{"id":8128,"date":"2023-11-29T11:04:16","date_gmt":"2023-11-29T05:34:16","guid":{"rendered":"https:\/\/envisionmathanswerkey.com\/?p=8128"},"modified":"2023-11-30T16:54:43","modified_gmt":"2023-11-30T11:24:43","slug":"envision-math-common-core-grade-3-answer-key-topic-13","status":"publish","type":"post","link":"https:\/\/envisionmathanswerkey.com\/envision-math-common-core-grade-3-answer-key-topic-13\/","title":{"rendered":"enVision Math Common Core Grade 3 Answer Key Topic 13 Fraction Equivalence and Comparison"},"content":{"rendered":"

Go through the\u00a0enVision Math Common Core Grade 3 Answer Key<\/a>\u00a0Topic 13 Fraction Equivalence and Comparison<\/strong>\u00a0regularly and improve your accuracy in solving questions.<\/p>\n

enVision Math Common Core 3rd Grade Answers Key Topic 13 Fraction Equivalence and Comparison<\/h2>\n

Essential Question:<\/strong>
\nWhat are different ways to compare fractions?
\n\"Envision<\/p>\n

enVision STEM Project: Life Cycles<\/strong>
\nDo Research A frog egg hatches into a tadpole that lives in water. The tadpole will change and eventually become an adult frog. Use the Internet or another source to gather information about the life cycle of a frog and other animals.<\/p>\n

Journal: Write a Report Include what you found. Also in your report:<\/p>\n

    \n
  • Tell about what is in a frog’s habitat to support changes the frog goes through in its life cycle.<\/li>\n
  • Compare the life cycles of the different animals you studied.<\/li>\n
  • For the animals you studied, make up and solve problems using fractions. Draw fraction strips to represent the fractions.<\/li>\n<\/ul>\n

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

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

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

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

      Question 1.
      \nThe symbol ___________ means is greater than.<\/p>\n

      Answer:
      \nThe symbol > means greater than.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ngreater than symbol is used to compare numbers.
      \nfor example:
      \n3 > 1.
      \nso the symbol > is used for large numbers when compared with small numbers.<\/p>\n

      \"Fraction<\/p>\n

      Question 2.
      \nThe symbol _________ means is less than.<\/p>\n

      Answer:
      \nThe symbol < means less than.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nless than a symbol is used to compare numbers.
      \nfor example:
      \n1 < 3.
      \nso the symbol < is used for small numbers when compared with large numbers.<\/p>\n

      Question 3.
      \nA ________ represents one equal part of a whole.<\/p>\n

      Answer:
      \nThe fraction represents one equal part of a whole.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \na fraction represents one equal part of a whole.
      \nfor example:
      \n3\/4.
      \nthe whole part is 4.
      \nthe 3\/4 of the portion is filled.
      \nso the fraction represents one equal part of a whole.<\/p>\n

      Comparing Whole Numbers<\/strong><\/p>\n

      Compare. Write <, >, or =.
      \nQuestion 4.
      \n48 \"Envision 30<\/p>\n

      Answer:
      \n48 > 30.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 48 and 30.
      \n30 is less than 48.
      \n48 is greater than 30.
      \n48 > 30.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 5.
      \n6 \"Envision 6<\/p>\n

      Answer:
      \n6 = 6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 6 and 6.
      \n6 is equal to 6.
      \n6 = 6.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 6.
      \n723 \"Envision 732<\/p>\n

      Answer:
      \n723 < 732.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 723 and 732.
      \n723 is less than 732.
      \n732 is greater than 723.
      \n723 < 732.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 7.
      \n152 \"Envision 183<\/p>\n

      Answer:
      \n152 < 183.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 152 and 183.
      \n152 is less than 183.
      \n183 is greater than 152.
      \n152 < 183.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 8.
      \n100 \"Envision 10<\/p>\n

      Answer:
      \n100 > 10.<\/p>\n

      \"Fraction<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 100 and 10.
      \n100 is greater than 10.
      \n10 is less than 100.
      \n100 > 10.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 9.
      \n189 \"Envision 99<\/p>\n

      Answer:
      \n189 > 99.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 189 and 99.
      \n189 is greater than 99.
      \n99 is less than 189.
      \n189 > 99.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 10.
      \n456 \"Envision 456<\/p>\n

      Answer:
      \n456 = 456.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 456 and 456.
      \n456 is equal to 456.
      \n456 = 456.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 11.
      \n123 \"Envision 223<\/p>\n

      Answer:
      \n123 < 223.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 123 and 223.
      \n123 is less than 223.
      \n223 is greater than 123.
      \n123 < 223.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 12.
      \n421 \"Envision 399<\/p>\n

      Answer:
      \n421 > 399.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 421 and 399.
      \n421 is greater than 399.
      \n399 is less than 421.
      \n421 > 399.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 13.
      \n158 \"Envision 185<\/p>\n

      Answer:
      \n158 < 185.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 158 and 185.
      \n158 is less than 185.
      \n185 is greater than 158.
      \n158 < 185.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 14.
      \n117 \"Envision 117<\/p>\n

      Answer:
      \n117 = 117.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 117 and 117.
      \n117 is equal to 117.
      \n117 = 117.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 15.
      \n900 \"Envision 893<\/p>\n

      Answer:
      \n900 > 893.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 900 and 893.
      \n900 is greater than 893.
      \n893 is less than 900.
      \n900 > 893.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      For each shape, write the fraction that is shaded.
      \nQuestion 16.
      \n\"Envision<\/p>\n

      Answer:
      \nThe fraction is 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe figure contains 8 boxes.
      \n4 boxes are filled.
      \n4\/8 portion of the boxes are filled.
      \n4\/8 = 1\/2.
      \nso half portion of the boxes is filled.<\/p>\n

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

      Answer:
      \nThe fraction is 1\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthere are 6 boxes in the figure.
      \n1 box is filled.
      \nso 1\/6 portion is filled.<\/p>\n

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

      Answer:
      \nThe fraction is 2\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe figure contains 4 boxes.
      \n2 boxes are filled.
      \n2\/4 portion of the boxes are filled.
      \n2\/4 = 1\/2.
      \nso half portion of the boxes is filled.<\/p>\n

      Division<\/p>\n

      Divide.
      \nQuestion 19.
      \n30 \u00f7 5<\/p>\n

      Answer:
      \nThe answer is 6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 30 and 5.
      \n5 x 6 = 30.
      \n30 \/ 5 = 6.<\/p>\n

      Question 20.
      \n72 \u00f7 8<\/p>\n

      Answer:
      \n72 \/ 8 = 9.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 72 and 8.
      \n8 x 9 = 72.
      \n72 \/ 8 = 9.<\/p>\n

      Question 21.
      \n28 \u00f7 4<\/p>\n

      Answer:
      \n28 \/ 4 = 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 28 and 4.
      \n4 x 7 = 28.
      \n28 \/ 4 = 7.<\/p>\n

      Question 22.
      \n48 \u00f7 6<\/p>\n

      Answer:
      \n48 \/ 6 = 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 48 and 6.
      \n6 x 8 = 48.
      \n48 \/ 6 = 8.<\/p>\n

      Question 23.
      \n81 \u00f7 9<\/p>\n

      Answer:
      \n81 \/ 9 = 9.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 81 and 9.
      \n9 x 9 = 81.
      \n81 \/ 9 = 9.<\/p>\n

      Question 24.
      \n45 \u00f7 5<\/p>\n

      Answer:
      \n45 \/ 5 = 9.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 45 and 5.
      \n5 x 9 = 45.
      \n45 \/ 5 = 9.<\/p>\n

      Question 25.
      \n32 \u00f7 8<\/p>\n

      Answer:
      \n32 \/ 8 = 4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 32 and 8.
      \n8 x 4 = 32.
      \n32 \/ 8 = 4.<\/p>\n

      Question 26.
      \n42 \u00f7 6<\/p>\n

      Answer:
      \n42 \/ 6 = 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 42 and 6.
      \n6 x 7 = 42.
      \n42 \/ 6 = 7.<\/p>\n

      Question 27.
      \n49 \u00f7 7<\/p>\n

      Answer:
      \n49 \/ 7 = 7.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 49 and 7.
      \n7 x 7 = 49.
      \n49 \/ 7 = 7.<\/p>\n

      Question 28.
      \nHow can you check if the answer to 40 \u00f7 5 is 8?<\/p>\n

      Answer:
      \n40 \/ 5 = 8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 40 and 5.
      \n40 \/ 5 = 8.
      \n8 x 5 = 40.<\/p>\n

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

      PROJECT 13A
      \nDo you want to ride a horse?
      \nProject: Design a Racetrack for Horses
      \n\"Envision<\/p>\n

      PROJECT 13B
      \nHow deep do you have to dig before you reach water?
      \nProject: Create a Picture of a Well
      \n\"Envision<\/p>\n

      PROJECT 13C
      \nHow many coffee beans does it take to fill up a container?
      \nProject: Plot Fractions on a Number Line
      \n\"Envision<\/p>\n

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

      Math Modeling
      \nWhat’s the Beef?
      \n\"Envision<\/p>\n

      Lesson 13.1 Equivalent Fractions: Use Models<\/h3>\n

      Solve & Share<\/strong>
      \nGregor threw a softball of the length of the yard in front of his house. Find as many fractions as you can that name the same part of the length of the yard that Gregor threw the ball. Explain how you decided
      \nI can … find equivalent fractions that name the same part of a whole.
      \n\"Envision<\/p>\n

      Answer:
      \n1\/9, 2\/9, 3\/9, 4\/9.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nGregor threw a softball off the length of the yard in front of his house.
      \nGregor threw the 1st ball at 1 yard.
      \n1\/9.
      \nthe length of the yard is 9.
      \nGregor threw the 2nd ball at 2 yards.
      \n2\/9.
      \nGregor threw the 3rd ball at 3 yards.
      \n3\/9.
      \nGregor threw the 4th ball at 4 yards.
      \n4\/9.
      \nso the fractions are 1\/9, 2\/9, 3\/9, and 4\/9.<\/p>\n

      Look Back! How can fraction strips help you tell if a fraction with a denominator of 2, 3, or 6 would name the same part of a whole as \\(\\frac{3}{4}\\)?<\/p>\n

      Answer:
      \n2\/4 and 6\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe denominators are 2, 3, and 6.
      \n3\/4 and 2\/4 = 1\/2.
      \n6\/4 = 3\/2.<\/p>\n

      Essentials Question<\/strong>
      \nHow Can Different Fractions Name the Same Part of a Whole?<\/p>\n

      Visual Learning Bridge
      \nThe Chisholm Trail was used to drive cattle to market. Ross’s herd has walked \\(\\frac{1}{2}\\) the distance to market. What is another way to name \\(\\frac{1}{2}\\)?
      \n\"Envision<\/p>\n

      \\(\\frac{1}{2}\\) = \\(\\frac{}{}\\) You can use fraction strips.
      \n\"Envision
      \nThe fractions \\(\\frac{1}{2}\\) and \\(\\frac{2}{4}\\) represent the same part of the whole.
      \nTwo \\(\\frac{1}{4}\\) strips are equal to \\(\\frac{1}{2}\\), so \\(\\frac{1}{2}\\) = \\(\\frac{2}{4}\\).
      \nAnother name for \\(\\frac{1}{2}\\) is \\(\\frac{2}{4}\\).<\/p>\n

      You can find other equivalent fractions. Think about fractions that name the same part of the whole.
      \n\"Envision
      \nFour \\(\\frac{1}{8}\\) strips are equal to \\(\\frac{1}{2}\\), so \\(\\frac{1}{2}\\) = \\(\\frac{4}{8}\\).
      \nAnother name for \\(\\frac{1}{2}\\) is \\(\\frac{4}{8}\\)<\/p>\n

      Convince Me! Look for Relationships In the examples above, what pattern do you see in the fractions that are equivalent to \\(\\frac{1}{2}\\)? What is another name for \\(\\frac{1}{2}\\) that is not shown above?<\/p>\n

      Answer:
      \nThe other name is 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nFour \\(\\frac{1}{8}\\) strips are equal to \\(\\frac{1}{2}\\).
      \n\\(\\frac{1}{2}\\) = \\(\\frac{4}{8}\\).
      \n\\(\\frac{1}{2}\\) is \\(\\frac{4}{8}\\).
      \nso the other name is 4\/8.<\/p>\n

      Another Example!<\/strong>
      \nYou can find an equivalent fraction for \\(\\frac{4}{6}\\) using an area model.
      \n\"Envision
      \nBoth area models have the same-sized whole. One is divided into sixths. The other shows thirds. The shaded parts show the same part of a whole. Because \\(\\frac{4}{6}\\) = \\(\\frac{2}{3}\\), another name for \\(\\frac{4}{6}\\) is \\(\\frac{2}{3}\\).<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nDivide the second area model into sixths. Shade it to show a fraction equivalent to \\(\\frac{1}{3}\\):
      \n\"Envision<\/p>\n

      Answer:
      \n1\/3 = 2\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ndivide the second area model into sixths.
      \n\\(\\frac{1}{3}\\) = \\(\\frac{2}{6}\\).
      \n\\(\\frac{1}{3}\\) is \\(\\frac{2}{6}\\).
      \n2\/6 = 1\/3.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Do You Know How?<\/strong>
      \nQuestion 2.
      \nUse the fraction strips to help find an equivalent fraction.
      \n\"Envision<\/p>\n

      Answer:
      \n1\/4 = 4\/16.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n\\(\\frac{1}{4}\\) = \\(\\frac{4}{16}\\).
      \n\\(\\frac{4}{16}\\) is \\(\\frac{1}{4}\\).
      \n1\/4 = 4\/16.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Question 3.
      \nUse the fraction strips to help find an equivalent fraction.
      \n\"Envision
      \nAnswer:
      \n1\/2 = 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n1\/4 + 1\/4 = 1\/2.
      \n1\/2 + 1\/2 = 1.
      \n4\/8 = 1\/2.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 4.
      \nDivide the second area model into eighths. Shade it to show a fraction equivalent to \\(\\frac{1}{2}\\).
      \n\"Envision<\/p>\n

      Answer:
      \n1\/2 = 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ndivide the second area model into eights.
      \n\\(\\frac{1}{2}\\) = \\(\\frac{4}{8}\\).
      \n\\(\\frac{1}{2}\\) is \\(\\frac{4}{8}\\).
      \n1\/2 = 4\/8.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      In 5-8, find each equivalent fraction. Use fraction strips or draw area models to help.
      \nQuestion 5.
      \n\\(\\frac{3}{4}\\) = \\(\\frac{}{8}\\)<\/p>\n

      Answer:
      \n\\(\\frac{3}{4}\\) = \\(\\frac{6}{8}\\).<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ndivide the 1st area model into fourths.
      \ndivide the second area model into eights.
      \n3\/4 = 6\/8.
      \n6\/8 = 3\/4.<\/p>\n

      Question 6.
      \n\\(\\frac{6}{6}\\) = \\(\\frac{}{8}\\)<\/p>\n

      Answer:
      \n\\(\\frac{6}{6}\\) = \\(\\frac{1}{8}\\).<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ndivide the 1st area model into sixths.
      \ndivide the second area model into eights.
      \n6\/6 = 1.
      \n1\/8 = 6\/6.<\/p>\n

      Question 7.
      \n\\(\\frac{2}{6}\\) = \\(\\frac{}{3}\\)<\/p>\n

      Answer:
      \n\\(\\frac{2}{6}\\) = \\(\\frac{1}{3}\\).<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ndivide the 1st area model into sixths.
      \ndivide the second area model into thirds.
      \n2\/6 = 1\/3.
      \n1\/3 = 2\/6.<\/p>\n

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

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ndivide the 1st area model into eigths.
      \ndivide the second area model into halfs.
      \n4\/8 = 1\/2.
      \n1\/2 = 4\/8.<\/p>\n

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

      In 9 and 10, use the fraction strips at the right.
      \n\"Envision
      \nQuestion 9.
      \nMarcy used fraction strips to show equivalent fractions. Complete the equation.
      \n\\(\\frac{}{4}\\) = ________<\/p>\n

