{"id":16217,"date":"2022-04-07T10:45:51","date_gmt":"2022-04-07T05:15:51","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=16217"},"modified":"2022-04-07T11:05:05","modified_gmt":"2022-04-07T05:35:05","slug":"big-ideas-math-answers-grade-5-chapter-8","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5-chapter-8\/","title":{"rendered":"Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions"},"content":{"rendered":"<p><strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5\/\">Big Ideas Math Answers Grade 5<\/a> Chapter 8 Add and Subtract Fractions<\/strong> is the best source to learn Add and Subtract Fractions concepts. Get free access to download Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions pdf. Learn how to solve a problem in different ways. We have provided a step-by-step process to solve the problems with real-time examples. Various tips and tricks are given to learn the concepts deeply. Follow the important notes for the quick learning of maths. Improve your math skills with the help of the Big Ideas Math Grade 5 Chapter 8 Add and Subtract Fractions Answers.<\/p>\n<h2>Big Ideas Math Book 5th Grade Chapter 8 Add and Subtract Fractions Answer Key<\/h2>\n<p>It is mandatory for the students to go through all the topics included in this chapter to kickstart their preparation. The list of topics is mentioned below along with the quick links. Understand each topic by referring to every link and solving every problem available below. Find the various methods to solve the questions and choose the best one to practice well for the exam. All the topics such as Simplest form, Subtract Fractions with Unlike Denominators, Find Common Denominators, Estimate Sums, and Differences of Fractions, Add Fractions with Unlike Denominators are prepared with a clear explanation in <em><strong>BIM Grade 5 Ch 8 Add and Subtract Fractions Solution key.<\/strong><\/em><\/p>\n<p><strong>Lesson: 1 Simplest Form<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_8.1_Simplest_Form\">Lesson 8.1 Simplest Form<\/a><\/li>\n<li><a href=\"#Lesson_8.1_Simplest_Form_Homework_&amp;_Practice_8.1\">Lesson 8.1 Simplest Form Homework &amp; Practice 8.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Estimate Sums and Differences of Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_8.2_Estimate_Sums_and_Differences_of_Fractions\">Lesson 8.2 Estimate Sums and Differences of Fractions<\/a><\/li>\n<li><a href=\"#Estimate_Sums_and_Differences_of_Fractions_Homework_&amp;_Practice_8.2\">Estimate Sums and Differences of Fractions Homework &amp; Practice 8.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Find Common Denominators<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_8.3_Find_Common_Denominators\">Lesson 8.3 Find Common Denominators<\/a><\/li>\n<li><a href=\"#Find_Common_Denominators_Homework_&amp;_Practice_8.3\">Find Common Denominators Homework &amp; Practice 8.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Add Fractions with Unlike Denominators<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_8.4_Add_Fractions_with_Unlike_Denominators\">Lesson 8.4 Add Fractions with Unlike Denominators<\/a><\/li>\n<li><a href=\"#Add_Fractions_with_Unlike_Denominators_Homework_&amp;_Practice_8.4\">Add Fractions with Unlike Denominators Homework &amp; Practice 8.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Subtract Fractions with Unlike Denominators<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_8.5_Subtract_Fractions_with_Unlike_Denominators\">Lesson 8.5 Subtract Fractions with Unlike Denominators<\/a><\/li>\n<li><a href=\"#Subtract_Fractions_with_Unlike_Denominators_Homework_&amp;_Practice_8.5\">Subtract Fractions with Unlike Denominators Homework &amp; Practice 8.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Add Mixed Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_8.6_Add_Mixed_Numbers\">Lesson 8.6 Add Mixed Numbers<\/a><\/li>\n<li><a href=\"#Add_Mixed_Numbers_Homework_&amp;_Practice_8.6\">Add Mixed Numbers Homework &amp; Practice 8.6<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 7 Subtract Mixed Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_8.7_Subtract_Mixed_Numbers\">Lesson 8.7 Subtract Mixed Numbers<\/a><\/li>\n<li><a href=\"#Subtract_Mixed_Numbers_Homework_&amp;_Practice_8.7\">Subtract Mixed Numbers Homework &amp; Practice 8.7<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 8 Problem Solving: Fractions<\/strong><\/p>\n<ul>\n<li><a href=\"_Fractions\">Lesson 8.8 Problem Solving: Fractions<\/a><\/li>\n<li><a href=\"_Fractions_Homework_&amp;_Practice_8.8\">Problem Solving: Fractions Homework &amp; Practice 8.8<\/a><\/li>\n<\/ul>\n<p><strong>Chapter 8 &#8211; Add and Subtract Fractions\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Add_and_Subtract_Fractions_Performance_Task_8\">Add and Subtract Fractions Performance Task 8<\/a><\/li>\n<li><a href=\"#Add_and_Subtract_Fractions_Activity\">Add and Subtract Fractions Activity<\/a><\/li>\n<li><a href=\"#Add_and_Subtract_Fractions_Performance_Chapter_Practice\">Add and Subtract Fractions Performance Chapter Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_8.1_Simplest_Form\"><\/a>Lesson 8.1 Simplest Form<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use the model to write as many fractions as possible that are equivalent to \\(\\frac{36}{72}\\) but have numerators less than 36 and denominators less than 72.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-8-Add-and-Subtract-Fractions-1.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions 1\" width=\"397\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-8-Add-and-Subtract-Fractions-1.png 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-8-Add-and-Subtract-Fractions-1-300x121.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><br \/>\nWhich of your fractions has the fewest equal parts? Explain.<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nWhen might it be helpful to write \\(\\frac{48}{72}\\) as \\(\\frac{2}{3}\\) in a math problem?<\/p>\n<p><strong>Think and Grow: Simplest Form<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nWhen the numerator and denominator of a fraction have no common factors other than 1, the fraction is in simplest form. To write a fraction in simplest form, divide the numerator and the denominator by the greatest of their common factors.<br \/>\n<strong>Example<\/strong><br \/>\nsimplify \\(\\frac{6}{8}\\) in the simplest form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-8-Add-and-Subtract-Fractions-2.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions 2\" width=\"196\" height=\"259\" \/><br \/>\n<strong>Step 1:<\/strong> Find the common factors of 6 and 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-3.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 3\" width=\"192\" height=\"70\" \/><br \/>\nThe common factors of 6 and 8 are 1 and 2.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-4.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 4\" width=\"608\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-4.png 608w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-4-300x128.png 300w\" sizes=\"(max-width: 608px) 100vw, 608px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-39746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-4-300x128.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-4\" width=\"300\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-4-300x128.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-4.jpg 608w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nUse the model to write \\(\\frac{2}{4}\\) in simplest form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-5.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 5\" width=\"134\" height=\"89\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 2 and 4.<br \/>\nFactors of 2:\u00a0 \u00a01, 2<br \/>\nFactors of 4:\u00a0 \u00a01, 2, 4<br \/>\nThe common factors of 2 and 4 are 1 and 2.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<a href=\"https:\/\/ccssmathanswers.com\/?attachment_id=27575\" rel=\"attachment wp-att-27575\"><img loading=\"lazy\" class=\"alignnone wp-image-27575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/1.jpg\" alt=\"\" width=\"130\" height=\"53\" \/><\/a>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-16278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-5.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 5\" width=\"134\" height=\"89\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1, \\(\\frac{2}{4}\\) is in simplest form.<\/p>\n<p>Question 2.<br \/>\nWrite \\(\\frac{8}{12}\\) in simplest form<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 8 and 12.<br \/>\nFactors of 8:\u00a0 \u00a0 1, 2, 4, 8<br \/>\nFactors of 12:\u00a0 1, 2, 3, 4, 6, 12<br \/>\nThe common factors of 8 and 12 are 1, 2 and 4.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<a href=\"https:\/\/ccssmathanswers.com\/big-ideas-math-answers-grade-5-chapter-8\/3-5\/\" rel=\"attachment wp-att-27713\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-27713\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/3.jpg\" alt=\"\" width=\"152\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/3.jpg 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/3-150x49.jpg 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><\/a><br \/>\nBecause 2 and 3 have no common factors other than 1, \\(\\frac{8}{12}\\) is in simplest form.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Use the model to write the fraction in simplest form.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-6.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 6\" width=\"202\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 8 and 10.<br \/>\nFactors of 8:\u00a0 \u00a0 1, 2, 4, 8<br \/>\nFactors of 10:\u00a0 1, 2, 5, 10<br \/>\nThe common factors of 8 and 10 are 1 and 2.<\/p>\n<p><strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B10%7D%3D%20%5Cfrac%7B8%20%5Cdiv%202%7D%7B10%20%5Cdiv%202%7D%20%3D%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{8}{10}= \\frac{8 \\div 2}{10 \\div 2} = \\frac{4}{5}\" \/><\/p>\n<p>Because 4 and 5 have no common factors other than 1, \\(\\frac{8}{10}\\) is in simplest form.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-7.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 7\" width=\"191\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 5 and 15.<br \/>\nFactors of 5: 1, 5<br \/>\nFactors of 15: 1, 3, 5,15<br \/>\nThe common factors of 5 and 15 are 1 and 5.<br \/>\nStep 2: Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B15%7D%3D%20%5Cfrac%7B5%20%5Cdiv%205%7D%7B15%20%5Cdiv%205%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{5}{15}= \\frac{5 \\div 5}{15 \\div 5} = \\frac{1}{3}\" \/><br \/>\nBecause 1 and 3 have no common factors other than 1, \\(\\frac{5}{15}\\) is in simplest form.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-8.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 8\" width=\"189\" height=\"137\" \/><\/p>\n<p>Write the fraction in simplest form.<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 10 and 12.<br \/>\nFactors of 10:\u00a0 1, 2, 5, 10<br \/>\nFactors of 12:\u00a0 1, 2, 3, 4, 6, 12<br \/>\nThe common factors of 10 and 12 are 1 and 2.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D%3D%20%5Cfrac%7B10%20%5Cdiv%202%7D%7B12%20%5Cdiv%202%7D%20%3D%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{10}{12}= \\frac{10 \\div 2}{12 \\div 2} = \\frac{5}{6}\" \/><br \/>\nBecause 5 and 6 have no common factors other than 1, \\(\\frac{10}{12}\\) is in simplest form.<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{3}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 3 and 6.<br \/>\nFactors of 3:\u00a0 1, 3<br \/>\nFactors of 6:\u00a0 1, 2, 3, 6<br \/>\nThe common factors of 3 and 6 are 1 and 3.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D%3D%20%5Cfrac%7B3%20%5Cdiv%203%7D%7B6%20%5Cdiv%203%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{3}{6}= \\frac{3 \\div 3}{6 \\div 3} = \\frac{1}{2}\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1, \\(\\frac{3}{6}\\) is in simplest form.<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{2}{10}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 2 and 10.<br \/>\nFactors of 2:\u00a0 1, 2<br \/>\nFactors of 10:\u00a0 1, 2, 5, 10<br \/>\nThe common factors of 2 and 10 are 1 and 2.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B10%7D%3D%20%5Cfrac%7B2%20%5Cdiv%202%7D%7B10%20%5Cdiv%202%7D%20%3D%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{2}{10}= \\frac{2 \\div 2}{10 \\div 2} = \\frac{1}{5}\" \/><br \/>\nBecause 1 and 5 have no common factors other than 1, \\(\\frac{2}{10}\\) is in simplest form.<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{6}{8}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 6 and 8.<br \/>\nFactors of 6:\u00a0 1, 2, 3, 6<br \/>\nFactors of 8:\u00a0 1, 2, 4, 8<br \/>\nThe common factors of 6 and 8 are 1 and 2.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D%3D%20%5Cfrac%7B6%20%5Cdiv%202%7D%7B8%20%5Cdiv%202%7D%20%3D%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{6}{8}= \\frac{6 \\div 2}{8 \\div 2} = \\frac{3}{4}\" \/><br \/>\nBecause 3 and 4 have no common factors other than 1, \\(\\frac{6}{8}\\) is in simplest form.<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{7}{14}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 7 and 14.<br \/>\nFactors of 7:\u00a0 1, 7<br \/>\nFactors of 14:\u00a0 1, 2, 7, 14<br \/>\nThe common factors of 7 and 14 are 1 and 7.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B14%7D%3D%20%5Cfrac%7B7%20%5Cdiv%207%7D%7B14%20%5Cdiv%207%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{7}{14}= \\frac{7 \\div 7}{14 \\div 7} = \\frac{1}{2}\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1, \\(\\frac{7}{14}\\) is in simplest form.<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{10}{100}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 10 and 100.<br \/>\nFactors of 10: 1, 2, 5, 10<br \/>\nFactors of 100:\u00a0 1, 2, 4, 5, 10, 20, 25, 50, 100<br \/>\nThe common factors of 10 and 100 are 1, 2, 5 and 10.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B100%7D%3D%20%5Cfrac%7B10%20%5Cdiv%2010%7D%7B100%20%5Cdiv%2010%7D%20%3D%20%5Cfrac%7B1%7D%7B10%7D\" alt=\"\\small \\frac{10}{100}= \\frac{10 \\div 10}{100 \\div 10} = \\frac{1}{10}\" \/><br \/>\nBecause 1 and 10 have no common factors other than 1, \\(\\frac{10}{100}\\) is in simplest form.<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{12}{4}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 12 and 4.<br \/>\nFactors of 12: 1, 2, 3, 4, 6, 12<br \/>\nFactors of 4:\u00a0 1, 2, 4<br \/>\nThe common factors of 12 and 4 are 1, 2 and 4.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B4%7D%3D%20%5Cfrac%7B12%20%5Cdiv%204%7D%7B4%20%5Cdiv%204%7D%20%3D%20%5Cfrac%7B3%7D%7B1%7D\" alt=\"\\small \\frac{12}{4}= \\frac{12 \\div 4}{4 \\div 4} = \\frac{3}{1}\" \/><br \/>\nBecause 3 and 1 have no common factors other than 1, \\(\\frac{12}{4}\\) is in simplest form.<\/p>\n<p>Question 12.<br \/>\nThree out of nine baseball players are in the outfield. In simplest form, what fraction of the players are in the outfield?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-9.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 9\" width=\"177\" height=\"134\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 3 and 9.<br \/>\nFactors of 3: 1, 3<br \/>\nFactors of 9:\u00a0 1, 3, 9<br \/>\nThe common factors of 3 and 9 are 1 and 3<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B9%7D%3D%20%5Cfrac%7B3%20%5Cdiv%203%7D%7B9%20%5Cdiv%203%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{3}{9}= \\frac{3 \\div 3}{9 \\div 3} = \\frac{1}{3}\" \/><br \/>\nBecause 1 and 3 have no common factors other than 1.<br \/>\nTherefore, <a href=\"https:\/\/ccssmathanswers.com\/big-ideas-math-answers-grade-5-chapter-8\/screenshot-2021-01-18-185530\/\" rel=\"attachment wp-att-30891\"><img loading=\"lazy\" class=\"alignnone size-full wp-image-30891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Screenshot-2021-01-18-185530.png\" alt=\"\" width=\"21\" height=\"45\" \/><\/a>players are in the outfield.<\/p>\n<p>Question 13.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend writes \\(\\frac{2}{6}\\) in simplest form. Is your friend correct? Explain<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-10.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 10\" width=\"134\" height=\"61\" \/><\/p>\n<p>Answer: No, the answer is wrong.<br \/>\nThe numerator and the denominator has to divide by the greatest of the common factors. You have divided only the denominator.<\/p>\n<p><strong>Explanation for \\(\\frac{2}{6}\\)<\/strong> in simplest form.<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 2 and 6.<br \/>\nFactors of 2: 1, 2<br \/>\nFactors of 6:\u00a0 1, 2, 3, 6<br \/>\nThe common factors of 2 and 6 are 1 and 2.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D%3D%20%5Cfrac%7B2%20%5Cdiv%202%7D%7B6%20%5Cdiv%202%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{2}{6}= \\frac{2 \\div 2}{6 \\div 2} = \\frac{1}{3}\" \/><br \/>\nBecause 1 and 3 have no common factors other than 1, \\(\\frac{2}{6}\\) is in simplest form.<\/p>\n<p>Question 14.<br \/>\n<strong>Reasoning<\/strong><br \/>\nThe numerator and denominator of a fraction have 1, 2, and 4 as common factors. After you divide the numerator and denominator by 2, the fraction is still not in simplest form. Why?<br \/>\nAnswer:<br \/>\nGiven that, common factors are 1, 2 and 4<br \/>\nFor the fraction to be in the simplest form, the numerator and denominator has to divide by the greatest of the common factors.<br \/>\nHere 4 is the greatest common factor. So, divide both the numerator and denominator by 4 to get the simplest form.<br \/>\nFor example 4 and 8<br \/>\nFactors for 4: 1, 2, 4<br \/>\nFactors for 8: 1, 2, 4, 8<br \/>\ncommon factors: 1, 2 and 4<br \/>\nSimplest form:\u00a0 \u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D%3D%20%5Cfrac%7B4%20%5Cdiv%204%7D%7B8%20%5Cdiv%204%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{4}{8}= \\frac{4 \\div 4}{8 \\div 4} = \\frac{1}{2}\" \/><\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA quarterback passes the ball 45 times during a game. The quarterback completes 35 passes. What fraction of the passes, in simplest form, does the quarterback complete?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-11.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 11\" width=\"175\" height=\"209\" \/><br \/>\nFind the number of passes that are not completed by subtracting the pass completions from the total number of passes.<br \/>\n45 &#8211; 35 = 10<br \/>\nWrite a fraction for the passes the quarterback does not complete.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-12.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 12\" width=\"402\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-12.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-12-300x49.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><br \/>\nFind common factors of 10 and 45. Then write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-13.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 13\" width=\"176\" height=\"251\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-14.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 14\" width=\"250\" height=\"142\" \/><br \/>\nThe quarterback does not complete __ of the passes.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-39748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-14.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-14\" width=\"250\" height=\"142\" \/><br \/>\nThe quarterback does not complete 2\/9 of the passes.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 15.<br \/>\nThere are 24 students in your class. Four of the students have blue eyes. What fraction of the class, in simplest form, do not have blue eyes?<br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nTotal no. of students in the class = 24<br \/>\nStudents have blue eyes = 4<br \/>\nStudents do not have blue eyes = 24 &#8211; 4 = 20<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 24 and 20.<br \/>\nFactors of 24: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nFactors of 20:\u00a0 1, 2, 4, 5, 10, 20<br \/>\nThe common factors of 24 and 20 are 1, 2 and 4.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B24%7D%3D%20%5Cfrac%7B20%20%5Cdiv%204%7D%7B24%20%5Cdiv%204%7D%20%3D%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{20}{24}= \\frac{20 \\div 4}{24 \\div 4} = \\frac{5}{6}\" \/><\/p>\n<p>Because 5 and 6 have no common factors other than 1.<br \/>\nTherefore, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/>th of the class do not have blue eyes.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA student answers 4 out of 12 questions on a test incorrectly. What fraction of the questions, in simplest form, does the student answer incorrectly? Interpret the fraction.<br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nTotal no. of questions = 12<br \/>\nNo. of incorrect answers = 4<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 12 and 4.<br \/>\nFactors of 12: 1, 2, 3, 4, 6, 12<br \/>\nFactors of 4:\u00a0 1, 2, 4<br \/>\nThe common factors of 12 and 4 are 1, 2 and 4.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D%20%3D%20%5Cfrac%7B4%20%5Cdiv%204%7D%7B12%20%5Cdiv%204%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{4}{12} = \\frac{4 \\div 4}{12 \\div 4} = \\frac{1}{3}\" \/><br \/>\nBecause 1 and 3 have no common factors other than 1.<br \/>\nTherefore, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> of the questions student answered incorrectly.<\/p>\n<h3><a id=\"Lesson_8.1_Simplest_Form_Homework_&amp;_Practice_8.1\"><\/a>Lesson 8.1 Simplest Form Homework &amp; Practice 8.1<\/h3>\n<p>Use the model to write the fraction in simplest form.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-16.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 16\" width=\"193\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 6 and 9.<br \/>\nFactors of 6: 1, 2, 3, 6<br \/>\nFactors of 9:\u00a0 1, 3, 9<br \/>\nThe common factors of 6 and 9 are 1 and 3.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D%20%3D%20%5Cfrac%7B6%20%5Cdiv%203%7D%7B9%20%5Cdiv%203%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{6}{9} = \\frac{6 \\div 3}{9 \\div 3} = \\frac{2}{3}\" \/><br \/>\nBecause 2 and 3 have no common factors other than 1, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/> is in simplest form.<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-17.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 17\" width=\"191\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 3 and 12.<br \/>\nFactors of 3: 1, 3<br \/>\nFactors of 12:\u00a0 1, 3, 4, 6, 12<br \/>\nThe common factors of 3 and 12 are 1 and 3.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D%20%3D%20%5Cfrac%7B3%20%5Cdiv%203%7D%7B12%20%5Cdiv%203%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{3}{12} = \\frac{3 \\div 3}{12 \\div 3} = \\frac{1}{4}\" \/><br \/>\nBecause 1 and 4 have no common factors other than 1, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/>\u00a0is in simplest form.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-18.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 18\" width=\"193\" height=\"150\" \/><\/p>\n<p>Write the fraction in simplest form<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 5 and 10.<br \/>\nFactors of 5: 1, 5<br \/>\nFactors of 10:\u00a0 1, 2, 5, 10<br \/>\nThe common factors of 5 and 10 are 1 and 5.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D%20%3D%20%5Cfrac%7B5%20%5Cdiv%205%7D%7B10%20%5Cdiv%205%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{5}{10} = \\frac{5 \\div 5}{10 \\div 5} = \\frac{1}{2}\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/> is in the simplest form.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{4}{8}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 4 and 8.<br \/>\nFactors of 4: 1, 2, 4<br \/>\nFactors of 8:\u00a0 1, 2, 4, 8<br \/>\nThe common factors of 4 and 8 are 1, 2 and 4.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D%20%3D%20%5Cfrac%7B4%20%5Cdiv%204%7D%7B8%20%5Cdiv%204%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{4}{8} = \\frac{4 \\div 4}{8 \\div 4} = \\frac{1}{2}\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1, \\(\\frac{4}{8}\\)\u00a0is in simplest form.<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{5}{100}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 5 and 100.<br \/>\nFactors of 5: 1, 5<br \/>\nFactors of 100:\u00a0 1, 2, 4, 5, 10, 20, 25, 50, 100<br \/>\nThe common factors of 5 and 100 are 1 and 5.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B100%7D%20%3D%20%5Cfrac%7B5%20%5Cdiv%205%7D%7B100%20%5Cdiv%205%7D%20%3D%20%5Cfrac%7B1%7D%7B20%7D\" alt=\"\\small \\frac{5}{100} = \\frac{5 \\div 5}{100 \\div 5} = \\frac{1}{20}\" \/><br \/>\nBecause 1 and 20 have no common factors other than 1, \\(\\frac{5}{100}\\) is in simplest form.<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{20}{15}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 20 and 15.<br \/>\nFactors of 20: 1, 2, 4, 5, 10, 20<br \/>\nFactors of 15:\u00a0 1, 3, 5, 15<br \/>\nThe common factors of 20 and 15 are 1 and 5.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B15%7D%20%3D%20%5Cfrac%7B20%20%5Cdiv%205%7D%7B15%20%5Cdiv%205%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D\" alt=\"\\small \\frac{20}{15} = \\frac{20 \\div 5}{15 \\div 5} = \\frac{4}{3}\" \/><br \/>\nBecause 4 and 3 have no common factors other than 1, \\(\\frac{20}{15}\\) is in simplest form.<\/p>\n<p>Question 7.<br \/>\nThere are 18 students in your class. Six of the students pack their lunch. In simplest form, what fraction of the students in your class pack their lunch?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-19.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 19\" width=\"107\" height=\"91\" \/><br \/>\nAnswer:<br \/>\nTotal students in the class = 18<br \/>\nNo. of students pack their lunch = 6<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 6 and 18.<br \/>\nFactors of 6: 1, 2, 3, 6<br \/>\nFactors of 18:\u00a0 1, 2, 3, 6, 9, 18<br \/>\nThe common factors of 6 and 18 are 1, 2, 3 and 6<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B18%7D%20%3D%20%5Cfrac%7B6%20%5Cdiv%206%7D%7B18%20%5Cdiv%206%7D%20%3D%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{6}{18} = \\frac{6 \\div 6}{18 \\div 6} = \\frac{1}{3}\" \/><br \/>\nBecause 1 and 3 have no common factors other than 1.<br \/>\nTherefore, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> of the students pack their lunch.<\/p>\n<p>Question 8.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWhy do you have to divide a numerator and a denominator by the greatest of their common factors to write a fraction in simplest form?<br \/>\nAnswer:<br \/>\nTo simplify a fraction to lowest terms, divide both the numerator and the denominator by their common factors. Repeat as needed until the only common factor is 1.<\/p>\n<p>Question 9.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how you know when a fraction is in simplest form.<br \/>\nAnswer:<br \/>\nIf the fraction has no common factors other than 1, then it is said to be the simplest form of the fraction.<\/p>\n<p>Question 10.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nWrite a fraction in which the numerator and the denominator have 1, 2, 4, and 8 as common factors. Then write the fraction in the simplest form.<br \/>\nAnswer:<br \/>\nThe fraction in which the numerator and the denominator is <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B16%7D\" alt=\"\\small \\frac{8}{16}\" \/>.<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 8 and 16.<br \/>\nFactors of 8: 1, 2, 4, 8<br \/>\nFactors of 16:\u00a0 1, 2, 4, 8, 16<br \/>\nThe common factors of 8 and 16 are 1, 2, 4 and 8.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B16%7D%20%3D%20%5Cfrac%7B8%20%5Cdiv%208%7D%7B16%20%5Cdiv%208%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{8}{16} = \\frac{8 \\div 8}{16 \\div 8} = \\frac{1}{2}\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1.<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA flight attendant has visited 30 of the 50 states. What fraction of the states, in simplest form, has he not visited?<br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nNo. of states = 50<br \/>\nA flight attendant has visited 30 states.<br \/>\nThe no. of states he has not visited = 50 &#8211; 30 = 20<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 20 and 50.<br \/>\nFactors of 20: 1, 2, 4, 5, 10, 20<br \/>\nFactors of 50: 1, 2, 5, 10, 25, 50<br \/>\nThe common factors of 20 and 50 are 1, 2, 5 and 10.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B50%7D%20%3D%20%5Cfrac%7B20%20%5Cdiv%2010%7D%7B50%20%5Cdiv%2010%7D%20%3D%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{20}{50} = \\frac{20 \\div 10}{50 \\div 10} = \\frac{2}{5}\" \/><br \/>\nBecause 2 and 5 have no common factors other than 1.<br \/>\nSo the flight attendant has not visited <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> of the states.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA bin has red, orange, yellow, green, blue, and purple crayons. There are 4 of each color in the bin. In simplest form, what fraction of the crayons are red, orange, yellow, or green?<br \/>\nAnswer:<br \/>\nGiven that, a bin has 6 colors(red, orange, yellow, green, blue, and purple) of crayons.<br \/>\nThere are 4 crayons in the each color = 4 x 6 = 24<br \/>\nIf the bin having only 3 colors(red, orange, yellow or green) = 4 x 3 = 12<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 12 and 24.<br \/>\nFactors of 12: 1, 2, 3, 4, 6, 12<br \/>\nFactors of 24: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThe common factors of 12 and 24 are 1, 2, 3, 4, 6 and 12.