer:
          \nIt is given that
          \nSamatha wrote \\(\\frac{1}{2}\\).
          \nHence, from the above,
          \nWe can conclude that
          \nThe 3 terms from the word list to describe Samantha’s fraction are:
          \na. Fraction
          \nb Unit fraction
          \nc Equivalent fraction<\/p>\n

          Topic 10 Reteaching<\/h3>\n

          Set A pages 385-388<\/strong><\/p>\n

          Talia used \\(\\frac{5}{8}\\) yard of ribbon.
          \n\"Envision<\/p>\n

          Remember<\/strong> a unit fraction will always have a numerator of 1<\/p>\n

          Write each fraction as a multiple of a unit fraction.
          \nQuestion 1.
          \n\\(\\frac{5}{5}\\)
          \nAnswer:
          \nThe given fraction is: \\(\\frac{5}{5}\\)
          \nSo,
          \nThe representation of the given fraction in the form of a unit fraction is:
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \nThe given fraction as a multiple of a unit fraction is:
          \n\\(\\frac{5}{5}\\) = 5 \u00d7 \\(\\frac{1}{5}\\)<\/p>\n

          Question 2.
          \n\\(\\frac{3}{8}\\)
          \nAnswer:
          \nThe given fraction is: \\(\\frac{3}{8}\\)
          \nSo,
          \nThe representation of the given fraction in the form of a unit fraction is:
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \nThe given fraction as a multiple of a unit fraction is:
          \n\\(\\frac{3}{8}\\) = 3 \u00d7 \\(\\frac{1}{8}\\)<\/p>\n

          Question 3.
          \n\\(\\frac{4}{3}\\)
          \nAnswer:
          \nThe given fraction is: \\(\\frac{4}{3}\\)
          \nSo,
          \nThe representation of the given fraction in the form of a unit fraction is:
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \nThe given fraction as a multiple of a unit fraction is:
          \n\\(\\frac{4}{3}\\) = 4 \u00d7 \\(\\frac{1}{3}\\)<\/p>\n

          Question 4.
          \n\\(\\frac{6}{5}\\)
          \nAnswer:
          \nThe given fraction is: \\(\\frac{6}{5}\\)
          \nSo,
          \nThe representation of the given fraction in the form of a unit fraction is:
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \nThe given fraction as a multiple of a unit fraction is:
          \n\\(\\frac{6}{5}\\) = 6 \u00d7 \\(\\frac{1}{5}\\)<\/p>\n

          Question 5.
          \n\\(\\frac{15}{8}\\)
          \nAnswer:
          \nThe given fraction is: \\(\\frac{15}{8}\\)
          \nSo,
          \nThe representation of the given fraction in the form of a unit fraction is:
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \nThe given fraction as a multiple of a unit fraction is:
          \n\\(\\frac{15}{8}\\) = 15 \u00d7 \\(\\frac{1}{8}\\)<\/p>\n

          Question 6.
          \n\\(\\frac{7}{4}\\)
          \nAnswer:
          \nThe given fraction is: \\(\\frac{7}{4}\\)
          \nSo,
          \nThe representation of the given fraction in the form of a unit fraction is:
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \nThe given fraction as a multiple of a unit fraction is:
          \n\\(\\frac{7}{4}\\) = 7 \u00d7 \\(\\frac{1}{4}\\)<\/p>\n

          Set B pages 389-392<\/strong><\/p>\n

          James runs \\(\\frac{3}{5}\\) mile each week. How far does James run after 2 weeks?
          \n\"Envision
          \nUse multiplication to find the product.
          \n\\(2 \\times \\frac{3}{5}=\\frac{3}{5}+\\frac{3}{5}=\\frac{6}{5}=\\frac{5}{5}+\\frac{1}{5}=1 \\frac{1}{5}\\)
          \nJames ran \\(\\frac{6}{5}\\) or 1\\(\\frac{1}{5}\\) miles.<\/p>\n