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ndivide the 1st area model into fourths.
      \ndivide the second area model into eights.
      \n1\/4 = 2\/8.
      \n2\/8 = 1\/4.<\/p>\n

      Question 10.
      \nRita says the fraction strips show fractions that are equivalent to \\(\\frac{1}{2}\\). Explain what you could do to the diagram to see if she is correct.<\/p>\n

      Answer:
      \n\\(\\frac{2}{4}\\) = \\(\\frac{1}{2}\\).<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \ndivide the 1st area model into fourths.
      \ndivide the second area model into halves.
      \n2\/4 = 1\/2.
      \n1\/2 = 2\/4.<\/p>\n

      Question 11.
      \nReasoning A band learns 4 to 6 new songs every month. What is a good estimate for the number of songs the band will learn in 8 months? Explain.<\/p>\n

      Answer:
      \nThe number of songs the band will learn in 8 months = 80 songs.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nA band learns 4 to 6 new songs every month.
      \n4 + 6 = 10.
      \n10 x 8 = 80.
      \nso the number of songs the band will learn in 8 months = 80 songs.<\/p>\n

      Question 12.
      \nThree-eighths of a playground is covered by grass. What fraction of the playground is NOT covered by grass?<\/p>\n

      Answer:
      \nThe fraction of the playground is not covered by grass = 5\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthree-eights of a playground is covered by grass.
      \n8 – 3 = 5.
      \nso the fraction of the playground is not covered by grass = 5\/8.<\/p>\n

      Question 13.
      \nHigher Order Thinking<\/strong> Aiden folded 2 strips of paper into eighths. He shaded a fraction equal to \\(\\frac{1}{4}\\) on the first strip and a fraction equal to \\(\\frac{3}{4}\\) on the second strip. Use eighths to show the fractions Aiden shaded on the pictures to the right. Which fraction of each strip did he shade?<\/p>\n

      Answer:
      \nThe fraction he shaded = 6\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nAiden folded 2 strips of paper into eighths.
      \n2\/8.
      \nHe shaded a fraction equal to \\(\\frac{1}{4}\\) on the first strip.
      \n1\/4.
      \nfraction equal to \\(\\frac{3}{4}\\) on the second strip.
      \n3\/4.
      \nhe shaded the 6\/8 portion of each strip.
      \n6\/8 = 3\/4.<\/p>\n

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

      Question 14.
      \nWhich fractions are equivalent? Select all that apply.
      \n\"Envision<\/p>\n

      Answer:
      \n1\/4 and 2\/8.
      \n3\/4 and 6\/8.
      \n2\/4 and 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthere are three equivalent fractions.
      \nthe fractions are:
      \n2\/8 = 1\/4.
      \n6\/8 = 3\/4.
      \n4\/8 = 2\/4.<\/p>\n

      Lesson 13.2 Equivalent Fractions: Use the Number Line<\/h3>\n

      Solve & Share<\/strong>
      \nThe top number line shows a point at \\(\\frac{1}{4}\\). Write the fraction for each of the points labeled A, B, C, D, E, and F. Which of these fractions show the same distance from 0 as \\(\\frac{1}{4}\\)?
      \nI can … use number lines to represent equivalent fractions.
      \n\"Envision<\/p>\n

      Look Back! How can number lines show that two fractions are equivalent?<\/p>\n

      Answer:
      \nThe fractions are 1\/2, 2\/4, 3\/4, 2\/8, 4\/8, and 4\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThe number line A shows the fraction 1\/2.
      \nB shows the fraction 2\/4.
      \nC shows the fraction 3\/4.
      \nD shows the fraction 2\/8.
      \nE shows the fraction 4\/8.
      \nF shows the fraction 4\/6.
      \n2\/4 = 1\/2.
      \n2\/8 = 1\/4.
      \n4\/8 = 1\/2.
      \n4\/6 = 2\/3.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Use Number Lines to Find Equivalent Fractions?<\/p>\n

      Visual Learning Bridge
      \nThe Circle W Ranch 1-mile trail has water for cattle at each \\(\\frac{1}{4}\\) mile mark. The Big T Ranch 1-mile trail has water for cattle at the \\(\\frac{1}{2}\\)-mile mark. What fractions name the points on the trails where there is water for cattle at the same distance from the start of each trail?
      \n\"Envision<\/p>\n

      You can use number lines to find the fractions.
      \n\"Envision
      \nThe fractions \\(\\frac{2}{4}\\) and \\(\\frac{1}{2}\\) name the same points on the trails where there is water for cattle. They are at the same distance from the start of the trails.<\/p>\n

      Convince Me! Model with Math lan paints \\(\\frac{6}{8}\\) of a fence. Anna paints \\(\\frac{3}{4}\\) of another fence of equal size and length. How can you show that lan and Anna have painted the same amount of each fence?<\/p>\n

      Answer:
      \nYes, both Anna and Lan have painted the same amount of each fence.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nLan paints \\(\\frac{6}{8}\\) of a fence.
      \nAnna paints \\(\\frac{3}{4}\\) of another fence of equal size and length.
      \n3\/4 = 6\/8.
      \n2 x 3 = 6.
      \n4 x 2 = 8.
      \nso both Anna and Lan have painted the same amount of each fence.<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nComplete the number line to show that \\(\\frac{2}{6}\\) and \\(\\frac{1}{3}\\) are equivalent fractions.
      \n\"Envision<\/p>\n

      Answer:
      \n2\/6 = 1\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions on the number line are:
      \n1\/6, 2\/6, 3\/6, 4\/6, and 5\/6.
      \n2\/6 = 1\/3.
      \n4\/6 = 2\/3.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 2.
      \nSheila compares \\(\\frac{4}{6}\\) and \\(\\frac{4}{8}\\) she discovers that the fractions are NOT equivalent. How does Sheila know?
      \n\"Envision<\/p>\n

      Answer:
      \nYes, both fractions are not equivalent.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nSheila compares \\(\\frac{4}{6}\\) and \\(\\frac{4}{8}\\).
      \n4\/6 = 2\/3.
      \n2 x 2 = 4.
      \n2 x 3 = 6.
      \n4\/8 = 2\/4.
      \n2 x 2 = 4.
      \n4 x 2 = 8.
      \nso 4\/6 is not equal to 4\/8.<\/p>\n

      Do You Know How?<\/strong>
      \nIn 3 and 4, find the missing equivalent fractions on the number line. Then write the equivalent fractions below.
      \nQuestion 3.
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing equivalent fractions on the number line is 3\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions on the number line are:
      \n1\/6, 2\/6, 3\/6, 4\/6, 5\/6, and 1.
      \n3\/6 = 1\/2.
      \nso the 3\/6 and 1\/2 are the equivalent fractions.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 4.
      \n\"Envision<\/p>\n

      Answer:
      \n6\/8 = 3\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions on the number line are:
      \n1\/8, 2\/8, 3\/8, 4\/8, 5\/8, 6\/8, and 7\/8.
      \n2\/8 = 1\/4.
      \n4\/8 = 1\/2.
      \n6\/8 = 3\/4.
      \n2 x 3 = 6.
      \n2 x 4 = 8.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      In 5-8, find the missing equivalent fractions on the number line. Then write the equivalent fractions below.
      \nQuestion 5.
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing equivalent fractions on the number line are 2\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions on the number line are 1\/8, 2\/8, 3\/8, 4\/8, 5\/8, 6\/8, and 7\/8.
      \n2\/8 = 1\/4.
      \n1 x 2 = 2.
      \n4 x 2 = 8.
      \nso the missing equivalent fraction is 2\/8 = 1\/4.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 6.
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing equivalent fractions on the number line are 4\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions on the number line are 1\/6, 2\/6, 3\/8, and 5\/6.
      \n2\/6 = 1\/3.
      \n1 x 2 = 2.
      \n3 x 2 = 6.
      \n4\/6 = 2\/3.
      \n2 x 2 = 4.
      \n3 x 2 = 6.
      \nso the missing equivalent fraction is 4\/6 = 2\/3.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Answer:
      \nThe missing equivalent fractions on the number line are 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions on the number line are 1\/8, 2\/8, 3\/8, 5\/8, 6\/8, and 7\/8.
      \n2\/8 = 1\/4.
      \n1 x 2 = 2.
      \n4 x 2 = 8.
      \n4\/8 = 2\/4.
      \n2 x 2 = 4.
      \n4 x 2 = 8.
      \nso the missing equivalent fraction is 4\/8 = 2\/4.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 8.
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing equivalent fractions on the number line are 6\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions on the number line are 1\/6, 2\/6, 3\/6, 4\/6, and 5\/6.
      \n2\/6 = 1\/3.
      \n1 x 2 = 2.
      \n3 x 2 = 6.
      \n4\/6 = 2\/3.
      \n2 x 2 = 4.
      \n3 x 2 = 6.
      \n6\/6 = 1.
      \n1 x 6 = 6.
      \nso the missing equivalent fraction is 6\/6 = 1.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Question 9.
      \nNumber Sense Bradley had 40 slices of pizza to share. How many pizzas did he have? Explain how you solved the problem.
      \n\"Envision<\/p>\n

      Answer:
      \nThe number of pizzas did he have = 5.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nBradley had 40 slices of pizza to share.
      \neach pizza was cut into 8 slices.
      \n40\/8 = 5.
      \n5 x 8 = 40.
      \nso the number of pizzas did he have = 5.<\/p>\n

      Question 10.
      \nMs. Owen has 15 magazines to share among 5 students for an art project. How many magazines will each student get? Use the bar diagram to write an equation that helps solve the problem.
      \n\"Envision<\/p>\n

      Answer:
      \nThe number of magazines will each student get = 3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nMs. Owen has 15 magazines to share among 5 students for an art project.
      \n15 \/ 5 = 3.
      \n3 + 3 + 3 + 3 + 3 = 15.
      \n3 x 5 = 15.
      \nso the number of magazines will each student get = 3.<\/p>\n

      Question 11.
      \nYonita has 28 different apps on her computer. Casey has 14 music apps and 20 game apps on his computer. How many more apps does Casey have than Yonita? Explain.<\/p>\n

      Answer:
      \nThe number of apps does Casey has more than Yonita = 6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nYonita has 28 different apps on her computer.
      \nCasey has 14 music apps and 20 game apps on his computer.
      \n14 + 20 = 34.
      \n34 – 28 = 6.
      \nso the number of apps does Casey has more than Yonita = 6.<\/p>\n

      Question 12.
      \nConstruct Arguments<\/strong> How can you tell, just by looking at the fractions, that \\(\\frac{2}{4}\\) and \\(\\frac{3}{4}\\) are NOT equivalent? Construct an argument to explain.<\/p>\n

      Answer:
      \nYes, 2\/4 and 3\/4 are not equivalent fractions.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fraction 2\/4 = 1\/2.
      \n1 x 2 = 2.
      \n2 x 2 = 4.
      \nthe fraction 3\/4 is not an equivalent fraction.
      \nso both the fractions are not equal.<\/p>\n

      Question 13.
      \nHigher Order Thinking<\/strong> Fiona and Gabe each had the same length of rope. Fiona used \\(\\frac{2}{3}\\) of her rope. Using sixths, what fraction of the length of rope will Gabe need to use to match the amount Fiona used? Draw a number line as part of your answer.<\/p>\n

      Answer:
      \nThe fraction of the rope Gabe used is 4\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nFiona and Gabe each had the same length of rope.
      \nFiona used \\(\\frac{2}{3}\\) of her rope.
      \n4\/6 = 2\/3.
      \n2 x 2 = 4.
      \n3 x 2 = 6.
      \nso the fraction of rope Gabe used is 4\/6.<\/p>\n

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

      Question 14.
      \nUse the number line to find which fraction is equivalent to \\(\\frac{3}{6}\\).
      \n\"Envision<\/p>\n

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n3\/6 = 1\/2.
      \n1 x 3 = 3.
      \n3 x 2 = 6.
      \n1\/2 = 3\/6.
      \nso option A is correct.<\/p>\n

      Question 15.
      \nUse the number line to find which fraction is equivalent to \\(\\frac{4}{8}\\).
      \n\"Envision<\/p>\n

      Answer:
      \nOption C is the correct answer.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n4\/8 = 2\/4.
      \n2 x 2 = 4.
      \n4 x 2 = 8.
      \n2\/4 = 4\/8.
      \nso option C is correct.<\/p>\n

      Lesson 13.3 Use Models to Compare Fractions: Same Denominator<\/h3>\n

      Solve & Share<\/strong>
      \nMaria and Evan are both jogging a mile. Maria has jogged mile, and Evan has jogged mile. Show how far each has jogged. Use any model you choose. Who jogged farther? How do you know?
      \nI can … compare fractions that refer to the same-sized whole and have the same denominator by comparing their numerators.
      \n\"Envision<\/p>\n

      Look Back! Suppose Evan had jogged \\(\\frac{5}{8}\\) mile instead of \\(\\frac{3}{8}\\) mile. Now, who has jogged farther? Explain.<\/p>\n

      Answer:
      \nEvan jogged farther than Maria.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nEvan had jogged \\(\\frac{5}{8}\\) mile instead of \\(\\frac{3}{8}\\).
      \n5\/8 – 3\/8 = 2\/8.
      \nso I think maria jogged very little when compared to Evan.
      \nso Evan jogged farther than Maria.<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Compare Fractions with the Same Denominator?<\/p>\n

      Visual Learning Bridge
      \nTwo banners with positive messages are the same size. One banner is \\(\\frac{4}{6}\\) yellow, and the other banner is \\(\\frac{2}{6}\\) yellow. Which is greater, \\(\\frac{4}{6}\\) or \\(\\frac{2}{6}\\)?
      \n\"Envision<\/p>\n

      \\(\\frac{4}{6}\\) is 4 of the unit fraction is \\(\\frac{1}{6}\\).
      \n\\(\\frac{2}{6}\\) of the unit fraction \\(\\frac{1}{6}\\).
      \nSo, \\(\\frac{4}{6}\\) is greater than \\(\\frac{2}{6}\\).
      \n\"Envision<\/p>\n

      Record the comparison using symbols or words.
      \n\\(\\frac{4}{6}\\) > \\(\\frac{2}{6}\\)
      \nFour sixths is greater than two sixths.
      \nIf two fractions have the same denominator, the fraction with the greater numerator is the greater fraction.<\/p>\n

      Convince Me! Reasoning Write a number for each numerator to make each comparison true. Use a picture and words to explain how you decided.
      \n\"Envision<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nExplain how you can use fraction strips to show whether \\(\\frac{5}{6}\\) or \\(\\frac{3}{6}\\) of the same whole is greater.<\/p>\n

      Answer:
      \n5\/6 > 3\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 5\/6 and 3\/6.
      \nso 5\/6 is greater than 3\/6.
      \n3\/6 < 5\/6.
      \n5\/6 > 3\/6.<\/p>\n

      Question 2.
      \nWhich is greater, \\(\\frac{3}{4}\\) or \\(\\frac{2}{4}\\)? Draw \\(\\frac{1}{4}\\)-strips to complete the diagram and answer the question.
      \n\"Envision<\/p>\n

      Answer:
      \n3\/4 is greater than 2\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n3\/4 is greater than 2\/4.
      \nthe whole is 4.
      \nbut one time it is divided into 3 parts.
      \nit is divided into 2 parts.
      \nso 3\/4 > 2\/4.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Do You Know How?<\/strong>
      \nIn 3 and 4, compare. Write <, >, or =. Use the fraction strips to help.
      \nQuestion 3.
      \n\"Envision<\/p>\n

      Answer:
      \n2\/8 > 1\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 2\/8 and 1\/8.
      \n1\/8 + 1\/8 = 2\/8.
      \n2\/8 is greater than 1\/8.
      \nso 2\/8 > 1\/8.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 4.
      \n\"Envision<\/p>\n

      Answer:
      \n3\/6 < 5\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 3\/6 and 5\/6.
      \n5\/6 is divided into 5 parts.
      \n1\/6 + 1\/6 + 1\/6 = 3\/6.
      \nso 3\/6 < 5\/6.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Leveled Practice In 5-14, compare. Write <, >, or =. Use or draw fraction strips to help. The fractions refer to the same whole.
      \nQuestion 5.
      \n\"Envision<\/p>\n