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B24%7D%20%3D%20%5Cfrac%7B12%20%5Cdiv%2012%7D%7B24%20%5Cdiv%2012%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{12}{24} = \\frac{12 \\div 12}{24 \\div 12} = \\frac{1}{2}\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> of the crayons are red, orange, yellow or green.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Estimate the sum or difference.<\/p>\n<p>Question 13.<br \/>\n598.44 &#8211; 45.61 =<strong>\u00a0<\/strong><br \/>\nAnswer: 550<br \/>\nThe number round to 598.44 is 600.<br \/>\nThe number round to 45.61 is 50.<br \/>\n600 &#8211; 50 = 550<br \/>\nThus the estimated difference is 550.<\/p>\n<p>Question 14.<br \/>\n93.8 + 4.3 =<br \/>\nAnswer: 98<br \/>\nThe number round to 93.8 is 94.<br \/>\nThe number round to 4.3 is 4.<br \/>\n94 + 4 = 98<br \/>\nThus the estimated addition is 98.<\/p>\n<h3><a id=\"Lesson_8.2_Estimate_Sums_and_Differences_of_Fractions\"><\/a>Lesson 8.2 Estimate Sums and Differences of Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Plot \\(\\frac{7}{12}\\), \\(\\frac{5}{6}\\) and \\(\\frac{1}{10}\\) on the number line.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-20.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 20\" width=\"397\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-20.png 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-20-300x58.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><br \/>\nHow can you estimate \\(\\frac{7}{12}\\) + \\(\\frac{5}{6}\\) ?<br \/>\nHow can you estimate \\(\\frac{2}{3}\\) &#8211; \\(\\frac{1}{10}\\)?<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nWrite two fractions that have a sum of about \\(\\frac{1}{2}\\). Then write two fractions that have a difference of about \\(\\frac{1}{2}\\). Explain your reasoning.<\/p>\n<p><strong>Think and Grow: Estimate Sums and Differences<\/strong><\/p>\n<p>You have used the benchmarks \\(\\frac{1}{2}\\) and 1 to compare fractions. You can use the benchmarks 0, \\(\\frac{1}{2}\\), and 1 to estimate sums and differences of fractions.<br \/>\n<strong>Example<\/strong><br \/>\nEstimate \\(\\frac{1}{6}\\) + \\(\\frac{5}{8}\\)<br \/>\n<strong>Step 1:<\/strong> Use a number line to estimate each fraction.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-21.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 21\" width=\"507\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-21.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-21-300x104.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{1}{6}\\) + \\(\\frac{5}{8}\\) is __ + __ = ___<br \/>\n<strong>Example<\/strong><br \/>\nEstimate \\(\\frac{9}{10}\\) &#8211; \\(\\frac{2}{5}\\).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-22.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 22\" width=\"617\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-22.png 617w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-22-300x125.png 300w\" sizes=\"(max-width: 617px) 100vw, 617px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Estimate the sum or difference<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{1}{3}\\) + \\(\\frac{11}{12}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> is between 0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> , but is closer to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to 1<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{1}{3}\\) + \\(\\frac{11}{12}\\) is\u00a0\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> +\u00a0 1 =\u00a0 <u><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/><\/u><\/p>\n<p>Question 2.<br \/>\n\\(\\frac{3}{5}\\) + \\(\\frac{5}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> is between\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1 , but is closer to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to 1<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{3}{5}\\) + \\(\\frac{5}{6}\\) is <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> +\u00a0 1 =\u00a0 <u><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/><\/u><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{15}{16}\\) &#8211; \\(\\frac{7}{8}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B16%7D\" alt=\"\\small \\frac{15}{16}\" \/>\u00a0is about <u><br \/>\n<\/u>Think : The numerator is about the same as the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/>\u00a0is about <u><br \/>\n<\/u>Think : The numerator is about the same as the denominator.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B16%7D\" alt=\"\\small \\frac{15}{16}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/>\u00a0 is 1 &#8211; 1 = 0.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Estimate the sum or difference.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{1}{6}\\) + \\(\\frac{3}{5}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> is between 0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>, but is closer to 0.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{1}{6}\\) + \\(\\frac{3}{5}\\) = 0 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{4}{5}\\) &#8211; \\(\\frac{5}{12}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/>\u00a0is about <u><br \/>\n<\/u>Think: The numerator is about the same as the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> is about <u><br \/>\n<\/u>Think: The numerator is about half of the denominator.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B16%7D\" alt=\"\\small \\frac{15}{16}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/>\u00a0 is 1 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> \u00a0= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{13}{16}\\) + \\(\\frac{5}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B16%7D\" alt=\"\\small \\frac{13}{16}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to 1.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to 1.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{13}{16}\\) + \\(\\frac{5}{6}\\) = 1+1 = 2<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{3}{6}\\) &#8211; \\(\\frac{1}{8}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/>\u00a0is about <u><br \/>\n<\/u>Think: The numerator is about half of the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/>\u00a0is about <u><br \/>\n<\/u>Think: The numerator is near to zero.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/>\u00a0is\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>\u00a0 &#8211; 0 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> .<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{1}{14}\\) + \\(\\frac{98}{100}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B14%7D\" alt=\"\\small \\frac{1}{14}\" \/> is closer to 0<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B98%7D%7B100%7D\" alt=\"\\small \\frac{98}{100}\" \/> is closer to 1.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{1}{14}\\) + \\(\\frac{98}{100}\\) = 0 +1 = 1<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{11}{12}\\) &#8211; \\(\\frac{1}{8}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> is about <u><br \/>\n<\/u>Think: The numerator is about the same as the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/>\u00a0is about <u><br \/>\n<\/u>Think: The numerator is near to zero.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/>\u00a0&#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> is\u00a0 1\u00a0 &#8211; 0 = 1.<\/p>\n<p>Question 10.<br \/>\nYou walk \\(\\frac{1}{10}\\) mile to your friend\u2019s house and then you both walk \\(\\frac{2}{5}\\) mile. Estimate how much farther you walk with your friend than you walk alone.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-23.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 23\" width=\"197\" height=\"167\" \/><br \/>\nAnswer:<br \/>\nTo find how much farther I walk with my friend than I walk alone, subtract the distance that I walk alone from we both walk.<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B10%7D\" alt=\"\\small \\frac{1}{10}\" \/> is about____<br \/>\nThink: The numerator is near to zero.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> is about____<br \/>\nThink: The numerator is about half of the denominator.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B10%7D\" alt=\"\\small \\frac{1}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> &#8211; 0 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><br \/>\nSo the distance I walk with my friend than I walk alone is <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> mile.<\/p>\n<p>Question 11.<br \/>\nA carpenter has two wooden boards. One board is \\(\\frac{3}{4}\\) foot long and the other board is \\(\\frac{1}{6}\\) foot long. To determine whether the total length of the boards is 1 foot, should the carpenter use an estimate, or is an exact answer required? Explain.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA carpenter has two wooden boards. One board is \\(\\frac{3}{4}\\) foot long and the other board is \\(\\frac{1}{6}\\) foot long.<br \/>\n\\(\\frac{3}{4}\\) + \\(\\frac{1}{6}\\)<br \/>\nThe fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.<br \/>\nLCM = 12<br \/>\n\\(\\frac{3}{4}\\) \u00d7 \\(\\frac{3}{3}\\) = \\(\\frac{9}{12}\\)<br \/>\n\\(\\frac{1}{6}\\) \u00d7 \\(\\frac{2}{2}\\) = \\(\\frac{2}{12}\\)<br \/>\n\\(\\frac{9}{12}\\) + \\(\\frac{2}{12}\\) = \\(\\frac{11}{12}\\)<br \/>\n\\(\\frac{11}{12}\\) is approximately equal to 1 foot.<\/p>\n<p>Question 12.<br \/>\n<strong>Number Sense<\/strong><br \/>\nA fraction has a numerator of 1 and a denominator greater than 4. Is the fraction closer to 0, \\(\\frac{1}{2}\\), or 1? Explain.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA fraction has a numerator of 1 and a denominator greater than 4.<br \/>\n\\(\\frac{1}{4}\\) = 0.25<br \/>\nIf the denominator is greater than 4. Let&#8217;s consider 8.<br \/>\n\\(\\frac{1}{8}\\) = 0.125<br \/>\nThe fraction will be close to 0.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nIn the human body, the small intestine is about 20\\(\\frac{1}{12}\\) feet long. The large intestine is about 4\\(\\frac{5}{6}\\) feet long. About how long are the intestines in the human body?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-24.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 24\" width=\"191\" height=\"207\" \/><br \/>\nTo \ufb01nd the total length of the intestines, estimate 20\\(\\frac{1}{12}\\) + 4\\(\\frac{5}{6}\\).<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-25.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 25\" width=\"688\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-25.png 688w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-25-300x105.png 300w\" sizes=\"(max-width: 688px) 100vw, 688px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-39866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-25-300x105.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-25\" width=\"300\" height=\"105\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-25-300x105.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-25.jpg 688w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nA bullfrog jumps 5\\(\\frac{11}{12}\\) feet. A leopard frog jumps 4\\(\\frac{1}{3}\\) feet. About how much farther does the bullfrog jump than the leopard frog?<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\n5<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> is about,\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> is closer to 1 than 0.<br \/>\n4<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> is about, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> is closer to 0 than 1.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference<br \/>\nAn estimate of 5<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/>\u00a0 &#8211; 4<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 1 &#8211; 0 = 1<br \/>\nSo, bullfrog jumps<strong> 1 feet<\/strong> farther than the leopard frog.<br \/>\nQuestion 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA cell phone has 32 gigabytes of storage. The amounts of storage used by photos, songs, and apps are shown. About how many gigabytes of storage are left?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-26.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 26\" width=\"302\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-26.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-26-300x120.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nNo. of gigabytes of storage in cellphone = 32<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\nPhotos &#8212;&gt;\u00a0 8<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> is about,\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/>\u00a0is closer to 1 than 0<br \/>\nSongs &#8212;&gt;\u00a0 \u00a02<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B100%7D\" alt=\"\\small \\frac{3}{100}\" \/> is about,\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B100%7D\" alt=\"\\small \\frac{3}{100}\" \/> is closer to 0 than 1<br \/>\nApps &#8212;&gt;\u00a0 \u00a0 \u00a06<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/>\u00a0 is about,\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> is closer to 1 than 0<br \/>\n<strong>Step 2:\u00a0<\/strong>Storage left in the phone = Total storage &#8211; storage(photos + songs + apps)<br \/>\n= 32 &#8211; (1 + 0 + 1)<br \/>\nTherefore, storage left = <strong>30 gigabytes.<\/strong><\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nUse two different methods to estimate how many cups of nut medley the recipe makes. Which estimate do you think is closer to the actual answer? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-27.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 27\" width=\"182\" height=\"153\" \/><br \/>\nAnswer:<br \/>\n1 \\(\\frac{3}{8}\\) + \\(\\frac{5}{8}\\) + 2 \\(\\frac{1}{3}\\)<br \/>\nFirst add the whole numbers<br \/>\n1 + 2 = 3<br \/>\n\\(\\frac{3}{8}\\) + \\(\\frac{5}{8}\\) + \\(\\frac{1}{3}\\)<br \/>\n1 \\(\\frac{1}{3}\\)<br \/>\n3 + 1 \\(\\frac{1}{3}\\) = 4 \\(\\frac{1}{3}\\)<br \/>\nThe fraction is 4 \\(\\frac{1}{3}\\)<br \/>\n4 is equal to the actual answer.<\/p>\n<h3><a id=\"Estimate_Sums_and_Differences_of_Fractions_Homework_&amp;_Practice_8.2\"><\/a>Estimate Sums and Differences of Fractions Homework &amp; Practice 8.2<\/h3>\n<p>Estimate the sum or difference<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{11}{12}\\) &#8211; \\(\\frac{5}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> is about <u><br \/>\n<\/u>Think : The numerator is about the same as the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/>\u00a0is about <u><br \/>\n<\/u>Think : The numerator is about same as the denominator.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/>\u00a0 is\u00a0 1\u00a0 &#8211; 1 = 0.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{17}{20}\\) + \\(\\frac{13}{20}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B20%7D\" alt=\"\\small \\frac{17}{20}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to 1.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B20%7D\" alt=\"\\small \\frac{13}{20}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{17}{20}\\) + \\(\\frac{13}{20}\\) = 1 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/>.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{3}{8}\\) &#8211; \\(\\frac{1}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> is about <u><br \/>\n<\/u>Think : The numerator is about half of the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> is about <u><br \/>\n<\/u>Think : The numerator is near to zero.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> \u00a0&#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> \u00a0 is\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>\u00a0 &#8211; 0 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{7}{12}\\) + \\(\\frac{2}{5}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> is between 0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>, but is closer to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{7}{12}\\) + \\(\\frac{2}{5}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 1.<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{4}{5}\\) &#8211; \\(\\frac{7}{12}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> is about <u><br \/>\n<\/u>Think: The numerator is about the same as the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> is about <u><br \/>\n<\/u>Think: The numerator is about half of the denominator.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> \u00a0&#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/>\u00a0 \u00a0is\u00a0 1 &#8211;\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>\u00a0 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{1}{5}\\) + 1\\(\\frac{10}{21}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\n\\(\\frac{1}{5}\\) is closer to 0<br \/>\n1\\(\\frac{10}{21}\\) is close to 1.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{1}{5}\\) + 1\\(\\frac{10}{21}\\)<br \/>\n= 0 + 1 = 1<\/p>\n<p>Question 7.<br \/>\n3\\(\\frac{5}{8}\\) &#8211; \\(\\frac{1}{10}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\n3<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/>\u00a0 is about, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> is closer to 1 than 0<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B10%7D\" alt=\"\\small \\frac{1}{10}\" \/> is near to 0<br \/>\n<strong>Step 2:<\/strong> Estimate the difference<br \/>\nAn estimate of 3<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/>\u00a0 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B10%7D\" alt=\"\\small \\frac{1}{10}\" \/> = 1 &#8211; 0 = 1.<\/p>\n<p>Question 8.<br \/>\n6\\(\\frac{1}{3}\\) + 2\\(\\frac{4}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\n\\(\\frac{1}{3}\\) is close to 0 than 1.<br \/>\n\\(\\frac{4}{6}\\) is to 1 than 0.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum<br \/>\nAn estimate of 6\\(\\frac{1}{3}\\) is 6.<br \/>\nAn estimate of 2\\(\\frac{4}{6}\\) is 3.<br \/>\n6 + 3 = 9<\/p>\n<p>Question 9.<br \/>\n5\\(\\frac{7}{8}\\) &#8211; 4\\(\\frac{49}{100}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\n5<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/>\u00a0 is about, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/>\u00a0is closer to 1 than 0<br \/>\n4<img class=\"\" src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B49%7D%7B100%7D\" alt=\"\\small \\frac{49}{100}\" \/>\u00a0 is about, <img class=\"\" src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B49%7D%7B100%7D\" alt=\"\\small \\frac{49}{100}\" \/> is closer to 0 than 1<br \/>\n<strong>Step 2:<\/strong> Estimate the difference<br \/>\nAn estimate of 5<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/>\u00a0 &#8211; 4<img class=\"\" src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B49%7D%7B100%7D\" alt=\"\\small \\frac{49}{100}\" \/>\u00a0 = 1 &#8211; 0 =\u00a0 1.<\/p>\n<p>Question 10.<br \/>\nYou make a bag of trail mix with \\(\\frac{2}{3}\\) cup of raisins and \\(\\frac{9}{8}\\) cups of peanuts. About how much trail mix do you make?<br \/>\nAnswer:<br \/>\nRaisins = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> cups<br \/>\nPeanuts = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B8%7D\" alt=\"\\small \\frac{9}{8}\" \/> cups<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B8%7D\" alt=\"\\small \\frac{9}{8}\" \/> is closer to 1.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{2}{3}\\) + \\(\\frac{9}{8}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + 1 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/>.<br \/>\nSo trail mix = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/>.<\/p>\n<p>Question 11.<br \/>\nYou have \\(\\frac{2}{3}\\) cup of \ufb02our in a bin and \\(\\frac{7}{8}\\) cup of \ufb02our in a bag. To determine whether you have enough \ufb02our for a recipe that needs 1\\(\\frac{3}{4}\\) cups of \ufb02our, should you use an estimate, or is an exact answer required? Explain.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou have \\(\\frac{2}{3}\\) cup of \ufb02our in a bin and \\(\\frac{7}{8}\\) cup of \ufb02our in a bag.<br \/>\n\\(\\frac{2}{3}\\) + \\(\\frac{7}{8}\\) = 1 \\(\\frac{13}{24}\\)<br \/>\nTh estimated fraction of 1 \\(\\frac{13}{24}\\) is 1\\(\\frac{3}{4}\\)<\/p>\n<p>Question 12.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how you know \\(\\frac{9}{10}\\) &#8211; \\(\\frac{3}{5}\\) is about \\(\\frac{1}{2}\\).<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> is about <u><br \/>\n<\/u>Think: The numerator is about the same as the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> is about <u><br \/>\n<\/u>Think : The numerator is about half of the denominator.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/>\u00a0 is 1 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> \u00a0= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>.<\/p>\n<p>Question 13.<br \/>\n<strong>Precision<\/strong><br \/>\nYour friend says \\(\\frac{5}{8}\\) + \\(\\frac{7}{12}\\) is about 2. Find a closer estimate. Explain why your estimate is closer.<br \/>\nAnswer:<br \/>\n\\(\\frac{5}{8}\\) + \\(\\frac{7}{12}\\) = 1 \\(\\frac{5}{24}\\)<br \/>\n\\(\\frac{5}{24}\\) is closer to 1 than 0.<br \/>\n1 \\(\\frac{5}{24}\\) is about 2.<\/p>\n<p>Question 14.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nAbout how much taller is Robot A than Robot B?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-28.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 28\" width=\"271\" height=\"243\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B10%7D\" alt=\"\\small \\frac{6}{10}\" \/> is about, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B10%7D\" alt=\"\\small \\frac{6}{10}\" \/> is closer to 1 than 0.<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/>\u00a0 is about, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> is closer to 0 than 1.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference<br \/>\nAn estimate of 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B10%7D\" alt=\"\\small \\frac{6}{10}\" \/>\u00a0 &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/>\u00a0\u00a0 = 1 &#8211; 0 =\u00a0 1.<br \/>\nRobot A is 1 meter taller than Robot B.<\/p>\n<p>Question 15.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA class makes a paper chain that is 5\\(\\frac{7}{12}\\) feet long. The class adds another 3\\(\\frac{5}{6}\\) feet to the chain. About how long is the chain now?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-29.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 29\" width=\"251\" height=\"111\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to round each mixed number to the nearest whole number.<br \/>\n5<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> is about,\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/>\u00a0is closer to 1 than 0.<br \/>\n3<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> is about, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> is closer to 1 than 0.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum<br \/>\nAn estimate of 5<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> \u00a0+ 3<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 1 + 1 = 2<br \/>\nTherefore, the chain is now <strong>2 feet<\/strong> long.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the product. Check whether your answer is reasonable.<\/p>\n<p>Question 16.<br \/>\n509 \u00d7 5 = ___<br \/>\nAnswer:<br \/>\nThe number 509 round to hundred is 500.<br \/>\n500 \u00d7 5 = 2500<br \/>\n509 \u00d7 5 = 2545<br \/>\nSo the answer is reasonable.<\/p>\n<p>Question 17.<br \/>\n7,692 \u00d7 6 = ___<br \/>\nAnswer:<br \/>\nThe number 7692 round to hundred is 7700.<br \/>\n7700 \u00d7 6 = 46200<br \/>\n7,692 \u00d7 6 = 46152<br \/>\nSo the answer is reasonable.<\/p>\n<p>Question 18.<br \/>\n31,435 \u00d7 7 = ___<br \/>\nAnswer:<br \/>\nThe number 31435 round to hundred is 31,400.<br \/>\n31,400 \u00d7 7 = 219800<br \/>\n31,435 \u00d7 7 = 220045<br \/>\nSo the answer is reasonable.<\/p>\n<h3><a id=\"Lesson_8.3_Find_Common_Denominators\"><\/a>Lesson 8.3 Find Common Denominators<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>You cut a rectangular pan of vegetable lasagna into equal-sized pieces. You serve \\(\\frac{1}{2}\\) of the lasagna to a large table and \\(\\frac{1}{3}\\) of the lasagna to a small table. Draw a diagram that shows how you cut the lasagna.<br \/>\nWhat fraction of the lasagna does each piece represent? How does the denominator of the fraction compare to the denominators of \\(\\frac{1}{2}\\) and \\(\\frac{1}{3}\\) ?<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nIs there another way you can cut the lasagna? Explain your reasoning.<\/p>\n<p><strong>Think and Grow: Find Common Denominators<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nFractions that have the same denominator are said to have a common denominator. You can find a common denominator either by finding a common multiple of the denominators or by finding the product of the denominators.<br \/>\n<strong>Example<\/strong><br \/>\nUse a common denominator to write equivalent fractions for \\(\\frac{1}{2}\\) and \\(\\frac{5}{8}\\).<br \/>\nList multiples of the denominators.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-30.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 30\" width=\"663\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-30.png 663w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-30-300x119.png 300w\" sizes=\"(max-width: 663px) 100vw, 663px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-39881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-30-300x119.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-30\" width=\"300\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-30-300x119.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-30.jpg 663w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nUse a common denominator to write equivalent fractions for \\(\\frac{2}{3}\\) and \\(\\frac{1}{4}\\). Use the product of the denominators: 3 \u00d7 4 = __.<br \/>\nWrite equivalent fractions with denominators of 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-31.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 31\" width=\"621\" height=\"257\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-31.png 621w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-31-300x124.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-39882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-31-300x124.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-31\" width=\"300\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-31-300x124.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-31.jpg 621w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Use a common denominator to write an equivalent fraction for each fraction.<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{2}{3}\\) and \\(\\frac{1}{6}\\)<br \/>\nAnswer:<br \/>\nUse the product of the denominators : 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 6 = 18<br \/>\nWrite equivalent fractions with denominators of 18<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%206%7D%7B3%20%5Ctimes%206%7D%20%3D%20%5Cfrac%7B12%7D%7B18%7D\" alt=\"\\small \\frac{2}{3} = \\frac{2 \\times 6}{3 \\times 6} = \\frac{12}{18}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%203%7D%7B6%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B3%7D%7B18%7D\" alt=\"\\small \\frac{1}{6} = \\frac{1 \\times 3}{6 \\times 3} = \\frac{3}{18}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B18%7D\" alt=\"\\small \\frac{12}{18}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B18%7D\" alt=\"\\small \\frac{3}{18}\" \/>.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{5}{6}\\) and \\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators : 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 4 = 24<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 24<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%204%7D%7B6%20%5Ctimes%204%7D%20%3D%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{5}{6} = \\frac{5 \\times 4}{6 \\times 4} = \\frac{20}{24}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%206%7D%7B4%20%5Ctimes%206%7D%20%3D%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{3}{4} = \\frac{3 \\times 6}{4 \\times 6} = \\frac{18}{24}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{20}{24}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{18}{24}\" \/>.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Use a common denominator to write an equivalent fraction for each fraction.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{2}{3}\\) and \\(\\frac{5}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators : 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 6 = 18<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 18<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%206%7D%7B3%20%5Ctimes%206%7D%20%3D%20%5Cfrac%7B12%7D%7B18%7D\" alt=\"\\small \\frac{2}{3} = \\frac{2 \\times 6}{3 \\times 6} = \\frac{12}{18}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%203%7D%7B6%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B15%7D%7B18%7D\" alt=\"\\small \\frac{5}{6} = \\frac{5 \\times 3}{6 \\times 3} = \\frac{15}{18}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B18%7D\" alt=\"\\small \\frac{12}{18}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B18%7D\" alt=\"\\small \\frac{15}{18}\" \/>.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{3}{4}\\) and \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators : 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 2 = 8<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 8<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%202%7D%7B4%20%5Ctimes%202%7D%20%3D%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{3}{4} = \\frac{3 \\times 2}{4 \\times 2} = \\frac{6}{8}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B2%20%5Ctimes%204%7D%20%3D%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{1}{2} = \\frac{1 \\times 4}{2 \\times 4} = \\frac{4}{8}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/>.