          Remember<\/strong> you can record answers as fractions or mixed numbers.<\/p>\n

          Write and solve an equation.
          \nQuestion 1.
          \n\"Envision
          \nAnswer:
          \nThe given model is:
          \n\"Envision
          \nNow,
          \nFrom the given model,
          \nWe can observe that
          \n3 \u00d7 \\(\\frac{1}{10}\\) + 3 \u00d7 \\(\\frac{1}{10}\\)
          \n= \\(\\frac{3}{10}\\) + \\(\\frac{3}{10}\\)
          \n= \\(\\frac{3 + 3}{10}\\)
          \n= \\(\\frac{6}{10}\\)
          \n= \\(\\frac{3}{5}\\)
          \nHence, from the above,
          \nWe can conclude that
          \nThe value for the given model is: \\(\\frac{3}{5}\\)<\/p>\n

          Question 2.
          \n\"Envision
          \nAnswer:
          \nThe given model is:
          \n\"Envision
          \nNow,
          \nFrom the given model,
          \nWe can observe that
          \nThe total number of parts are: 6
          \nThe number of shaded parts is: 4
          \nSo,
          \nThe fraction of the shaded part in the given model = \\(\\frac{The number of shaded parts}{The total number of parts}\\)
          \n= \\(\\frac{4}{6}\\)
          \n= \\(\\frac{2}{3}\\)
          \nHence, from the above,
          \nWe can conclude that
          \nThe value for the given model is: \\(\\frac{2}{3}\\)<\/p>\n

          Set C pages 393-396<\/strong><\/p>\n

          Alisa has 7 puppies. Each puppy eats \\(\\frac{2}{3}\\) cup of food each day. How many cups of food does Alisa need to feed the puppies each day?
          \nMultiply 7 \u00d7 \\(\\frac{2}{3}\\)
          \nMultiply the whole number and the numerator.
          \n\\(7 \\times \\frac{2}{3}=\\frac{7 \\times 2}{3}\\)
          \n= \\(\\frac{14}{3}\\)
          \n= \\(\\frac{3}{3}+\\frac{3}{3}+\\frac{3}{3}+\\frac{3}{3}+\\frac{2}{3}\\)
          \n= 4\\(\\frac{2}{3}\\) cups
          \nAlisa needs 4\\(\\frac{2}{3}\\) cups of food to feed the puppies each day.<\/p>\n

          Remember<\/strong> you multiply the whole number and the numerator and write the product above the denominator of the fraction.<\/p>\n

          Question 1.
          \nMilo makes 5 batches of muffins. In each batch he uses \\(\\frac{2}{3}\\) bag of walnuts. How many bags of walnuts does Milo use?
          \nAnswer:
          \nIt is given that
          \nMilo makes 5 batches of muffins. In each batch he uses \\(\\frac{2}{3}\\) bag of walnuts.
          \nSo,
          \nThe number of bags of walnuts does Milo use = (The number of batches of muffins) \u00d7 (The amount of bag of walnuts present in each batch)
          \n= 5 \u00d7 \\(\\frac{2}{3}\\)
          \n= \\(\\frac{5 \u00d7 2}{3}\\)
          \n= \\(\\frac{10}{3}\\) bags of walnuts
          \nHence, from the above,
          \nWe can conclude that
          \nThe number of bags of walnuts does Milo used is: \\(\\frac{10}{3}\\) bags of walnuts<\/p>\n

          Question 2.
          \nA bird feeder can hold \\(\\frac{7}{8}\\) pound of seeds. How many pounds of seeds can 4 bird feeders hold?
          \nAnswer:
          \nIt is given that
          \nA bird feeder can hold \\(\\frac{7}{8}\\) pound of seeds
          \nSo,
          \nThe number of pounds of seeds can 4 bird feeders hold = 4 \u00d7 (The number of pounds of seeds a bird feeder can hold)
          \n= 4 \u00d7 \\(\\frac{7}{8}\\)
          \n= \\(\\frac{4 \u00d7 7}{8}\\)
          \n= \\(\\frac{28}{8}\\)
          \n= \\(\\frac{7}{2}\\) pounds of seeds
          \nHence, from the above,
          \nWe can conclude that
          \nThe number of pounds of seeds can 4 bird feeders hold is: \\(\\frac{7}{2}\\) pounds of seeds<\/p>\n