      Answer:
      \n3\/8 < 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 3\/8 and 4\/8.
      \n1\/8 + 1\/8 + 1\/8 = 3\/8.
      \n1\/8 + 1\/8 + 1\/8 + 1\/8 = 4\/8.
      \nso 3\/8 < 4\/8.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 6.
      \n\"Envision<\/p>\n

      Answer:
      \n3\/4 = 3\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 3\/4 and 3\/4.
      \n1\/4 + 1\/4 + 1\/4 = 3\/4.
      \n3\/4 = 3\/4.
      \nso both of them are equal.<\/p>\n

      Question 7.
      \n\\(\\frac{6}{8}\\) \"Envision \\(\\frac{3}{8}\\)<\/p>\n

      Answer:
      \n6\/8 > 3\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 6\/8 and 3\/8.
      \n6\/8 = 3\/4.
      \n2 x 3 = 6.
      \n4 x 2 = 8.
      \n1\/8 + 1\/8 + 1\/8 = 3\/8.
      \n6\/8 > 3\/8.<\/p>\n

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

      Answer:
      \n5\/8 < 7\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 5\/8 and 7\/8.
      \n1\/8 + 1\/8 + 1\/8\u00a0 + 1\/8 + 1\/8 = 5\/8.
      \n1\/8 x 7 = 7\/8.
      \n5\/8 < 7\/8.<\/p>\n

      Question 9.
      \n\\(\\frac{1}{2}\\) \"Envision \\(\\frac{1}{2}\\)<\/p>\n

      Answer:
      \n1\/2 = 1\/2.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/2 and 1\/2.
      \n1\/2 x 1 = 1\/2.
      \n1\/2 x 1 =1\/2.
      \nso both of them are equal.<\/p>\n

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

      1\/3 < 2\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/3 and 2\/3.
      \n1\/3 x 1 = 1\/3.
      \n1\/3 + 1\/3 = 2\/3.
      \n1\/3 < 2\/3.<\/p>\n

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

      6\/6 > 3\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 6\/6 and 3\/6.
      \n1\/6 + 1\/6 + 1\/6\u00a0 + 1\/6 + 1\/6 + 1\/6 = 6\/6.
      \n1\/6 + 1\/6 + 1\/6 = 3\/6.
      \n6\/6 > 3\/6.<\/p>\n

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

      2\/8 < 3\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/8 and 3\/8.
      \n1\/8 + 1\/8 = 2\/8.
      \n1\/8 + 1\/8 +1\/8 = 3\/8.
      \n2\/8 < 3\/8.<\/p>\n

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

      3\/3 > 1\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 3\/3 and 1\/3.
      \n1\/3 + 1\/3 + 1\/3\u00a0 = 3\/3.
      \n1\/3 x 1 = 1\/3.
      \n3\/3 > 1\/3.<\/p>\n

      Question 14.
      \n\\(\\frac{1}{4}\\) \"Envision \\(\\frac{3}{4}\\)
      \nAnswer:<\/p>\n

      1\/4 < 3\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/4 and 3\/4.
      \n1\/4 x 1 = 1\/4.
      \n1\/4 +1\/4 + 1\/4\u00a0 = 3\/4.
      \n1\/4 < 3\/4.<\/p>\n

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

      In 15 and 16, use the pictures of the strips that have been partly shaded.
      \n\"Envision
      \nQuestion 15.
      \nCompare. Write <, >, or =
      \nThe green strips show \\(\\frac{1}{6}\\) \"Envision \\(\\frac{2}{6}\\)<\/p>\n

      Answer:
      \n1\/6 < 2\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/6 and 2\/6.
      \n1\/6 x 1 = 1\/6.
      \n1\/6 +1\/6 = 2\/6.
      \n1\/6 < 2\/6.<\/p>\n

      Question 16.
      \nDo the yellow strips show \\(\\frac{2}{4}\\) > \\(\\frac{3}{4}\\)? Explain.<\/p>\n

      Answer:
      \nNo, 2\/4 < 3\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/4 and 3\/4.
      \n1\/4 +1\/4 = 2\/4.
      \n1\/4 +1\/4 + 1\/4\u00a0 = 3\/4.
      \n2\/4 < 3\/4.<\/p>\n

      Question 17.
      \nIzzy and Henry have two different pizzas. Izzy ate \\(\\frac{3}{8}\\) of her pizza. Henry ate \\(\\frac{3}{8}\\) of his pizza. Izzy ate more pizza than Henry. How is this possible? Explain.<\/p>\n

      Answer:
      \nNo, it was not possible.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nIzzy and Henry have two different pizzas.
      \nIzzy ate \\(\\frac{3}{8}\\) of her pizza.
      \nHenry ate \\(\\frac{3}{8}\\) of his pizza.
      \n3\/8 = 1\/8 + 1\/8 + 1\/8.
      \n3\/8 x 1 = 3\/8.
      \n3\/8 = 3\/8.
      \nso both of them ate the equal.<\/p>\n

      Question 18.
      \nGeneralize Two fractions are equal. They also have the same denominator. What must be true of the numerators of the fractions? Explain.<\/p>\n

      Answer:
      \nYes, the two fractions are equal.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nIzzy and Henry have two different pizzas.
      \nIzzy ate \\(\\frac{3}{8}\\) of her pizza.
      \nHenry ate \\(\\frac{3}{8}\\) of his pizza.
      \n3\/8 = 1\/8 + 1\/8 + 1\/8.
      \n3\/8 x 1 = 3\/8.
      \n3\/8 = 3\/8.
      \nso both of them ate the equal.<\/p>\n

      Question 19.
      \nNumber Sense<\/strong> Mr. Domini had $814 in the bank on Wednesday. On Thursday, he withdrew $250, and on Friday, he withdrew $185. How much money did he have in the bank then?<\/p>\n

      Answer:
      \nThe money he has in the bank = $379.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nMr. Domini had $814 in the bank on Wednesday.
      \nOn Thursday, he withdrew $250.
      \nOn Friday, he withdrew $185.
      \n250 + 185 = 435.
      \n814 – 435 = 379.
      \nso Mr. Domini had $814 in the bank on Wednesday.<\/p>\n

      Question 20.
      \nHigher Order Thinking<\/strong> Tom’s parents let him choose whether to play his favorite board game for \\(\\frac{7}{8}\\) hour or for \\(\\frac{8}{8}\\) hour. Explain which amount of time you think Tom should choose and why.<\/p>\n

      Answer:
      \nTom should choose 8\/8 hour.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nTom’s parents let him choose whether to play his favorite board game for 7\/8 hours.
      \n8\/8 hour = 1.
      \n7\/8 x 1 = 7\/8.
      \n1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 = 8\/8.
      \n1 = 8\/8.
      \nso i think Tom should choose 1 hour.<\/p>\n

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

      Question 21.
      \nPaul and Enrique each have equal-sized pizzas cut into 8 equal slices. Paul eats 3 slices. Enrique eats 2 slices. Select numbers and symbols from the box to write a comparison for the fraction of pizza Paul and Enrique have each eaten.
      \n\"Envision<\/p>\n

      Answer:
      \nPaul eats more slices than Enriques.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nPaul and Enrique each have equal-sized pizzas cut into 8 equal slices.
      \nPaul eats 3 slices.
      \nEnrique eats 2 slices.
      \n1\/8 + 1\/8 + 1\/8 = 3\/8.
      \n1\/8 + 1\/8 = 2\/8.
      \nso paul eats more slices than Enriques.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Lesson 13.4 Use Models to Compare Fractions: Same Numerator<\/h3>\n

      Solve & Share<\/strong>
      \nKrista, Jamal, and Rafe each had 1 serving of vegetables. Krista ate \\(\\frac{2}{6}\\), Jamal ate \\(\\frac{2}{3}\\), and Rafe ate \\(\\frac{2}{8}\\) of his serving. Arrange the fractions in order from least to greatest to show who ate the least and who ate the greatest amount of vegetables.
      \nI can … compare fractions that refer to the same whole and have the same numerator by comparing their denominators.
      \n\"Envision<\/p>\n

      Answer:
      \nRafe, Krista, and Jamal.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nKrista, Jamal, and Rafe each had 1 serving of vegetables.
      \nKrista ate \\(\\frac{2}{6}\\), Jamal ate \\(\\frac{2}{3}\\).
      \nRafe ate \\(\\frac{2}{8}\\) of his serving.
      \n2\/6 = 1\/6 + 1\/6.
      \n2\/3 = 1\/3 + 1\/3.
      \n2\/8 = 1\/8 + 1\/8.
      \nso Rafe ate least when compared to Krista and Jamal.
      \nso the order from least to highest.
      \nRafe, Krista, and Jamal.<\/p>\n

      Look Back! Tamika ate \\(\\frac{2}{2}\\) of a serving of vegetables. In order from least to greatest, arrange the fractions of a serving Krista, Jamal, Rafe, and Tamika each ate. Explain your reasoning.<\/p>\n

      Answer:
      \nRafe, Krista, Jamal, and Tamika.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nTamika ate \\(\\frac{2}{2}\\) of a serving of vegetables.
      \n2\/2 = 1.
      \nso Tamika at more than Rafe, Krista, and Jamal.<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Compare Fractions with the Same Numerator?<\/p>\n

      Visual Learning Bridge
      \nClaire bought 2 scarves as souvenirs from her visit to a Florida university. The scarves are the same size. One scarf is \\(\\frac{5}{6}\\) orange, and the other scarf is \\(\\frac{5}{8}\\) orange. Which is greater, \\(\\frac{5}{6}\\) or \\(\\frac{5}{8}\\)?
      \n\"Envision<\/p>\n

      What You Show
      \nUse fraction strips to reason about the size of \\(\\frac{5}{6}\\) a compared to the size of \\(\\frac{5}{8}\\).
      \n\"Envision
      \nThere are 5 sixths. There are 5 eighths. The parts are different sizes.
      \nThe greater the denominator, the smaller each part will be.<\/p>\n

      What You Write
      \nDescribe the comparison using symbols or words.
      \n\\(\\frac{5}{6}\\) > \\(\\frac{5}{8}\\)
      \nFive sixths is greater than five eighths.
      \nIf two fractions have the same numerator, the fraction with the lesser denominator is the greater fraction.<\/p>\n

      Convince Me! Critique Reasoning Julia says \\(\\frac{1}{8}\\) is greater than \\(\\frac{1}{4}\\) because 8 is greater than 4. Critique Julia’s reasoning. Is she correct? Explain.<\/p>\n

      Answer:
      \nYes, Julia’s reasoning was correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nJulia says \\(\\frac{1}{8}\\) is greater than \\(\\frac{1}{4}\\).
      \n1\/8 = 1 x 1\/8.
      \n1\/4 = 1 x 1\/4.
      \nso Julia’s reasoning was correct.<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nHow can fraction strips help you reason about whether \\(\\frac{4}{6}\\) or \\(\\frac{4}{8}\\) of the same whole is greater?<\/p>\n

      Answer:
      \n4\/6 > 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 4\/6 and 4\/8.
      \n4\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6.
      \n4\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n4\/6 x 1 = 4\/6.
      \n4\/8 x 1 = 4\/8.
      \nso 4\/6 > 4\/8.<\/p>\n

      Question 2.
      \nWhich is greater, \\(\\frac{1}{4}\\) or \\(\\frac{1}{6}\\)? Draw fraction strips to complete the diagram and answer the question.
      \n\"Envision<\/p>\n

      Answer:
      \n1\/4 > 1\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/4 and 1\/6.
      \n1\/4 x 1 = 1\/4.
      \n1\/6 x 1 = 1\/6.
      \n1 is divided into 1\/4 and 1\/6.
      \n1\/4 > 1\/6.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Do You Know How?<\/strong>
      \nIn 3 and 4, compare. Write <, >, or =. Use fraction strips to help.
      \nQuestion 3.
      \n\"Envision<\/p>\n

      Answer:
      \n3\/6 < 3\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 3\/6 and 3\/3.
      \n3\/6 = 1\/6 + 1\/6 + 1\/6.
      \n3\/3 = 1.
      \nso 3\/6 < 3\/3.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 4.
      \n\"Envision<\/p>\n

      Answer:
      \n4\/6 < 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 4\/6 and 4\/8.
      \n4\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6.
      \n4\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \nso 4\/6 = 1 x 4\/6.
      \nso 4\/6 < 4\/8.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Leveled Practice In 5-14, compare. Write <, >, or =. Use or draw fraction strips to help. The fractions refer to the same whole.
      \nQuestion 5.
      \n\"Envision<\/p>\n

      Answer:
      \n2\/4 < 2\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/4 and 2\/3.
      \n2\/4 = 1\/4 + 1\/4.
      \n2\/3 = 1\/3 + 1\/3.
      \nso 2\/4 < 2\/3.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 6.
      \n\"Envision<\/p>\n

      Answer:
      \n4\/4 > 4\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 4\/4 and 4\/6.
      \n4\/4 = 1.
      \n1\/6 + 1\/6 + 1\/6 + 1\/6 = 4\/6.
      \nso 4\/4 > 4\/6.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 7.
      \n\\(\\frac{2}{3}\\) \"Envision \\(\\frac{2}{2}\\)<\/p>\n

      Answer:
      \n2\/3 > 2\/2.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/3 and 2\/2.
      \n2\/2 = 1.
      \n1\/3 + 1\/3 = 2\/3.
      \nso 2\/3 > 2\/2.<\/p>\n

      Question 8.
      \n\\(\\frac{4}{8}\\) \"Envision \\(\\frac{4}{8}\\)<\/p>\n

      Answer:
      \n4\/8 = 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 4\/8 and 4\/8.
      \n4\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n4\/8 x 1 = 4\/8.
      \nso 4\/8 = 4\/8.<\/p>\n

      Question 9.
      \n\\(\\frac{5}{6}\\) \"Envision \\(\\frac{5}{8}\\)<\/p>\n

      Answer:
      \n5\/6 > 5\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 5\/6 and 5\/8.
      \n5\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6 + 1\/6.
      \n5\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \nso 5\/6 > 5\/8.<\/p>\n

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

      Answer:
      \n1\/4 > 1\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/4 and 1\/3.
      \n1\/4 = 1\/4 x 1.
      \n1\/3 x 1 = 2\/3.
      \nso 1\/4 > 1\/3.<\/p>\n

      Question 11.
      \n\\(\\frac{1}{3}\\) \"Envision \\(\\frac{1}{6}\\)<\/p>\n

      Answer:
      \n1\/3 > 1\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/3 and 1\/2.
      \n1\/3 = 1 x 1\/3.
      \n1\/2 x 1 = 1\/3.
      \nso 1\/3 > 1\/6.<\/p>\n

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

      Answer:
      \n4\/6 = 4\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 4\/6 and 4\/6.
      \n4\/6 = 1 x 4\/6.
      \n1\/6 + 1\/6 + 1\/6 + 1\/6 = 4\/6.
      \nso 4\/6 = 4\/6.<\/p>\n

      Question 13.
      \n\\(\\frac{1}{8}\\) \"Envision \\(\\frac{1}{2}\\)<\/p>\n

      Answer:
      \n1\/8 < 1\/2.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/8 and 1\/2.
      \n1\/8 = 1 x 1\/8.
      \n1\/2 x 1 = 1\/2.
      \nso 1\/8 < 1\/2.<\/p>\n

      Question 14.
      \n\\(\\frac{2}{6}\\) \"Envision \\(\\frac{2}{3}\\)<\/p>\n

      Answer:
      \n2\/6 < 2\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/6 and 2\/3.
      \n2\/6 = 1\/6 + 1\/6.
      \n1\/3 + 1\/3 = 2\/3.
      \nso 2\/6 < 2\/3.<\/p>\n

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

      Question 15.
      \nJames uses blue and white tiles to make the two designs shown here. James says that the total blue area in the top design is the same as the total blue area in the bottom design. Is he correct? Explain.
      \n\"Envision<\/p>\n

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nJames uses blue and white tiles to make the two designs.
      \nJames says that the total blue area in the top design is the same as the total blue area in the bottom design.
      \n4\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n1\/8 x 4 = 4\/8.
      \nso James was correct.<\/p>\n