<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{5}{9}\\) and \\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 3 = 27<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 27<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B9%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%203%7D%7B9%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B15%7D%7B27%7D\" alt=\"\\small \\frac{5}{9} = \\frac{5 \\times 3}{9 \\times 3} = \\frac{15}{27}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%209%7D%7B3%20%5Ctimes%209%7D%20%3D%20%5Cfrac%7B18%7D%7B27%7D\" alt=\"\\small \\frac{2}{3} = \\frac{2 \\times 9}{3 \\times 9} = \\frac{18}{27}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B27%7D\" alt=\"\\small \\frac{15}{27}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B27%7D\" alt=\"\\small \\frac{18}{27}\" \/>.<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{8}{21}\\) and \\(\\frac{3}{7}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 21 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 7 = 147<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 147<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B21%7D%20%3D%20%5Cfrac%7B8%20%5Ctimes%207%7D%7B21%20%5Ctimes%207%7D%20%3D%20%5Cfrac%7B56%7D%7B147%7D\" alt=\"\\small \\frac{8}{21} = \\frac{8 \\times 7}{21 \\times 7} = \\frac{56}{147}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B7%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%2021%7D%7B7%20%5Ctimes%2021%7D%20%3D%20%5Cfrac%7B63%7D%7B147%7D\" alt=\"\\small \\frac{3}{7} = \\frac{3 \\times 21}{7 \\times 21} = \\frac{63}{147}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B56%7D%7B147%7D\" alt=\"\\small \\frac{56}{147}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B63%7D%7B147%7D\" alt=\"\\small \\frac{63}{147}\" \/>.<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{1}{5}\\) and \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 2 = 10<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 10<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B5%20%5Ctimes%202%7D%20%3D%20%5Cfrac%7B2%7D%7B10%7D\" alt=\"\\small \\frac{1}{5} = \\frac{1 \\times 2}{5 \\times 2} = \\frac{2}{10}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%205%7D%7B2%20%5Ctimes%205%7D%20%3D%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{1}{2} = \\frac{1 \\times 5}{2 \\times 5} = \\frac{5}{10}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B10%7D\" alt=\"\\small \\frac{2}{10}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/>.<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{3}{4}\\) and \\(\\frac{1}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 6 = 24<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 24<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%206%7D%7B4%20%5Ctimes%206%7D%20%3D%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{3}{4} = \\frac{3 \\times 6}{4 \\times 6} = \\frac{18}{24}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B6%20%5Ctimes%204%7D%20%3D%20%5Cfrac%7B4%7D%7B24%7D\" alt=\"\\small \\frac{1}{6} = \\frac{1 \\times 4}{6 \\times 4} = \\frac{4}{24}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{18}{24}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B24%7D\" alt=\"\\small \\frac{4}{24}\" \/>.<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{3}{7}\\) and \\(\\frac{2}{9}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 9 = 63<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 63<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B7%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%209%7D%7B7%20%5Ctimes%209%7D%20%3D%20%5Cfrac%7B27%7D%7B63%7D\" alt=\"\\small \\frac{3}{7} = \\frac{3 \\times 9}{7 \\times 9} = \\frac{27}{63}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B9%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%207%7D%7B9%20%5Ctimes%207%7D%20%3D%20%5Cfrac%7B14%7D%7B63%7D\" alt=\"\\small \\frac{2}{9} = \\frac{2 \\times 7}{9 \\times 7} = \\frac{14}{63}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B27%7D%7B63%7D\" alt=\"\\small \\frac{27}{63}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B63%7D\" alt=\"\\small \\frac{14}{63}\" \/>.<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{3}{8}\\) and \\(\\frac{5}{11}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 11 = 88<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 88<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%2011%7D%7B8%20%5Ctimes%2011%7D%20%3D%20%5Cfrac%7B33%7D%7B88%7D\" alt=\"\\small \\frac{3}{8} = \\frac{3 \\times 11}{8 \\times 11} = \\frac{33}{88}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B11%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%208%7D%7B11%20%5Ctimes%208%7D%20%3D%20%5Cfrac%7B40%7D%7B88%7D\" alt=\"\\small \\frac{5}{11} = \\frac{5 \\times 8}{11 \\times 8} = \\frac{40}{88}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B33%7D%7B88%7D\" alt=\"\\small \\frac{33}{88}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B40%7D%7B88%7D\" alt=\"\\small \\frac{40}{88}\" \/>.<\/p>\n<p>Question 11.<br \/>\nYou walk your dog \\(\\frac{3}{4}\\) mile on Saturday and \\(\\frac{5}{8}\\) mile on Sunday. Use a common denominator to write an equivalent fraction for each fraction.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-32.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 32\" width=\"184\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 8 = 32<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 32<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%208%7D%7B4%20%5Ctimes%208%7D%20%3D%20%5Cfrac%7B24%7D%7B32%7D\" alt=\"\\small \\frac{3}{4} = \\frac{3 \\times 8}{4 \\times 8} = \\frac{24}{32}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%204%7D%7B8%20%5Ctimes%204%7D%20%3D%20%5Cfrac%7B20%7D%7B32%7D\" alt=\"\\small \\frac{5}{8} = \\frac{5 \\times 4}{8 \\times 4} = \\frac{20}{32}\" \/><br \/>\nDog walk on Saturday, equivalent fraction = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B32%7D\" alt=\"\\small \\frac{24}{32}\" \/><br \/>\nDog walk on Sunday, equivalent fraction = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B32%7D\" alt=\"\\small \\frac{20}{32}\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how to use the models to \ufb01nd a common denominator for \\(\\frac{1}{2}\\) and \\(\\frac{3}{5}\\). Then write an equivalent fraction for each fraction.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-33.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 33\" width=\"256\" height=\"80\" \/><br \/>\nAnswer:<br \/>\nInitially find the product of the denominators and that product value is the denominator for both fractions.<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 5 = 10<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 10<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%205%7D%7B2%20%5Ctimes%205%7D%20%3D%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{1}{2} = \\frac{1 \\times 5}{2 \\times 5} = \\frac{5}{10}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%202%7D%7B5%20%5Ctimes%202%7D%20%3D%20%5Cfrac%7B6%7D%7B10%7D\" alt=\"\\small \\frac{3}{5} = \\frac{3 \\times 2}{5 \\times 2} = \\frac{6}{10}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B10%7D\" alt=\"\\small \\frac{6}{10}\" \/>.<\/p>\n<p>Question 13.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich pairs of fractions are equivalent to \\(\\frac{1}{2}\\) and \\(\\frac{2}{3}\\) ?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-34.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 34\" width=\"253\" height=\"128\" \/><br \/>\nAnswer:<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B12%7D\" alt=\"\\small \\frac{6}{12}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><br \/>\nThese two fractions are equivalent to \\(\\frac{1}{2}\\) and \\(\\frac{2}{3}\\).<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou and your friend make woven key chains. Your key chain is \\(\\frac{2}{4}\\) foot long. Your friend\u2019s is \\(\\frac{3}{6}\\) foot long. Are the key chains the same length?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-35.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 35\" width=\"175\" height=\"127\" \/><br \/>\nUse a common denominator to write equivalent fractions for the lengths of the key chains. Use the product of the denominators.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-36.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 36\" width=\"134\" height=\"39\" \/><br \/>\nWrite equivalent fractions with denominators of 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-37.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 37\" width=\"326\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-37.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-37-300x58.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nCompare the lengths of the key chains.<br \/>\nSo, the key chains __ the same length.<\/p>\n<p>Answer:<br \/>\n4 \u00d7 6 = 24<br \/>\nWrite equivalent fractions with denominators of 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-39883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-37-300x58.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-37\" width=\"300\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-37-300x58.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-37.jpg 326w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nSo, the key chains has the same length.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nYour hamster weighs \\(\\frac{13}{16}\\) ounce. Your friend\u2019s hamster weighs \\(\\frac{6}{8}\\) ounce. Do the hamsters weigh the same amount?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-38.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 38\" width=\"110\" height=\"164\" \/><br \/>\nAnswer:<br \/>\nUse a common denominator to write equivalent fractions for the hamsters weight.<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 16 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 8 = 128<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 128<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B16%7D%20%3D%20%5Cfrac%7B13%20%5Ctimes%208%7D%7B16%20%5Ctimes%208%7D%20%3D%20%5Cfrac%7B104%7D%7B128%7D\" alt=\"\\small \\frac{13}{16} = \\frac{13 \\times 8}{16 \\times 8} = \\frac{104}{128}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D%20%3D%20%5Cfrac%7B6%20%5Ctimes%2016%7D%7B8%20%5Ctimes%2016%7D%20%3D%20%5Cfrac%7B96%7D%7B128%7D\" alt=\"\\small \\frac{6}{8} = \\frac{6 \\times 16}{8 \\times 16} = \\frac{96}{128}\" \/><br \/>\nHamsters weigh the different amount. One is <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B104%7D%7B128%7D\" alt=\"\\small \\frac{104}{128}\" \/> ounce and the other one is <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B96%7D%7B128%7D\" alt=\"\\small \\frac{96}{128}\" \/> ounce.<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have three vegetable pizzas of the same size. One has 4 equal slices. The second has 8 equal slices. The third has 6 equal slices. You cut the pizzas until all of them have the same number of slices. How many slices does each pizza have?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou have three vegetable pizzas of the same size.<br \/>\nOne has 4 equal slices. The second has 8 equal slices.<br \/>\nThe third has 6 equal slices. You cut the pizzas until all of them have the same number of slices.<br \/>\n4 + 6 + 8 = 18<br \/>\none has \\(\\frac{4}{18}\\)<br \/>\nsecond has \\(\\frac{6}{18}\\)<br \/>\nThird has \\(\\frac{8}{18}\\)<br \/>\nTotal there are 18 slices.<\/p>\n<h3><a id=\"Find_Common_Denominators_Homework_&amp;_Practice_8.3\"><\/a>Find Common Denominators Homework &amp; Practice 8.3<\/h3>\n<p>Use a common denominator to write an equivalent fraction for each fraction.<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{1}{2}\\) and \\(\\frac{3}{8}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 8 = 16<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 16<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%208%7D%7B2%20%5Ctimes%208%7D%20%3D%20%5Cfrac%7B8%7D%7B16%7D\" alt=\"\\small \\frac{1}{2} = \\frac{1 \\times 8}{2 \\times 8} = \\frac{8}{16}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%202%7D%7B8%20%5Ctimes%202%7D%20%3D%20%5Cfrac%7B6%7D%7B16%7D\" alt=\"\\small \\frac{3}{8} = \\frac{3 \\times 2}{8 \\times 2} = \\frac{6}{16}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B16%7D\" alt=\"\\small \\frac{8}{16}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B16%7D\" alt=\"\\small \\frac{6}{16}\" \/>.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{7}{9}\\) and \\(\\frac{2}{3}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 3 = 27<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 27.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B9%7D%20%3D%20%5Cfrac%7B7%20%5Ctimes%203%7D%7B9%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B21%7D%7B27%7D\" alt=\"\\small \\frac{7}{9} = \\frac{7 \\times 3}{9 \\times 3} = \\frac{21}{27}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%209%7D%7B3%20%5Ctimes%209%7D%20%3D%20%5Cfrac%7B18%7D%7B27%7D\" alt=\"\\small \\frac{2}{3} = \\frac{2 \\times 9}{3 \\times 9} = \\frac{18}{27}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B21%7D%7B27%7D\" alt=\"\\small \\frac{21}{27}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B27%7D\" alt=\"\\small \\frac{18}{27}\" \/>.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{5}{6}\\) and \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 2 = 12<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 12.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%202%7D%7B6%20%5Ctimes%202%7D%20%3D%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{5}{6} = \\frac{5 \\times 2}{6 \\times 2} = \\frac{10}{12}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%206%7D%7B2%20%5Ctimes%206%7D%20%3D%20%5Cfrac%7B6%7D%7B12%7D\" alt=\"\\small \\frac{1}{2} = \\frac{1 \\times 6}{2 \\times 6} = \\frac{6}{12}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B12%7D\" alt=\"\\small \\frac{6}{12}\" \/>.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{3}{4}\\) and \\(\\frac{5}{16}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 16 = 64<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 64.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%2016%7D%7B4%20%5Ctimes%2016%7D%20%3D%20%5Cfrac%7B48%7D%7B64%7D\" alt=\"\\small \\frac{3}{4} = \\frac{3 \\times 16}{4 \\times 16} = \\frac{48}{64}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B16%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%204%7D%7B16%20%5Ctimes%204%7D%20%3D%20%5Cfrac%7B20%7D%7B64%7D\" alt=\"\\small \\frac{5}{16} = \\frac{5 \\times 4}{16 \\times 4} = \\frac{20}{64}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B48%7D%7B64%7D\" alt=\"\\small \\frac{48}{64}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B64%7D\" alt=\"\\small \\frac{20}{64}\" \/>.<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{18}{24}\\) and \\(\\frac{5}{6}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 24 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 6 = 144<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 144.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D%20%3D%20%5Cfrac%7B18%20%5Ctimes%206%7D%7B24%20%5Ctimes%206%7D%20%3D%20%5Cfrac%7B108%7D%7B144%7D\" alt=\"\\small \\frac{18}{24} = \\frac{18 \\times 6}{24 \\times 6} = \\frac{108}{144}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%2024%7D%7B6%20%5Ctimes%2024%7D%20%3D%20%5Cfrac%7B120%7D%7B144%7D\" alt=\"\\small \\frac{5}{6} = \\frac{5 \\times 24}{6 \\times 24} = \\frac{120}{144}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B108%7D%7B144%7D\" alt=\"\\small \\frac{108}{144}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B120%7D%7B144%7D\" alt=\"\\small \\frac{120}{144}\" \/>.<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{1}{3}\\) and \\(\\frac{1}{5}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 5 = 15<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 15.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%205%7D%7B3%20%5Ctimes%205%7D%20%3D%20%5Cfrac%7B5%7D%7B15%7D\" alt=\"\\small \\frac{1}{3} = \\frac{1 \\times 5}{3 \\times 5} = \\frac{5}{15}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%203%7D%7B5%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B3%7D%7B15%7D\" alt=\"\\small \\frac{1}{5} = \\frac{1 \\times 3}{5 \\times 3} = \\frac{3}{15}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B15%7D\" alt=\"\\small \\frac{5}{15}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B15%7D\" alt=\"\\small \\frac{3}{15}\" \/>.<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{3}{5}\\) and \\(\\frac{4}{7}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 7= 35<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 35.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%207%7D%7B5%20%5Ctimes%207%7D%20%3D%20%5Cfrac%7B21%7D%7B35%7D\" alt=\"\\small \\frac{3}{5} = \\frac{3 \\times 7}{5 \\times 7} = \\frac{21}{35}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B7%7D%20%3D%20%5Cfrac%7B4%20%5Ctimes%205%7D%7B7%20%5Ctimes%205%7D%20%3D%20%5Cfrac%7B20%7D%7B35%7D\" alt=\"\\small \\frac{4}{7} = \\frac{4 \\times 5}{7 \\times 5} = \\frac{20}{35}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B21%7D%7B35%7D\" alt=\"\\small \\frac{21}{35}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B35%7D\" alt=\"\\small \\frac{20}{35}\" \/>.<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{5}{8}\\) and \\(\\frac{2}{9}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators: 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 9 = 72<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 72.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%209%7D%7B8%20%5Ctimes%209%7D%20%3D%20%5Cfrac%7B45%7D%7B72%7D\" alt=\"\\small \\frac{5}{8} = \\frac{5 \\times 9}{8 \\times 9} = \\frac{45}{72}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B9%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%208%7D%7B9%20%5Ctimes%208%7D%20%3D%20%5Cfrac%7B16%7D%7B72%7D\" alt=\"\\small \\frac{2}{9} = \\frac{2 \\times 8}{9 \\times 8} = \\frac{16}{72}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B45%7D%7B72%7D\" alt=\"\\small \\frac{45}{72}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B72%7D\" alt=\"\\small \\frac{16}{72}\" \/>.<\/p>\n<p>Question 9.<br \/>\nA mint plant grows \\(\\frac{7}{8}\\) inch in 1 week and \\(\\frac{13}{16}\\) inch the next week. Use a common denominator to write an equivalent fraction for each fraction.<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators : 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 16 = 128<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with denominators of 128.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D%20%3D%20%5Cfrac%7B7%20%5Ctimes%2016%7D%7B8%20%5Ctimes%2016%7D%20%3D%20%5Cfrac%7B112%7D%7B128%7D\" alt=\"\\small \\frac{7}{8} = \\frac{7 \\times 16}{8 \\times 16} = \\frac{112}{128}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B16%7D%20%3D%20%5Cfrac%7B13%20%5Ctimes%208%7D%7B16%20%5Ctimes%208%7D%20%3D%20%5Cfrac%7B104%7D%7B128%7D\" alt=\"\\small \\frac{13}{16} = \\frac{13 \\times 8}{16 \\times 8} = \\frac{104}{128}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B112%7D%7B128%7D\" alt=\"\\small \\frac{112}{128}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B104%7D%7B128%7D\" alt=\"\\small \\frac{104}{128}\" \/>.<\/p>\n<p>Question 10.<br \/>\nWhich One Doesn\u2019t Belong? Which pair of fractions is not equivalent to \\(\\frac{2}{5}\\) and \\(\\frac{1}{10}\\)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-39.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 39\" width=\"243\" height=\"115\" \/><br \/>\nAnswer:<br \/>\nSo, <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B15%7D\" alt=\"\\small \\frac{5}{15}\" \/> is not equivalent to \\(\\frac{2}{5}\\) and \\(\\frac{1}{10}\\) and remaining all the pairs are equivalent.<\/p>\n<p>Question 11.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says she used a common denominator to \ufb01nd fractions equivalent to \\(\\frac{2}{3}\\) and \\(\\frac{8}{9}\\). Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-39.1.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 39.1\" width=\"161\" height=\"137\" \/><br \/>\nAnswer:<br \/>\nNo, she is wrong because 9 and 12 are not common denominators.<br \/>\n<strong>Step 1:<\/strong> Use the product of the denominators : 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 9 = 27<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with common denominator of 27.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%209%7D%7B3%20%5Ctimes%209%7D%20%3D%20%5Cfrac%7B18%7D%7B27%7D\" alt=\"\\small \\frac{2}{3} = \\frac{2 \\times 9}{3 \\times 9} = \\frac{18}{27}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B9%7D%20%3D%20%5Cfrac%7B8%20%5Ctimes%203%7D%7B9%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B24%7D%7B27%7D\" alt=\"\\small \\frac{8}{9} = \\frac{8 \\times 3}{9 \\times 3} = \\frac{24}{27}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B27%7D\" alt=\"\\small \\frac{18}{27}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B27%7D\" alt=\"\\small \\frac{24}{27}\" \/>.<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nSome friends spend \\(\\frac{1}{3}\\) hour collecting sticks and \\(\\frac{5}{6}\\) hour building a fort. Do they spend the same amount of time on each? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-40.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 40\" width=\"264\" height=\"116\" \/><br \/>\nAnswer:<br \/>\nNo, they can not spend the same time on each because <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> is not equivalent to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/>.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> is equivalent to <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/>.<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nUse a common denominator to write an equivalent fraction for each fraction. Which two students are the same distance from the school? Are they closer to or farther from the school than the other student?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-41.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 41\" width=\"346\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-41.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-41-300x189.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use the LCM of the denominators. LCM of 12, 8 and 6 = 24<br \/>\n<strong>Step 2:<\/strong> Write equivalent fractions with common denominator of 24.<br \/>\nStudent A &#8211;&gt;\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D%20%3D%20%5Cfrac%7B10%20%5Ctimes%202%7D%7B12%20%5Ctimes%202%7D%20%3D%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{10}{12} = \\frac{10 \\times 2}{12 \\times 2} = \\frac{20}{24}\" \/><br \/>\nStudent B &#8211;&gt;\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D%20%3D%20%5Cfrac%7B7%20%5Ctimes%203%7D%7B8%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B21%7D%7B24%7D\" alt=\"\\small \\frac{7}{8} = \\frac{7 \\times 3}{8 \\times 3} = \\frac{21}{24}\" \/><br \/>\nStudent C &#8211;&gt;\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%204%7D%7B6%20%5Ctimes%204%7D%20%3D%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{5}{6} = \\frac{5 \\times 4}{6 \\times 4} = \\frac{20}{24}\" \/><br \/>\nTherefore, student A and student C are the same distance from the school i.e. <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{20}{24}\" \/> mile.<br \/>\nThey are closer to student B.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the value of the expression.<\/p>\n<p>Question 14.<br \/>\n10<sup>2<br \/>\n<\/sup>Answer: 100<\/p>\n<p>Question 15.<br \/>\n8 \u00d7 10<sup>4<br \/>\n<\/sup>Answer: 80,000<\/p>\n<p>Question 16.<br \/>\n6 \u00d7 10<sup>3<br \/>\n<\/sup>Answer: 6000<\/p>\n<p>Question 17.<br \/>\n9 \u00d7 10<sup>5<br \/>\n<\/sup>Answer: 9,00,000<\/p>\n<h3><a id=\"Lesson_8.4_Add_Fractions_with_Unlike_Denominators\"><\/a>Lesson 8.4 Add Fractions with Unlike Denominators<\/h3>\n<p>Use a model to find the sum.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-16315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-42.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 42\" width=\"384\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-42.png 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-42-300x135.png 300w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/p>\n<p>Explain how you can use a model to add fifths and tenths.<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nHow can you add two fractions with unlike denominators without using a model? Explain why your method makes sense.<\/p>\n<p><strong>Think and Grow: Add Fractions with Unlike Denominators<\/strong><\/p>\n<p>You can use equivalent fractions to add fractions that have unlike denominators.<br \/>\n<strong>Example<\/strong><br \/>\nFind \\(\\frac{1}{4}\\) + \\(\\frac{3}{8}\\)<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 8 is a multiple of 4, so rewrite \\(\\frac{1}{4}\\) with a denominator of 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-43.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 43\" width=\"576\" height=\"165\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-43.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-43-300x86.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-39884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-43-300x86.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-43\" width=\"300\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-43-300x86.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-43.jpg 576w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\n<strong>Example<\/strong><br \/>\nFind \\(\\frac{7}{8}\\) + \\(\\frac{1}{6}\\) Estimate __<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 8 is not a multiple of 6, so rewrite each fraction with a denominator of 8 \u00d7 6 = 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-44.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 44\" width=\"606\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-44.png 606w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-44-300x120.png 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-39885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-44-300x120.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-44\" width=\"300\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-44-300x120.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-44.jpg 606w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Add.<\/p>\n<p>Question 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-45.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 45\" width=\"125\" height=\"52\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 6 is a multiple of 3, so rewrite it with a denominator of 6.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%202%7D%7B3%20%5Ctimes%202%7D\" alt=\"\\small \\frac{2 \\times 2}{3 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/>\u00a0 =\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B6%7D\" alt=\"\\small \\frac{9}{6}\" \/> or <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/><\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-46.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 46\" width=\"130\" height=\"67\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 5 is not a multiple of 4, so rewrite each fraction with a denominator of 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 4 = 20<\/p>\n<p>Rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B5%20%5Ctimes%204%7D\" alt=\"\\small \\frac{1 \\times 4}{5 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B20%7D\" alt=\"\\small \\frac{4}{20}\" \/>\u00a0 and\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%205%7D%7B4%20%5Ctimes%205%7D\" alt=\"\\small \\frac{3 \\times 5}{4 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{15}{20}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B20%7D\" alt=\"\\small \\frac{4}{20}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{15}{20}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B20%7D\" alt=\"\\small \\frac{19}{20}\" \/><\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-47.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 47\" width=\"116\" height=\"59\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 6 is not a multiple of 4, so rewrite each fraction with a denominator of 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 4 = 24<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B6%20%5Ctimes%204%7D\" alt=\"\\small \\frac{1 \\times 4}{6 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B24%7D\" alt=\"\\small \\frac{4}{24}\" \/>\u00a0 and\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%206%7D%7B4%20%5Ctimes%206%7D\" alt=\"\\small \\frac{1 \\times 6}{4 \\times 6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B24%7D\" alt=\"\\small \\frac{6}{24}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B24%7D\" alt=\"\\small \\frac{4}{24}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B24%7D\" alt=\"\\small \\frac{6}{24}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B24%7D\" alt=\"\\small \\frac{10}{24}\" \/> or <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/><\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Add.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-48.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 48\" width=\"122\" height=\"60\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 8 is a multiple of 4, so rewrite it with a denominator of 8.