          Set D pages 397-400<\/strong><\/p>\n

          \"Envision<\/p>\n

          Remember<\/strong> you may need to regroup when solving problems with time.<\/p>\n

          Question 1.
          \n\"Envision
          \nAnswer:
          \nWe know that,
          \nIf the number of minutes is greater than 60 and we know that
          \n1 hour = 60 minutes
          \nAdd that hour to the hours present in the result and keep the extra minutes intact
          \nHence,
          \n\"\"<\/p>\n

          Question 2.
          \n7 \u00d7 \\(\\frac{3}{4}\\) hour
          \nAnswer:
          \nThe given fraction is: 7 \u00d7 \\(\\frac{3}{4}\\) hours
          \nSo,
          \n7 \u00d7 \\(\\frac{3}{4}\\)
          \n= \\(\\frac{7 \u00d7 3}{4}\\)
          \n= \\(\\frac{21]{4}\\) hours
          \nHence, from the above,
          \nWe can conclude that
          \nThe value of the given fraction is: \\(\\frac{21}{4}\\) hours<\/p>\n

          Question 3.
          \n\"Envision
          \nAnswer:
          \nWe know that,
          \n1 week = 7 days
          \nSo,
          \nWhen the number of days is less than 7, borrow that 7 days from the number of weeks and add it to the number that is less than 7 and do the subtraction
          \nHence,
          \n\"\"<\/p>\n

          Question 4.
          \nDivide 560 days into groups of 8.
          \nAnswer:
          \nIt is given that
          \nDivide 560 days into groups of 8.
          \nSo,
          \nUsing the method of Long division,
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \n560 days is divided into 70 equal parts when divided by 8<\/p>\n

          Question 5.
          \nLi Marie practices piano 1\\(\\frac{2}{3}\\) hours during the week and 2\\(\\frac{1}{3}\\) hours on the weekend. Show each time on the number line. How many more hours does she practice on the weekend than on the weekdays?
          \n\"Envision
          \nAnswer:
          \nIt is given that
          \nLi Marie practices piano 1\\(\\frac{2}{3}\\) hours during the week and 2\\(\\frac{1}{3}\\) hours on the weekend
          \nNow,
          \nWe know that,
          \nThe number of weekdays is: 5 days
          \nThe number of days in a weekend are: 2 days
          \nSo,
          \nThe number of hours Li Marie practices piano during the week = 5 \u00d7 1\\(\\frac{2}{3}\\)
          \n= 5 \u00d7 \\(\\frac{5}{3}\\)
          \n= \\(\\frac{5 \u00d7 5}{3}\\)
          \n= \\(\\frac{25}{3}\\) hours
          \nSo,
          \nThe number of hours Li Marie practices piano on the weekend = 2 \u00d7 2\\(\\frac{1}{3}\\)
          \n= 2 \u00d7 \\(\\frac{7}{3}\\)
          \n= \\(\\frac{2 \u00d7 7}{3}\\)
          \n= \\(\\frac{14}{3}\\) hours
          \nSo,
          \nThe difference between the number of hours Li Marie practices on the weekend and during the week =
          \n\\(\\frac{25}{3}\\) – \\(\\frac{14}{3}\\)
          \n= \\(\\frac{25 – 14}{3}\\)
          \n= \\(\\frac{11}{3}\\) hours
          \nSo,
          \nThe representation of the number f hours Li Mario practices piano during the week and on the weekend on a number line is:
          \n\"\"
          \nHence, from the above,
          \nWe can conclude that
          \nLi Mario practices \\(\\frac{11}{3}\\) hours more on the weekend than the weekdays<\/p>\n

          Set E pages 401-404<\/strong><\/p>\n

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

            \n
          • How can I use the math I know to help solve this problem?<\/li>\n
          • How can I use pictures, objects, or an equation to represent the problem?<\/li>\n
          • How can I use numbers, words, and symbols to solve the problem?
            \n\"Envision<\/li>\n<\/ul>\n