      Question 16.
      \nAmy sold 8 large quilts and 1 baby quilt. How much money did she make from selling quilts?
      \n\"Envision<\/p>\n

      Answer:
      \nThe money did she make from selling quilts = $520.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nAmy sold 8 large quilts and 1 baby quilt.
      \n60 x 8 = 480.
      \n40 x 1 = 40.
      \n480 + 40 = 520.
      \nso the money did she make from selling quilts = $520.<\/p>\n

      Question 17.
      \nBe Precise Write two comparison statements about the fractions shown below.
      \n\"Envision<\/p>\n

      Answer:
      \n3\/3 > 3\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 3\/3 and 3\/4.
      \n3\/3 = 1\/3 + 1\/3 + 1\/3.
      \n3\/4 = 1\/4 + 1\/4 + 1\/4.
      \nso 3\/3 > 3\/4.<\/p>\n

      Question 18.
      \nHigher Order Thinking<\/strong> John says that when you compare two fractions with the same numerator, you look at the denominators because the fraction with the greater denominator is greater. Is he correct? Explain, and give an example.<\/p>\n

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nJohn says that when you compare two fractions with the same numerator,
      \n3\/3 and 3\/4.
      \n3\/3 = 1.
      \n3\/4 = 1\/4 + 1\/4 + 1\/4.
      \n1 > 1\/4.
      \nso he was correct.<\/p>\n

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

      Question 19.
      \nThese fractions refer to the same whole. Which of these comparisons are correct? Select all that apply.
      \n\"Envision<\/p>\n

      Answer:
      \n2\/4 > 2\/3, 1\/2 > 1\/4, 5\/6 = 5\/6, and 3\/4 > 3\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 2\/4 and 2\/3.
      \n2\/4 = 1\/4 + 1\/4.
      \n2\/3 = 1\/3 + 1\/3.
      \nthe fractions are 1\/2 and 1\/4.
      \n1\/4 x 1 = 1\/4.
      \n1\/2 x 1 = 1\/2.
      \nthe fractions are 3\/4 and 3\/6.
      \n3\/4 = 1\/4 + 1\/4 + 1\/4.
      \n3\/6 = 1\/6 + 1\/6 + 1\/6.
      \nso the four fractions are correct.<\/p>\n

      Lesson 13.5 Compare Fractions: Use Benchmarks<\/h3>\n

      Solve & Share<\/strong>
      \nMr. Evans wrote \\(\\frac{2}{8}, \\frac{4}{8}, \\frac{6}{8}, \\frac{1}{8}, \\frac{3}{8}, \\frac{5}{8}\\) on and \\(\\frac{7}{8}\\) on the board. Then he circled the fractions that are closer to 0 than to 1. Which fractions did he circle? Which fractions did he not circle? Explain how you decided.
      \nI can … use what I know about the size of benchmark numbers to compare fractions.
      \n\"Envision<\/p>\n

      Look Back! Eric says that \\(\\frac{3}{8}\\) is closer to 1 than to 0 because \\(\\frac{3}{8}\\) is greater than \\(\\frac{1}{8}\\). Is he correct? Use benchmark numbers to evaluate Eric’s reasoning and justify your answer.<\/p>\n

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nEric says that 3\/8 is closer to 1.
      \n3\/8 is greater than 1\/8.
      \n3\/8 = 1\/8 + 1\/8 + 1\/8.
      \nso 3\/8 > 1\/8.
      \nso Eric was correct.<\/p>\n

      Essential Question<\/strong>
      \nHow Can Benchmark Numbers Be Used to Compare Fractions?<\/p>\n

      Visual Learning Bridge
      \nKeri wants to buy of a container of roasted peanuts. Alan wants to buy of a container of roasted peanuts. The containers are the same size. Who will buy more peanuts?
      \n\"Envision<\/p>\n

      Compare each fraction to the benchmark number \\(\\frac{1}{2}\\). Then see how they relate to each other in size.
      \n\"Envision<\/p>\n

      So, \\(\\frac{2}{6}\\) is less than \\(\\frac{2}{3}\\).
      \n\\(\\frac{2}{6}\\) < \\(\\frac{2}{3}\\)
      \nAlan will buy more peanuts than Keri.<\/p>\n

      Convince Me! Make Sense and Persevere Candice buys \\(\\frac{2}{8}\\) of a container of roasted peanuts. The container is the same size as those used by Keri and Alan. She says \\(\\frac{2}{8}\\) is between \\(\\frac{1}{2}\\) and 1, so she buys more peanuts than Alan. Is Candice correct? Explain.<\/p>\n

      Answer:
      \nCandice, she was correct.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nCandice buys \\(\\frac{2}{8}\\) of a container of roasted peanuts.
      \nThe container is the same size as those used by Keri and Alan.
      \nShe says \\(\\frac{2}{8}\\) is between \\(\\frac{1}{2}\\) and 1.
      \n2\/8 = 1\/8 + 1\/8.
      \n1\/2 x 1 = 1\/2.
      \nso Candice was correct.<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nTina used benchmark numbers to decide that \\(\\frac{3}{8}\\) is less than \\(\\frac{7}{8}\\). Do you agree? Explain.<\/p>\n

      Answer:
      \nYes, 3\/8 is less than 7\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nTina used benchmark numbers to decide that 3\/8 is less than 7\/8.
      \n3\/8 = 1\/8 + 1\/8 + 1\/8.
      \n7\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \nso 3\/8 is less than 7\/8.<\/p>\n

      Question 2.
      \nWrite two fractions with a denominator of 6 that are closer to 0 than to 1.<\/p>\n

      Answer:
      \nThe two fractions are 3\/6 and 4\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 3\/6 and 4\/6
      \n3\/6 = 1\/6 + 1\/6 + 1\/6.
      \n4\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6.
      \nso 3\/6 and 4\/6 equal to 0 and 1.<\/p>\n

      Question 3.
      \nWrite two fractions with a denominator of 8 that are closer to 1 than to 0.<\/p>\n

      Answer:
      \nThe two fractions are 2\/8 and 7\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions with a denominator of 8 that are closer to 1 than to 0.
      \n2\/8 = 1\/8 + 1\/8.
      \n7\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \nso the two fractions are 2\/8 and 7\/8 is equal to 0 and 1.<\/p>\n

      Do You Know How?<\/strong>
      \nIn 4-6, choose from the fractions \\(\\frac{1}{8}, \\frac{1}{4}, \\frac{6}{8}\\) and \\(\\frac{3}{4}\\). Use fraction strips to help.
      \nQuestion 4.
      \nWhich fractions are closer to 0 than to 1?<\/p>\n

      Answer:
      \nThe two fractions are 3\/4 and 1\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 1\/8, 1\/4, 6\/8, and 3\/4.
      \n3\/4 = 1\/4 + 1\/4 + 1\/4.
      \n1\/4 x 1 = 1\/4
      \nso the two fractions are 3\/4 and 1\/4.<\/p>\n

      Question 5.
      \nWhich fractions are closer to 1 than to 0?<\/p>\n

      Answer:
      \nThe fractions are 6\/8 and 3\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 1\/8, 1\/4, 6\/8, and 3\/4.
      \n6\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n3\/4 = 1\/4 + 1\/4 + 1\/4.
      \nso the fractions closer to 1 than to 0 are 6\/8 and 3\/4.<\/p>\n

      Question 6.
      \nUse the two fractions with a denominator of 8 to write a true statement: < .<\/p>\n

      Answer:
      \n1\/8 < 6\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 1\/8, 1\/4, 6\/8, and 3\/4.
      \n6\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n3\/4 = 1\/4 + 1\/4 + 1\/4.
      \nthe two fractions with a denominator of 8.
      \nso 1\/8 < 6\/8.<\/p>\n

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

      In 7 and 8, choose from the fractions, \\(\\frac{2}{3}, \\frac{7}{8}, \\frac{1}{4}\\), and \\(\\frac{2}{6}\\).
      \nQuestion 7.
      \nWhich of the fractions are closer to 0 than to 1?<\/p>\n

      Answer:
      \nThe fractions are closer to 0 than to 1 are 2\/3 and 1\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 2\/3, 7\/8, 1\/4, and 2\/6.
      \n2\/3 = 1\/3 + 1\/3.
      \n1\/4 x 1 = 1\/4.
      \nso the fractions are closer to 0 than to 1 are 2\/3 and 1\/4.<\/p>\n

      Question 8.
      \nWhich of the fractions are closer to 1 than to 0?<\/p>\n

      Answer:
      \nThe fractions are closer to 1 than to 0 are 7\/8 and 2\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 2\/3, 7\/8, 1\/4, and 2\/6.
      \n7\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n2\/6 = 1\/6 + 1\/6.
      \nso the fractions are closer to 1 than to 0 are 7\/8 and 2\/6.<\/p>\n

      In 9-14, use a strategy to compare. Write <, >, or =.
      \n\"Envision
      \nQuestion 9.
      \n\\(\\frac{5}{8}\\) \"Envision \\(\\frac{7}{8}\\)<\/p>\n

      Answer:
      \n5\/8 < 7\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 5\/8 and 7\/8.
      \n5\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n7\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \nso 5\/8 < 7\/8.<\/p>\n

      Question 10.
      \n\\(\\frac{5}{8}\\) \"Envision \\(\\frac{2}{8}\\)<\/p>\n

      Answer:
      \n5\/8 > 2\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 5\/8 and 2\/8.
      \n5\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n2\/8 = 1\/8 + 1\/8.
      \nso 5\/8 > 2\/8.<\/p>\n

      Question 11.
      \n\\(\\frac{3}{4}\\) \"Envision \\(\\frac{3}{6}\\)<\/p>\n

      Answer:
      \n3\/4 > 3\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 3\/4 and 3\/6.
      \n3\/4 = 1\/4 + 1\/4 + 1\/4.
      \n3\/6 = 1\/6 + 1\/6 + 1\/6.
      \nso 3\/4 < 3\/6.<\/p>\n

      Question 12.
      \n\\(\\frac{4}{6}\\) \"Envision \\(\\frac{4}{8}\\)<\/p>\n

      Answer:
      \n4\/6 < 4\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 4\/6 and 4\/8.
      \n4\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6.
      \n4\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \nso 4\/6 < 4\/8.<\/p>\n

      Question 13.
      \n\\(\\frac{2}{6}\\) \"Envision \\(\\frac{2}{4}\\)<\/p>\n

      Answer:
      \n2\/6 > 2\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/6 and 2\/4.
      \n2\/6 = 1\/6 + 1\/6.
      \n2\/4 = 1\/4 + 1\/4.
      \nso 2\/6 > 2\/4.<\/p>\n

      Question 14.
      \n\\(\\frac{2}{3}\\) \"Envision \\(\\frac{1}{3}\\)<\/p>\n

      Answer:
      \n2\/3 > 1\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/3 and 1\/3.
      \n2\/3 = 1\/3 + 1\/3.
      \n1\/3 = 1\/3 x 1.
      \nso 2\/3 > 1\/3.<\/p>\n

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

      In 15-17, use the table at the right.
      \n\"Envision
      \nQuestion 15.
      \nWhich people have walked closer to 1 mile than to 0 miles?<\/p>\n

      Answer:
      \nMr. Nunez and Miss Lee have walked closer to 1 mile than to 0 miles.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthere are 5 people in the chart.
      \nthey are 1\/6, 5\/6, 1\/3, 4\/8, and 4\/6.
      \nthe people closer to 1 mile than to 0 miles are Mr. Nunez and Miss.
      \nthe fractions closer to 1 mile is 5\/6 and 4\/6.<\/p>\n

      Question 16.
      \nWhich people have walked closer to 0 miles than to 1 mile?<\/p>\n

      Answer:
      \nMrs. Avery and Miss Chang have walked closer to 0 miles than to 1 mile.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthere are 5 people in the chart.
      \nthey are 1\/6, 5\/6, 1\/3, 4\/8, and 4\/6.
      \nthe people closer to 0 miles than to 1 mile are Mrs. Avery and Miss chang.
      \nthe fractions closer to 0 miles is 1\/6 and 1\/3.<\/p>\n

      Question 17.
      \nWho has walked a fraction of a mile that is closer to neither 0 nor 1? Explain.<\/p>\n

      Answer:
      \nMr. O’Leary has walked closer to neither 0 nor 1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthere are 5 people in the chart.
      \nthey are 1\/6, 5\/6, 1\/3, 4\/8, and 4\/6.
      \nthe people closer to neither 0 nor 1.
      \nthe fractions are 4\/8.<\/p>\n

      Question 18.
      \nRahul compares two wholes that are the same size. He says that \\(\\frac{2}{6}\\) < \\(\\frac{2}{3}\\) because \\(\\frac{2}{6}\\) is less than \\(\\frac{1}{2}\\), and \\(\\frac{2}{3}\\) is greater than \\(\\frac{1}{2}\\). Is he correct? Explain.
      \n\"Envision<\/p>\n

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nRahul compares two wholes that are the same size.
      \nHe says that \\(\\frac{2}{6}\\) < \\(\\frac{2}{3}\\).
      \n\\(\\frac{2}{6}\\) is less than \\(\\frac{1}{2}\\).
      \n2\/6 < 2\/3.
      \n2\/6 < 1\/2.
      \n2\/3 > 1\/2.
      \nso he was correct.<\/p>\n

      Question 19.
      \nMake Sense and Persevere Manish drives 265 more miles than Janice. Manish drives 642 miles. How many miles does Janice drive?<\/p>\n

      Answer:
      \nThe number of miles does Janice drive =<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nManish drives 265 more miles than Janice.
      \nManish drives 642 miles.
      \n642 – 265 = 377.
      \nso the number of miles does Janice drives = 377.<\/p>\n

      Question 20.
      \nAlgebra Nika has 90 pencils. Forty of them are yellow, 13 are green, 18 are red, and the rest are blue. How many blue pencils does Nika have?<\/p>\n

      Answer:
      \nThe number of blue pencils does Nika have = 47.<\/p>\n

      Explanation:
      \nIn the above-given that,
      \ngiven that,
      \nAlgebra Nika has 90 pencils.
      \nForty of them are yellow, 13 are green, 18 are red, and the rest are blue.
      \n13 + 18 = 43.
      \n90 – 43 = 47.
      \nso the number of blue pencils does Nika have = 47.<\/p>\n

      Question 21.
      \nHigher Order Thinking<\/strong> Omar says that \\(\\frac{2}{6}\\) < \\(\\frac{4}{6}\\) because \\(\\frac{2}{6}\\) is between 0 and \\(\\frac{1}{2}\\), and \\(\\frac{4}{6}\\) is between \\(\\frac{1}{2}\\) and 1. Is he correct? Explain.
      \n\"Envision<\/p>\n

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n2\/6 < 4\/6.
      \n2\/6 is between 0 and 1\/2.
      \n4\/6 is between 1\/2 and 1.
      \n0, 2\/6, and 1\/2.
      \n1\/2, 4\/6, and 1.
      \nso Omar was correct.<\/p>\n

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

      Question 22.
      \nEach of the fractions in the comparisons at the right refer to the same whole. Use benchmark fractions to reason about the size of each fraction. Select all the correct comparisons.
      \n\"Envision<\/p>\n

      Answer:
      \n2\/3 < 2\/4, 3\/6 > 3\/8, and 3\/8 > 5\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe fractions are 2\/3 < 2\/4, 2\/4 < 2\/3, 3\/8 > 5\/8, 1\/4 < 2\/4, and 3\/6 > 3\/8.
      \nso the 2\/3 < 2\/4.
      \n2\/3 < 1 and 1\/2 > 1.
      \n3\/6 > 3\/8.
      \n3\/8 > 5\/8.
      \nso the correct fractions are 2\/3 < 2\/4, 3\/6 > 3\/8, and 3\/8 > 5\/8.<\/p>\n

      Lesson 13.6 Compare Fractions: Use the Number Line<\/h3>\n

      Solve & Share<\/strong>
      \nTanya, Riaz, and Ryan each used a bag of flour to make modeling clay. The bags were labeled lb, \u00e1 lb, and \u0179 lb. Show these fractions on a number line. How can you use the number line to compare two of these fractions?
      \nI can … compare two fractions by locating them on a number line.
      \n\"Envision<\/p>\n