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B4%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{4 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B8%7D\" alt=\"\\small \\frac{2}{8}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B8%7D\" alt=\"\\small \\frac{2}{8}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/><\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-49.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 49\" width=\"131\" height=\"71\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 12 is a multiple of 3, so rewrite it with a denominator of 12.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%204%7D%7B3%20%5Ctimes%204%7D\" alt=\"\\small \\frac{2 \\times 4}{3 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> =\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B12%7D\" alt=\"\\small \\frac{15}{12}\" \/> or <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-50.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 50\" width=\"129\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 15 is a multiple of 5 , so rewrite it with a denominator of 15.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%203%7D%7B5%20%5Ctimes%203%7D\" alt=\"\\small \\frac{2 \\times 3}{5 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B15%7D\" alt=\"\\small \\frac{10}{15}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B15%7D\" alt=\"\\small \\frac{10}{15}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B15%7D\" alt=\"\\small \\frac{16}{15}\" \/><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-51.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 51\" width=\"120\" height=\"62\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 8 is not a multiple of 6, so rewrite each fraction with a denominator of 8 \u00d7 6 = 48.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%208%7D%7B6%20%5Ctimes%208%7D\" alt=\"\\small \\frac{1 \\times 8}{6 \\times 8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B48%7D\" alt=\"\\small \\frac{8}{48}\" \/>\u00a0 and\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%20%5Ctimes%206%7D%7B8%20%5Ctimes%206%7D\" alt=\"\\small \\frac{4 \\times 6}{8 \\times 6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B48%7D\" alt=\"\\small \\frac{24}{48}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B48%7D\" alt=\"\\small \\frac{8}{48}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B48%7D\" alt=\"\\small \\frac{24}{48}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B32%7D%7B48%7D\" alt=\"\\small \\frac{32}{48}\" \/> or <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-52.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 52\" width=\"120\" height=\"58\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 12 is not a multiple of 5, so rewrite each fraction with a denominator of 12 \u00d7 5 = 60.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%20%5Ctimes%205%7D%7B12%20%5Ctimes%205%7D\" alt=\"\\small \\frac{11 \\times 5}{12 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B55%7D%7B60%7D\" alt=\"\\small \\frac{55}{60}\" \/>\u00a0 and\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%2012%7D%7B5%20%5Ctimes%2012%7D\" alt=\"\\small \\frac{3 \\times 12}{5 \\times 12}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B36%7D%7B60%7D\" alt=\"\\small \\frac{36}{60}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B55%7D%7B60%7D\" alt=\"\\small \\frac{55}{60}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B36%7D%7B60%7D\" alt=\"\\small \\frac{36}{60}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B91%7D%7B60%7D\" alt=\"\\small \\frac{91}{60}\" \/><\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-53.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 53\" width=\"144\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 9 is a multiple of 3 , so rewrite it with a denominator of 9.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B3%7D\" alt=\"\\small \\frac{4}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%20%5Ctimes%203%7D%7B3%20%5Ctimes%203%7D\" alt=\"\\small \\frac{4 \\times 3}{3 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B9%7D\" alt=\"\\small \\frac{12}{9}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B9%7D\" alt=\"\\small \\frac{2}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B3%7D\" alt=\"\\small \\frac{4}{3}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B9%7D\" alt=\"\\small \\frac{5}{9}\" \/>\u00a0 =\u00a0 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B9%7D\" alt=\"\\small \\frac{2}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B9%7D\" alt=\"\\small \\frac{12}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B9%7D\" alt=\"\\small \\frac{5}{9}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B9%7D\" alt=\"\\small \\frac{19}{9}\" \/><\/p>\n<p>Question 10.<br \/>\nYour friend buys \\(\\frac{1}{8}\\) pound of green lentils and \\(\\frac{3}{4}\\) pound of brown lentils. What fraction of a pound of lentils does she buy?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-54.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 54\" width=\"208\" height=\"120\" \/><br \/>\nAnswer:<br \/>\nGiven that,<br \/>\npound of green lentils = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/><br \/>\nPound of brown lentils = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 8 is a multiple of 4, so rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> with a denominator of 8.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%202%7D%7B4%20%5Ctimes%202%7D\" alt=\"\\small \\frac{3 \\times 2}{4 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\nPound of lentils = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\nFraction of pound of lentils = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/><\/p>\n<p>Question 11.<br \/>\n<strong>Reasoning<\/strong><br \/>\nNewton and Descartes find \\(\\frac{1}{2}\\) + \\(\\frac{1}{6}\\). Newton says the sum is \\(\\frac{4}{6}\\). Descartes says the sum is \\(\\frac{2}{3}\\). Who is correct? Explain.<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><br \/>\nThink: 6 is a multiple of 2, so rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> with a denominator of 6.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%203%7D%7B2%20%5Ctimes%203%7D\" alt=\"\\small \\frac{1 \\times 3}{2 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/>\u00a0+ <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/> or <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/><br \/>\nTherefore, both Newton and Descartes answers are correct.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWrite two fractions that have a sum of 1 and have different denominators.<br \/>\nAnswer:<br \/>\n\\(\\frac{1}{2}\\) + \\(\\frac{3}{6}\\)<br \/>\n= \\(\\frac{1}{2}\\) \u00d7 \\(\\frac{3}{3}\\) + \\(\\frac{3}{6}\\)<br \/>\n= \\(\\frac{3}{6}\\) + \\(\\frac{3}{6}\\)<br \/>\n= \\(\\frac{6}{6}\\)<br \/>\n= 1<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nAbout \\(\\frac{17}{15}\\) of Earth\u2019s surface is covered by ocean water.<br \/>\nAbout \\(\\frac{3}{100}\\) of Earth\u2019s surface is covered by other water resources.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-55.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 55\" width=\"137\" height=\"140\" \/><br \/>\nAbout how much of Earth\u2019s surface is covered by water?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-56.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 56\" width=\"677\" height=\"345\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-56.png 677w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-56-300x153.png 300w\" sizes=\"(max-width: 677px) 100vw, 677px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-39886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-56-300x153.jpg\" alt=\"Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-56\" width=\"300\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-56-300x153.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-56.jpg 677w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nThe George Washington Bridge links Manhattan, NY, to FortLee, NJ. The part of the bridge in New Jersey is about \\(\\frac{1}{2}\\) mile long. The part in New York is about \\(\\frac{2}{5}\\) mile long. About how long is the George Washington Bridge?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-57.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 57\" width=\"241\" height=\"191\" \/><br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nNew Jersey bridge = \\(\\frac{1}{2}\\) mile long<br \/>\nNew York bridge = \\(\\frac{2}{5}\\) mile long<br \/>\nAdd <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> to find how long is the George Washington Bridge<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think:<\/strong> 5 is not a multiple of 2, so rewrite each fraction with a denominator of 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 2 = 10<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%205%7D%7B2%20%5Ctimes%205%7D\" alt=\"\\small \\frac{1 \\times 5}{2 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%202%7D%7B5%20%5Ctimes%202%7D\" alt=\"\\small \\frac{2 \\times 2}{5 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/>\u00a0 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/><br \/>\nSo, George Washington Bridge is about <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> mile long.<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYour goal is to practice playing the saxophone for at least 2 hours in 1 week. Do you reach your goal? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-58.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 58\" width=\"319\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-58.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-58-300x93.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/><br \/>\n<strong>Think:\u00a0<\/strong>Rewrite the denominators as 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 3 = 24<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%206%7D%7B4%20%5Ctimes%206%7D\" alt=\"\\small \\frac{3 \\times 6}{4 \\times 6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{18}{24}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%2012%7D%7B2%20%5Ctimes%2012%7D\" alt=\"\\small \\frac{1 \\times 12}{2 \\times 12}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B24%7D\" alt=\"\\small \\frac{12}{24}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%208%7D%7B3%20%5Ctimes%208%7D\" alt=\"\\small \\frac{2 \\times 8}{3 \\times 8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B24%7D\" alt=\"\\small \\frac{16}{24}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{18}{24}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B24%7D\" alt=\"\\small \\frac{12}{24}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B24%7D\" alt=\"\\small \\frac{16}{24}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B46%7D%7B24%7D\" alt=\"\\small \\frac{46}{24}\" \/> or <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B12%7D\" alt=\"\\small \\frac{23}{12}\" \/><br \/>\nTotal practice time in a week = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B12%7D\" alt=\"\\small \\frac{23}{12}\" \/> = 1.91 hours<br \/>\nSo, goal does not reached.<\/p>\n<h3><a id=\"Add_Fractions_with_Unlike_Denominators_Homework_&amp;_Practice_8.4\"><\/a>Add Fractions with Unlike Denominators Homework &amp; Practice 8.4<\/h3>\n<p>Add<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{1}{9}\\) + \\(\\frac{2}{3}\\) = ___<br \/>\nAnswer:<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/><br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think: <\/strong>9 is a multiple of 3, so rewrite it with a denominator of 9<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%203%7D%7B3%20%5Ctimes%203%7D\" alt=\"\\small \\frac{2 \\times 3}{3 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B9%7D\" alt=\"\\small \\frac{7}{9}\" \/><br \/>\n\\(\\frac{1}{9}\\) + \\(\\frac{2}{3}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B9%7D\" alt=\"\\small \\frac{7}{9}\" \/><\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{2}\\) + \\(\\frac{3}{4}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think: <\/strong>4 is a multiple of 2, so rewrite it with a denominator of 4<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B2%20%5Ctimes%202%7D%20%3D%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{1 \\times 2}{2 \\times 2} = \\frac{2}{4}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/><br \/>\n\\(\\frac{1}{2}\\) + \\(\\frac{3}{4}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{4}{6}\\) + \\(\\frac{5}{12}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think: <\/strong>12 is a multiple of 6, so rewrite it with a denominator of 12<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%20%5Ctimes%202%7D%7B6%20%5Ctimes%202%7D\" alt=\"\\small \\frac{4 \\times 2}{6 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B12%7D\" alt=\"\\small \\frac{13}{12}\" \/><br \/>\n\\(\\frac{4}{6}\\) + \\(\\frac{5}{12}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B12%7D\" alt=\"\\small \\frac{13}{12}\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{1}{3}\\) + \\(\\frac{1}{4}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think:<\/strong> 4 is not a multiple of 3, so rewrite each fraction with a denominator of 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 3 = 12<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B3%20%5Ctimes%204%7D\" alt=\"\\small \\frac{1 \\times 4}{3 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%203%7D%7B4%20%5Ctimes%203%7D\" alt=\"\\small \\frac{1 \\times 3}{4 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/>\u00a0 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/><br \/>\n\\(\\frac{1}{3}\\) + \\(\\frac{1}{4}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{3}{2}\\) + \\(\\frac{4}{5}\\) = __<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think:<\/strong> 5 is not a multiple of 2, so rewrite each fraction with a denominator of 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 2 = 10<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%205%7D%7B2%20%5Ctimes%205%7D\" alt=\"\\small \\frac{3 \\times 5}{2 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B10%7D\" alt=\"\\small \\frac{15}{10}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%20%5Ctimes%202%7D%7B5%20%5Ctimes%202%7D\" alt=\"\\small \\frac{4 \\times 2}{5 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B10%7D\" alt=\"\\small \\frac{8}{10}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/>\u00a0 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B10%7D\" alt=\"\\small \\frac{15}{10}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B10%7D\" alt=\"\\small \\frac{8}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B10%7D\" alt=\"\\small \\frac{23}{10}\" \/><br \/>\n\\(\\frac{3}{2}\\) + \\(\\frac{4}{5}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B10%7D\" alt=\"\\small \\frac{23}{10}\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{6}{8}\\) + \\(\\frac{9}{10}\\) + \\(\\frac{1}{8}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think:<\/strong> 10 is not a multiple of 8, so rewrite each fraction with a denominator of 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 8 = 80<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%20%5Ctimes%2010%7D%7B8%20%5Ctimes%2010%7D\" alt=\"\\small \\frac{6 \\times 10}{8 \\times 10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B60%7D%7B80%7D\" alt=\"\\small \\frac{60}{80}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%20%5Ctimes%208%7D%7B10%20%5Ctimes%208%7D\" alt=\"\\small \\frac{9 \\times 8}{10 \\times 8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B72%7D%7B80%7D\" alt=\"\\small \\frac{72}{80}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%2010%7D%7B8%20%5Ctimes%2010%7D\" alt=\"\\small \\frac{1 \\times 10}{8 \\times 10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B80%7D\" alt=\"\\small \\frac{10}{80}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/>\u00a0= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B60%7D%7B80%7D\" alt=\"\\small \\frac{60}{80}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B72%7D%7B80%7D\" alt=\"\\small \\frac{72}{80}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B80%7D\" alt=\"\\small \\frac{10}{80}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B142%7D%7B80%7D\" alt=\"\\small \\frac{142}{80}\" \/><br \/>\n\\(\\frac{6}{8}\\) + \\(\\frac{9}{10}\\) + \\(\\frac{1}{8}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B142%7D%7B80%7D\" alt=\"\\small \\frac{142}{80}\" \/><\/p>\n<p>Question 7.<br \/>\nYou use beads to make a design. Of the beads, \\(\\frac{1}{3}\\) are red and \\(\\frac{1}{6}\\) are blue. The rest are white.What fraction of the beads are red or blue?<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think:<\/strong> 6 is a multiple of 3, so rewrite it with a denominator of 6<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B3%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{3 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/><br \/>\nThe fraction of beads are red or blue = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><br \/>\nRest are white = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><\/p>\n<p>Question 8.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says the sum of \\(\\frac{1}{5}\\) and \\(\\frac{9}{10}\\) is \\(\\frac{10}{15}\\). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think:<\/strong> 10 is a multiple of 5, so rewrite it with a denominator of 10<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B5%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{5 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B10%7D\" alt=\"\\small \\frac{2}{10}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B10%7D\" alt=\"\\small \\frac{2}{10}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B10%7D\" alt=\"\\small \\frac{11}{10}\" \/><br \/>\nTherefore, the sum of \\(\\frac{1}{5}\\) and \\(\\frac{9}{10}\\) is <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B10%7D\" alt=\"\\small \\frac{11}{10}\" \/>.<br \/>\nSo, my friend answer is wrong.<\/p>\n<p>Question 9.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWhich expressions are equal to \\(\\frac{14}{15}\\)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-8-Add-and-Subtract-Fractions-59.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 8 Add and Subtract Fractions 59\" width=\"220\" height=\"109\" \/><br \/>\nAnswer:<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B15%7D\" alt=\"\\small \\frac{11}{15}\" \/> are equal to \\(\\frac{14}{15}\\) and these two expressions only having denominator of 15.<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThere are 100 senators in the 115th Congress. Democrats make up of the senators, and Republicans make up \\(\\frac{13}{25}\\) of the 25 senators. The rest are Independents. What fraction of the senators are Democrat or Republican?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nThere are 100 senators in the 115th Congress.<br \/>\nDemocrats make up of the senators, and Republicans make up \\(\\frac{13}{25}\\) of the 25 senators.<br \/>\n\\(\\frac{100}{115}\\) + \\(\\frac{13}{25}\\)<br \/>\n= \\(\\frac{100}{115}\\) \u00d7 \\(\\frac{5}{5}\\) + \\(\\frac{13}{25}\\) \u00d7 \\(\\frac{23}{23}\\)<br \/>\n= \\(\\frac{799}{575}\\)<br \/>\n= 1 \\(\\frac{224}{575}\\)<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour friend needs 1 cup of homemade orange juice. He squeezes \\(\\frac{1}{2}\\) cup of orange juice from one orange and \\(\\frac{3}{8}\\) cup from another orange. Does your friend need to squeeze another orange? Explain.<br \/>\nAnswer:<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/><br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think:<\/strong> 8 is a multiple of 2, so rewrite it with a denominator of 8<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B2%20%5Ctimes%204%7D\" alt=\"\\small \\frac{1 \\times 4}{2 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/><br \/>\nJuice from 2 oranges = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/><br \/>\nMy friend needs 1 cup of orange juice = 1 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/><br \/>\nSo, my friend needs to squeeze <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> cup from another orange.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nOf all the atoms in caffeine, \\(\\frac{1}{12}\\) are oxygen atoms, \\(\\frac{1}{6}\\) are nitrogen atoms, and \\(\\frac{1}{3}\\) are carbon atoms. The rest of the atoms are hydrogen. What fraction of the atoms in caffeine are oxygen, nitrogen, or hydrogen?<br \/>\nAnswer:<br \/>\nFrom the given information, hydrogen atoms = 1- (<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/>) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> = ?<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\n<strong>Think:<\/strong> 12 is a multiple of 6, so rewrite it with a denominator of 12<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B6%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{6 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B12%7D\" alt=\"\\small \\frac{2}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B12%7D\" alt=\"\\small \\frac{2}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/><br \/>\nSo <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> of the atoms in caffeine are oxygen, nitrogen, or hydrogen.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Use properties to find the sum or product.<\/p>\n<p>Question 13.<br \/>\n5 \u00d7 84<br \/>\nAnswer: 420<\/p>\n<p>Explanation:<br \/>\nWe can find the product by using the distributive property.<br \/>\n5 \u00d7 84 = 5 \u00d7 (80 + 4)<br \/>\n= (5 \u00d7 80) + (5 \u00d7 4)<br \/>\n= 400 + 20<br \/>\n= 420<\/p>\n<p>Question 14.<br \/>\n521 + 0 + 67<br \/>\nAnswer: 588<\/p>\n<p>Explanation:<br \/>\nWe can find the sum of the given expression using the additive identity.<br \/>\n521 + 0 + 67 = 521 + 67<br \/>\n= 588<\/p>\n<p>Question 15.<br \/>\n25 \u00d7 8 \u00d7 4<br \/>\nAnswer: 800<\/p>\n<p>Explanation:<br \/>\n25 \u00d7 8 \u00d7 4<br \/>\n= 25 \u00d7 32<br \/>\n= 800<\/p>\n<h3><a id=\"Lesson_8.5_Subtract_Fractions_with_Unlike_Denominators\"><\/a>Lesson 8.5 Subtract Fractions with Unlike Denominators<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use a model to find the difference.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16249\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-60.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 60\" width=\"323\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-60.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-60-300x150.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nExplain how you can use a model to subtract fourths from twelfths.<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nHow can you subtract two fractions with unlike denominators without using a model? Explain why your method makes sense.<\/p>\n<p><strong>Think and Grow: Subtract Fractions with Unlike Denominators<\/strong><\/p>\n<p>You can use equivalent fractions to subtract fractions that have unlike denominators.<br \/>\n<strong>Example<\/strong><br \/>\nFind \\(\\frac{9}{10}\\) &#8211; \\(\\frac{1}{2}\\).<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 10 is a multiple of 2, so rewrite \\(\\frac{1}{2}\\) with a denominator of 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16250\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-61.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 61\" width=\"618\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-61.png 618w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-61-300x84.png 300w\" sizes=\"(max-width: 618px) 100vw, 618px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-40476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-61-300x84.jpg\" alt=\"Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-61\" width=\"300\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-61-300x84.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-61.jpg 618w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nFind \\(\\frac{4}{3}\\) &#8211; \\(\\frac{1}{4}\\). Estimate _____<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 4 is not a multiple of 3, so rewrite each fraction with a denominator of 3 \u00d7 4 = 12.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Subtract.<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{1}{2}\\) &#8211; \\(\\frac{1}{4}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think: <\/strong>4 is a multiple of 2, so rewrite \\(\\frac{1}{2}\\) with a denominator of 4.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B2%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{2 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/><br \/>\n= \\(\\frac{1}{4}\\)<br \/>\n\\(\\frac{1}{2}\\) &#8211; \\(\\frac{1}{4}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{7}{9}\\) &#8211; \\(\\frac{2}{3}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 9 is a multiple of 3, so rewrite \\(\\frac{2}{3}\\) with a denominator of 9.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%203%7D%7B3%20%5Ctimes%203%7D\" alt=\"\\small \\frac{2 \\times 3}{3 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B9%7D\" alt=\"\\small \\frac{7}{9}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B9%7D\" alt=\"\\small \\frac{7}{9}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/><br \/>\n\\(\\frac{7}{9}\\) &#8211; \\(\\frac{2}{3}\\) = \\(\\frac{1}{9}\\)<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{6}{5}\\) &#8211; \\(\\frac{3}{8}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 8 is not a multiple of 5, so rewrite each fraction with a denominator of 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 8 = 40<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B5%7D\" alt=\"\\small \\frac{6}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%20%5Ctimes%208%7D%7B5%20%5Ctimes%208%7D\" alt=\"\\small \\frac{6 \\times 8}{5 \\times 8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B48%7D%7B40%7D\" alt=\"\\small \\frac{48}{40}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%205%7D%7B8%20%5Ctimes%205%7D\" alt=\"\\small \\frac{3 \\times 5}{8 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B40%7D\" alt=\"\\small \\frac{15}{40}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B5%7D\" alt=\"\\small \\frac{6}{5}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B48%7D%7B40%7D\" alt=\"\\small \\frac{48}{40}\" \/>\u00a0&#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B40%7D\" alt=\"\\small \\frac{15}{40}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B33%7D%7B40%7D\" alt=\"\\small \\frac{33}{40}\" \/><br \/>\n\\(\\frac{6}{5}\\) &#8211; \\(\\frac{3}{8}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B33%7D%7B40%7D\" alt=\"\\small \\frac{33}{40}\" \/><\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Subtract.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{10}{12}\\) &#8211; \\(\\frac{3}{4}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 12 is a multiple of 4, so rewrite \\(\\frac{3}{4}\\) with a denominator of 12.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%203%7D%7B4%20%5Ctimes%203%7D\" alt=\"\\small \\frac{3 \\times 3}{4 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><br \/>\n=<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/><br \/>\n\\(\\frac{10}{12}\\) &#8211; \\(\\frac{3}{4}\\) = \\(\\frac{1}{12}\\)<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{1}{3}\\) &#8211; \\(\\frac{1}{6}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 6 is a multiple of 3, so rewrite \\(\\frac{1}{3}\\) with a denominator of 6.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B3%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{3 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><br \/>\n\\(\\frac{1}{3}\\) &#8211; \\(\\frac{1}{6}\\) = \\(\\frac{1}{6}\\)<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{9}{10}\\) &#8211; \\(\\frac{2}{5}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 10 is a multiple of 5, so rewrite \\(\\frac{2}{5}\\) with a denominator of 10.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/>\u00a0as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%202%7D%7B5%20%5Ctimes%202%7D\" alt=\"\\small \\frac{2 \\times 2}{5 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/> or <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><br \/>\n\\(\\frac{9}{10}\\) &#8211; \\(\\frac{2}{5}\\) = \\(\\frac{1}{2}\\)<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{5}{4}\\) &#8211; \\(\\frac{2}{5}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 5 is not a multiple of 4, so rewrite each fraction with a denominator of 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 5 = 20<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%20%5Ctimes%205%7D%7B4%20%5Ctimes%205%7D\" alt=\"\\small \\frac{5 \\times 5}{4 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B25%7D%7B20%7D\" alt=\"\\small \\frac{25}{20}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%204%7D%7B5%20%5Ctimes%204%7D\" alt=\"\\small \\frac{2 \\times 4}{5 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B20%7D\" alt=\"\\small \\frac{8}{20}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B25%7D%7B20%7D\" alt=\"\\small \\frac{25}{20}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B20%7D\" alt=\"\\small \\frac{8}{20}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B20%7D\" alt=\"\\small \\frac{17}{20}\" \/><br \/>\n\\(\\frac{5}{4}\\) &#8211; \\(\\frac{2}{5}\\) = \\(\\frac{17}{20}\\)<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{13}{16}\\) &#8211; \\(\\frac{3}{16}\\) &#8211; \\(\\frac{5}{8}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 16 is a multiple of 8, so rewrite \\(\\frac{5}{8}\\) with a denominator of 16.