            Julie makes chili with 2\\(\\frac{3}{8}\\) cups of red beans, 4\\(\\frac{1}{8}\\) cups of chili beans, and \\(\\frac{7}{8}\\) cup of onions. How many more cups of chili beans did Julie use than red beans and onions combined?<\/p>\n

            Question 1.
            \nWrite and solve an equation to find r, how many cups of red beans and onions Julie uses.
            \nAnswer:
            \nIt is given that
            \nJulie makes chili with 2\\(\\frac{3}{8}\\) cups of red beans, 4\\(\\frac{1}{8}\\) cups of chili beans, and \\(\\frac{7}{8}\\) cup of onions
            \nSo,
            \nThe number of cups of red beans and onions Julie uses to make chili (r) = (The number of cups of red beans used to make chili) + (The number of cups of onions used to make chili)
            \n= 2\\(\\frac{3}{8}\\) + \\(\\frac{7}{8}\\)
            \n= \\(\\frac{19}{8}\\) + \\(\\frac{7}{8}\\)
            \n= \\(\\frac{19 + 7}{8}\\)
            \n= \\(\\frac{26}{8}\\)
            \n= \\(\\frac{13}{4}\\) cups
            \nHence, from the above,
            \nWe can conclude that
            \nThe number of cups of red beans and onions Julie uses to make chili is: \\(\\frac{13}{4}\\) cups<\/p>\n

            Question 2.
            \nWrite and solve an equation to find c, how many more cups of chili beans Julie used than red beans and onions.
            \nAnswer:
            \nIt is given that
            \nJulie makes chili with 2\\(\\frac{3}{8}\\) cups of red beans, 4\\(\\frac{1}{8}\\) cups of chili beans, and \\(\\frac{7}{8}\\) cup of onions
            \nNow,
            \nFrom Question 1,
            \nThe number of cups of red beans and onions Julie uses to make chili is: \\(\\frac{13}{4}\\) cups
            \nNow,
            \nThe number of more cups of chili beans Julie used than red beans and onions (c) = (The number of cups of chili beans Julie used to amke chili) – (The number of cups of red beans and onions Julie uses to make chili)
            \n= 4\\(\\frac{1}{8}\\) – \\(\\frac{13}{4}\\)
            \n= \\(\\frac{33}{8}\\) – \\(\\frac{26}{8}\\)
            \n= \\(\\frac{33 – 26}{8}\\)
            \n= \\(\\frac{7}{8}\\) cups
            \nHence, from the above,
            \nWe can conclude that
            \nThe number of more cups of chili beans Julie used than red beans and onions (c) is: \\(\\frac{7}{8}\\) cups<\/p>\n

            Topic 10 Assessment Practice<\/h3>\n

            Question 1.
            \nMargo practices her flute \\(\\frac{1}{4}\\) hour each day.
            \n\"Envision
            \nA. Write and solve an equation to find how many hours Margo practices her flute in 1 week.
            \nAnswer:
            \nIt is given that
            \nMargo practices her flute \\(\\frac{1}{4}\\) hour each day.
            \nNow,
            \nThe given information is:
            \n\"Envision
            \nSo,
            \nThe number of hours Margo practices her flute in 1 week = (The number of days in 1 week) \u00d7 (The number of hours Margo practices her flute each day)
            \n= 7 \u00d7 \\(\\frac{1}{4}\\)
            \n= \\(\\frac{7 \u00d7 1}{4}\\)
            \n= \\(\\frac{7}{4}\\) hours
            \nHence, from the above,
            \nWe can conclude that
            \nThe number of hours Margo practices her flute in 1 week is: \\(\\frac{7}{4}\\) hours<\/p>\n