      Look Back! If the bags were labeled \\(\\frac{4}{8}\\) lb, \\(\\frac{3}{8}\\) lb, and \\(\\frac{6}{8}\\) lb, how could a number line help you solve this problem?<\/p>\n

      Answer:
      \n3\/8 < 4\/8 < 6\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nif the bags were labeled 4\/8 lb, 3\/8 lb, and 6\/8 lb.
      \nso the fractions from least to greatest are 3\/8, 4\/8, and 6\/8.
      \n3\/8 is near to 0.
      \n4\/8 is in between 0 and 1.
      \n6\/8 is near to 1.<\/p>\n

      Essentials Question<\/strong>
      \nHow Can You Compare Fractions Using the Number Line?<\/p>\n

      Visual Learning Bridge
      \nTalia has two different lengths of blue and red ribbon. Does she have more blue ribbon or more red ribbon?
      \n\"Envision<\/p>\n

      The fractions both refer to 1 yard of ribbon. This is the whole.
      \nYou can use a number line to compare \\(\\frac{1}{3}\\) and \\(\\frac{2}{3}\\).
      \nThe farther the distance of the fraction from zero on the number line, the greater the fraction.
      \n\"Envision
      \nOn the number line, \\(\\frac{2}{3}\\) is farther to the right than \\(\\frac{1}{3}\\).
      \nSo, \\(\\frac{2}{3}\\) > \\(\\frac{1}{3}\\).
      \nTalia has more blue ribbon than red ribbon.<\/p>\n

      Convince Me! Use Structure Talia has an additional length of green ribbon that measures \\(\\frac{2}{4}\\) yard. How can you compare the length of the green ribbon to the lengths of the blue and red ribbons?<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nWhen two fractions refer to the same whole, what do you notice when the denominators you are comparing are the same?<\/p>\n

      Answer:
      \nThe denominators are greater than the numerators.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nif two fractions are the same.
      \nthe denominators are greater than the numerators.<\/p>\n

      Question 2.
      \nWrite a problem that compares two fractions with different numerators.<\/p>\n

      Answer:
      \n1\/3 > 2\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two different fractions are 1\/3 and 2\/5.
      \n1\/3 x 1 = 1\/3.
      \n2\/3 = 1\/3 + 1\/3.
      \nso 1\/3 > 2\/3.<\/p>\n

      Do You Know How?<\/strong>
      \nIn 3-5, compare fractions using <, >, or =. Use the number lines to help.
      \nQuestion 3.
      \n\"Envision<\/p>\n

      Answer:
      \n2\/4 < 2\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/4 and 2\/3.
      \n2\/4 = 1\/4 + 1\/4.
      \n2\/3 = 1\/3 + 1\/3.
      \n2\/4 is the half portion in the number line.
      \nso 2\/4 > 2\/3.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 4.
      \n\"Envision<\/p>\n

      Answer:
      \n2\/6 < 2\/3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 2\/6 and 2\/3.
      \n2\/6 = 1\/6 + 1\/6.
      \n2\/3 = 1\/3 + 1\/3.
      \n2\/6 is below the half portion in the number line.
      \nso 2\/6 < 2\/3.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Answer:
      \n5\/8 > 3\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 5\/8 and 3\/8.
      \n5\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n3\/8 = 1\/8 + 1\/8 + 1\/8.
      \n3\/8 is the half portion in the number line.
      \nso 5\/8 > 3\/8.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      In 6-9, use the number lines to compare the fractions. Write >, <, or =.
      \nQuestion 6.
      \n\"Envision<\/p>\n

      Answer:
      \n1\/4 > 3\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/4 and 3\/4.
      \n1\/4 = 1\/4 x 1.
      \n3\/4 = 1\/4 + 1\/4 + 1\/4.
      \n1\/4 is nearest to 0.
      \nso 1\/4 > 3\/4.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Answer:
      \n4\/6 < 3\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 4\/6 and 3\/6.
      \n4\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6.
      \n3\/6 = 1\/6 + 1\/6 + 1\/6.
      \nso 4\/6 < 3\/6.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 8.
      \n\"Envision<\/p>\n

      Answer:
      \n1\/2 > 1\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/4 and 1\/2.
      \n1\/2 = 1\/2 x 1.
      \n1\/4 = 1\/4 x 1
      \n1\/4 is nearest to 0.
      \nso 1\/2 > 1\/4.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 9.
      \n\"Envision<\/p>\n

      Answer:
      \n1\/3 > 1\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two fractions are 1\/3 and 1\/8.
      \n1\/3 = 1\/3 x 1.
      \n1\/8 = 1\/8 x 1.
      \n1\/8 is nearest to 0.
      \nso 1\/3 > 1\/8.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Question 10.
      \nNumber Sense Randy wants to save $39. The table shows how much money he has saved. Explain how you can use estimation to decide if he has saved enough money.
      \n\"Envision<\/p>\n

      Answer:
      \nYes, he has saved enough money.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nRandy wants to save $39.
      \nin march month he saved $14.
      \nin April he saved $11.
      \nin May he saved $22.
      \n14 + 11 + 22 = 47.
      \nso he has saved enough money.<\/p>\n

      Question 11.
      \nScott ate \\(\\frac{2}{8}\\) of a fruit bar. Anne ate \\(\\frac{4}{8}\\) of a same-sized fruit bar. Can you tell who ate more of a fruit bar, Scott or Anne? Explain.<\/p>\n

      Answer:
      \nAnne ate more of a fruit bar.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nScott ate \\(\\frac{2}{8}\\) of a fruit bar.
      \nAnne ate \\(\\frac{4}{8}\\) of a same-sized fruit bar.
      \n2\/8 = 1\/8 + 1\/8.
      \n4\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8.
      \n4 > 2.
      \nso the whole is 8.
      \nso Anne ate more of a fruit bar.<\/p>\n

      Question 12.
      \nBe Precise Matt and Adara have identical pieces of cardboard for an art project. Matt uses \\(\\frac{2}{3}\\) of his piece. Adara uses \\(\\frac{2}{6}\\) of her piece. Who uses more, Matt or Adara? Draw two number lines to help explain your answer.<\/p>\n

      Answer:
      \nMatt uses more cardboard.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nMatt and Adara have identical pieces of cardboard for an art project.
      \nmatt uses 2\/3 of his piece.
      \nAdara uses 2\/6 of her piece.
      \n2\/3 = 1\/3 + 1\/3.
      \n2\/6 = 1\/6 + 1\/6.
      \nin 1st 3 is the whole part.
      \n2 is near to 3.
      \nso matt uses more cardboard.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 13.
      \nHigher Order Thinking<\/strong> Some friends shared a pizza. Nicole ate \\(\\frac{2}{8}\\) of the pizza. Chris ate \\(\\frac{1}{8}\\) more than Johan. Mike ate \\(\\frac{1}{8}\\) of the pizza. Johan ate more than Mike. Who ate the most pizza?
      \n\"Envision<\/p>\n

      Answer:
      \nChris ate more pizza.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nSome friends shared a pizza.
      \nNicole ate \\(\\frac{2}{8}\\) of the pizza.
      \nChris ate \\(\\frac{1}{8}\\) more than Johan.
      \nMike ate \\(\\frac{1}{8}\\) of the pizza.
      \n1\/8 + 1 = 2\/8.
      \n2\/8 + 1 = 3\/8.
      \nso Chris ate more pizza.<\/p>\n

      Question 14.
      \nInez has 2 rows of plants. There are 8 plants in each row. Each plant has 3 flowers. How many flowers are there in all?<\/p>\n

      Answer:
      \nThe number of flowers is there = 48.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nInez has 2 rows of plants.
      \nthere are 8 plants in each row.
      \neach plant has 3 flowers.
      \n8 x 2 =16.
      \n16 x 3 = 48.
      \nso the number of flowers is there = 48.<\/p>\n

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

      Question 15.
      \nDaniel walked \\(\\frac{3}{4}\\) of a mile. Theo walked \\(\\frac{3}{8}\\) of a mile. Use the number lines to show 0 the fraction of a mile Daniel and Theo each walked. Then select all the correct statements that describe the fractions.
      \n\"Envision
      \n\u2610 \\(\\frac{3}{4}\\) is equivalent to \\(\\frac{3}{8}\\) because the fractions mark the same point.
      \n\u2610 \\(\\frac{3}{4}\\) is greater than \\(\\frac{3}{8}\\) because it is farther from zero.
      \n\u2610 \\(\\frac{3}{4}\\) is less than \\(\\frac{3}{8}\\) because it is farther from zero.
      \n\u2610 \\(\\frac{3}{8}\\) is less than \\(\\frac{3}{4}\\) because it is closer to zero.
      \n\u2610 \\(\\frac{3}{8}\\) is greater than \\(\\frac{3}{4}\\) because it is closer to zero.<\/p>\n

      Answer:
      \nOption B is the correct answer.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nDaniel walked \\(\\frac{3}{4}\\) of a mile.
      \nTheo walked \\(\\frac{3}{8}\\) of a mile.
      \nin the 1st line, the 3 is farther from the 0.
      \nso 3\/4 > 3\/8.
      \nso option B is the correct answer.<\/p>\n

      Lesson 13.7 Whole Numbers and Fractions<\/h3>\n

      Solve & Share<\/strong>
      \nJamie’s family ate 12 pieces of apple pie during the week. Each piece was \\(\\frac{1}{6}\\) of a whole pie. How many whole pies did Jamie’s family eat? What fraction of a pie was left over? Explain how you decided.
      \nI can … use representations to find fraction names for whole numbers.
      \n\"Envision<\/p>\n

      Look Back! Jamie cuts another pie into smaller pieces. Each piece of pie is \\(\\frac{1}{8}\\) of the whole. Jamie gives away 8 pieces. Does Jamie have any pie left over? Explain how you know.<\/p>\n

      Answer:
      \nJamie does not have left any pie.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nJamie cuts another pie into smaller pieces.
      \nEach piece of pie is \\(\\frac{1}{8}\\) of the whole.
      \nJamie gives away 8 pieces.
      \n8 – 8 = 0.
      \nso Jamie does not have left any pie.<\/p>\n

      Essential Question<\/strong>
      \nHow Can You Use Fraction Names to Represent Whole Numbers?<\/p>\n

      Visual Learning Bridge
      \nWhat are some equivalent fraction names for 1, 2, and 3?
      \nYou can write a whole number as a fraction by writing the whole number as the numerator and
      \n\"Envision
      \nThe number line shows 3 wholes. Each whole is divided into 1 equal part.
      \n1 whole divided into 1 equal part can be written as \\(\\frac{1}{1}\\).
      \n2 wholes each divided into 1 equal part can be written as \\(\\frac{2}{1}\\).
      \n3 wholes each divided into 1 equal part can be written as \\(\\frac{1}{1}\\)
      \n1 = \\(\\frac{1}{2}\\)
      \n2 = \\(\\frac{2}{1}\\)
      \n3 = \\(\\frac{3}{1}\\)<\/p>\n

      You can find other equivalent fraction names for whole numbers.
      \n\"Envision<\/p>\n

      Convince Me! Reasoning What equivalent fraction names can you write for 4 using denominators of 1, 2, or 4?<\/p>\n

      Another Example!<\/strong>
      \nYou can use fractions to name whole numbers.
      \n\"Envision
      \nTwelve \\(\\frac{1}{3}\\) fraction strips equal 4 whole fraction strips.
      \nAll whole numbers have fraction names. You can write 4 = \\(\\frac{12}{3}\\).
      \nYou also know 4 = \\(\\frac{4}{1}\\), so you can write 4 = \\(\\frac{4}{1}\\) = \\(\\frac{12}{3}\\).<\/p>\n

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

      Do You Understand?<\/strong>
      \nQuestion 1.
      \nExplain how you know that \\(\\frac{4}{1}\\) = 4.<\/p>\n

      Answer:
      \n4\/1 = 4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \n12\/3 = 4\/1.
      \n3 x 1 = 3.
      \n3 x 4 = 12.
      \nso 4\/1 = 4.<\/p>\n

      Do You Know How?<\/strong>
      \nQuestion 2.
      \nComplete the number line.
      \n\"Envision<\/p>\n

      Answer:
      \nThe missing numbers in upside are 1\/3, 3\/3, 4\/3, and 6\/3.
      \nthe missing numbers on the downside are 1\/6, 2\/6, 4\/6, 5\/6, 6\/6, 7\/6, 9\/6, 10\/6, 11\/6, and 12\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number line is 1\/3, 2\/3, 3\/3, 4\/3, 5\/3, 6\/3.
      \n2\/6 = 1\/3.
      \n1 x 2 = 2.
      \n3 x 2 = 6.
      \n6\/6 = 1.
      \n9\/6 = 3\/2.
      \n3 x 3 = 9.
      \n3 x 2 = 6.
      \nso the missing numbers are 1\/3, 3\/3, 4\/3, and 6\/3.
      \n1\/6, 2\/6, 4\/6, 5\/6, 6\/6, 7\/6, 9\/6, 10\/6, 11\/6, and 12\/6.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 3.
      \nLook at the number line. Write two equivalent fractions for each whole number.
      \n\"Envision<\/p>\n

      Answer:
      \n1 = 3\/3 = 6\/6.
      \n2 = 6\/3 = 12\/6.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe two numbers are 1 and 2.
      \n1 = 3\/3.
      \n6 \/ 6 = 1.
      \n6\/3 = 2.
      \n12 \/ 6 = 2.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      In 4-7, write two equivalent fractions for each whole number. You can draw number lines to help.
      \nQuestion 4.
      \n\"Envision<\/p>\n

      Answer:
      \n4 = 8\/2 = 4\/1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 4.
      \n8\/2 = 4.
      \n2 x 1 = 2.
      \n2 x 4 = 8.
      \n4 \/ 1 = 4.
      \nso the missing numbers are 8 and 4.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Answer:
      \n1 = 4\/4 = 1\/1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 1.
      \n4\/4 = 1.
      \n4 x 1 = 4.
      \n1 x 4 = 4.
      \n1 \/ 1 = 1.
      \nso the missing numbers are 4 and 1.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Question 6.
      \n\"Envision<\/p>\n

      Answer:
      \n2 = 6\/3 = 2\/1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 2.
      \n6\/3 = 2.
      \n3 x 1 = 3.
      \n3 x 2 = 6.
      \n2 \/ 1 = 2.
      \nso the missing numbers are 6 and 1.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

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

      Answer:
      \n5 = 10\/2 = 5\/1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe number is 5.
      \n10\/2 = 5.
      \n2 x 1 = 2.
      \n2 x 5 = 10.
      \n5 \/ 1 = 5.
      \nso the missing numbers are 10 and 5.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      In 8-11, for each pair of fractions, write the equivalent whole number.
      \nQuestion 8.
      \n\\(\\frac{6}{2}\\) = \\(\\frac{3}{1}\\) =<\/p>\n

      Answer:
      \n\\(\\frac{6}{2}\\) = \\(\\frac{3}{1}\\) = 3.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nfor each pair of fractions, write the equivalent whole number.
      \n6\/2 = 3.
      \n3\/1 = 3.
      \nso \\(\\frac{6}{2}\\) = \\(\\frac{3}{1}\\) = 3.<\/p>\n

      Question 9.
      \n\\(\\frac{3}{3}\\) = \\(\\frac{6}{6}\\) =<\/p>\n

      Answer:
      \n\\(\\frac{3}{3}\\) = \\(\\frac{6}{6}\\) = 1.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nfor each pair of fractions, write the equivalent whole number.
      \n3\/3 = 1.
      \n6\/6 = 1.
      \nso \\(\\frac{3}{3}\\) = \\(\\frac{6}{6}\\) = 1.<\/p>\n

      Question 10.
      \n\\(\\frac{8}{4}\\) = \\(\\frac{6}{3}\\) =<\/p>\n

      Answer:
      \n\\(\\frac{8}{4}\\) = \\(\\frac{6}{3}\\) = 2.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nfor each pair of fractions, write the equivalent whole number.
      \n8\/4 = 2.
      \n6\/3 = 2.
      \nso \\(\\frac{8}{4}\\) = \\(\\frac{6}{3}\\) = 2.<\/p>\n