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%20%5Ctimes%202%7D%7B8%20%5Ctimes%202%7D\" alt=\"\\small \\frac{5 \\times 2}{8 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B16%7D\" alt=\"\\small \\frac{10}{16}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B16%7D\" alt=\"\\small \\frac{13}{16}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B16%7D\" alt=\"\\small \\frac{3}{16}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B16%7D\" alt=\"\\small \\frac{10}{16}\" \/> = 0<br \/>\n\\(\\frac{13}{16}\\) &#8211; \\(\\frac{3}{16}\\) &#8211; \\(\\frac{5}{8}\\) = 0<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{8}{9}\\) &#8211; (\\(\\frac{2}{3}\\) + \\(\\frac{1}{6}\\)) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator.<br \/>\ncommon denominator for 9, 3 and 6 = 18<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B9%7D\" alt=\"\\small \\frac{8}{9}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B18%7D\" alt=\"\\small \\frac{16}{18}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B18%7D\" alt=\"\\small \\frac{12}{18}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B18%7D\" alt=\"\\small \\frac{3}{18}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B9%7D\" alt=\"\\small \\frac{8}{9}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B18%7D\" alt=\"\\small \\frac{16}{18}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B18%7D\" alt=\"\\small \\frac{12}{18}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B18%7D\" alt=\"\\small \\frac{3}{18}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B18%7D\" alt=\"\\small \\frac{1}{18}\" \/><br \/>\n\\(\\frac{8}{9}\\) &#8211; (\\(\\frac{2}{3}\\) + \\(\\frac{1}{6}\\)) = \\(\\frac{1}{18}\\)<\/p>\n<p>Question 10.<br \/>\nYou have \\(\\frac{1}{3}\\) yard of wire. You use \\(\\frac{1}{3}\\) yard to make an electric circuit. How much wire do you have left?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16252\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-63.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 63\" width=\"233\" height=\"128\" \/><br \/>\nAnswer: Left with 0 wire<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 0<\/p>\n<p>Question 11.<br \/>\nYour friend finds \\(\\frac{5}{8}\\) &#8211; \\(\\frac{2}{5}\\). Explain why his answer is unreasonable. What did he do wrong?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16253\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-64.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 64\" width=\"137\" height=\"56\" \/><br \/>\nAnswer: For subtracting two fractions, the denominators must be same. Here, denominators are different.<br \/>\nSo, the answer is wrong<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 8 is not a multiple of 5, so rewrite each fraction with a denominator of 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 5 = 40<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%20%5Ctimes%205%7D%7B8%20%5Ctimes%205%7D\" alt=\"\\small \\frac{5 \\times 5}{8 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B25%7D%7B40%7D\" alt=\"\\small \\frac{25}{40}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%208%7D%7B5%20%5Ctimes%208%7D\" alt=\"\\small \\frac{2 \\times 8}{5 \\times 8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B40%7D\" alt=\"\\small \\frac{16}{40}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B25%7D%7B40%7D\" alt=\"\\small \\frac{25}{40}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B40%7D\" alt=\"\\small \\frac{16}{40}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B40%7D\" alt=\"\\small \\frac{9}{40}\" \/><br \/>\n\\(\\frac{5}{8}\\) &#8211; \\(\\frac{2}{5}\\) = \\(\\frac{9}{40}\\)<\/p>\n<p>Question 12.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich two fractions have a difference of \\(\\frac{1}{8}\\) ?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16254\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-65.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 65\" width=\"238\" height=\"51\" \/><br \/>\nAnswer:<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/><br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 8 is a multiple of 2, so rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> with a denominator of 8.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B2%20%5Ctimes%204%7D\" alt=\"\\small \\frac{1 \\times 4}{2 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/><br \/>\nSo, fractions <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> have the difference of <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/>.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA geologist needs \\(\\frac{1}{2}\\) cup of volcanic sand to perform an experiment. She has \\(\\frac{3}{2}\\) cups of quartz sand. She has \\(\\frac{2}{3}\\) cup more quartz sand than volcanic sand. Can she perform the experiment?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16255\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-66.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 66\" width=\"206\" height=\"121\" \/><br \/>\nFind how many cups of volcanic sand the geologist has by subtracting \\(\\frac{2}{3}\\) from \\(\\frac{3}{2}\\).<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 3 is not a multiple of 2, so rewrite each fraction with a denominator 2 \u00d7 3 = 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16256\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-67.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 67\" width=\"603\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-67.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-67-300x137.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-40479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-67-300x137.jpg\" alt=\"Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-67\" width=\"300\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-67-300x137.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-67.jpg 603w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nThe world record for the longest dog tail is \\(\\frac{77}{100}\\) meter. The previous record was \\(\\frac{1}{20}\\) meter. shorter than the current record. Was the previous record longer than \\(\\frac{3}{4}\\) meter?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16257\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-68.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 68\" width=\"176\" height=\"122\" \/><br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nWorld record for the longest dog tail is <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B77%7D%7B100%7D\" alt=\"\\small \\frac{77}{100}\" \/> meter.<br \/>\nPrevious record was <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B20%7D\" alt=\"\\small \\frac{1}{20}\" \/> meter shorter than the current record<br \/>\nSo subtract <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B20%7D\" alt=\"\\small \\frac{1}{20}\" \/> meter from the current record\u00a0to find previous record.<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B20%7D\" alt=\"\\small \\frac{1}{20}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B100%7D\" alt=\"\\small \\frac{5}{100}\" \/><br \/>\nPrevious record = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B77%7D%7B100%7D\" alt=\"\\small \\frac{77}{100}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B100%7D\" alt=\"\\small \\frac{5}{100}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B72%7D%7B100%7D\" alt=\"\\small \\frac{72}{100}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B25%7D\" alt=\"\\small \\frac{18}{25}\" \/> meter<br \/>\nSo the previous record is not longer than <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> meter.<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA woodworker has 1 gallon of paint for a tree house. He uses \\(\\frac{3}{8}\\) gallon to paint the walls and \\(\\frac{1}{5}\\) gallon to paint the ladder. He needs \\(\\frac{1}{4}\\) gallon to paint the roof. Does he have enough paint? Explain.<br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nWoodworker has 1 gallon of paint<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> gallon is used to paint the walls.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> gallon is used to paint the ladder.<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B40%7D\" alt=\"\\small \\frac{15}{40}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B40%7D\" alt=\"\\small \\frac{8}{40}\" \/><br \/>\n1 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B40%7D\" alt=\"\\small \\frac{15}{40}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B40%7D\" alt=\"\\small \\frac{8}{40}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B40%7D\" alt=\"\\small \\frac{17}{40}\" \/><br \/>\nTherefore, he has more than <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> gallon to paint the roof.<\/p>\n<h3><a id=\"Subtract_Fractions_with_Unlike_Denominators_Homework_&amp;_Practice_8.5\"><\/a>Subtract Fractions with Unlike Denominators Homework &amp; Practice 8.5<\/h3>\n<p>Subtract<\/p>\n<p>Question 1.<br \/>\n\\(\\frac{3}{4}\\) &#8211; \\(\\frac{1}{8}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 8 is a multiple of 4, so rewrite \\(\\frac{3}{4}\\) with a denominator of 8<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%202%7D%7B4%20%5Ctimes%202%7D\" alt=\"\\small \\frac{3 \\times 2}{4 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/><br \/>\n\\(\\frac{3}{4}\\) &#8211; \\(\\frac{1}{8}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/><\/p>\n<p>Question 2.<br \/>\n\\(\\frac{4}{5}\\) &#8211; \\(\\frac{6}{15}\\) = __<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 15 is a multiple of 5, so rewrite \\(\\frac{4}{5}\\) with a denominator of 15<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%20%5Ctimes%203%7D%7B5%20%5Ctimes%203%7D\" alt=\"\\small \\frac{4 \\times 3}{5 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B15%7D\" alt=\"\\small \\frac{12}{15}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B15%7D\" alt=\"\\small \\frac{12}{15}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/><br \/>\n\\(\\frac{4}{5}\\) &#8211; \\(\\frac{6}{15}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{2}\\) &#8211; \\(\\frac{1}{8}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 8 is a multiple of 2, so rewrite \\(\\frac{1}{2}\\) with a denominator of 8<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B2%20%5Ctimes%204%7D\" alt=\"\\small \\frac{1 \\times 4}{2 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/><br \/>\n\\(\\frac{1}{2}\\) &#8211; \\(\\frac{1}{8}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/><\/p>\n<p>Question 4.<br \/>\n\\(\\frac{5}{3}\\) &#8211; \\(\\frac{3}{4}\\) = _____<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 4 is not a multiple of 3, so rewrite each fraction with a denominator of 4 x 3 =12<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B3%7D\" alt=\"\\small \\frac{5}{3}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%20%5Ctimes%204%7D%7B3%20%5Ctimes%204%7D\" alt=\"\\small \\frac{5 \\times 4}{3 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B12%7D\" alt=\"\\small \\frac{20}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%203%7D%7B4%20%5Ctimes%203%7D\" alt=\"\\small \\frac{3 \\times 3}{4 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B3%7D\" alt=\"\\small \\frac{5}{3}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B12%7D\" alt=\"\\small \\frac{20}{12}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/><br \/>\n\\(\\frac{5}{3}\\) &#8211; \\(\\frac{3}{4}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/><\/p>\n<p>Question 5.<br \/>\n\\(\\frac{6}{8}\\) &#8211; \\(\\frac{7}{10}\\) = _____<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 10 is not a multiple of 8, so rewrite each fraction with a denominator of 10 x 8 =80<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%20%5Ctimes%2010%7D%7B8%20%5Ctimes%2010%7D\" alt=\"\\small \\frac{6 \\times 10}{8 \\times 10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B60%7D%7B80%7D\" alt=\"\\small \\frac{60}{80}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%20%5Ctimes%208%7D%7B10%20%5Ctimes%208%7D\" alt=\"\\small \\frac{7 \\times 8}{10 \\times 8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B56%7D%7B80%7D\" alt=\"\\small \\frac{56}{80}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B60%7D%7B80%7D\" alt=\"\\small \\frac{60}{80}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B56%7D%7B80%7D\" alt=\"\\small \\frac{56}{80}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B80%7D\" alt=\"\\small \\frac{4}{80}\" \/><br \/>\n\\(\\frac{6}{8}\\) &#8211; \\(\\frac{7}{10}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B80%7D\" alt=\"\\small \\frac{4}{80}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B20%7D\" alt=\"\\small \\frac{1}{20}\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{5}{6}\\) &#8211; \\(\\frac{1}{4}\\) &#8211; \\(\\frac{3}{12}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 12 is a multiple of 4 and 6, so rewrite each fraction with a denominator of 12<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%20%5Ctimes%202%7D%7B6%20%5Ctimes%202%7D\" alt=\"\\small \\frac{5 \\times 2}{6 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%203%7D%7B4%20%5Ctimes%203%7D\" alt=\"\\small \\frac{1 \\times 3}{4 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/><br \/>\n\\(\\frac{5}{6}\\) &#8211; \\(\\frac{1}{4}\\) &#8211; \\(\\frac{3}{12}\\) = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/><\/p>\n<p>Question 7.<br \/>\nYou eat \\(\\frac{1}{12}\\) of a vegetable casserole. Your friend eats \\(\\frac{1}{6}\\) of the same casserole. How much more does your friend eat than you?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16258\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-69.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 69\" width=\"174\" height=\"125\" \/><br \/>\nAnswer:<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/><br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 12 is a multiple of 6, so rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> with a denominator of 12<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B6%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{6 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B12%7D\" alt=\"\\small \\frac{2}{12}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B12%7D\" alt=\"\\small \\frac{2}{12}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/><br \/>\nSo, my friend eats <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/> of a vegetable casserole than me.<\/p>\n<p>Question 8.<br \/>\n<strong>Writing<\/strong><br \/>\nWhy do fractions need a common denominator before you can add or subtract them?<br \/>\nAnswer:<br \/>\nIn order to add fractions, the fractions must have a common denominator. We need the pieces of each fraction to be the same size to combine them together. These two fractions have the same denominator, so the equal parts that the whole has been split into are the same size.<\/p>\n<p>Question 9.<br \/>\n<strong>Logic<\/strong><br \/>\nFind a.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16259\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-70.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 70\" width=\"106\" height=\"54\" \/><br \/>\nAnswer:<br \/>\na = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 10 is a multiple of 2, so rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> with a denominator of 10<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%205%7D%7B2%20%5Ctimes%205%7D\" alt=\"\\small \\frac{1 \\times 5}{2 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/><br \/>\na = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/><br \/>\na = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B10%7D\" alt=\"\\small \\frac{2}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/><\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWrite and solve an equation to find the difference between Length A and Length B on the ruler.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16260\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-71.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 71\" width=\"198\" height=\"138\" \/><br \/>\nAnswer:<br \/>\n\\(\\frac{1}{10}\\) \u00d7 \\(\\frac{2}{2}\\) = \\(\\frac{2}{20}\\)<br \/>\n\\(\\frac{9}{10}\\) \u00d7 \\(\\frac{2}{2}\\) = \\(\\frac{18}{20}\\)<br \/>\n\\(\\frac{18}{20}\\) &#8211; \\(\\frac{2}{20}\\) = \\(\\frac{16}{20}\\)<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou want to stack cups in \\(\\frac{1}{4}\\) minute. Your first attempt takes \\(\\frac{1}{2}\\) minute. Your second attempt takes \\(\\frac{3}{10}\\) minute less than your first attempt. Do you meet your goal?<br \/>\nAnswer:<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/><br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 10 is a multiple of 2, so rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> with a denominator of 10<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%205%7D%7B2%20%5Ctimes%205%7D\" alt=\"\\small \\frac{1 \\times 5}{2 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B10%7D\" alt=\"\\small \\frac{2}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/><br \/>\nSo my second attempt takes <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> minute and I did not meet my goal.<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou and your friend each have a canvas of the same size. You divide your canvas into 5 sections and paint 3 of them. Your friend divides her canvas into 7 sections and paints 4 of them. Who paints more? How much more?<br \/>\nAnswer:<br \/>\nMy canvas = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/><br \/>\nMy friend canvas = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B7%7D\" alt=\"\\small \\frac{4}{7}\" \/><br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\n<strong>Think:<\/strong> 7 is a multiple of 5, so rewrite both with a denominator of 7 x 5 = 35<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%207%7D%7B5%20%5Ctimes%207%7D\" alt=\"\\small \\frac{3 \\times 7}{5 \\times 7}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B21%7D%7B35%7D\" alt=\"\\small \\frac{21}{35}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B7%7D\" alt=\"\\small \\frac{4}{7}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%20%5Ctimes%205%7D%7B7%20%5Ctimes%205%7D\" alt=\"\\small \\frac{4 \\times 5}{7 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B35%7D\" alt=\"\\small \\frac{20}{35}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B7%7D\" alt=\"\\small \\frac{4}{7}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B21%7D%7B35%7D\" alt=\"\\small \\frac{21}{35}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B35%7D\" alt=\"\\small \\frac{20}{35}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B35%7D\" alt=\"\\small \\frac{1}{35}\" \/><br \/>\nI paint <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B35%7D\" alt=\"\\small \\frac{1}{35}\" \/> more canvas than my friend.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Evaluate. Check whether your answer is reasonable.<\/p>\n<p>Question 13.<br \/>\n1.7 + 5 + 4.3 = ___<br \/>\nAnswer: 11<\/p>\n<p>Question 14.<br \/>\n15.24 + 6.13 &#8211; 7 = ___<br \/>\nAnswer: 14.37<\/p>\n<h3><a id=\"Lesson_8.6_Add_Mixed_Numbers\"><\/a>Lesson 8.6 Add Mixed Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use a model to find the sum.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16261\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-72.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 72\" width=\"78\" height=\"52\" \/><\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nHow can you add mixed numbers with unlike denominators without using a model? Explain why your method makes sense.<\/p>\n<p><strong>Think and Grow: Add Mixed Numbers<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nA proper fraction is a fraction less than 1. An improper fraction is a fraction greater than 1. A mixed number represents the sum of a whole number and a proper fraction. You can use equivalent fractions to add mixed numbers.<br \/>\n<strong>Example<\/strong><br \/>\nFind 1\\(\\frac{1}{2}\\) + 2\\(\\frac{5}{6}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16262\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-73.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 73\" width=\"689\" height=\"462\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-73.png 689w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-73-300x201.png 300w\" sizes=\"(max-width: 689px) 100vw, 689px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Add.<\/p>\n<p>Question 1.<br \/>\n2\\(\\frac{2}{3}\\) + 2\\(\\frac{1}{6}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/>\u00a0 = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/>\u00a0 = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/>\u00a0 + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/><\/p>\n<p>Question 2.<br \/>\n1\\(\\frac{5}{12}\\) + 3\\(\\frac{3}{4}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B12%7D\" alt=\"\\small \\frac{14}{12}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B6%7D\" alt=\"\\small \\frac{7}{6}\" \/><\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Add.<\/p>\n<p>Question 3.<br \/>\n5\\(\\frac{4}{9}\\) + 1\\(\\frac{2}{3}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B9%7D\" alt=\"\\small \\frac{4}{9}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B9%7D\" alt=\"\\small \\frac{4}{9}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B9%7D\" alt=\"\\small \\frac{4}{9}\" \/> + 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B9%7D\" alt=\"\\small \\frac{10}{9}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B64%7D%7B9%7D\" alt=\"\\small \\frac{64}{9}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/><\/p>\n<p>Question 4.<br \/>\n3\\(\\frac{1}{2}\\) + \\(\\frac{5}{12}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B12%7D\" alt=\"\\small \\frac{6}{12}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B12%7D\" alt=\"\\small \\frac{6}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/><br \/>\n= 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/><\/p>\n<p>Question 5.<br \/>\n4\\(\\frac{5}{6}\\) + 3\\(\\frac{5}{12}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B12%7D\" alt=\"\\small \\frac{15}{12}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B99%7D%7B12%7D\" alt=\"\\small \\frac{99}{12}\" \/> = 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\frac{4}{5}\\) + 8\\(\\frac{7}{20}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B20%7D\" alt=\"\\small \\frac{16}{20}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> + 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B20%7D\" alt=\"\\small \\frac{16}{20}\" \/> + 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/><br \/>\n= 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B20%7D\" alt=\"\\small \\frac{23}{20}\" \/><\/p>\n<p>Question 7.<br \/>\n2\\(\\frac{1}{3}\\) + \\(\\frac{1}{6}\\) + 3\\(\\frac{2}{3}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><br \/>\n= 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B6%7D\" alt=\"\\small \\frac{7}{6}\" \/><\/p>\n<p>Question 8.<br \/>\n5\\(\\frac{1}{2}\\) + 4\\(\\frac{3}{4}\\) + 6\\(\\frac{5}{8}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/>\u00a0 + 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> + 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/><br \/>\n= 15 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B8%7D\" alt=\"\\small \\frac{15}{8}\" \/><\/p>\n<p>Question 9.<br \/>\nYour science class makes magic milk using 1\\(\\frac{1}{8}\\) cups of watercolor paint and 1\\(\\frac{3}{4}\\) cups of milk. How many cups of magic milk does your class make?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16263\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-74.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 74\" width=\"207\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nGiven data,<br \/>\nWatercolor paint = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> cups<br \/>\nMilk = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> cups<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> + 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B8%7D\" alt=\"\\small \\frac{23}{8}\" \/><br \/>\nSo the class makes 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> cups of magic milk<\/p>\n<p>Question 10.<br \/>\n<strong>Structure<\/strong><br \/>\nFind 2\\(\\frac{3}{10}\\) + 4\\(\\frac{2}{5}\\) two different ways.<br \/>\nAnswer:<br \/>\n<strong>Method 1:<br \/>\n<\/strong>Add the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/><br \/>\n= 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/><br \/>\n<strong>Method 2:<br \/>\n<\/strong>Write the mixed numbers as improper fractions with a common denominator and then add.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = 2 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B10%7D\" alt=\"\\small \\frac{20}{10}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B10%7D\" alt=\"\\small \\frac{23}{10}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = 4 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B22%7D%7B5%7D\" alt=\"\\small \\frac{22}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B44%7D%7B10%7D\" alt=\"\\small \\frac{44}{10}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B10%7D\" alt=\"\\small \\frac{23}{10}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B44%7D%7B10%7D\" alt=\"\\small \\frac{44}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B67%7D%7B10%7D\" alt=\"\\small \\frac{67}{10}\" \/><br \/>\n= 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/><\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nFind the missing numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16264\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-75.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 75\" width=\"146\" height=\"57\" \/><br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\nRewrite 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/>\u00a0 as 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\nwe can write 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B35%7D%7B8%7D\" alt=\"\\small \\frac{35}{8}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B8%7D\" alt=\"\\small \\frac{11}{8}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> + 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B8%7D\" alt=\"\\small \\frac{11}{8}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/><br \/>\nSo the missing numbers are 1 and 5.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> + 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/><\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou kayak 1\\(\\frac{8}{10}\\) miles and then take a break. You kayak 1\\(\\frac{1}{4}\\) more miles. How many miles do you kayak altogether?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16265\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-76.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 76\" width=\"273\" height=\"148\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16266\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-77.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 77\" width=\"586\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-77.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-77-300x153.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-40491\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-77-300x153.jpg\" alt=\"Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-77\" width=\"300\" height=\"153\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-77-300x153.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-77.jpg 586w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 12.<br \/>\nYou listen to a song that is 2\\(\\frac{3}{4}\\) minutes long. Then you listen to a song that is 3\\(\\frac{1}{3}\\) minutes long. How many minutes do you spend listening to the two songs altogether?<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator 4 x 3 = 12.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/><br \/>\n= 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B12%7D\" alt=\"\\small \\frac{13}{12}\" \/> min<br \/>\nSo I spend 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B12%7D\" alt=\"\\small \\frac{13}{12}\" \/> min listening to the two songs altogether.<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA beekeeper collects 3\\(\\frac{3}{4}\\) more pounds of honey from Hive 3 than Hive 1. Which hive produces the most honey? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16267\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-79.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 79\" width=\"293\" height=\"280\" \/><br \/>\nAnswer:<br \/>\nFrom the given information,<br \/>\nHoney from Hive 3 = Hive 1 honey + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\n= 23 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\n= 23 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n= 26 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B8%7D\" alt=\"\\small \\frac{11}{8}\" \/><br \/>\nUse a common denominator for all the hives<br \/>\nHive 1 honey = 23 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/><br \/>\nHive 2 honey = 27 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 27 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/><br \/>\nHive 3 honey = 26 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B8%7D\" alt=\"\\small \\frac{11}{8}\" \/><br \/>\nTherefore, <strong>Hive 2<\/strong> produces the most honey.<\/p>\n<h3><a id=\"Add_Mixed_Numbers_Homework_&amp;_Practice_8.6\"><\/a>Add Mixed Numbers Homework &amp; Practice 8.6<\/h3>\n<p>Add<\/p>\n<p>Question 1.<br \/>\n6\\(\\frac{2}{5}\\) + 1\\(\\frac{3}{10}\\)<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/>= 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/><br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> +\u00a01 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/> + 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/><br \/>\n= 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/><\/p>\n<p>Question 2.