            B. Write and solve an equation to find how many minutes Margo practices her flute in 1 day. Then use that to find the number of minutes she practices in 1 week.
            \nAnswer:
            \nIt is given that
            \nMargo practices her flute \\(\\frac{1}{4}\\) hour each day.
            \nNow,
            \nThe given information is:
            \n\"Envision
            \nNow,
            \nWe know that,
            \n1 day = 24 hours
            \nSo,
            \nThe number of minutes Margo practices her flute in 1 day = (The number of hours Margo practices her flute in 1 day) \u00d7 60
            \n= \\(\\frac{1}{4}\\) \u00d7 60
            \n= \\(\\frac{60}{4}\\)
            \n= 15 minutes
            \nSo,
            \nThe number of minutes Margo practices her flute in 1 week = (The number of days in 1 week) \u00d7 (The number of minutes Margo practices her flute in 1 day)
            \n= 7 \u00d7 15
            \n= 7 \u00d7 (10 + 5)
            \n= (7 \u00d7 10) + (7 \u00d7 5)
            \n= 70 + 35
            \n= 105 minutes
            \nHence, from the above,
            \nWe can conclude that
            \nThe number of minutes Margo practices her flute in 1 day is: 15 minutes
            \nThe number of minutes Margo practices her flute in 1 week is: 105 minutes<\/p>\n

            Question 2.
            \nWhich of the following represents the fraction \\(\\frac{8}{9}\\) as a multiple of a unit fraction?
            \nA. \\(\\frac{8}{8}\\) = 1 \u00d7 \\(\\frac{8}{9}\\)
            \nB. \\(\\frac{8}{9}\\) = 8 \u00d7 9
            \nC. \\(\\frac{8}{9}\\) = 8 \u00d7 \\(\\frac{1}{9}\\)
            \nD. \\(\\frac{8}{9}\\) = 4 \u00d7 \\(\\frac{2}{9}\\)
            \nAnswer:
            \nThe given fraction is: \\(\\frac{8}{9}\\)
            \nSo,
            \nThe representation of the given fraction as a multiple of a unit fraction is:
            \n\\(\\frac{8}{9}\\) = 8 \u00d7 \\(\\frac{1}{9}\\)
            \nHence, from the above,
            \nWe can conclude that
            \nThe following equations represent the fraction \\(\\frac{8}{9}\\) as a multiple of a unit fraction are:
            \n\"\"<\/p>\n

            Question 3.
            \nBen played at a friend’s house for 2 hours 35 minutes. Later he played at a park for 1 hour 10 minutes. He played for another 1 hour 20 minutes in his backyard. How long did Ben play in all?
            \nA. 6 hours 27 minutes
            \nB. 5 hours 15 minutes
            \nC. 5 hours 5 minutes
            \nD. 5 hours
            \nAnswer:
            \nIt is given that
            \nBen played at a friend’s house for 2 hours 35 minutes. Later he played at a park for 1 hour 10 minutes. He played for another 1 hour 20 minutes in his backyard
            \nSo,
            \nThe total amount of time taken by Ben to play in all = 2 hours 35 minutes + 1 hour 10 minutes + 1 hour 20 minutes
            \n= 4 hours 65 minutes
            \n= 5 hours 05 minutes
            \nHence, from the above,
            \nWe can conclude that
            \nThe time taken by Ben to play in all is:
            \n\"\"<\/p>\n

            Question 4.
            \nChoose numbers from the list to fill in the missing values in the multiplication equations. Use each number once.
            \n\"Envision
            \nAnswer:
            \nThe given number list is:
            \n\"\"
            \nHence, from the above,
            \nWe can conclude that
            \nThe numbers from the list that filled in the missing values in the multiplication equations are:
            \n\"\"<\/p>\n

            Question 5.
            \nChris found the products of whole numbers and fractions. Match each expression with its product.
            \n\"Envision
            \nAnswer:
            \nThe given expressions with their matched products are:
            \n\"\"<\/p>\n