      Question 11.
      \n\\(\\frac{9}{3}\\) = \\(\\frac{12}{4}\\) =<\/p>\n

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

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nfor each pair of fractions, write the equivalent whole number.
      \n9\/3 = 3.
      \n12\/4 = 3.
      \nso \\(\\frac{9}{3}\\) = \\(\\frac{12}{4}\\) = 3.<\/p>\n

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

      Question 12.
      \nHenry needs to fix or replace his refrigerator. It will cost $376 to fix it. How much more will it cost to buy a new refrigerator than to fix the current one?
      \n\"Envision<\/p>\n

      Answer:
      \nThe more it costs to buy a new refrigerator = $593.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nHenry needs to fix or replace his refrigerator.
      \nIt will cost $376 to fix.
      \nthe new refrigerator cost is $969.
      \n969 – 376 = 593.
      \nso more it costs to buy a new refrigerator = $593.<\/p>\n

      Question 13.
      \nDeclan says, \u201cTo write an equivalent fraction name for 5, I can write 5 as the denominator and 1 as the numerator.” Do you agree with Declan? Explain.<\/p>\n

      Answer:
      \nNo, Declan was wrong.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nTo write an equivalent fraction name for 5, I can write 5 as the denominator and 1 as the numerator.
      \n5\/1 = 5.
      \nso Declan was wrong.<\/p>\n

      Question 14.
      \nLook for Relationships Describe a pattern in fractions equivalent to 1 whole.<\/p>\n

      Answer:<\/p>\n

      Question 15.
      \nenVision\u00ae STEM There are four stages in a butterfly’s life cycle: egg, caterpillar, chrysalis, and butterfly. Dan makes one whole poster for each stage. Use a fraction to show the number of whole posters Dan makes.<\/p>\n

      Answer:
      \nDan makes the fractions 1\/4, 2\/4, 3\/4, and 4\/4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nThere are four stages in a butterfly’s life cycle: egg, caterpillar, chrysalis, and butterfly.
      \n1st stage is egg = 1\/4.
      \n2nd stage is caterpillar = 2\/4.
      \n3rd stage is chrysalis = 3\/4.
      \n4th stage is butterfly = 4\/4.
      \nso the fractions are 1\/4, 2\/4, 3\/4, and 4\/4.<\/p>\n

      Question 16.
      \nKaren bought 4 movie tickets for $9 each. She has $12 left over. How much money did Karen have to start? Explain.<\/p>\n

      Answer:
      \nThe money Karen has to start = $48.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nKaren bought 4 movie tickets for $9 each. She has $12 left over
      \n4 x 9 = 36.
      \n36 + 12 = 48.
      \nso the money Karen has to start = $48.<\/p>\n

      Question 17.
      \nHigher Order Thinking<\/strong> Peggy has 4 whole sandwiches. She cuts each whole into halves. Then Peggy gives away 1 whole sandwich. Show the number of sandwiches Peggy has left as a fraction.<\/p>\n

      Each sandwich is cut into equal parts.<\/p>\n

      Answer:
      \nThe number of sandwiches Peggy has left as a fraction = 6\/8.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nPeggy has 4 whole sandwiches.
      \nShe cuts each whole into halves.
      \n4 x 2 = 8.
      \nThen Peggy gives away 1 whole sandwich.
      \n8 – 2 = 6.
      \nso the number of sandwiches Peggy has left as a fraction = 6\/8.<\/p>\n

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

      Question 18.
      \nComplete the equations. Match the fractions with their equivalent whole numbers.
      \n\"Envision<\/p>\n

      Answer:
      \n6\/1 = 12\/2 = 6.
      \n6\/3 = 4\/2 = 2.
      \n4\/4 = 1\/1 = 1.
      \n8\/2 = 16\/4 = 4.<\/p>\n

      Explanation:
      \nIn the above-given question,
      \ngiven that,
      \nthe numbers are 1, 2, 4, and 6.
      \n6\/1 = 12\/2 = 6.
      \n6\/3 = 4\/2 = 2.
      \n4\/4 = 1\/1 = 1.
      \n8\/2 = 16\/4 = 4.
      \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

      Lesson 13.8 Problem Solving<\/h3>\n

      Construct Arguments<\/strong>
      \nSolve & Share<\/strong>
      \nLindsey and Matt are running in a 1-mile race. They have both run the same distance so far. Write a fraction that shows how far Lindsey could have run. Write a different fraction that shows how far Matt could have run. Construct a math argument to support your answer.
      \nI can … construct math arguments using what I know about fractions.
      \n\"Envision<\/p>\n

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

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

        Look Back! Construct Arguments Are the two fractions you wrote equivalent? Construct a math argument using pictures, words, and numbers to support your answer.<\/p>\n

        Essential Question<\/strong>
        \nHow Can You Construct Arguments?<\/p>\n

        Visual Learning Bridge
        \nClara and Ana are making rugs. The rugs will be the same size. Clara has finished of her rug. Ana has finished of her rug. Who has finished more of her rug? Conjecture: Clara has finished a greater portion of her rug than Ana.<\/p>\n

        A conjecture is a statement that you think is true. It needs to be proved.<\/p>\n

        How can I explain why my conjecture is correct?
        \nI need to construct an argument to justify my conjecture.<\/p>\n

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

          \n
        • use numbers, objects, drawings, or actions correctly to explain my thinking.<\/li>\n
        • make sure my explanation is simple, complete, and easy to understand.<\/li>\n<\/ul>\n

          Here’s my thinking…
          \nI will use drawings and numbers to explain my thinking.
          \nThe number lines represent the same whole. One is divided into fourths. One is divided into eighths.
          \n\"Envision
          \nThe number lines show that 3 of the fourths is greater than 3 of the eighths.
          \nSo, \\(\\frac{3}{4}\\) > \\(\\frac{3}{8}\\). The conjecture is correct.<\/p>\n

          Convince Me! Construct Arguments Use numbers to construct another math argument to justify the conjecture above. Think about how you can look at the numerator and the denominator.<\/p>\n

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

          Construct Arguments<\/strong> Paul and Anna were eating burritos. The burritos were the same size. Paul ate \\(\\frac{2}{6}\\) of a burrito. Anna ate \\(\\frac{2}{3}\\) of a burrito. Conjecture: Paul and Anna ate the same amount.
          \nQuestion 1.
          \nDraw a diagram to help justify the conjecture.
          \n\"Envision<\/p>\n

          Answer:
          \nNo, Paul and Anna were correct.<\/p>\n

          Explanation:
          \nIn the above-given question,
          \ngiven that,
          \nPaul and Anna were eating burritos.
          \nThe burritos were the same size.
          \nPaul ate \\(\\frac{2}{6}\\) of a burrito.
          \nAnna ate \\(\\frac{2}{3}\\) of a burrito.
          \npaul ate 2 of the sixths is less than the 2 of the thirds.
          \n2\/6 = 1\/6 + 1\/6.
          \n2\/3 = 1\/3 + 1\/3.
          \nyes, the conjecture is not correct.<\/p>\n

          Question 2.
          \nIs the conjecture correct? Construct an argument to justify your answer.<\/p>\n

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

          Explanation:
          \nIn the above-given question,
          \ngiven that,
          \nPaul and Anna were eating burritos.
          \nThe burritos were the same size.
          \nPaul ate \\(\\frac{2}{6}\\) of a burrito.
          \nAnna ate \\(\\frac{2}{3}\\) of a burrito.
          \npaul ate 2 of the sixths is less than the 2 of the thirds.
          \n2\/6 = 1\/6 + 1\/6.
          \n2\/3 = 1\/3 + 1\/3.
          \nyes, the conjecture is not correct.<\/p>\n

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

          Construct Arguments<\/strong> Reyna has a blue ribbon that is 1 yard long and a red ribbon that is 2 yards long. She uses \\(\\frac{2}{4}\\) of the red ribbon and \\(\\frac{2}{4}\\) of the blue ribbon.<\/p>\n

          Conjecture: Reyna uses the same amount of red and blue ribbon.
          \nQuestion 3.
          \nDraw a diagram to help justify the conjecture.<\/p>\n

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

          Explanation:
          \nIn the above-given question,
          \ngiven that,
          \nReyna has a blue ribbon that is 1 yard long and a red ribbon that is 2 yards long.
          \nShe uses \\(\\frac{2}{4}\\) of the red ribbon and \\(\\frac{2}{4}\\) of the blue ribbon.
          \n2\/4 = 1\/4 + 1\/4.
          \n2\/4 = 1\/4 + 1\/4.
          \nyes, the conjecture is correct.
          \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

          Question 4.
          \nIs the conjecture correct? Construct an argument to justify your answer.<\/p>\n

          Answer:
          \nYes, the conjecture is correct.<\/p>\n

          Explanation:
          \nIn the above-given question,
          \ngiven that,
          \nReyna has a blue ribbon that is 1 yard long and a red ribbon that is 2 yards long.
          \nShe uses \\(\\frac{2}{4}\\) of the red ribbon and \\(\\frac{2}{4}\\) of the blue ribbon.
          \n2\/4 = 1\/4 + 1\/4.
          \n2\/4 = 1\/4 + 1\/4.
          \nyes, the conjecture is correct.<\/p>\n

          Question 5.
          \nExplain another way you could justify the conjecture.
          \nAnswer:<\/p>\n

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

          Performance Task<\/strong> School Fair Twenty-one students worked at the school fair. Mrs. Gold’s students worked at a class booth. The table shows the fraction of 1 hour that her students worked. Mrs. Gold wants to know the order of the work times for the students from least to greatest.
          \n\"Envision<\/p>\n

          Question 6.
          \nMake Sense and Persevere What comparisons do you need to make to find out who worked the least?<\/p>\n

          Answer:
          \nThe student who worked least is Pedro.<\/p>\n

          Explanation:
          \nIn the above-given question,
          \ngiven that,
          \nSchool Fair Twenty-one students worked at the school fair.
          \nGold’s students worked at a class booth.
          \nThe table shows the fraction of 1 hour that her students worked.
          \nTim worked 4 hours.
          \nCathy worked 2\/4 hours.
          \nJose worked 2\/6 hours.
          \nPedro worked 3\/4 hours.
          \n3\/4 < 2\/4 < 2\/6.
          \nso the student who worked least is Pedro.<\/p>\n

          Question 7.
          \nBe Precise What is the whole for each student’s time? Do all the fractions refer to the same whole?<\/p>\n

          Answer:
          \nThe same whole is 4.<\/p>\n

          Explanation:
          \nIn the above-given question,
          \ngiven that,
          \nSchool Fair Twenty-one students worked at the school fair.
          \nGold’s students worked at a class booth.
          \nThe table shows the fraction of 1 hour that her students worked.
          \nTim worked 4 hours.
          \nCathy worked 2\/4 hours.
          \nJose worked 2\/6 hours.
          \nPedro worked 3\/4 hours.
          \n3\/4 < 2\/4 < 2\/6.
          \nso the students who worked least is Pedro.<\/p>\n

          Question 8.
          \nUse Appropriate Tools What tool could you use to solve this problem? Explain how you would use this tool.
          \n\"Envision<\/p>\n

          Answer:<\/p>\n

          Question 9.
          \nConstruct Arguments<\/strong> What is the order of the work times from least to greatest? Construct a math argument to justify your answer.<\/p>\n

          Answer:
          \nThe student who worked the least is Pedro.<\/p>\n

          Explanation:
          \nIn the above-given question,
          \ngiven that,
          \nSchool Fair Twenty-one students worked at the school fair.
          \nGold’s students worked at a class booth.
          \nThe table shows the fraction of 1 hour that her students worked.
          \nTim worked 4 hours.
          \nCathy worked 2\/4 hours.
          \nJose worked 2\/6 hours.
          \nPedro worked 3\/4 hours.
          \n3\/4 < 2\/4 < 2\/6.
          \nso the student who worked least is Pedro.<\/p>\n

          Topic 13 Fluency Practice Activity<\/h3>\n

          Find a Match<\/strong>
          \nWork with a partner. Point to a clue. Read the clue.
          \nLook below the clues to find a match. Write the clue letter in the box next to the match.
          \nFind a match for every clue.
          \nI can … multiply and divide within 100.<\/p>\n

          Clues
          \nA. ls equal to 3 \u00d7 3
          \nB. is equal to 4 \u00d7 4
          \nC. is equal to 9 \u00d7 4
          \nD. is equal to 0 \u00f7 10
          \nE. is equal to 35 \u00f7 5
          \nF. is equal to 12 \u00f7 4
          \nG. is equal to 5 \u00d7 4
          \nH. is equal to 3 \u00d7 8
          \nI. Is equal to 2 \u00d7 5
          \nJ. Is equal to 3 \u00d7 10
          \nK. is equal to 9 \u00d7 2
          \nL. is equal to 2 \u00d7 4
          \n\"Envision<\/p>\n

          Answer:
          \n6 x 6 = 36, 40 \/ 4 = 10, 0 x 9 = 0, 3 x 6 = 18, 32 \/ 4 = 8, 10 x 2 = 20, 5 x 6 = 30, 7 \/ 21 = 3, 8 x 2 = 16, and 6 x 4 = 24.<\/p>\n

          Explanation:
          \nIn the above-given question,
          \ngiven that,
          \nA is not equal to 9.
          \nB is equal to 16.
          \nC is equal to 36.
          \nD is equal to 0.
          \nE is equal to 35 \/ 5 = 7.
          \nF is equal to 3.
          \nG is equal to 20.
          \nH is equal to 24.
          \nI is equal to 10.
          \nJ is equal to 30.
          \nK is equal to 18.
          \nL is equal to 8.
          \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

          Topic 13 Vocabulary Review<\/h3>\n

          Word List<\/p>\n

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

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

            Write T for true or F for false.
            \nQuestion 1.
            \n______ \\(\\frac{1}{6}\\) and \\(\\frac{2}{6}\\) have the same numerator.<\/p>\n

            Answer:
            \nTrue.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe fractions are 1\/6 and 2\/6.
            \n2\/6 = 1\/3.
            \n2 x 1 = 2.
            \n2 x 3 = 6.
            \nso both the fractions have the same numerator.<\/p>\n

            Question 2.
            \n________ \\(\\frac{1}{2}\\) and \\(\\frac{4}{8}\\) are equivalent fractions.<\/p>\n

            Answer:
            \nTrue.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe fractions are 1\/2 and 4\/8.
            \n4\/8 = 1\/2.
            \n4 x 1 = 4.
            \n4 x 2 = 8.
            \nso both the fractions are equivalent fractions.<\/p>\n

            Question 3.
            \n_______ \\(\\frac{3}{8}\\) is a unit fraction.<\/p>\n

            Answer:
            \nTrue.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe fraction is 3\/8.
            \n3\/8 = 1\/8 + 1\/8 + 1\/8.
            \nso 3\/8 is a unit fraction.<\/p>\n

            Question 4.
            \n_________ A whole number can be written as a fraction.<\/p>\n

            Answer:
            \nTrue.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nA whole number can be written as a fraction.
            \n2 \/ 2 = 1.
            \nso the whole number can be written as a fraction.<\/p>\n

            Question 5.
            \n________ The denominators in \\(\\frac{1}{3}\\) and \\(\\frac{2}{3}\\) in are the same.<\/p>\n

            Answer:
            \nTrue.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe fractions are 1\/3 and 2\/3.
            \n2\/3 = 1\/3 + 1\/3.
            \nin both the fractions, the numerator, and denominator are the same.
            \nso both the fractions have the same denominators.<\/p>\n

            Question 6.
            \n_______ A number line always shows fractions.<\/p>\n

            Answer:
            \nA unit fraction is a number line that always shows fractions.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \n3\/8 is a unit fraction.
            \n3 is the numerator and 8 is a denominator.
            \nso the unit fraction is a number line that always shows fractions.<\/p>\n