<br \/>\n2\\(\\frac{2}{3}\\) + 5\\(\\frac{3}{6}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/>= 2\u00a0<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> + 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/> = 2\u00a0<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/> + 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/><br \/>\n= 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B6%7D\" alt=\"\\small \\frac{7}{6}\" \/><\/p>\n<p>Question 3.<br \/>\n\\(\\frac{1}{4}\\) + 3\\(\\frac{2}{5}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator 4 x 5 = 20<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B20%7D\" alt=\"\\small \\frac{5}{20}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B20%7D\" alt=\"\\small \\frac{8}{20}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/>\u00a0 = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B20%7D\" alt=\"\\small \\frac{5}{20}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B20%7D\" alt=\"\\small \\frac{8}{20}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B20%7D\" alt=\"\\small \\frac{13}{20}\" \/><\/p>\n<p>Question 4.<br \/>\n9\\(\\frac{5}{7}\\) + \\(\\frac{2}{3}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator 7 x 3 = 21<br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B7%7D\" alt=\"\\small \\frac{5}{7}\" \/> = 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B21%7D\" alt=\"\\small \\frac{15}{21}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B21%7D\" alt=\"\\small \\frac{14}{21}\" \/><br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B7%7D\" alt=\"\\small \\frac{5}{7}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B21%7D\" alt=\"\\small \\frac{15}{21}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B21%7D\" alt=\"\\small \\frac{14}{21}\" \/> = 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B29%7D%7B21%7D\" alt=\"\\small \\frac{29}{21}\" \/><\/p>\n<p>Question 5.<br \/>\n2\\(\\frac{1}{2}\\) + 1\\(\\frac{3}{4}\\) + \\(\\frac{1}{2}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/>\u00a0 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/> +1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B4%7D\" alt=\"\\small \\frac{7}{4}\" \/><\/p>\n<p>Question 6.<br \/>\n2\\(\\frac{2}{3}\\) + 4\\(\\frac{1}{2}\\) + 3\\(\\frac{5}{6}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>\u00a0 + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/>\u00a0 + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B6%7D\" alt=\"\\small \\frac{12}{6}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>\u00a0 + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 11<\/p>\n<p>Question 7.<br \/>\nA veterinarian spends 3\\(\\frac{3}{4}\\) hours helping cats and 5\\(\\frac{1}{2}\\) hours helping dogs. How many hours does she spend helping cats and dogs altogether?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16268\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-80.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 80\" width=\"135\" height=\"143\" \/><br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator<br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/><br \/>\n= 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/><br \/>\nSo veterinarian spends 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/> hours helping cats and dogs altogether.<\/p>\n<p>Question 8.<br \/>\n<strong>Writing<\/strong><br \/>\nHow is adding mixed numbers with unlike denominators similar to adding fractions with unlike denominators? How is it different?<br \/>\nAnswer:<br \/>\nFor both adding mixed numbers and adding fractions we have to use a common denominator.<br \/>\n<strong>How it is different?<br \/>\n<\/strong>For adding fractions, directly add the fractions with common denominator.<br \/>\nBut for adding mixed numbers, add the fractional parts and add the whole number parts.<\/p>\n<p>Question 9.<br \/>\n<strong>Logic<\/strong><br \/>\nCan you add two mixed numbers and get a sum of 2? Explain.<br \/>\nAnswer:<br \/>\nYes, the sum of two mixed numbers can be equal to 2 but only of one of the mixed numbers is negative.<\/p>\n<p>Question 10.<br \/>\n<strong>Structure<\/strong><br \/>\nShade the model to represent the sum. Then write an equation to represent your model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-81.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 81\" width=\"380\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-81.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-81-300x60.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><br \/>\nAnswer: 4 \\(\\frac{1}{4}\\)<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nAn emperor tamarin has a body length of 9\\(\\frac{5}{10}\\) inches and a tail length of 14\\(\\frac{1}{4}\\) inches. How long is the emperor tamarin?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-82.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 82\" width=\"137\" height=\"154\" \/><br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator 10 x 4 = 40<br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/> = 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B40%7D\" alt=\"\\small \\frac{20}{40}\" \/><br \/>\n14 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = 14 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B40%7D\" alt=\"\\small \\frac{10}{40}\" \/><br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/> + 14 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B40%7D\" alt=\"\\small \\frac{20}{40}\" \/> + 14 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B40%7D\" alt=\"\\small \\frac{10}{40}\" \/><br \/>\n= 23 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B30%7D%7B40%7D\" alt=\"\\small \\frac{30}{40}\" \/><br \/>\nSo, an emperor tamarin is 23 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> inches long.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA long jumper jumps 1\\(\\frac{2}{3}\\) feet farther on her third attempt than her second attempt. On which attempt does she jump the farthest? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-83.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 83\" width=\"298\" height=\"92\" \/><br \/>\nAnswer:<br \/>\nThird attempt = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> + 13 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator 3 x 4 = 12<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><br \/>\n13 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 13 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> + 13 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/> + 13 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/> = 14 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B12%7D\" alt=\"\\small \\frac{17}{12}\" \/><br \/>\nTherefore, she jumps the farthest on her first attempt.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the product. Check whether your answer is reasonable.<\/p>\n<p>Question 13.<br \/>\n354 \u00d7 781<br \/>\nAnswer:<br \/>\nThe number close to 354 is 350<br \/>\nThe number close to 781 is 800.<br \/>\n350 \u00d7 800 = 280000<br \/>\n354 \u00d7 781 = 276474<br \/>\nYes, the answer is reasonable.<\/p>\n<p>Question 14.<br \/>\n4,029 \u00d7 276<br \/>\nAnswer:<br \/>\nThe number close to 4029 is 4000<br \/>\nThe number close to 276 is 300<br \/>\n4000 \u00d7 300 = 1200000<br \/>\n4029 \u00d7 276 = 1112004<br \/>\nYes, the answer is reasonable.<\/p>\n<p>Question 15.<br \/>\n950 \u00d7 326<br \/>\nAnswer:<br \/>\nThe number close to 950 is 1000<br \/>\nThe number close to 326 is 300<br \/>\n1000 \u00d7 300 = 300000<br \/>\n950 \u00d7 326 = 309700<br \/>\nYes, the answer is reasonable.<\/p>\n<h3><a id=\"Lesson_8.7_Subtract_Mixed_Numbers\"><\/a>Lesson 8.7 Subtract Mixed Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use a model to find the difference<br \/>\n3\\(\\frac{5}{6}\\) &#8211; 2\\(\\frac{1}{3}\\)<\/p>\n<p><strong>Construct Arguments<\/strong><br \/>\nHow can you subtract mixed numbers with unlike denominators without using a model? Explain why your method makes sense.<\/p>\n<p><strong>Think and Grow: Subtract Mixed Numbers<\/strong><\/p>\n<p>You can use equivalent fractions to subtract mixed numbers that have fractional parts with unlike denominators.<br \/>\n<strong>Example<\/strong><br \/>\nFind 3\\(\\frac{1}{4}\\) &#8211; 1\\(\\frac{1}{2}\\).<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-16272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-84.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 84\" width=\"622\" height=\"589\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-84.png 622w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-84-300x284.png 300w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Subtract.<\/p>\n<p>Question 1.<br \/>\n1\\(\\frac{4}{5}\\) &#8211; 1\\(\\frac{3}{10}\\)<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B10%7D\" alt=\"\\small \\frac{8}{10}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B10%7D\" alt=\"\\small \\frac{8}{10}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = 0 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B10%7D\" alt=\"\\small \\frac{5}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><\/p>\n<p>Question 2.<br \/>\n5\\(\\frac{7}{12}\\) &#8211; 3\\(\\frac{5}{6}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> &#8211; 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> &#8211; 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/>\u00a0 = 4 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B12%7D\" alt=\"\\small \\frac{12}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B12%7D\" alt=\"\\small \\frac{19}{12}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> &#8211; 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B12%7D\" alt=\"\\small \\frac{19}{12}\" \/> &#8211; 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B12%7D\" alt=\"\\small \\frac{10}{12}\" \/><br \/>\n= 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Subtract.<\/p>\n<p>Question 3.<br \/>\n8\\(\\frac{11}{12}\\) &#8211; 5\\(\\frac{2}{3}\\) = _____<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><br \/>\n8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> &#8211; 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> &#8211; 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><br \/>\n8\\(\\frac{11}{12}\\) &#8211; 5\\(\\frac{2}{3}\\) = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/><\/p>\n<p>Question 4.<br \/>\n6 &#8211; 4\\(\\frac{3}{4}\\) = ___<br \/>\nAnswer:<br \/>\n6 &#8211; 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 6 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B4%7D\" alt=\"\\small \\frac{19}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/><\/p>\n<p>Question 5.<br \/>\n21\\(\\frac{2}{9}\\) &#8211; 10\\(\\frac{1}{3}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B9%7D\" alt=\"\\small \\frac{3}{9}\" \/><br \/>\n21 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B9%7D\" alt=\"\\small \\frac{2}{9}\" \/> = 20 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B9%7D\" alt=\"\\small \\frac{9}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B9%7D\" alt=\"\\small \\frac{2}{9}\" \/> = 20 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B9%7D\" alt=\"\\small \\frac{11}{9}\" \/><br \/>\n21 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B9%7D\" alt=\"\\small \\frac{2}{9}\" \/> &#8211; 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 20 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B9%7D\" alt=\"\\small \\frac{11}{9}\" \/> &#8211; 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B9%7D\" alt=\"\\small \\frac{3}{9}\" \/><br \/>\n= 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B9%7D\" alt=\"\\small \\frac{8}{9}\" \/><\/p>\n<p>Question 6.<br \/>\n7\\(\\frac{1}{2}\\) &#8211; \\(\\frac{5}{8}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> = 6 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B8%7D\" alt=\"\\small \\frac{8}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B8%7D\" alt=\"\\small \\frac{12}{8}\" \/><br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B8%7D\" alt=\"\\small \\frac{12}{8}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/><br \/>\n= 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/><\/p>\n<p>Question 7.<br \/>\n9\\(\\frac{7}{20}\\) &#8211; 1\\(\\frac{3}{5}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B20%7D\" alt=\"\\small \\frac{12}{20}\" \/><br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/> = 8 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B20%7D\" alt=\"\\small \\frac{20}{20}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/> = 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B27%7D%7B20%7D\" alt=\"\\small \\frac{27}{20}\" \/><br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B5%7D\" alt=\"\\small \\frac{3}{5}\" \/> = 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B27%7D%7B20%7D\" alt=\"\\small \\frac{27}{20}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B20%7D\" alt=\"\\small \\frac{12}{20}\" \/><br \/>\n= 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{15}{20}\" \/><br \/>\n= 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><\/p>\n<p>Question 8.<br \/>\n7\\(\\frac{5}{6}\\) &#8211; 1\\(\\frac{1}{6}\\) &#8211; 2\\(\\frac{2}{3}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 6 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B6%7D\" alt=\"\\small \\frac{6}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B6%7D\" alt=\"\\small \\frac{11}{6}\" \/><br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B6%7D\" alt=\"\\small \\frac{11}{6}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/><br \/>\n= 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B6%7D\" alt=\"\\small \\frac{6}{6}\" \/><br \/>\n= 3 + 1<br \/>\n7\\(\\frac{5}{6}\\) &#8211; 1\\(\\frac{1}{6}\\) &#8211; 2\\(\\frac{2}{3}\\) = 4<\/p>\n<p>Question 9.<br \/>\nA volunteer at a food bank buys 3\\(\\frac{3}{4}\\) pounds of cheese to make sandwiches. She uses 2\\(\\frac{7}{8}\\) pounds. How much cheese does she have left?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-8-Add-and-Subtract-Fractions-87.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 8 Add and Subtract Fractions 87\" width=\"189\" height=\"112\" \/><br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nA volunteer buys 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> pounds of cheese<br \/>\nShe uses 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> pounds<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> = 2 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B8%7D\" alt=\"\\small \\frac{8}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B8%7D\" alt=\"\\small \\frac{14}{8}\" \/><br \/>\nCheese left = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B8%7D\" alt=\"\\small \\frac{14}{8}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = 0 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/><br \/>\nSo she left with <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> pounds of cheese.<\/p>\n<p>Question 10.<br \/>\n<strong>Writing<\/strong><br \/>\nHow is adding mixed numbers the same as subtracting mixed numbers? How is it different?<br \/>\nAnswer:<br \/>\nAdding and subtracting mixed numbers is same because we need to use a common denominator for both.<br \/>\nAdding and subtracting mixed numbers is different because<br \/>\nFor subtracting mixed numbers, the first fraction should be greater than the second number.<\/p>\n<p>Question 11.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWrite the words as an expression. Then evaluate.<br \/>\nSubtract the sum of four and three-fourths and two and five-eighths from eleven and seven-eighths.<br \/>\nAnswer:<br \/>\n11 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> &#8211; (4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/>)<br \/>\nTo subtract or add the fractional parts, use a common denominator.<br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B8%7D\" alt=\"\\small \\frac{11}{8}\" \/><br \/>\n11 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> &#8211; (4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/>) = 11 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> &#8211; 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B8%7D\" alt=\"\\small \\frac{11}{8}\" \/><br \/>\n11 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = 10 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B8%7D\" alt=\"\\small \\frac{8}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B8%7D\" alt=\"\\small \\frac{15}{8}\" \/><br \/>\n11 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> &#8211; (4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/>) = 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B8%7D\" alt=\"\\small \\frac{15}{8}\" \/> &#8211; 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B8%7D\" alt=\"\\small \\frac{11}{8}\" \/><br \/>\n11 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> &#8211; (4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/>) = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nFind the missing number.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16227\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-88.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 88\" width=\"133\" height=\"62\" \/><br \/>\nAnswer:<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/><\/p>\n<p>3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/>\u00a0= 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B12%7D\" alt=\"\\small \\frac{3}{12}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/><br \/>\n= 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B12%7D\" alt=\"\\small \\frac{2}{12}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><br \/>\nSo the missing number is <strong>1.<\/strong><\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA dragonfly is 1\\(\\frac{1}{2}\\) inches long. How much longer is the walking leaf than the dragonfly?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16228\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-89.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 89\" width=\"248\" height=\"176\" \/><br \/>\nTo find how much longer the walking leaf is than the dragonfly, subtract the length of the dragonfly from the length of the walking leaf.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-90.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 90\" width=\"379\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-90.png 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-90-300x142.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><br \/>\nThe walking leaf is __ inches longer than the dragonfly.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-40498\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-90-300x142.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-90\" width=\"300\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-90-300x142.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-90.jpg 379w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe walking leaf is 1 \\(\\frac{1}{6}\\) inches longer than the dragonfly.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nYou volunteer 5\\(\\frac{3}{4}\\) hours in 1 month. You spend 3\\(\\frac{1}{3}\\) hours volunteering at an animal shelter. You spend the remaining hours picking up litter on the side of the road. How many hours do you spend picking up litter?<br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nVolunteering hours in 1 month = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\nTime spent at an animal shelter = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/><br \/>\nRemaining hours in a month are for picking up litter = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> &#8211; 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/><br \/>\nTo subtract the fractional parts, use a common denominator 4 x 3 =12<br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/><br \/>\nTime spend for picking up litter = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B12%7D\" alt=\"\\small \\frac{9}{12}\" \/> &#8211; 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/>.<\/p>\n<p>Question 14.<br \/>\nA professional basketball player is 6\\(\\frac{3}{4}\\) feet tall. Your friend is 4\\(\\frac{5}{6}\\) feet tall. How much taller is the basketball player than your friend?<br \/>\nAnswer:<br \/>\nTo find how much taller is the basketball player than the friend, subtract the height of the friend from the height of the basketball player.<br \/>\nGiven that,<br \/>\nBasketball player is 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> feet tall.<br \/>\nMy friend is 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> feet tall.<br \/>\nTo subtract the fractional parts, use a common denominator 4 x 6 = 24<br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{18}{24}\" \/> = 5 + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B24%7D\" alt=\"\\small \\frac{24}{24}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{18}{24}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B42%7D%7B24%7D\" alt=\"\\small \\frac{42}{24}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{20}{24}\" \/><br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> &#8211; 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B42%7D%7B24%7D\" alt=\"\\small \\frac{42}{24}\" \/> &#8211; 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{20}{24}\" \/><br \/>\n= 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B22%7D%7B24%7D\" alt=\"\\small \\frac{22}{24}\" \/><br \/>\n= 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/><br \/>\nThe basketball player is 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> feet taller than my friend.<\/p>\n<p>Question 15.<br \/>\nYour rain gauge has 2\\(\\frac{1}{2}\\) inches of water. After a rainstorm, your rain gauge has 1\\(\\frac{3}{4}\\) more inches of water. It is sunny for a week. Now your rain gauge has 2\\(\\frac{2}{3}\\) inches of water. How many inches of water evaporated?<br \/>\nAnswer:<br \/>\nAfter a rainstorm, water in the rain gauge = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/><br \/>\nTo subtract or add the fractional parts, use a common denominator.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/><br \/>\nWater in the rain gauge = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> +1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B4%7D\" alt=\"\\small \\frac{2}{4}\" \/> + 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/> inches<br \/>\nWater evaporated = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B12%7D\" alt=\"\\small \\frac{15}{12}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><\/p>\n<p>3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B4%7D\" alt=\"\\small \\frac{5}{4}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B12%7D\" alt=\"\\small \\frac{15}{12}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/><br \/>\nSo, 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B12%7D\" alt=\"\\small \\frac{7}{12}\" \/> inches of water evaporated.<\/p>\n<h3><a id=\"Subtract_Mixed_Numbers_Homework_&amp;_Practice_8.7\"><\/a>Subtract Mixed Numbers Homework &amp; Practice 8.7<\/h3>\n<p>Subtract<\/p>\n<p>Question 1.<br \/>\n9\\(\\frac{5}{6}\\) &#8211; 4\\(\\frac{1}{2}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/><br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> &#8211; 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> &#8211; 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/><br \/>\n= 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/><br \/>\n9\\(\\frac{5}{6}\\) &#8211; 4\\(\\frac{1}{2}\\) = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/>\u00a0= 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/><\/p>\n<p>Question 2.<br \/>\n3\\(\\frac{2}{3}\\) &#8211; \\(\\frac{1}{9}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B9%7D\" alt=\"\\small \\frac{5}{9}\" \/><\/p>\n<p>Question 3.<br \/>\n6\\(\\frac{1}{3}\\) &#8211; 1\\(\\frac{11}{12}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B12%7D\" alt=\"\\small \\frac{4}{12}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B12%7D\" alt=\"\\small \\frac{16}{12}\" \/><br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B12%7D\" alt=\"\\small \\frac{16}{12}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/><br \/>\n= 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B12%7D\" alt=\"\\small \\frac{5}{12}\" \/><\/p>\n<p>Question 4.<br \/>\n12\\(\\frac{5}{6}\\) &#8211; 7\\(\\frac{3}{10}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator 6 x 10 = 60<br \/>\n12 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 12 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B50%7D%7B60%7D\" alt=\"\\small \\frac{50}{60}\" \/><br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B60%7D\" alt=\"\\small \\frac{18}{60}\" \/><br \/>\n12 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> &#8211; 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = 12 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B50%7D%7B60%7D\" alt=\"\\small \\frac{50}{60}\" \/> &#8211; 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B60%7D\" alt=\"\\small \\frac{18}{60}\" \/><br \/>\n= 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B32%7D%7B60%7D\" alt=\"\\small \\frac{32}{60}\" \/><br \/>\n12\\(\\frac{5}{6}\\) &#8211; 7\\(\\frac{3}{10}\\) = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B32%7D%7B60%7D\" alt=\"\\small \\frac{32}{60}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B15%7D\" alt=\"\\small \\frac{8}{15}\" \/><\/p>\n<p>Question 5.<br \/>\n5 &#8211; 2\\(\\frac{3}{4}\\) = ___<br \/>\nAnswer:<br \/>\n5 &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 5 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B4%7D\" alt=\"\\small \\frac{11}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B4%7D\" alt=\"\\small \\frac{9}{4}\" \/><\/p>\n<p>Question 6.<br \/>\n4\\(\\frac{1}{5}\\) &#8211; 2\\(\\frac{1}{4}\\) = __<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator 5 x 4 = 20<br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B20%7D\" alt=\"\\small \\frac{4}{20}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B20%7D\" alt=\"\\small \\frac{24}{20}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B20%7D\" alt=\"\\small \\frac{5}{20}\" \/><\/p>\n<p>4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B20%7D\" alt=\"\\small \\frac{24}{20}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B20%7D\" alt=\"\\small \\frac{5}{20}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B20%7D\" alt=\"\\small \\frac{19}{20}\" \/><\/p>\n<p>Subtract.<\/p>\n<p>Question 7.<br \/>\n7\\(\\frac{5}{8}\\) &#8211; 1\\(\\frac{5}{6}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator 8 x 6 = 48<br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B30%7D%7B48%7D\" alt=\"\\small \\frac{30}{48}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B78%7D%7B48%7D\" alt=\"\\small \\frac{78}{48}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B40%7D%7B48%7D\" alt=\"\\small \\frac{40}{48}\" \/><br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B78%7D%7B48%7D\" alt=\"\\small \\frac{78}{48}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B40%7D%7B48%7D\" alt=\"\\small \\frac{40}{48}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B38%7D%7B48%7D\" alt=\"\\small \\frac{38}{48}\" \/><br \/>\n= 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B24%7D\" alt=\"\\small \\frac{19}{24}\" \/><\/p>\n<p>Question 8.<br \/>\n8\\(\\frac{1}{9}\\) &#8211; 6\\(\\frac{7}{8}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator 8 x 9 = 72<br \/>\n8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/> = 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B72%7D\" alt=\"\\small \\frac{8}{72}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B80%7D%7B72%7D\" alt=\"\\small \\frac{80}{72}\" \/><br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B63%7D%7B72%7D\" alt=\"\\small \\frac{63}{72}\" \/><br \/>\n8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B9%7D\" alt=\"\\small \\frac{1}{9}\" \/> &#8211; 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B80%7D%7B72%7D\" alt=\"\\small \\frac{80}{72}\" \/> &#8211; 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B63%7D%7B72%7D\" alt=\"\\small \\frac{63}{72}\" \/><br \/>\n= 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B72%7D\" alt=\"\\small \\frac{17}{72}\" \/><\/p>\n<p>Question 9.<br \/>\n1\\(\\frac{6}{7}\\) + 5\\(\\frac{13}{14}\\) &#8211; 2\\(\\frac{1}{2}\\) = ___<br \/>\nAnswer:<br \/>\nTo subtract or add the fractional parts, use a common denominator<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B7%7D\" alt=\"\\small \\frac{6}{7}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B14%7D\" alt=\"\\small \\frac{12}{14}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B14%7D\" alt=\"\\small \\frac{7}{14}\" \/><\/p>\n<p>1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B7%7D\" alt=\"\\small \\frac{6}{7}\" \/> + 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B14%7D\" alt=\"\\small \\frac{13}{14}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B14%7D\" alt=\"\\small \\frac{12}{14}\" \/> + 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B14%7D\" alt=\"\\small \\frac{13}{14}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B14%7D\" alt=\"\\small \\frac{7}{14}\" \/><br \/>\n= 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B14%7D\" alt=\"\\small \\frac{18}{14}\" \/><br \/>\n= 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B7%7D\" alt=\"\\small \\frac{9}{7}\" \/><\/p>\n<p>Question 10.<br \/>\nYour friend says the difference of 8 and 3\\(\\frac{7}{10}\\) is 5\\(\\frac{7}{10}\\). Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n8 &#8211; 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> = 8 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B37%7D%7B10%7D\" alt=\"\\small \\frac{37}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B43%7D%7B10%7D\" alt=\"\\small \\frac{43}{10}\" \/><\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nUse a symbol card to complete the equation. Then \ufb01nd b.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-91.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 91\" width=\"193\" height=\"111\" \/><br \/>\nAnswer:<br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B20%7D\" alt=\"\\small \\frac{17}{20}\" \/> &#8211; b = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B20%7D\" alt=\"\\small \\frac{5}{20}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B45%7D%7B20%7D\" alt=\"\\small \\frac{45}{20}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B20%7D\" alt=\"\\small \\frac{10}{20}\" \/><br \/>\nb = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B20%7D\" alt=\"\\small \\frac{17}{20}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/><br \/>\n= 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B45%7D%7B20%7D\" alt=\"\\small \\frac{45}{20}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B20%7D\" alt=\"\\small \\frac{17}{20}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B20%7D\" alt=\"\\small \\frac{10}{20}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B20%7D\" alt=\"\\small \\frac{18}{20}\" \/><br \/>\nb = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B20%7D\" alt=\"\\small \\frac{18}{20}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/><\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThe world record for the heaviest train pulled with a human beard is 2\\(\\frac{3}{4}\\) metric tons. The world record for the heaviest train pulled by human teeth is 4\\(\\frac{1}{5}\\) metric tons. How much heavier is the train pulled by teeth than the train pulled with a beard?<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator 4 x 5 = 20<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{15}{20}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B20%7D\" alt=\"\\small \\frac{4}{20}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B20%7D\" alt=\"\\small \\frac{24}{20}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B24%7D%7B20%7D\" alt=\"\\small \\frac{24}{20}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{15}{20}\" \/><br \/>\n= 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B20%7D\" alt=\"\\small \\frac{9}{20}\" \/><br \/>\nThe train pulled by teeth 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B20%7D\" alt=\"\\small \\frac{9}{20}\" \/> metric tons heavier than the train pulled with a beard.<\/p>\n<p>Question 13.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour friend\u2019s hair is 50\\(\\frac{4}{5}\\) centimeters long. Your hair is 8\\(\\frac{9}{10}\\) centimeters long. How much longer is your friend\u2019s hair than yours?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-92.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 92\" width=\"116\" height=\"228\" \/><br \/>\nAnswer:<br \/>\nMy friend&#8217;s hair = 50 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> cm<br \/>\nMy hair = 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> cm<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator<br \/>\n50 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> = 50 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B10%7D\" alt=\"\\small \\frac{8}{10}\" \/> = 49 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B10%7D\" alt=\"\\small \\frac{18}{10}\" \/><br \/>\n50 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> &#8211; 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> = 49 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B10%7D\" alt=\"\\small \\frac{18}{10}\" \/> &#8211; 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> = 41 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/><br \/>\nMy friend&#8217;s hair is 41 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> cms longer than my hair.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Question 14.<br \/>\nRound 6.294.<br \/>\nNearest whole number:<br \/>\nNearest tenth:<br \/>\nNearest hundredth:<br \/>\nAnswer:<br \/>\nNearest whole number: 6<br \/>\nNearest tenth: 60<br \/>\nNearest hundredth: 600<\/p>\n<p>Question 15.<br \/>\nRound 10.571.<br \/>\nNearest whole number:<br \/>\nNearest tenth:<br \/>\nNearest hundredth:<br \/>\nAnswer:<br \/>\nNearest whole number: 11<br \/>\nNearest tenth: 110<br \/>\nNearest hundredth: 1100<\/p>\n<h3><a id=\"Lesson_8.8_Problem_Solving:_Fractions\"><\/a>Lesson 8.8 Problem Solving: Fractions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p><strong>Make a plan to solve the problem.<\/strong><\/p>\n<p>At a state park, every \\(\\frac{1}{10}\\) mile of walking trail is marked. Every \\(\\frac{1}{4}\\) mile of a separate biking trail is marked. The table shows the number of mileage markers you and your friend pass while walking and biking on the trails. Who travels farther? How much farther?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-93.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 93\" width=\"230\" height=\"256\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-94.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 94\" width=\"321\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-94.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-94-300x127.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p><strong>Make Sense of Problems<\/strong><br \/>\nYou decide to walk farther and you pass 4 more mileage markers on the walking trail. Does this change your plan to solve the problem? Explain.<br \/>\nAnswer:<br \/>\nAt a state park, every \\(\\frac{1}{10}\\) mile of the walking trail is marked.<br \/>\n8 \u00d7 \\(\\frac{1}{10}\\) = \\(\\frac{8}{10}\\)<br \/>\nEvery \\(\\frac{1}{4}\\) mile of a separate biking trail is marked.<br \/>\n9 \u00d7 \\(\\frac{1}{4}\\) = 2 \\(\\frac{1}{4}\\)<br \/>\n\\(\\frac{8}{10}\\) + \\(\\frac{4}{10}\\) = \\(\\frac{12}{10}\\)<br \/>\n= 1 \\(\\frac{2}{10}\\)<br \/>\nYour friend travels more farther.<\/p>\n<p><strong>Think and Gow: Problem Solving: Fractions<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nTo repair a skate ramp, you cut a piece of wood from a 9\\(\\frac{1}{2}\\)-foot-long board. Then you cut the remaining piece in half. Each half is 3\\(\\frac{5}{12}\\) feet long. How long is the first piece you cut?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-95.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 95\" width=\"167\" height=\"111\" \/><\/p>\n<p><strong>Understand the Problem<\/strong><\/p>\n<p>What do you know?<\/p>\n<ul>\n<li>The board is 9 feet long.2first piece you cut.<\/li>\n<li>You cut a piece from the board.<\/li>\n<li>You cut the rest into two pieces that are each 3\\(\\frac{5}{12}\\) feet long.<\/li>\n<\/ul>\n<p>What do you need tofind?<\/p>\n<ul>\n<li>You need to find the length of the first piece you cut.<\/li>\n<\/ul>\n<p><strong>Make a Plan<\/strong><\/p>\n<p>How will you solve?<br \/>\nWrite and solve an equation: Subtract the sum of the lengths of the last two pieces you cut from the total length of the board.<\/p>\n<p>Solve<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-96.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 96\" width=\"545\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-96.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-96-300x32.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><br \/>\nLet g represent the length of the first piece you cut.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-97.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 97\" width=\"183\" height=\"163\" \/><br \/>\nSo, the length of the first piece you cut is __ feet.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40505\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-97.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-97\" width=\"183\" height=\"163\" \/><br \/>\nSo, the length of the first piece you cut is 2 \\(\\frac{2}{3}\\) feet.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nExplain how you can check your answer in the example above.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40505\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-97.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-97\" width=\"183\" height=\"163\" \/><\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Understand the problem. What do you know? What do you need to find? Explain.<\/p>\n<p>Question 2.<br \/>\nA racehorse eats 38\\(\\frac{1}{2}\\) pounds of food each day. He eats 22\\(\\frac{3}{4}\\) pounds of hay and 7\\(\\frac{1}{2}\\) pounds of grains. How many pounds of his daily diet is not hay or grains?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-98.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 98\" width=\"131\" height=\"192\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA racehorse eats 38\\(\\frac{1}{2}\\) pounds of food each day.<br \/>\nHe eats 22\\(\\frac{3}{4}\\) pounds of hay and 7\\(\\frac{1}{2}\\) pounds of grains.<br \/>\n38\\(\\frac{1}{2}\\) &#8211; 22\\(\\frac{3}{4}\\)<br \/>\n= 15 \\(\\frac{3}{4}\\)<br \/>\nThus 15 \\(\\frac{3}{4}\\) pounds of his daily diet is not grains.<\/p>\n<p>Question 3.<br \/>\nIn 2015, American Pharoah won all of the horse races shown in the table. How many kilometers did American Pharoah run in the races altogether?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-99.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 99\" width=\"200\" height=\"212\" \/><\/p>\n<p>Understand the problem. Then make a plan. How will you solve? Explain.<br \/>\nAnswer:<br \/>\nAdd all the lengths to find how many kilometers did American Pharoah run in the races altogether.<br \/>\n2 + 1 \\(\\frac{9}{10}\\) + 2 \\(\\frac{2}{5}\\)<br \/>\nFirst add all the whole numbers.<br \/>\n2 + 1 + 2 = 5<br \/>\nNow add the fractions<br \/>\n\\(\\frac{9}{10}\\) + \\(\\frac{4}{10}\\) = 1 \\(\\frac{3}{10}\\)<br \/>\n5 + 1 \\(\\frac{3}{10}\\) = 6\u00a0\\(\\frac{3}{10}\\)<\/p>\n<p>Question 4.<br \/>\nYou have 2\\(\\frac{1}{2}\\) cups of blueberries. You use 1\\(\\frac{1}{4}\\) cups for pancakes and \\(\\frac{1}{2}\\) cup for muffins. What fraction of a cup of blueberries do you have left?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou have 2\\(\\frac{1}{2}\\) cups of blueberries.<br \/>\nYou use 1\\(\\frac{1}{4}\\) cups for pancakes and \\(\\frac{1}{2}\\) cup for muffins.<br \/>\n1\\(\\frac{1}{4}\\) + \\(\\frac{1}{2}\\) = 1 \\(\\frac{3}{4}\\)<br \/>\n2\\(\\frac{1}{2}\\) &#8211; 1 \\(\\frac{3}{4}\\) = \\(\\frac{3}{4}\\)<\/p>\n<p>Question 5.<br \/>\nA customer orders 2 pounds of cheese at a deli. The deli worker places some cheese in a bowl and weighs it. The scale shows 1\\(\\frac{1}{4}\\) pounds. The bowl weighs \\(\\frac{1}{8}\\) pound. What fraction of a pound of cheese does the worker need to add to the bowl?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA customer orders 2 pounds of cheese at a deli. The deli worker places some cheese in a bowl and weighs it.<br \/>\nThe scale shows 1\\(\\frac{1}{4}\\) pounds. The bowl weighs \\(\\frac{1}{8}\\) pound.<br \/>\n1\\(\\frac{1}{4}\\) + \\(\\frac{1}{8}\\) = 1 \\(\\frac{3}{8}\\)<br \/>\n2 &#8211; 1 \\(\\frac{3}{8}\\) = \\(\\frac{5}{8}\\)<\/p>\n<p>Question 6.<br \/>\n<strong>Reasoning<\/strong><br \/>\nStudent A is 8\\(\\frac{1}{2}\\) inches shorter than Student B. Student B is 3\\(\\frac{1}{4}\\) inches taller than Student C. Student C is 56\\(\\frac{3}{8}\\) inches tall. How tall is Student A? Student B?<br \/>\nAnswer:<br \/>\nStudent A is 8\\(\\frac{1}{2}\\) inches shorter than Student B.<br \/>\nStudent B is 3\\(\\frac{1}{4}\\) inches taller than Student C.<br \/>\nStudent C is 56\\(\\frac{3}{8}\\) inches tall.<br \/>\nStudent B is 56\\(\\frac{3}{8}\\) + 3\\(\\frac{1}{4}\\) = 59 \\(\\frac{5}{8}\\)<br \/>\nThus the height of student B is 59 \\(\\frac{5}{8}\\) inches.<br \/>\nStudent A is 59 \\(\\frac{5}{8}\\) &#8211; 8\\(\\frac{1}{2}\\) = 51 \\(\\frac{1}{8}\\)<br \/>\nThus the height of Student A is 51 \\(\\frac{1}{8}\\) inches.<\/p>\n<p>Question 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA police dog spends \\(\\frac{1}{8}\\) of his workday in a police car, \\(\\frac{3}{4}\\) of his workday in public, and the rest of his workday at the police station. What fraction of the dog\u2019s day is spent at the police station?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA police dog spends \\(\\frac{1}{8}\\) of his workday in a police car, \\(\\frac{3}{4}\\) of his workday in public, and the rest of his workday at the police station.<br \/>\n\\(\\frac{1}{8}\\) + \\(\\frac{3}{4}\\) = \\(\\frac{7}{8}\\)<br \/>\n1 &#8211; \\(\\frac{7}{8}\\) = \\(\\frac{1}{8}\\)<br \/>\nThus \\(\\frac{1}{8}\\) fraction of the dog\u2019s day is spent at the police station<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThe Magellan spacecraft, launched by the United States, spent 5\\(\\frac{5}{12}\\) years in space before it burned in Venus\u2019s atmosphere. Its first 4 cycles around Venus each lasted \\(\\frac{2}{3}\\) year. The remaining cycles around Venus lasted a total of 1\\(\\frac{1}{2}\\) years. How long did it take to travel from Earth to Venus?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16239\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-100.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 100\" width=\"206\" height=\"189\" \/><br \/>\nThink: What do you know? What do you need to find? How will you solve?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16240\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-101.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 101\" width=\"579\" height=\"459\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-101.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-101-300x238.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-40512\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-101-300x238.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-101\" width=\"300\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-101-300x238.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-101.jpg 579w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 8.<br \/>\nYou have one of each euro coin shown. Your friend has four euro coins that have a total weight of 21\\(\\frac{3}{10}\\) grams. Whose coins weigh more? How much more?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16241\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-102.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 102\" width=\"322\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-102.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-102-300x115.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nAnswer:<br \/>\n2 \\(\\frac{3}{10}\\) + 5 \\(\\frac{3}{4}\\) + 7 \\(\\frac{4}{5}\\) + 7 \\(\\frac{1}{2}\\)<br \/>\n= 23 \\(\\frac{7}{20}\\)<br \/>\n23 \\(\\frac{7}{20}\\) &#8211; 21\\(\\frac{3}{10}\\)<br \/>\n= 2 \\(\\frac{1}{20}\\)<\/p>\n<h3><a id=\"Problem_Solving:_Fractions_Homework_&amp;_Practice_8.8\"><\/a>Problem Solving: Fractions Homework &amp; Practice 8.8<\/h3>\n<p>Understand the problem. What do you know? What do you need to find? Explain.<\/p>\n<p>Question 1.<br \/>\nYour goal is to exercise for 15 hours this month. You exercise for 3\\(\\frac{1}{2}\\) hours the \ufb01rst week and 3\\(\\frac{3}{4}\\) hours the next week. How many more hours do you need to exercise to reach your goal?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYour goal is to exercise for 15 hours this month.<br \/>\nYou exercise for 3\\(\\frac{1}{2}\\) hours the \ufb01rst week and 3\\(\\frac{3}{4}\\) hours the next week.<br \/>\n3\\(\\frac{1}{2}\\) + 3\\(\\frac{3}{4}\\) = 7 \\(\\frac{1}{4}\\)<br \/>\n15 &#8211; 7 \\(\\frac{1}{4}\\) = 7 \\(\\frac{3}{4}\\) hours<\/p>\n<p>Question 2.<br \/>\nA taxi driver travels 4\\(\\frac{5}{8}\\) miles to his \ufb01rst stop. He travels 1\\(\\frac{3}{4}\\) miles less to his second stop. How many miles does the taxi driver travel for the two stops?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16242\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-103.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 103\" width=\"154\" height=\"98\" \/><\/p>\n<p>Understand the problem. Then make a plan. How will you solve? Explain.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA taxi driver travels 4\\(\\frac{5}{8}\\) miles to his \ufb01rst stop. He travels 1\\(\\frac{3}{4}\\) miles less to his second stop.<br \/>\n4\\(\\frac{5}{8}\\) + 1\\(\\frac{3}{4}\\) = 7 \\(\\frac{1}{4}\\)<\/p>\n<p>Question 3.<br \/>\nDuring the U.S. Civil War, \\(\\frac{5}{9}\\) of the states fought for the Union, and \\(\\frac{11}{36}\\) of the states fought for the Confederacy. The rest of the states were border states. What fraction of the states were border states?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nDuring the U.S. Civil War, \\(\\frac{5}{9}\\) of the states fought for the Union, and \\(\\frac{11}{36}\\) of the states fought for the Confederacy. The rest of the states were border states.<br \/>\n\\(\\frac{5}{9}\\) + \\(\\frac{11}{36}\\) = \\(\\frac{31}{36}\\)<\/p>\n<p>Question 4.<br \/>\nYou have 6\\(\\frac{3}{4}\\) pounds of clay. You use 4\\(\\frac{1}{6}\\) pounds to make a medium-sized bowl and 1\\(\\frac{1}{2}\\) pounds to make a small bowl. How many pounds of clay do you have left?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYou have 6\\(\\frac{3}{4}\\) pounds of clay.<br \/>\nYou use 4\\(\\frac{1}{6}\\) pounds to make a medium-sized bowl and 1\\(\\frac{1}{2}\\) pounds to make a small bowl.<br \/>\n4\\(\\frac{1}{6}\\) + 1\\(\\frac{1}{2}\\) = 5 \\(\\frac{2}{3}\\)<br \/>\n6\\(\\frac{3}{4}\\) &#8211; 5 \\(\\frac{2}{3}\\) = 1 \\(\\frac{1}{12}\\)<\/p>\n<p>Question 5.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nNewton and Descartes have a 70-day summer vacation. They go to camp for \\(\\frac{23}{70}\\) of their vacation, and they travel for \\(\\frac{6}{35}\\) of their vacation. They stay home the rest of their vacation. How many weeks do Newton and Descartes spend at home?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nNewton and Descartes have a 70-day summer vacation. They go to camp for \\(\\frac{23}{70}\\) of their vacation, and they travel for \\(\\frac{6}{35}\\) of their vacation.<br \/>\n\\(\\frac{23}{70}\\) + \\(\\frac{6}{35}\\) = \\(\\frac{1}{2}\\)<br \/>\nThat means Newton and Descartes spend 5 weeks at home.<\/p>\n<p>Question 6.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA farmer plants beets in a square garden with side lengths of 12\\(\\frac{2}{3}\\) feet. He plants squash in a garden with a perimeter of 50\\(\\frac{1}{2}\\) feet. Which garden has a greater perimeter? How much greater is it?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA farmer plants beets in a square garden with side lengths of 12\\(\\frac{2}{3}\\) feet.<br \/>\nThe perimeter of the square = 4s<br \/>\nP = 4 \u00d7 12\\(\\frac{2}{3}\\)<br \/>\nP = 50 \\(\\frac{2}{3}\\)<br \/>\n50 \\(\\frac{2}{3}\\) is greater than 50\\(\\frac{1}{2}\\)<\/p>\n<p>Question 7.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWhich grade uses more leafy greens daily for its classroom rabbits? How much more does it use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16243\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-104.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 104\" width=\"321\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-104.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-104-300x145.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer: 4th Grade uses more leafy greens.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the product.<\/p>\n<p>Question 1.<br \/>\n0.43 \u00d7 1,000 = <strong>430<\/strong><br \/>\nAnswer:<br \/>\n43 x 10<sup>-2<\/sup>\u00a0x 10<sup>3<\/sup> = 43 x 10<sup>1<br \/>\n<\/sup>= 430<\/p>\n<p>Question 2.<br \/>\n25.8 \u00d7 0.1 = <strong>2.58<\/strong><br \/>\nAnswer:<br \/>\n258 x 10<sup>-1<\/sup>\u200b\u200b\u200b\u200b\u200b\u200b\u200b x 10<sup>-1<\/sup>= 2.58<\/p>\n<h3><a id=\"Add_and_Subtract_Fractions_Performance_Task_8\"><\/a>Add and Subtract Fractions Performance Task 8<\/h3>\n<p>Many historic landmarks are located in Washington, D.C.<\/p>\n<p>Question 1.<br \/>\nInitial construction of the Washington Monument began in 1848. When the height of the monument reached 152 feet, construction halted due to lack of funds. How many feet were added to the height of the monument when construction resumed 23 years later?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16244\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-105.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 105\" width=\"225\" height=\"279\" \/><br \/>\nAnswer:<br \/>\nThe initial construction of the Washington Monument began in 1848. When the height of the monument reached 152 feet, construction halted due to lack of funds.<br \/>\n554 \\(\\frac{3}{4}\\) &#8211; 152 = 402 \\(\\frac{3}{4}\\)<\/p>\n<p>Question 2.<br \/>\nYou visit several historic landmarks. You start at the Capitol Building and walk to the Washington Monument, then the Lincoln Memorial, then the White House, and then back to the Capitol Building.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16245\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-106.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 106\" width=\"606\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-106.png 606w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-106-300x93.png 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><br \/>\na. You walk 3 miles each hour. It takes you \\(\\frac{1}{2}\\) hour to walk from the Lincoln Memorial to the White House. What is the distance from the Lincoln Memorial to the White House? Label the map.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-41053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-106-300x93.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-106\" width=\"300\" height=\"93\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-106-300x93.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-106.jpg 606w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. What is the total distance you walk visiting the landmarks?<br \/>\nAnswer: 1 \\(\\frac{1}{5}\\) + \\(\\frac{4}{5}\\) + 1 \\(\\frac{4}{5}\\) + 1 \\(\\frac{3}{5}\\)<br \/>\n= 5 \\(\\frac{2}{5}\\)<\/p>\n<p>Question 3.<br \/>\nA law in Washington, D.C., restricts a new building\u2019s height to no more than 20 feet taller than the width of the street it faces. You design a building with stories that are each 15 feet tall for a street that is 88\\(\\frac{2}{3}\\) feet wide. What is the greatest number of stories your building can have? How much shorter is your building than the height restriction?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA law in Washington, D.C., restricts a new building\u2019s height to no more than 20 feet taller than the width of the street it faces.<br \/>\n20 \u00d7 88\\(\\frac{2}{3}\\) = 1773 \\(\\frac{1}{3}\\)<br \/>\nYou design a building with stories that are each 15 feet tall for a street that is 88\\(\\frac{2}{3}\\) feet wide.<br \/>\n15 \u00d7 88\\(\\frac{2}{3}\\) = 1330<br \/>\n1773 \\(\\frac{1}{3}\\) &#8211; 1330 = 443 \\(\\frac{1}{3}[\/latex<\/p>\n<h3><a id=\"Add_and_Subtract_Fractions_Activity\"><\/a>Add and Subtract Fractions Activity<\/h3>\n<p><strong>Mixed Number Number<\/strong><br \/>\n<strong>Subtract and Add<\/strong><br \/>\n<strong>Directions:<\/strong><\/p>\n<ol>\n<li>Each player flips four Mixed Number Cards.<\/li>\n<li>Each player arranges the cards to create two differences that will have the greatest possible sum.<\/li>\n<li>Each player records the two differences, and then adds the differences.<\/li>\n<li>Players repeat Steps 1\u20133.<\/li>\n<li>Each player adds Sum A and Sum B to find the total. The player with the greatest total wins!<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-16247\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-107.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 107\" width=\"546\" height=\"554\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-107.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-107-296x300.png 296w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-41056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-107-296x300.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-107\" width=\"296\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-107-296x300.jpg 296w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-107.jpg 546w\" sizes=\"(max-width: 296px) 100vw, 296px\" \/><\/p>\n<h3><a id=\"Add_and_Subtract_Fractions_Performance_Chapter_Practice\"><\/a>Add and Subtract Fractions Performance Chapter Practice<\/h3>\n<p><strong>8.1 Simplest Form<\/strong><\/p>\n<p>Write the fraction in simplest form.<\/p>\n<p>Question 1.<br \/>\n[latex]\\frac{2}{12}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 2 and 12.<br \/>\nFactors of 2:\u00a0 \u00a0 1, 2<br \/>\nFactors of 12:\u00a0 1, 2, 3, 4, 6, 12<br \/>\nThe common factors of 2 and 12 are 1 and 2.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B12%7D%20%3D%20%5Cfrac%7B2%20%5Cdiv%202%7D%7B12%20%5Cdiv%202%7D%20%3D%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{2}{12} = \\frac{2 \\div 2}{12 \\div 2} = \\frac{1}{6}\" \/><br \/>\nBecause 1 and 6 have no common factors other than 1, \\(\\frac{2}{12}\\) is in simplest form.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{15}{30}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 15 and 30.<br \/>\nFactors of 15:\u00a0 \u00a0 1, 3, 5, 15<br \/>\nFactors of 30:\u00a0 1, 2, 3, 5, 6, 10, 15, 30<br \/>\nThe common factors of 15 and 30 are 1, 3, 5 and 15.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B30%7D%20%3D%20%5Cfrac%7B15%20%5Cdiv%2015%7D%7B30%20%5Cdiv%2015%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{15}{30} = \\frac{15 \\div 15}{30 \\div 15} = \\frac{1}{2}\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1, \\(\\frac{15}{30}\\) is in simplest form.<\/p>\n<p>Question 3.<br \/>\n\\(\\frac{16}{24}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 16 and 24.<br \/>\nFactors of 16:\u00a0 \u00a0 1, 2, 4, 8, 16<br \/>\nFactors of 24:\u00a0 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThe common factors of 16 and 24 are 1, 2, 4 and 8.<br \/>\n<strong>Step 2:<\/strong> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B24%7D%20%3D%20%5Cfrac%7B16%20%5Cdiv%208%7D%7B24%20%5Cdiv%208%7D%20%3D%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{16}{24} = \\frac{16 \\div 8}{24 \\div 8} = \\frac{2}{3}\" \/><br \/>\nBecause 2 and 3 have no common factors other than 1, \\(\\frac{16}{24}\\) is in simplest form.<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{18}{36}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 18 and 36.<br \/>\nFactors of 18:\u00a0 1, 2, 3, 6, 9,\u00a018<br \/>\nFactors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36<br \/>\nThe common factors of 18 and 36 are 1, 2, 3, 6, 9 and 18.<br \/>\n<strong style=\"font-size: 16px;\">Step 2:<\/strong><span style=\"font-size: 16px;\"> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<\/span><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B36%7D%20%3D%20%5Cfrac%7B18%20%5Cdiv%2018%7D%7B36%20%5Cdiv%2018%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{18}{36} = \\frac{18 \\div 18}{36 \\div 18} = \\frac{1}{2}\" \/><br \/>\nBecause 1 and 2 have no common factors other than 1, \\(\\frac{18}{36}\\) is in simplest form.<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{8}{32}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 8 and 32.<br \/>\nFactors of 8:\u00a0 1, 2, 4, 8<br \/>\nFactors of 32: 1, 2, 4, 8, 16, 32<br \/>\nThe common factors of 8 and 32 are 1, 2, 4 and 8.<br \/>\n<strong style=\"font-size: 16px;\">Step 2:<\/strong><span style=\"font-size: 16px;\"> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<\/span><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B32%7D%20%3D%20%5Cfrac%7B8%20%5Cdiv%208%7D%7B32%20%5Cdiv%208%7D%20%3D%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{8}{32} = \\frac{8 \\div 8}{32 \\div 8} = \\frac{1}{4}\" \/><br \/>\nBecause 1 and 4 have no common factors other than 1, \\(\\frac{8}{32}\\) is in simplest form.<\/p>\n<p>Question 6.<br \/>\n\\(\\frac{25}{10}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Find the common factors of 25 and 10.<br \/>\nFactors of 25:\u00a0 1, 5, 25<br \/>\nFactors of 10: 1, 2, 5, 10<br \/>\nThe common factors of 25 and 10 are 1 and 5.<br \/>\n<strong style=\"font-size: 16px;\">Step 2:<\/strong><span style=\"font-size: 16px;\"> Write an equivalent fraction by dividing the numerator and the denominator by the greatest of the common factors.<br \/>\n<\/span><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B25%7D%7B10%7D%20%3D%20%5Cfrac%7B25%20%5Cdiv%205%7D%7B10%20%5Cdiv%205%7D%20%3D%20%5Cfrac%7B5%7D%7B2%7D\" alt=\"\\small \\frac{25}{10} = \\frac{25 \\div 5}{10 \\div 5} = \\frac{5}{2}\" \/><br \/>\nBecause 5 and 2 have no common factors other than 1, \\(\\frac{25}{10}\\) is in simplest form.<\/p>\n<p><strong>8.2 Estimate Sums and Differences of Fractions<\/strong><\/p>\n<p>Estimate the sum or difference.<\/p>\n<p>Question 7.<br \/>\n\\(\\frac{7}{8}\\) &#8211; \\(\\frac{1}{5}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> is about <u><br \/>\n<\/u>Think: The numerator is about the same as the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/> is about <u><br \/>\n<\/u>Think: The numerator is near to zero.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B5%7D\" alt=\"\\small \\frac{1}{5}\" \/>\u00a0 is 1 &#8211; 0 = 1.<\/p>\n<p>Question 8.<br \/>\n\\(\\frac{5}{6}\\) + \\(\\frac{9}{10}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to 1.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B10%7D\" alt=\"\\small \\frac{9}{10}\" \/> is between <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> and 1, but is closer to 1.