            Question 6.
            \nWhat is the product of 4 and \\(\\frac{4}{8}\\)? Write another expression that is equal to the product of 4 and \\(\\frac{4}{8}\\).
            \nAnswer:
            \nThe given numbers are: 4 and \\(\\frac{4}{8}\\)
            \nSo,
            \n4 \u00d7 \\(\\frac{4}{8}\\)
            \n= 4 \u00d7 4 \u00d7 \\(\\frac{1}{8}\\)
            \n= \\(\\frac{4 \u00d7 4}{8}\\)
            \n= \\(\\frac{16}{8}\\)
            \n= 2
            \nHence, from the above,
            \nWe can conclude that
            \nThe product of 4 \u00d7 \\(\\frac{4}{8}\\) is: 2
            \nThe another expression that is equal to 4 \u00d7 \\(\\frac{4}{8}\\) is: 4 \u00d7 4 \u00d7 \\(\\frac{1}{8}\\)<\/p>\n

            Question 7.
            \nComplete the multiplication equation that describes that is shown by the model.
            \n\"Envision
            \nAnswer:
            \nThe given model is:
            \n\"\"
            \nNow,
            \nFrom the given model,
            \nWe can observe that
            \n\\(\\frac{1}{6}\\) is repeated 8 times and \\(\\frac{2}{6}\\) is repeated 4 times
            \nSo,
            \n\"\"
            \nHence, from the above,
            \nWe can conclude that
            \nThe completed multiplication equation that is shown by the model is:
            \n\"\"<\/p>\n

            Question 8.
            \nUse a unit fraction and a whole number to write a multiplication equation equal to a \\(\\frac{7}{8}\\).
            \nAnswer:
            \nThe given fraction is: \\(\\frac{7}{8}\\)
            \nSo,
            \nThe representation of the given fraction in the form of a unit fraction and a whole number is:
            \n\\(\\frac{7}{8}\\) = 7 \u00d7 \\(\\frac{1}{8}\\)
            \nHence, from the above,
            \nWe can conclude that
            \nThe multiplication equation for the given fraction in the form of a unit fraction and a whole number is:
            \n\\(\\frac{7}{8}\\) = 7 \u00d7 \\(\\frac{1}{8}\\)<\/p>\n

            Question 9.
            \nJuan is making cookies. He makes 2 batches on Monday and 4 batches on Tuesday. He uses \\(\\frac{3}{4}\\) cup of flour in each batch. How much flour does Juan use? Explain.
            \nAnswer:
            \nIt is given that
            \nJuan is making cookies. He makes 2 batches on Monday and 4 batches on Tuesday. He uses \\(\\frac{3}{4}\\) cup of flour in each batch
            \nSo,
            \nThe total number of batches = (The number of batches made by Juan on Monday) + (The number of batches made by Juan on Tuesday)
            \n= 2 + 4
            \n= 6 batches
            \nSo,
            \nThe total amount of flour Juan used = (The total number of batches) \u00d7 (The amount of flour used in each batch)
            \n= 6 \u00d7 \\(\\frac{3}{4}\\)
            \n= \\(\\frac{6 \u00d7 3}{4}\\)
            \n= \\(\\frac{18}{4}\\)
            \n= \\(\\frac{9}{2}\\) cups of flour
            \nHence, from the above,
            \nWe can conclude that
            \nThe total amount of flour Juan used is: \\(\\frac{9}{2}\\) cups of flour<\/p>\n

            Question 10.
            \nLee uses \\(\\frac{1}{5}\\) yard of wire for each ornament he makes. He makes 3 ornaments for his grandmother and 2 ornaments for his mother. How many yards of wire did Lee use?
            \nA. \\(\\frac{3}{5}\\)
            \nB. 1\\(\\frac{2}{5}\\)
            \nC. \\(\\frac{2}{5}\\)
            \nD. 1
            \nAnswer:
            \nIt is given that
            \nLee uses \\(\\frac{1}{5}\\) yard of wire for each ornament he makes. He makes 3 ornaments for his grandmother and 2 ornaments for his mother
            \nSo,
            \nThe total number of ornaments Lee made = (The number of ornaments he made for his grandmother) + (The number of ornaments made for his mother)
            \n= 3 + 2
            \n= 5 ornaments
            \nSo,
            \nThe total number of yards of wire Lee used = (The total number of ornaments Lee made) \u00d7 (The number of yards of wire he used for each ornament)
            \n= 5 \u00d7 \\(\\frac{1}{5}\\)
            \n= \\(\\frac{5 \u00d7 1}{5}\\)
            \n= \\(\\frac{5}{5}\\)
            \n= 1 yard
            \nHence, from the above,
            \nWe can conclude that
            \nThe total number of yards of wire Lee used is:
            \n\"\"<\/p>\n