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

            Answer:
            \n1\/2 is a fraction.
            \n3\/8 is a unit fraction.
            \n1\/2 = 2\/4 are equivalent fractions.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe terms are fraction, unit fraction, and equivalent fractions.
            \n1\/2 is a fraction.
            \n3\/8 is a unit fraction.
            \n1\/2 = 2\/4 are equivalent fractions.
            \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Use Vocabulary in Writing<\/strong>
            \nQuestion 10.
            \nUse at least 2 terms from the Word List to explain how to compare \\(\\frac{1}{2}\\) and \\(\\frac{1}{3}\\).<\/p>\n

            Answer:
            \nThe two terms have different denominators.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 1\/2 and 1\/3.
            \n1\/2 = 2\/4.
            \n1\/3 = 2\/6.
            \nso both the fractions have different denominators.<\/p>\n

            Topic 13 Reteaching<\/h3>\n

            Set A pages 485-488<\/strong><\/p>\n

            Two fractions are equivalent if they name the same part of a whole.
            \nWhat is one fraction that is equivalent to \\(\\frac{6}{8}\\)?
            \nYou can use fraction strips to find equivalent fractions.
            \n\"Envision
            \n\\(\\frac{6}{8}\\) = \\(\\frac{3}{4}\\)
            \nYou also can use area models to see that a I are equivalent fractions. The shaded fractions both show the same part of the whole.
            \n\"Envision<\/p>\n

            Remember<\/strong> to check that both sets of strips are the same length<\/p>\n

            In 1 and 2, find an equivalent fraction. Use fraction strips and models to help.
            \nQuestion 1.
            \n\"Envision<\/p>\n

            Answer:
            \n4\/6 = 2\/3.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe fraction is 4\/6.
            \n4\/6 = 2\/3.
            \n2 x 2 = 4.
            \n2 x 3 = 6.
            \nso the equivalent fraction is 2\/3.
            \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Question 2.
            \n\"Envision<\/p>\n

            Answer:
            \n2\/6 = 1\/3.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe fraction is 2\/6.
            \n2\/6 = 1\/3.
            \n1 x 2 = 2.
            \n2 x 3 = 6.
            \nso the equivalent fraction is 1\/3.
            \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Set B pages 489-492<\/strong><\/p>\n

            Riley says the library is \\(\\frac{2}{8}\\) of a mile from their house. Sydney says it is \\(\\frac{1}{4}\\) of a mile.
            \nUse the number lines to find who is correct.
            \n\"Envision
            \nThe fractions \\(\\frac{2}{8}\\) and \\(\\frac{1}{4}\\) are equivalent. They are the same distance from 0 on a number line. Riley and Sydney are both correct.<\/p>\n

            Remember<\/strong> that equivalent fractions have different names, but they represent the same point on a number line.<\/p>\n

            In 1 and 2, write two fractions that name the same location on the number line.
            \nQuestion 1.
            \n\"Envision<\/p>\n

            Answer:
            \nThe two fractions that name the same location on the number line = 1.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe fractions are 8\/8 and 4\/4.
            \n8\/8 = 1.
            \n4\/4 = 1.
            \nso the two fractions that name the same location on the number line = 1.
            \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Question 2.
            \n\"Envision<\/p>\n

            Answer:
            \nThe two fractions that name the same location on the number line = 3\/6 and 1\/2.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe fractions are 3\/6 and 1\/2.
            \n3\/6 = 1\/2.
            \n3 x 1 = 3.
            \n3 x 2 = 6.
            \nso the two fractions that name the same location on the number line = 3\/6 and 1\/2.
            \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Set C pages 493-496<\/strong><\/p>\n

            You can use fraction strips to compare fractions with the same denominator.
            \nCompare \\(\\frac{3}{4}\\) to \\(\\frac{2}{4}\\).
            \n\"Envision
            \nThe denominator of each fraction is 4.
            \nThree \\(\\frac{1}{4}\\) fraction strips show \\(\\frac{3}{4}\\).
            \nTwo \\(\\frac{1}{4}\\) fraction strips show \\(\\frac{2}{4}\\).
            \nThe fraction strips showing \\(\\frac{3}{4}\\) have 1 more unit fraction than the strips showing \\(\\frac{2}{4}\\).
            \nSo \\(\\frac{3}{4}\\) > \\(\\frac{2}{4}\\).<\/p>\n

            Remember<\/strong> that if fractions have the same denominator, the greater fraction has a greater numerator.<\/p>\n

            In 1-3, compare. Write <, >, or =. Use fraction strips to help.
            \nQuestion 1.
            \n\"Envision<\/p>\n

            Answer:
            \n3\/6 < 5\/6.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 3\/6 and 5\/6.
            \n3\/6 = 1\/6 + 1\/6 + 1\/6.
            \n5\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6 + 1\/6.
            \n3\/6 < 5\/6.<\/p>\n

            \"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Question 2.
            \n\\(\\frac{4}{6}\\) \"Envision \\(\\frac{5}{6}\\)<\/p>\n

            Answer:
            \n4\/6 < 5\/6.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 4\/6 and 5\/6.
            \n4\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6.
            \n5\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6 + 1\/6.
            \n4\/6 < 5\/6.<\/p>\n

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

            Answer:
            \n5\/8 > 3\/8.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 5\/8 and 3\/8.
            \n5\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
            \n3\/8 = 1\/8 + 1\/8 + 1\/8.
            \n5\/8 > 3\/8.<\/p>\n

            Set D pages 497-500<\/strong><\/p>\n

            You can use fraction strips to compare fractions with the same numerator.
            \nCompare \\(\\frac{1}{6}\\) to \\(\\frac{1}{2}\\).
            \n\"Envision
            \nThe numerator of each fraction is 1.
            \nThe \\(\\frac{1}{6}\\) fraction strip is less than the \\(\\frac{1}{2}\\) strip.
            \nSo \\(\\frac{1}{6}\\) < \\(\\frac{1}{2}\\)
            \nYou can use reasoning to understand. Think about dividing a whole into 6 pieces and dividing it into 2 pieces. One of 6 pieces is less than 1 of 2 pieces.<\/p>\n

            Remember<\/strong> that if fractions have the same numerator, the greater fraction has a lesser denominator.<\/p>\n

            In 1-3, compare. Write <, >, or=. Use fraction strips to help.
            \nQuestion 1.
            \n\"Envision<\/p>\n

            Answer:
            \n3\/4 < 3\/8.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 3\/4 and 3\/8.
            \n3\/4 = 1\/4 + 1\/4 + 1\/4.
            \n3\/8 = 1\/8 + 1\/8 + 1\/8.
            \n3\/4 < 3\/8.
            \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Question 2.
            \n\\(\\frac{5}{6}\\) \"Envision \\(\\frac{5}{8}\\)<\/p>\n

            Answer:
            \n5\/6 < 5\/8.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 5\/6 and 5\/8.
            \n5\/6 = 1\/6 + 1\/6 + 1\/6 + 1\/6 + 1\/6.
            \n5\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8 + 1\/8.
            \n5\/6 < 5\/8.<\/p>\n

            Question 3.
            \n\\(\\frac{1}{3}\\) \"Envision \\(\\frac{1}{2}\\)<\/p>\n

            Answer:
            \n1\/3 > 1\/2.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 1\/3 and 1\/2.
            \n1\/3 = 2\/6.
            \n2\/6 = 1\/6 + 1\/6.
            \n1\/3 > 1\/2.<\/p>\n

            Set E pages 501-504<\/strong><\/p>\n

            You can compare fractions using benchmark numbers such as 0, \\(\\frac{1}{2}\\), and 1.<\/p>\n

            Chris and Mary are painting pictures. The pictures are the same size. Chris painted \\(\\frac{3}{4}\\) of his picture. Mary painted her picture. Who painted the greater amount?
            \n\\(\\frac{3}{4}\\) is greater than \\(\\frac{1}{2}\\).
            \n\\(\\frac{3}{8}\\) is less than \\(\\frac{1}{2}\\).
            \nChris painted the greater amount.<\/p>\n

            Remember<\/strong> that you can compare each fraction to a benchmark number to see how they relate to each other.<\/p>\n

            In 1 and 2, use benchmark numbers to help solve.
            \nQuestion 1.
            \nMike had \\(\\frac{2}{6}\\) of a candy bar. Sally had \\(\\frac{4}{6}\\) of a candy bar. Whose fraction of a candy bar was closer to 1? Closer to 0?<\/p>\n

            Answer:
            \nSally was closer to 1.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nMike had \\(\\frac{2}{6}\\) of a candy bar.
            \nSally had \\(\\frac{4}{6}\\) of a candy bar.
            \n2\/6 = 1\/3.
            \n4\/6 = 2\/3.
            \n2\/3 is closer to 1.
            \nso sally was closer to 1.<\/p>\n

            Question 2.
            \nPaul compared two bags of rice. One weighs \\(\\frac{4}{6}\\) pound, and the other weighs \\(\\frac{4}{8}\\) pound. Which bag is heavier?<\/p>\n

            Answer:
            \nThe 4\/6 pounds bag is heavier.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nPaul compared two bags of rice.
            \nOne weighs 4\/6 pound.
            \nthe other weighs 4\/8 pound.
            \n4\/6 = 2\/3.
            \n4\/8 = 2\/4.
            \nso the 4\/6 pounds bag is heavier.<\/p>\n

            Set F pages 505-508<\/strong><\/p>\n

            You can use a number line to compare fractions.
            \nWhich is greater, \\(\\frac{3}{6}\\) or \\(\\frac{4}{6}\\)?
            \n\"Envision
            \n\\(\\frac{4}{6}\\) is farther from zero than \\(\\frac{3}{6}\\), so \\(\\frac{4}{6}\\) is greater.
            \nYou also can compare two fractions with the same numerator by drawing two number lines.<\/p>\n

            Which is greater, \\(\\frac{2}{4}\\) or \\(\\frac{2}{3}\\)?
            \n\"Envision
            \n\\(\\frac{2}{3}\\) is farther from zero than \\(\\frac{2}{4}\\), so \\(\\frac{2}{3}\\) is greater.<\/p>\n

            Remember<\/strong> to draw two number lines that are equal in length when comparing fractions with different denominators.<\/p>\n

            In 1 and 2, compare. Write <, >, or=. Use number lines to help.
            \nQuestion 1.
            \n\"Envision<\/p>\n

            Answer:
            \n2\/6 < 3\/6.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 2\/6 and 3\/6.
            \n2\/6 = 1\/3.
            \n2\/6 = 1\/6 + 1\/6.
            \n3\/6 = 1\/2.
            \n3\/6 = 1\/6 + 1\/6 + 1\/6.
            \nso 2\/6 < 3\/6.
            \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Question 2.
            \n\"Envision<\/p>\n

            Answer:
            \n3\/4 > 3\/6.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe two fractions are 3\/4 and 3\/6.
            \n3\/4 = 1\/4 + 1\/4 + 1\/4.
            \n3\/6 = 1\/6 + 1\/6 + 1\/6.
            \n3\/6 = 1\/2.
            \nso 3\/4 > 3\/6.
            \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

            Set G pages 509-512<\/strong><\/p>\n

            How many thirds are in 2 wholes?
            \nYou can use a number line or fraction strips to find a fraction name for 2 using thirds.
            \n\"Envision
            \n2 = \\(\\frac{6}{3}\\)
            \nThe whole number 2 can also be written as the fraction \\(\\frac{6}{3}\\).<\/p>\n

            Remember<\/strong> that when you write whole numbers as fractions, the numerator can be greater than the denominator.<\/p>\n

            In 1-4, write an equivalent fraction for each whole number.
            \nQuestion 1.
            \n3<\/p>\n

            Answer:
            \nThe equivalent fraction is 12\/4.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe whole number is 3.
            \n12\/4 = 3.
            \n3 x 4 = 12.
            \n3 x 1 = 3.
            \nso the equivalent fraction is 12\/4.<\/p>\n

            Question 2.
            \n2<\/p>\n

            Answer:
            \nThe equivalent fraction is 4\/2.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe whole number is 2.
            \n4\/2 = 2\/1.
            \n2 x 2 = 4.
            \n2 x 1 = 2.
            \nso the equivalent fraction is 4\/2.<\/p>\n

            Question 3.
            \n5<\/p>\n

            Answer:
            \nThe equivalent fraction is 15\/3.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe whole number is 5.
            \n15\/3 = 5.
            \n3 x 1 = 3.
            \n3 x 5 = 15.
            \nso the equivalent fraction is 15\/3.<\/p>\n

            Question 4.
            \n1<\/p>\n

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

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nthe whole number is 1.
            \n3\/3 = 1.
            \nso the equivalent fraction is 3\/3.<\/p>\n

            In 5-8, write the equivalent whole number for each fraction.
            \nQuestion 5.
            \n\\(\\frac{6}{3}\\)<\/p>\n

            Answer:
            \nThe equivalent whole number is 2.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nThe fraction is 6\/3.
            \n6\/3 = 2.
            \n3 x 1 = 3.
            \n3 x 2 = 6.
            \nso the equivalent whole number is 2.<\/p>\n

            Question 6.
            \n\\(\\frac{10}{2}\\)<\/p>\n

            Answer:
            \nThe equivalent whole number is 5.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nThe fraction is 10\/2.
            \n10\/2 = 5.
            \n2 x 1 = 2.
            \n2 x 5 = 10.
            \nso the equivalent whole number is 5.<\/p>\n

            Question 7.
            \n\\(\\frac{14}{2}\\)<\/p>\n

            Answer:
            \nThe equivalent whole number is 7.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nThe fraction is 14\/2.
            \n14\/2 = 7.
            \n2 x 1 = 2.
            \n7 x 2 = 14.
            \nso the equivalent whole number is 7.<\/p>\n

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

            Answer:
            \nThe equivalent whole number is 1.<\/p>\n

            Explanation:
            \nIn the above-given question,
            \ngiven that,
            \nThe fraction is 8\/8.
            \n8\/8 = 1.
            \n8 x 1 = 8.
            \n1 x 8 = 8.
            \nso the equivalent whole number is 1.<\/p>\n

            Set H pages 513-516<\/strong><\/p>\n

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

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

              Remember<\/strong> that when you construct an argument, you explain why your work is correct.<\/p>\n

              Odell and Tamra paint two walls with the same dimensions. Odell paints \\(\\frac{1}{6}\\) of a wall. Tamra paints \\(\\frac{1}{3}\\) of the other wall. Conjecture: Odell paints less than Tamra.
              \nQuestion 1.
              \nDraw a diagram to justify the conjecture.<\/p>\n

              Answer:
              \nYes, Odell paints less than Tamra.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nOdell and Tamra paint two walls with the same dimensions.
              \nOdell paints \\(\\frac{1}{6}\\) of a wall.
              \nTamra paints \\(\\frac{1}{3}\\) of the other wall.
              \n1\/6 < 1\/3.
              \nso Odell paints less than Tamra.<\/p>\n

              Question 2.
              \nUse the diagram to justify the conjecture.
              \nAnswer:<\/p>\n

              Topic 13 Assessment Practice<\/h3>\n

              Question 1.
              \nTwo friends are working on a project. So far, Cindy has done \\(\\frac{4}{8}\\) of the project, and Kim has done \\(\\frac{3}{8}\\) of the project. Who has done more of the project? Explain.<\/p>\n

              Answer:
              \nCindy has done more of the project.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nTwo friends are working on a project.
              \nCindy has done \\(\\frac{4}{8}\\) of the project.
              \nKim has done \\(\\frac{3}{8}\\) of the project.
              \n4\/8 = 1\/8 + 1\/8 + 1\/8 + 1\/8.
              \n3\/8 = 1\/8 + 1\/8 + 1\/8.
              \nso Cindy has done more of the project.<\/p>\n

              Question 2.
              \nSerena can compare \\(\\frac{3}{4}\\) and \\(\\frac{3}{6}\\) without using fraction strips. She says that a whole divided into 4 equal parts will have larger parts than the same whole divided into 6 equal parts. Three larger parts must be more than three smaller parts, so \\(\\frac{3}{4}\\) is greater than \\(\\frac{3}{6}\\). Is Serena correct? If not, explain Serena’s error. Then, write the correct comparison using symbols.<\/p>\n

              Answer:
              \nYes, Serena is correct.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nSerena can compare 3\/4 and 3\/6 without using fraction strips.
              \n3\/4 = 1\/4 + 1\/4 + 1\/4.
              \n3\/6 = 1\/2.
              \n3 x 1 = 3.
              \n3 x 2 = 6.
              \nso Serena is correct.<\/p>\n