            Question 11.
            \nLucas is making one dozen snacks for his team. He uses \\(\\frac{1}{4}\\) cup of dried cherries and \\(\\frac{2}{4}\\) cup of dried apricots for each snack. How many cups of dried fruit does Lucas need for his one dozen snacks? Remember, there are 12 snacks in one dozen. Write and solve equations to show how you found the answer.
            \nAnswer:
            \nIt is given that
            \nLucas is making one dozen snacks for his team. He uses \\(\\frac{1}{4}\\) cup of dried cherries and \\(\\frac{2}{4}\\) cup of dried apricots for each snack.
            \nSo,
            \nThe total number of cups of dried cherries and dried apricots for each snack = \\(\\frac{1}{4}\\) + \\(\\frac{2}{4}\\)
            \n= \\(\\frac{1 + 2}{4}\\)
            \n= \\(\\frac{3}{4}\\)
            \nSo,
            \nThe total number of cups of dried cherries and dried apricot for his 1 dozen snacks = 12 \u00d7 (The total number of cups of dried cherries and dried apricots for each snack)
            \n= 12 \u00d7 \\(\\frac{3}{4}\\)
            \n= \\(\\frac{12 \u00d7 3}{4}\\)
            \n= \\(\\frac{36}{4}\\)
            \n= 9 cups
            \nHence, from the above,
            \nWe can conclude that
            \nThe total number of cups of dried cherries and dried apricot for his 1 dozen snacks are: 9 cups<\/p>\n

            Topic 10 Performance Task<\/h3>\n

            School Mural
            \nPaul has permission to paint a 20-panel mural for his school. Part of the mural is shown in the Painting a Mural figure. Paul decides he needs help. The Helpers table shows how much several of his friends can paint each day and how many days a week they can paint.
            \n\"Envision<\/p>\n

            Question 1.
            \nThe students want to find how long it will take to paint the mural if each works on a different part of the panels a different number of days a week.
            \nPart A
            \nHow many panels can Leeza paint in a week? Use fraction strips to explain.
            \nAnswer:
            \nIt is given that
            \nPaul has permission to paint a 20-panel mural for his school. Part of the mural is shown in the Painting a Mural figure. Paul decides he needs help. The Helpers table shows how much several of his friends can paint each day and how many days a week they can paint.
            \nNow,
            \nThe given table is:
            \n\"\"
            \nNow,
            \nFrom the given table,
            \nWe can observe that
            \nLeeza can paint \\(\\frac{3}{4}\\) panels a day for 3 days a week
            \nSo,
            \nThe number of panels Leeza can paint in a week = (The amount Leeza can paint a day) \u00d7 (The number of days she can paint a week)
            \n= \\(\\frac{3}{4}\\) \u00d7 3
            \n= \\(\\frac{3 \u00d7 3}{4}\\)
            \n= \\(\\frac{9}{4}\\) panels
            \nHence,
            \nThe representation of the number of panels Leeza can paint in a week in the form of a bar diagram is:
            \n\"\"
            \nThe number of panels Leeza can paint in a week is: \\(\\frac{9}{4}\\) panels<\/p>\n