              Question 3.
              \nJill finished reading \\(\\frac{2}{3}\\) of a book for a summer reading project. Owen read \\(\\frac{2}{8}\\) of the same book. Use the number lines to compare how much Jill and Owen each read. Who reads more of the book?
              \n\"Envision<\/p>\n

              Answer:
              \nThe missing fractions are 1\/3 and 2\/3.
              \n1\/8, 2\/8, 3\/8, 4\/8, 5\/8, 6\/8, and 7\/8.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nJill finished reading \\(\\frac{2}{3}\\) of a book for a summer reading project
              \nOwen read \\(\\frac{2}{8}\\) of the same book.
              \n2\/8 = 1\/4.
              \n2 x 1 = 2.
              \n4 x 2 = 8.
              \nso Jill read more of the book.
              \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

              Question 4.
              \nA small cake is cut into 4 equal pieces. What fraction represents the entire cake? Explain.<\/p>\n

              Answer:
              \nThe fraction 4\/4 represents the entire cake.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nA small cake is cut into 4 equal pieces.
              \n4 \/ 4 = 1.
              \nso the fraction 4\/4 represents the entire cake.<\/p>\n

              Question 5.
              \nMark and Sidney each have a piece of wood that is the same size. Mark paints \\(\\frac{2}{8}\\) of his piece of wood. Sidney paints \\(\\frac{5}{8}\\) of her piece of wood. Who painted a fraction that is closer to 1 than to 0? Explain how you found your answer. Then tell who painted less of his or her piece of wood.<\/p>\n

              Answer:
              \nSidney is closer to 1 than to 0.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nMark and Sidney each have a piece of wood that is the same size.
              \nMark paints \\(\\frac{2}{8}\\) of his piece of wood.
              \nSidney paints \\(\\frac{5}{8}\\) of her piece of wood.
              \n2\/8 is near to 0.
              \n5\/8 is closer to 1.
              \nso Sidney is closer to 1 than to 0.<\/p>\n

              Question 6.
              \nGreg colored the fraction model below.
              \nA. Which fractions name the purple part of the model? Select all that apply.
              \n\"Envision<\/p>\n

              Answer:
              \nThe fraction 6\/8 names the purple part of the model.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nthe fractions are 1\/2, 3\/4, 2\/3, 4\/6, 6\/8.
              \n6 boxes are filled with purple color.
              \nso the fraction 6\/8 names the purple part of the model.<\/p>\n

              B. Does \\(\\frac{1}{4}\\) name the unshaded part of the model? Explain.<\/p>\n

              Answer:
              \nYes, the fraction 1\/4 names the unshaded part of the model.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nthe fractions are 1\/2, 3\/4, 2\/3, 4\/6, 6\/8.
              \n2 boxes are not filled with purple color.
              \nso the fraction 2\/8 names the unshaded part of the model.<\/p>\n

              Question 7.
              \nCarl, Fiona, and Jen each had a sandwich. The sandwiches were the same size and cut into eighths. Carl ate \\(\\frac{7}{8}\\) of a sandwich, Fiona ate \\(\\frac{3}{8}\\) of a sandwich, and Jen ate \\(\\frac{6}{8}\\) of a sandwich. Who ate the most? Explain.<\/p>\n

              Answer:
              \nCarl ate more sandwiches.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nCarl, Fiona, and Jen each had a sandwich.
              \nThe sandwiches were the same size and cut into eighths.
              \nCarl ate \\(\\frac{7}{8}\\) of a sandwich.
              \nFiona ate \\(\\frac{3}{8}\\) of a sandwich.
              \nJen ate \\(\\frac{6}{8}\\) of a sandwich.
              \n3\/8, 6\/8, 7\/8.
              \nso carl ate more sandwiches.<\/p>\n

              Question 8.
              \nGeorge wants to know if two pieces of wire are the same length. One wire is \\(\\frac{6}{8}\\) foot. The other is \\(\\frac{3}{4}\\) foot. Are they the same length? Fill in the fractions on the number line to compare the lengths of the pieces of wire. Then explain your answer.
              \n\"Envision
              \nAnswer:
              \nThe missing fractions are 1\/4, 2\/4, and 3\/4.
              \n2\/8, 4\/8, and 6\/8.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nGeorge wants to know if two pieces of wire are the same length.
              \nOne wire is \\(\\frac{6}{8}\\) foot.
              \nThe other is \\(\\frac{3}{4}\\) foot.
              \n6\/8 = 3\/4.
              \n2 x 3 = 6.
              \n2 x 4 = 8.
              \nso the missing fractions are 1\/4, 2\/4, and 3\/4.
              \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

              Question 9.
              \nLezlie hiked \\(\\frac{3}{8}\\) mile on Monday. On Wednesday she hiked \\(\\frac{3}{6}\\) mile. She hiked a mile on Friday. Use benchmark fractions to arrange the lengths of the hikes in order from shortest to longest hike.<\/p>\n

              Answer:
              \nThe lengths of hikes in order from shortest and longest = 3\/4, 3\/6, and 3\/8.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nLezlie hiked \\(\\frac{3}{8}\\) mile on Monday.
              \nOn Wednesday she hiked \\(\\frac{3}{6}\\) mile.
              \nShe hiked a mile on Friday.
              \n8 – 2 = 6, 6 – 2 = 4.
              \nso the lengths of hikes in order from shortest and longest = 3\/4, 3\/6, and 3\/8.<\/p>\n

              Question 10.
              \nA mural is divided into 3 equal parts. What fraction represents the entire mural? Explain.<\/p>\n

              Answer:
              \nThe entire mural is 3\/3.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nA mural is divided into 3 equal parts.
              \n3\/3 = 1.
              \nso the entire mural is divided into 3 parts.<\/p>\n

              Question 11.
              \nMeagan ate \\(\\frac{3}{4}\\) of a cookie. Write an equivalent fraction for the amount of cookie Meagan did NOT eat. Then write a fraction that is equivalent to the amount of the cookie that Meagan did eat, and explain why your answer is correct.<\/p>\n

              Answer:
              \nMegan did not eat = 1\/4.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nMeagan ate \\(\\frac{3}{4}\\) of a cookie.
              \n3\/4 + 1\/4 = 1.
              \n3\/4 = 1\/4 + 1\/4 + 1\/4.
              \nso megan did not ate = 1\/4.<\/p>\n

              Question 12.
              \nCircle each fraction that is equivalent to 1. Explain your reasoning. Then give another fraction that is equal to 1.
              \n\"Envision<\/p>\n

              Answer:
              \nThe fraction that is equivalent to 1 is 3\/3 and 6\/6.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nthe fractions are 2\/4, 3\/3, 3\/6, 4\/6, and 6\/6.
              \ncircle each fraction that is equivalent to 1.
              \n3\/3 = 1, and 6\/6 = 1.
              \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

              Question 13.
              \nUse the number line to help order the fractions from least to greatest. Then explain how you found your answer.
              \n\"Envision<\/p>\n

              Answer:
              \nThe fractions from least to greatest = 0\/4, 1\/2, 1\/4, 6\/8, and 4\/4.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nThe fractions are 6\/8, 4\/4, 1\/4, 1\/2, and 0\/4.
              \n6\/8 = 3\/4.
              \n2 x 3 = 6.
              \n2 x 4 = 8.
              \nso the fractions from least to greatest = 0\/4, 1\/2, 1\/4, 6\/8, and 4\/4.<\/p>\n

              Question 14.
              \nEva and Landon had the same math homework. Eva finished the homework. Landon finished of the homework. Conjecture: Eva and Landon finished the same amount of their homework.
              \nA. Complete the number lines to help think about the conjecture.
              \n\"Envision<\/p>\n

              Answer:
              \nThe fractions are 1\/4, 2\/4, 3\/4, and 4\/4.
              \n1\/8, 2\/8, 3\/8, 4\/8, 5\/8, 6\/8, 7\/8, and 8\/8.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nEva and Landon had the same math homework.
              \nEva finished the homework.
              \n2\/4 = 1\/2.
              \n2 x 1 = 2.
              \n2 x 2 = 4.
              \nso the missing fractions are 1\/4, 2\/4, 3\/4, and 4\/4.
              \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

              B. Use your diagram to decide if the conjecture is correct. Explain.
              \nAnswer:<\/p>\n

              Question 15.
              \nFor each pair of fractions, write the equivalent whole number in the box.
              \n\"Envision<\/p>\n

              Answer:
              \n16\/4 = 8\/2 = 4.
              \n6\/3 = 4\/2 = 2.
              \n8\/8 = 6\/6 = 1.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nthe pair of fractions are 16\/4, 8\/2, 6\/3, 4\/2, 8\/8, and 6\/6.
              \n16\/4 = 8\/2 = 4.
              \n6\/3 = 4\/2 = 2.
              \n8\/8 = 6\/6 = 1.
              \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

              Topic 13 Performance Task<\/h3>\n

              Clothing Store Devin, Jenna, Eli, and Gabby work at a clothing store. On Saturday they each worked the same number of hours.<\/p>\n

              The Time Spent at Cash Register table shows the fraction of time each person spent checking out customers. The Time Spent on Customer Calls table shows the fraction of an hour Jenna spent answering phone calls for the store.<\/p>\n

              Use the Time Spent at Cash Register table to answer Questions 1-3.
              \n\"Envision
              \nQuestion 1.
              \nDraw fraction strips to show the fraction of time each person worked at the cash register.
              \n\"Envision<\/p>\n

              Answer:
              \nThe fraction of time each person worked at the cash register = 3\/6, 2\/6, 6\/6, and 5\/6.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nDevin, Jenna, Eli, and Gabby work at a clothing store.
              \nDevin worked 3\/6 hours a day.
              \nJenna worked 2\/6 hours a day.
              \nEli worked 6\/6 hours a day.
              \nGabby worked 5\/6 hours a day.
              \nthe fraction of hours is 3\/6, 2\/6, 6\/6, and 5\/6.
              \nso the fraction of time each person worked at the cash register = 3\/6, 2\/6, 6\/6, and 5\/6.
              \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

              Question 2.
              \nWho spent the most time at the cash register?<\/p>\n

              Answer:
              \nThe most time spent at the cash register = Gabby.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nDevin, Jenna, Eli, and Gabby work at a clothing store.
              \nDevin worked 3\/6 hours a day.
              \nJenna worked 2\/6 hours a day.
              \nEli worked 6\/6 hours a day.
              \nGabby worked 5\/6 hours a day.
              \n3\/6 = 1\/2.
              \n3 x 1 = 3.
              \n3 x 2 = 6.
              \n2\/6 = 1\/3.
              \n2 x 1 = 2.
              \n2 x 3 = 6.
              \n6 \/ 6 = 1.
              \nso the number of hours Gabby worked = 5\/6.<\/p>\n

              Question 3.
              \nWrite a comparison to show the time Gabby spent at the cash register compared to the time Devin spent. Use >, <, or =.<\/p>\n

              Answer:
              \nGabby worked more hours than Devin.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nDevin, Jenna, Eli, and Gabby work at a clothing store.
              \nDevin worked 3\/6 hours a day.
              \nJenna worked 2\/6 hours a day.
              \nEli worked 6\/6 hours a day.
              \nGabby worked 5\/6 hours a day.
              \n5\/6 is greater than 3\/6.
              \nso Gabby worked more hours than Devin.<\/p>\n

              Question 4.
              \nUse the Time Spent on Customer Calls table to answer this question: On which day did Jenna spend closest to one hour on the phone? Explain how you know.
              \n\"Envision<\/p>\n

              Answer:
              \nJenna spends the closest to one hour on Monday.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \non Saturday he spends a 3\/6 fraction of an hour.
              \non Sunday he spends 3\/5 fraction of an hour.
              \non Monday he spends 3\/4 fraction of an hour.
              \n3\/6 = 1\/2.
              \n3\/4 is nearest to the 1.
              \nso Jenna spends the closest to one hour on Monday.<\/p>\n

              The store sells different colors of men’s socks. The Socks table shows the fraction for each sock color in the store.<\/p>\n

              Use the Socks table to answer Questions 5 and 6.
              \n\"Envision<\/p>\n

              Question 5.
              \nPart A
              \nComplete the fractions on the number line. Label the fraction that represents each sock color.
              \n\"Envision<\/p>\n

              Answer:
              \nThe fraction that represents each sock color = 1\/4, 2\/4, 3\/4, and 1.
              \n1\/8, 2\/8, 3\/8, 4\/8, 5\/8, 6\/8, 7\/8, and 1.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nThe store sells different colors of men’s socks.
              \nthe white color socks are 1\/8.
              \nthe black color sock is 1\/4.
              \nthe brown color socks are 3\/8.
              \nthe gray color socks are 2\/8.
              \nso the fraction that represents each sock color = 1\/4, 2\/4, 3\/4, and 1.
              \n1\/8, 2\/8, 3\/8, 4\/8, 5\/8, 6\/8, 7\/8, and 1.
              \n\"Envision-Math-Common-Core-3rd-Grade-Answer-Key-Topic-13-<\/p>\n

              Part B
              \nDoes the store have more brown socks or more white socks?<\/p>\n

              Answer:
              \nThe store has more brown socks = 3\/8.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nThe store sells different colors of men’s socks.
              \nthe white color socks are 1\/8.
              \nthe black color sock is 1\/4.
              \nthe brown color socks are 3\/8.
              \nthe gray color socks are 2\/8.
              \n3\/8 is greater than 1\/8.
              \nso brown color socks are more than white color socks.<\/p>\n

              Question 6.
              \nUse the number line in Exercise 5 Part A to construct an argument to justify the following conjecture: The store has an equal number of gray socks and black socks.<\/p>\n

              Answer:
              \nYes, the store has an equal number of gray socks and white socks.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nThe store sells different colors of men’s socks.
              \nthe white color socks are 1\/8.
              \nthe black color sock is 1\/4.
              \nthe brown color socks are 3\/8.
              \nthe gray color socks are 2\/8.
              \n2\/8 = 1\/4.
              \n2 x 1 = 2.
              \n4 x 2 = 8.
              \nso the store has the equal number of gray socks and white socks.<\/p>\n

              Question 7.
              \nUse the Miguel’s Socks table to answer the question.
              \n\"Envision
              \nMiguel bought some socks at the clothing store. After he washed them, he counted the number of individual socks he has. Each sock is \\(\\frac{1}{2}\\) of a pair. How many pairs of black socks does he have? Write this number as a fraction.<\/p>\n

              Answer:
              \nThe number of pairs of black socks does he have = 3 pairs.<\/p>\n

              Explanation:
              \nIn the above-given question,
              \ngiven that,
              \nMiguel bought some socks at the clothing store.
              \nthe number of black color socks = 6.
              \nthe number of gray color socks = 8.
              \n3\/6 and 4\/8.
              \n3\/6 = 1\/2.
              \n4\/8 = 1\/2.
              \nso the number of pairs of black socks does he have = 3 pairs.<\/p>\n","protected":false},"excerpt":{"rendered":"

              Go through the\u00a0enVision Math Common Core Grade 3 Answer Key\u00a0Topic 13 Fraction Equivalence and Comparison\u00a0regularly and improve your accuracy in solving questions. enVision Math Common Core 3rd Grade Answers Key Topic 13 Fraction Equivalence and Comparison Essential Question: What are different ways to compare fractions? enVision STEM Project: Life Cycles Do Research A frog egg …<\/p>\n","protected":false},"author":1,"featured_media":25595,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/envisionmathanswerkey.com\/wp-content\/uploads\/2021\/06\/enVision-Math-Common-Core-Grade-3-Answer-Key-Topic-13-Fraction-Equivalence-and-Comparison.png","_links":{"self":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/8128"}],"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=8128"}],"version-history":[{"count":4,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/8128\/revisions"}],"predecessor-version":[{"id":27580,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/posts\/8128\/revisions\/27580"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media\/25595"}],"wp:attachment":[{"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/media?parent=8128"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/categories?post=8128"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/envisionmathanswerkey.com\/wp-json\/wp\/v2\/tags?post=8128"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}