            Part B
            \nHow many panels can Kelsey paint in a week? Use equations to explain.
            \nAnswer:
            \nThe given table is:
            \n\"\"
            \nNow,
            \nFrom the given table,
            \nWe can observe that
            \nKelsey paints \\(\\frac{7}{8}\\) panels a day for 4 days a week
            \nSo,
            \nThe number of panels Kelsey can paint in a week = (The number of days can Kelsey paint in a week) \u00d7 (The number of panels Kelsey can paint in a day)
            \n= 4 \u00d7 \\(\\frac{7}{8}\\)
            \n= \\(\\frac{4 \u00d7 7}{8}\\)
            \n= \\(\\frac{28}{8}\\)
            \n= \\(\\frac{7}{2}\\) panels
            \nHence, from the above,
            \nWe can conclude that
            \nThe number of panels Kelsey can paint in a week is: \\(\\frac{7}{2}\\) panels<\/p>\n

            Part C
            \nPaul can work 5 days a week. How many panels can Paul paint in a week? Explain.
            \nAnswer:
            \nIt is given that
            \nPaul works \\(\\frac{9}{10}\\) panels a day
            \nSo,
            \nThe number of panels Paul can paint in a week = (The number of days Paul can paint in a week) \u00d7 (The number of panels Paul can paint in a day)
            \n= 5 \u00d7 \\(\\frac{9}{10}\\)
            \n= \\(\\frac{5 \u00d7 9}{10}\\)
            \n= \\(\\frac{45}{10}\\)
            \n= \\(\\frac{9}{2}\\) panels
            \nHence, from the above,
            \nWe can conclude that
            \nThe number of panels Paul can paint in a week is: \\(\\frac{9}{2}\\) panels<\/p>\n

            Part D
            \nHow many panels can Tony paint in a week? Draw a bar diagram. Write and solve an equation.
            \nAnswer:
            \nThe given table is:
            \n\"\"
            \nNow,
            \nFrom the given table,
            \nWe can observe that
            \nTony paints \\(\\frac{5}{6}\\) panels a day for 3 days a week
            \nSo,
            \nThe number of panels Tony can paint in a week = (The number of days can Tony paint in a week) \u00d7 (The number of panels Tony can paint in a day)
            \n= 3 \u00d7 \\(\\frac{5}{6}\\)
            \n= \\(\\frac{3 \u00d7 5}{6}\\)
            \n= \\(\\frac{15}{6}\\)
            \n= \\(\\frac{5}{2}\\) panels
            \nHence,
            \nThe representation of the number of panels Tony can make in a week in the form of a bar diagram is:
            \n\"\"
            \nThe number of panels Tony can paint in a week is: \\(\\frac{5}{2}\\) panels<\/p>\n

            Question 2.
            \nThe Time Spent Painting Each Day table shows how much time each of Paul’s friends helped with the mural each day that they worked on it.
            \n\"Envision
            \nHow much more time did Kelsey spend each day than Tony and Leeza combined? Explain.
            \nAnswer:
            \nIt is given that
            \nThe Time Spent Painting Each Day table shows how much time each of Paul’s friends helped with the mural each day that they worked on it.
            \nNow,
            \nThe given table is:
            \n\"Envision
            \nNow,
            \nFrom the given table,
            \nWe can observe that
            \nThe time spent painting each day by Tony and Leeza combined = 1 hour 45 minutes + 30 minutes
            \n= 1 hour 75 minutes
            \n= 2 hours 15 minutes
            \nSo,
            \nThe difference between the time spent each day by Kelsey and Tony and Leeza combined = 2 hours 30 minutes – 2 hours 15 minutes
            \n= 15 minutes
            \nHence, from the above,
            \nWe can conclude that
            \nKelsey spent each day 15 minutes more than Tony and Leeza combined<\/p>\n","protected":false},"excerpt":{"rendered":"

            Go through the\u00a0enVision Math Common Core Grade 4 Answer Key\u00a0Topic 10 Extend Multiplication Concepts to Fractions\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 4th Grade Answers Key Topic 10 Extend Multiplication Concepts to Fractions Essential Questions: How can you describe a fraction using a unit fraction? How can you multiply 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\/11697"}],"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=11697"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/11697\/revisions"}],"predecessor-version":[{"id":27771,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/11697\/revisions\/27771"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=11697"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=11697"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=11697"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}