<br \/>\n<strong>Step 2:<\/strong> Estimate the sum.<br \/>\nAn estimate of \\(\\frac{5}{6}\\) + \\(\\frac{9}{10}\\) = 1 + 1 = 2.<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{11}{12}\\) &#8211; \\(\\frac{89}{100}\\)<br \/>\nAnswer:<br \/>\n<strong>Step 1:<\/strong> Use mental math to estimate each fraction.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> is about <u><br \/>\n<\/u>Think : The numerator is about the same as the denominator.<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B89%7D%7B100%7D\" alt=\"\\small \\frac{89}{100}\" \/> is about <u><br \/>\n<\/u>Think : The numerator is closer to denominator.<br \/>\n<strong>Step 2:<\/strong> Estimate the difference.<br \/>\nAn estimate of <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B89%7D%7B100%7D\" alt=\"\\small \\frac{89}{100}\" \/>\u00a0 is 1 &#8211; 1 = 0.<\/p>\n<p>Question 10.<br \/>\n<strong>Precision<\/strong><br \/>\nYour friend says \\(\\frac{7}{8}\\) &#8211; \\(\\frac{5}{12}\\) is about 0. Find a closer estimate. Explain why your estimate is closer.<br \/>\nAnswer:<br \/>\n\\(\\frac{7}{8}\\) &#8211; \\(\\frac{5}{12}\\) = \\(\\frac{11}{24}\\)<br \/>\n\\(\\frac{11}{24}\\) = 0.45<br \/>\nThe number 0.45 is close to 0.<\/p>\n<p><strong>8.3 Find Common Denominators<\/strong><\/p>\n<p>Use a common denominator to write an equivalent fraction for each fraction.<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{4}\\) and \\(\\frac{1}{2}\\)<br \/>\nAnswer:<br \/>\nUse the product of the denominators: 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 2 = 8<br \/>\nWrite equivalent fractions with denominators of 8<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D%20%3D%20%5Cfrac%7B1%5Ctimes%202%7D%7B4%5Ctimes%202%7D%20%3D%20%5Cfrac%7B2%7D%7B8%7D\" alt=\"\\small \\frac{1}{4} = \\frac{1\\times 2}{4\\times 2} = \\frac{2}{8}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%204%7D%7B2%20%5Ctimes%204%7D%20%3D%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{1}{2} = \\frac{1 \\times 4}{2 \\times 4} = \\frac{4}{8}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B8%7D\" alt=\"\\small \\frac{2}{8}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/>.<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{2}{3}\\) and \\(\\frac{2}{9}\\)<br \/>\nAnswer:<br \/>\nUse the product of the denominators : 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 9 = 27<br \/>\nWrite equivalent fractions with denominators of 27<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%209%7D%7B3%20%5Ctimes%209%7D%20%3D%20%5Cfrac%7B18%7D%7B27%7D\" alt=\"\\small \\frac{2}{3} = \\frac{2 \\times 9}{3 \\times 9} = \\frac{18}{27}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B9%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%203%7D%7B9%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B6%7D%7B27%7D\" alt=\"\\small \\frac{2}{9} = \\frac{2 \\times 3}{9 \\times 3} = \\frac{6}{27}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B27%7D\" alt=\"\\small \\frac{18}{27}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B27%7D\" alt=\"\\small \\frac{6}{27}\" \/>.<\/p>\n<p>Question 13.<br \/>\n\\(\\frac{2}{3}\\) and \\(\\frac{5}{6}\\)<br \/>\nAnswer:<br \/>\nUse the product of the denominators : 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 6 = 18<br \/>\nWrite equivalent fractions with denominators of 18<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D%20%3D%20%5Cfrac%7B2%20%5Ctimes%206%7D%7B3%20%5Ctimes%206%7D%20%3D%20%5Cfrac%7B12%7D%7B18%7D\" alt=\"\\small \\frac{2}{3} = \\frac{2 \\times 6}{3 \\times 6} = \\frac{12}{18}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%203%7D%7B6%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B15%7D%7B18%7D\" alt=\"\\small \\frac{5}{6} = \\frac{5 \\times 3}{6 \\times 3} = \\frac{15}{18}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B18%7D\" alt=\"\\small \\frac{12}{18}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B18%7D\" alt=\"\\small \\frac{15}{18}\" \/>.<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{4}{5}\\) and \\(\\frac{1}{3}\\)<br \/>\nAnswer:<br \/>\nUse the product of the denominators : 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 3 = 15<br \/>\nWrite equivalent fractions with denominators of 15<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D%20%3D%20%5Cfrac%7B4%20%5Ctimes%203%7D%7B5%20%5Ctimes%203%7D%20%3D%20%5Cfrac%7B12%7D%7B15%7D\" alt=\"\\small \\frac{4}{5} = \\frac{4 \\times 3}{5 \\times 3} = \\frac{12}{15}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D%20%3D%20%5Cfrac%7B1%20%5Ctimes%205%7D%7B3%20%5Ctimes%205%7D%20%3D%20%5Cfrac%7B5%7D%7B15%7D\" alt=\"\\small \\frac{1}{3} = \\frac{1 \\times 5}{3 \\times 5} = \\frac{5}{15}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B15%7D\" alt=\"\\small \\frac{12}{15}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B15%7D\" alt=\"\\small \\frac{5}{15}\" \/>.<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{5}{6}\\) and \\(\\frac{8}{9}\\)<br \/>\nAnswer:<br \/>\nUse the product of the denominators : 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 9 = 54<br \/>\nWrite equivalent fractions with denominators of 54<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D%20%3D%20%5Cfrac%7B5%20%5Ctimes%209%7D%7B6%20%5Ctimes%209%7D%20%3D%20%5Cfrac%7B45%7D%7B54%7D\" alt=\"\\small \\frac{5}{6} = \\frac{5 \\times 9}{6 \\times 9} = \\frac{45}{54}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B9%7D%20%3D%20%5Cfrac%7B8%20%5Ctimes%206%7D%7B9%20%5Ctimes%206%7D%20%3D%20%5Cfrac%7B48%7D%7B54%7D\" alt=\"\\small \\frac{8}{9} = \\frac{8 \\times 6}{9 \\times 6} = \\frac{48}{54}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B45%7D%7B54%7D\" alt=\"\\small \\frac{45}{54}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B48%7D%7B54%7D\" alt=\"\\small \\frac{48}{54}\" \/>.<\/p>\n<p>Question 16.<br \/>\n\\(\\frac{4}{5}\\) and \\(\\frac{3}{4}\\)<br \/>\nAnswer:<br \/>\nUse the product of the denominators : 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Ctimes\" alt=\"\\small \\times\" \/> 4 = 20<br \/>\nWrite equivalent fractions with denominators of 20<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D%20%3D%20%5Cfrac%7B4%20%5Ctimes%204%7D%7B5%20%5Ctimes%204%7D%20%3D%20%5Cfrac%7B16%7D%7B20%7D\" alt=\"\\small \\frac{4}{5} = \\frac{4 \\times 4}{5 \\times 4} = \\frac{16}{20}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D%20%3D%20%5Cfrac%7B3%20%5Ctimes%205%7D%7B4%20%5Ctimes%205%7D%20%3D%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{3}{4} = \\frac{3 \\times 5}{4 \\times 5} = \\frac{15}{20}\" \/><br \/>\nTherefore, equivalent fractions are <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B16%7D%7B20%7D\" alt=\"\\small \\frac{16}{20}\" \/>\u00a0 and <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{15}{20}\" \/>.<\/p>\n<p><strong>8.4 Add Fractions with Unlike Denominators<\/strong><\/p>\n<p>Add<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{2}{15}\\) + \\(\\frac{2}{3}\\) = __<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 15 is a multiple of 3, so rewrite \\(\\frac{2}{3}\\) with a denominator of 15.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%205%7D%7B3%20%5Ctimes%205%7D\" alt=\"\\small \\frac{2 \\times 5}{3 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B15%7D\" alt=\"\\small \\frac{10}{15}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B15%7D\" alt=\"\\small \\frac{2}{15}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B15%7D\" alt=\"\\small \\frac{2}{15}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B15%7D\" alt=\"\\small \\frac{10}{15}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B15%7D\" alt=\"\\small \\frac{12}{15}\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\frac{3}{4}\\) + \\(\\frac{1}{8}\\) = __<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 8 is a multiple of 4, so rewrite \\(\\frac{3}{4}\\) with a denominator of 8.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%202%7D%7B4%20%5Ctimes%202%7D\" alt=\"\\small \\frac{3 \\times 2}{4 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/><\/p>\n<p>Question 19.<br \/>\n\\(\\frac{7}{2}\\) + \\(\\frac{1}{6}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 6 is a multiple of 2, so rewrite \\(\\frac{7}{2}\\) with a denominator of 6.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B2%7D\" alt=\"\\small \\frac{7}{2}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%20%5Ctimes%203%7D%7B2%20%5Ctimes%203%7D\" alt=\"\\small \\frac{7 \\times 3}{2 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B21%7D%7B6%7D\" alt=\"\\small \\frac{21}{6}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B2%7D\" alt=\"\\small \\frac{7}{2}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B21%7D%7B6%7D\" alt=\"\\small \\frac{21}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B22%7D%7B6%7D\" alt=\"\\small \\frac{22}{6}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B3%7D\" alt=\"\\small \\frac{11}{3}\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{5}{9}\\) + \\(\\frac{1}{2}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 9 is not a multiple of 2, so rewrite each fraction with a denominator of 9 x 2 = 18.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B9%7D\" alt=\"\\small \\frac{5}{9}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%20%5Ctimes%202%7D%7B9%20%5Ctimes%202%7D\" alt=\"\\small \\frac{5 \\times 2}{9 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B18%7D\" alt=\"\\small \\frac{10}{18}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%209%7D%7B2%20%5Ctimes%209%7D\" alt=\"\\small \\frac{1 \\times 9}{2 \\times 9}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B18%7D\" alt=\"\\small \\frac{9}{18}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B9%7D\" alt=\"\\small \\frac{5}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B10%7D%7B18%7D\" alt=\"\\small \\frac{10}{18}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B9%7D%7B18%7D\" alt=\"\\small \\frac{9}{18}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B18%7D\" alt=\"\\small \\frac{19}{18}\" \/><\/p>\n<p>Question 21.<br \/>\n\\(\\frac{7}{10}\\) + \\(\\frac{5}{6}\\) = ___<br \/>\nAnswer:<\/p>\n<p>Use equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 10 is not a multiple of 6, so rewrite each fraction with a denominator of 10 x 6 = 60.<\/p>\n<p>Rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%20%5Ctimes%206%7D%7B10%20%5Ctimes%206%7D\" alt=\"\\small \\frac{7 \\times 6}{10 \\times 6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B42%7D%7B60%7D\" alt=\"\\small \\frac{42}{60}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%20%5Ctimes%2010%7D%7B6%20%5Ctimes%2010%7D\" alt=\"\\small \\frac{5 \\times 10}{6 \\times 10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B50%7D%7B60%7D\" alt=\"\\small \\frac{50}{60}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B42%7D%7B60%7D\" alt=\"\\small \\frac{42}{60}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B50%7D%7B60%7D\" alt=\"\\small \\frac{50}{60}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B92%7D%7B60%7D\" alt=\"\\small \\frac{92}{60}\" \/><\/p>\n<p>Question 22.<br \/>\n\\(\\frac{1}{6}\\) + \\(\\frac{11}{12}\\) + \\(\\frac{4}{6}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the sum.<br \/>\nThink: 12 is a multiple of 6, so rewrite each fraction with a denominator of 12.<\/p>\n<p>Rewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B6%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{6 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B12%7D\" alt=\"\\small \\frac{2}{12}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%20%5Ctimes%202%7D%7B6%20%5Ctimes%202%7D\" alt=\"\\small \\frac{4 \\times 2}{6 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B6%7D\" alt=\"\\small \\frac{4}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B12%7D\" alt=\"\\small \\frac{2}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B12%7D\" alt=\"\\small \\frac{11}{12}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B12%7D\" alt=\"\\small \\frac{8}{12}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B21%7D%7B12%7D\" alt=\"\\small \\frac{21}{12}\" \/><\/p>\n<p>= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B4%7D\" alt=\"\\small \\frac{7}{4}\" \/><\/p>\n<p><strong>8.5 Subtract Fractions with Unlike Denominators<\/strong><\/p>\n<p>Subtract<\/p>\n<p>Question 23.<br \/>\n\\(\\frac{1}{4}\\) &#8211; \\(\\frac{1}{8}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 8 is a multiple of 4, so rewrite \\(\\frac{1}{4}\\) with a denominator of 8.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%20%5Ctimes%202%7D%7B4%20%5Ctimes%202%7D\" alt=\"\\small \\frac{1 \\times 2}{4 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B8%7D\" alt=\"\\small \\frac{2}{8}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B4%7D\" alt=\"\\small \\frac{1}{4}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B8%7D\" alt=\"\\small \\frac{2}{8}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B8%7D\" alt=\"\\small \\frac{1}{8}\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\frac{3}{2}\\) &#8211; \\(\\frac{7}{10}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 10 is a multiple of 2, so rewrite \\(\\frac{3}{2}\\) with a denominator of 10.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%205%7D%7B2%20%5Ctimes%205%7D\" alt=\"\\small \\frac{3 \\times 5}{2 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B10%7D\" alt=\"\\small \\frac{15}{10}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B2%7D\" alt=\"\\small \\frac{3}{2}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B10%7D\" alt=\"\\small \\frac{15}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B10%7D\" alt=\"\\small \\frac{8}{10}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/><\/p>\n<p>Question 25.<br \/>\n\\(\\frac{15}{16}\\) &#8211; \\(\\frac{7}{8}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 16 is a multiple of 8, so rewrite \\(\\frac{7}{8}\\) with a denominator of 16.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%20%5Ctimes%202%7D%7B8%20%5Ctimes%202%7D\" alt=\"\\small \\frac{7 \\times 2}{8 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B16%7D\" alt=\"\\small \\frac{14}{16}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B16%7D\" alt=\"\\small \\frac{15}{16}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B16%7D\" alt=\"\\small \\frac{15}{16}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B16%7D\" alt=\"\\small \\frac{14}{16}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B16%7D\" alt=\"\\small \\frac{1}{16}\" \/><\/p>\n<p>Question 26.<br \/>\n\\(\\frac{4}{3}\\) &#8211; \\(\\frac{2}{5}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 5 is not a multiple of 3, so rewrite each fraction with a denominator of 5 x 3 = 15.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B3%7D\" alt=\"\\small \\frac{4}{3}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%20%5Ctimes%205%7D%7B3%20%5Ctimes%205%7D\" alt=\"\\small \\frac{4 \\times 5}{3 \\times 5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B15%7D\" alt=\"\\small \\frac{20}{15}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%203%7D%7B5%20%5Ctimes%203%7D\" alt=\"\\small \\frac{2 \\times 3}{5 \\times 3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B3%7D\" alt=\"\\small \\frac{4}{3}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B15%7D\" alt=\"\\small \\frac{20}{15}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B15%7D\" alt=\"\\small \\frac{6}{15}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B15%7D\" alt=\"\\small \\frac{14}{15}\" \/><\/p>\n<p>Question 27.<br \/>\n\\(\\frac{5}{6}\\) &#8211; \\(\\frac{3}{4}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 6 is not a multiple of 4, so rewrite each fraction with a denominator of 6 x 4 = 24.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%20%5Ctimes%204%7D%7B6%20%5Ctimes%204%7D\" alt=\"\\small \\frac{5 \\times 4}{6 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{20}{24}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%20%5Ctimes%206%7D%7B4%20%5Ctimes%206%7D\" alt=\"\\small \\frac{3 \\times 6}{4 \\times 6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{18}{24}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B20%7D%7B24%7D\" alt=\"\\small \\frac{20}{24}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B18%7D%7B24%7D\" alt=\"\\small \\frac{18}{24}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B24%7D\" alt=\"\\small \\frac{2}{24}\" \/><br \/>\n= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B12%7D\" alt=\"\\small \\frac{1}{12}\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\frac{7}{10}\\) &#8211; \\(\\frac{2}{5}\\) + \\(\\frac{11}{20}\\) = ___<br \/>\nAnswer:<br \/>\nUse equivalent fractions to write the fractions with a common denominator. Then find the difference.<br \/>\nThink: 20 is a multiple of 10 and 5, so rewrite each fraction with a denominator of 20.<br \/>\nRewrite <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/>\u00a0 as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%20%5Ctimes%202%7D%7B10%20%5Ctimes%202%7D\" alt=\"\\small \\frac{7 \\times 2}{10 \\times 2}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B20%7D\" alt=\"\\small \\frac{14}{20}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> as <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%20%5Ctimes%204%7D%7B5%20%5Ctimes%204%7D\" alt=\"\\small \\frac{2 \\times 4}{5 \\times 4}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B20%7D\" alt=\"\\small \\frac{8}{20}\" \/><\/p>\n<p><img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B20%7D\" alt=\"\\small \\frac{11}{20}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B20%7D\" alt=\"\\small \\frac{14}{20}\" \/> &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B20%7D\" alt=\"\\small \\frac{8}{20}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B20%7D\" alt=\"\\small \\frac{11}{20}\" \/><\/p>\n<p><strong>8.6 Add Mixed Numbers<\/strong><\/p>\n<p>Add<\/p>\n<p>Question 29.<br \/>\n1\\(\\frac{3}{4}\\) + 7\\(\\frac{5}{8}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> + 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/> + 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/><br \/>\n= 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B8%7D\" alt=\"\\small \\frac{11}{8}\" \/><\/p>\n<p>Question 30.<br \/>\n3\\(\\frac{3}{10}\\) + 2\\(\\frac{7}{20}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator<br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B20%7D\" alt=\"\\small \\frac{6}{20}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B20%7D\" alt=\"\\small \\frac{6}{20}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/><br \/>\n= 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B20%7D\" alt=\"\\small \\frac{13}{20}\" \/><\/p>\n<p>Question 31.<br \/>\n\\(\\frac{1}{3}\\) + 6\\(\\frac{4}{5}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator 3 x 5 = 15<br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B15%7D\" alt=\"\\small \\frac{5}{15}\" \/><br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B15%7D\" alt=\"\\small \\frac{12}{15}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> + 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B5%7D\" alt=\"\\small \\frac{4}{5}\" \/> \u00a0= <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B15%7D\" alt=\"\\small \\frac{5}{15}\" \/> + 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B12%7D%7B15%7D\" alt=\"\\small \\frac{12}{15}\" \/><br \/>\n= 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B17%7D%7B15%7D\" alt=\"\\small \\frac{17}{15}\" \/><\/p>\n<p>Question 32.<br \/>\n5\\(\\frac{8}{9}\\) + \\(\\frac{5}{6}\\) = _____<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator 9 x 6 = 54<br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B9%7D\" alt=\"\\small \\frac{8}{9}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B48%7D%7B54%7D\" alt=\"\\small \\frac{48}{54}\" \/><br \/>\n<img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B45%7D%7B54%7D\" alt=\"\\small \\frac{45}{54}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B9%7D\" alt=\"\\small \\frac{8}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/>\u00a0 = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B48%7D%7B54%7D\" alt=\"\\small \\frac{48}{54}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B45%7D%7B54%7D\" alt=\"\\small \\frac{45}{54}\" \/><br \/>\n= 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B93%7D%7B54%7D\" alt=\"\\small \\frac{93}{54}\" \/><\/p>\n<p>Question 33.<br \/>\n2\\(\\frac{2}{3}\\) + \\(\\frac{4}{9}\\) + 4\\(\\frac{1}{3}\\) = ___<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/><br \/>\n4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B9%7D\" alt=\"\\small \\frac{3}{9}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B3%7D\" alt=\"\\small \\frac{2}{3}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B9%7D\" alt=\"\\small \\frac{4}{9}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> \u00a0 = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B9%7D\" alt=\"\\small \\frac{6}{9}\" \/> + <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B9%7D\" alt=\"\\small \\frac{4}{9}\" \/> + 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B9%7D\" alt=\"\\small \\frac{3}{9}\" \/><br \/>\n= 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B9%7D\" alt=\"\\small \\frac{13}{9}\" \/><\/p>\n<p>Question 34.<br \/>\n5\\(\\frac{1}{2}\\) + 2\\(\\frac{5}{8}\\) + 3\\(\\frac{3}{4}\\) = _____<br \/>\nAnswer:<br \/>\nAdd the fractional parts and add the whole number parts.<br \/>\nTo add the fractional parts, use a common denominator<br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/><br \/>\n3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/>\u00a0 \u00a0=5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B8%7D\" alt=\"\\small \\frac{4}{8}\" \/> + 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B8%7D\" alt=\"\\small \\frac{5}{8}\" \/> + 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B8%7D\" alt=\"\\small \\frac{6}{8}\" \/><br \/>\n= 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B8%7D\" alt=\"\\small \\frac{15}{8}\" \/><\/p>\n<p><strong>8.7 Subtract Mixed Numbers<\/strong><\/p>\n<p>Subtract<\/p>\n<p>Question 35.<br \/>\n8\\(\\frac{7}{10}\\) &#8211; 1\\(\\frac{2}{5}\\) = ___<br \/>\nAnswer:<\/p>\n<p>Subtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/><br \/>\n8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" data-cke-saved-src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" \/>\u00a0&#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> \u00a0= 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" alt=\"\\small \\frac{7}{10}\" data-cke-saved-src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B10%7D\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B4%7D%7B10%7D\" alt=\"\\small \\frac{4}{10}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B10%7D\" alt=\"\\small \\frac{3}{10}\" \/><\/p>\n<p>Question 36.<br \/>\n15\\(\\frac{97}{100}\\) &#8211; 10\\(\\frac{7}{20}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/> = 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B35%7D%7B100%7D\" alt=\"\\small \\frac{35}{100}\" \/><br \/>\n15 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B97%7D%7B100%7D\" alt=\"\\small \\frac{97}{100}\" \/> &#8211; 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B20%7D\" alt=\"\\small \\frac{7}{20}\" \/>\u00a0 = 15 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B97%7D%7B100%7D\" alt=\"\\small \\frac{97}{100}\" \/> &#8211; 10 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B35%7D%7B100%7D\" alt=\"\\small \\frac{35}{100}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B62%7D%7B100%7D\" alt=\"\\small \\frac{62}{100}\" \/><\/p>\n<p>Question 37.<br \/>\n4 &#8211; 3\\(\\frac{5}{6}\\) = ___<br \/>\nAnswer:<br \/>\n4 &#8211; 3 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/> = 4 &#8211; <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B23%7D%7B6%7D\" alt=\"\\small \\frac{23}{6}\" \/> = <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B6%7D\" alt=\"\\small \\frac{1}{6}\" \/><\/p>\n<p>Question 38.<br \/>\n5\\(\\frac{1}{3}\\) &#8211; 2\\(\\frac{1}{2}\\) = _____<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator 3 x 2 = 6.<br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> = 5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B6%7D\" alt=\"\\small \\frac{2}{6}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B6%7D\" alt=\"\\small \\frac{8}{6}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/><br \/>\n5 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B3%7D\" alt=\"\\small \\frac{1}{3}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B6%7D\" alt=\"\\small \\frac{8}{6}\" \/> &#8211; 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B6%7D\" alt=\"\\small \\frac{3}{6}\" \/><br \/>\n= 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B6%7D\" alt=\"\\small \\frac{5}{6}\" \/><\/p>\n<p>Question 39.<br \/>\n9\\(\\frac{2}{5}\\) &#8211; 6\\(\\frac{3}{4}\\) = ___<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator 5 x 4 = 20.<br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> = 9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B20%7D\" alt=\"\\small \\frac{8}{20}\" \/> = 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B28%7D%7B20%7D\" alt=\"\\small \\frac{28}{20}\" \/><br \/>\n6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{15}{20}\" \/><br \/>\n9 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B2%7D%7B5%7D\" alt=\"\\small \\frac{2}{5}\" \/> &#8211; 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B4%7D\" alt=\"\\small \\frac{3}{4}\" \/> = 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B28%7D%7B20%7D\" alt=\"\\small \\frac{28}{20}\" \/> &#8211; 6 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B15%7D%7B20%7D\" alt=\"\\small \\frac{15}{20}\" \/><br \/>\n= 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B13%7D%7B20%7D\" alt=\"\\small \\frac{13}{20}\" \/><\/p>\n<p>Question 40.<br \/>\n2\\(\\frac{3}{8}\\) + 7\\(\\frac{1}{2}\\) &#8211; 1\\(\\frac{11}{16}\\) = ____<br \/>\nAnswer:<br \/>\nTo add or subtract the fractional parts, use a common denominator.<br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B16%7D\" alt=\"\\small \\frac{6}{16}\" \/><br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B16%7D\" alt=\"\\small \\frac{8}{16}\" \/><br \/>\n2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B8%7D\" alt=\"\\small \\frac{3}{8}\" \/> + 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B1%7D%7B2%7D\" alt=\"\\small \\frac{1}{2}\" \/>\u00a0 &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B16%7D\" alt=\"\\small \\frac{11}{16}\" \/> = 2 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B6%7D%7B16%7D\" alt=\"\\small \\frac{6}{16}\" \/> + 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B8%7D%7B16%7D\" alt=\"\\small \\frac{8}{16}\" \/> &#8211; 1 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B11%7D%7B16%7D\" alt=\"\\small \\frac{11}{16}\" \/><br \/>\n= 8 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B16%7D\" alt=\"\\small \\frac{3}{16}\" \/><\/p>\n<p>Question 41.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA family adopts a puppy that weighs 7\\(\\frac{7}{8}\\) pounds. They take him to the vet 2 weeks later, and he weighs 12\\(\\frac{3}{16}\\) pounds. How much weight did the puppy gain?<br \/>\nAnswer:<br \/>\nSubtract the fractional parts and subtract the whole number parts.<br \/>\nTo subtract the fractional parts, use a common denominator.<br \/>\n7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B16%7D\" alt=\"\\small \\frac{14}{16}\" \/><br \/>\n12 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B16%7D\" alt=\"\\small \\frac{3}{16}\" \/> &#8211; 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B7%7D%7B8%7D\" alt=\"\\small \\frac{7}{8}\" \/> = 12 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B3%7D%7B16%7D\" alt=\"\\small \\frac{3}{16}\" \/> \u00a0&#8211; 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B16%7D\" alt=\"\\small \\frac{14}{16}\" \/><br \/>\n= 11 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B19%7D%7B16%7D\" alt=\"\\small \\frac{19}{16}\" \/> &#8211; 7 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B14%7D%7B16%7D\" alt=\"\\small \\frac{14}{16}\" \/><br \/>\n= 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B16%7D\" alt=\"\\small \\frac{5}{16}\" \/><br \/>\nSo the puppy gains 4 <img src=\"https:\/\/private.codecogs.com\/gif.latex?%5Cdpi%7B100%7D%20%5Csmall%20%5Cfrac%7B5%7D%7B16%7D\" alt=\"\\small \\frac{5}{16}\" \/> pounds weight.<\/p>\n<p><strong>8.8 Problem Solving: Fractions<\/strong><\/p>\n<p>Question 42.<br \/>\nA radio station plays three commercials between two songs. The commercials play for 2 minutes altogether. The first commercial is \\(\\frac{1}{2}\\) minute, and the second commercial is 1\\(\\frac{1}{4}\\) minutes. How long is the third commercial?<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nA radio station plays three commercials between two songs.<br \/>\nThe commercials play for 2 minutes altogether. The first commercial is \\(\\frac{1}{2}\\) minute, and the second commercial is 1\\(\\frac{1}{4}\\) minutes.<br \/>\n\\(\\frac{1}{2}\\) + 1\\(\\frac{1}{4}\\) = 1 \\(\\frac{3}{4}\\)<br \/>\n2 &#8211; 1 \\(\\frac{3}{4}\\) = \\(\\frac{1}{4}\\)<\/p>\n<p>Question 43.<br \/>\nYour friend plants a tree seedling on Earth Day that is 1\\(\\frac{1}{3}\\) feet tall. In 1 year, the tree grows 1\\(\\frac{5}{6}\\) feet. After 2 years, the tree is 4\\(\\frac{11}{12}\\) feet tall. How much did the tree grow in the second year?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-16248\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-8-Add-and-Subtract-Fractions-109.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 8 Add and Subtract Fractions 109\" width=\"131\" height=\"236\" \/><br \/>\nAnswer:<br \/>\nGiven,<br \/>\nYour friend plants a tree seedling on Earth Day that is 1\\(\\frac{1}{3}\\) feet tall.<br \/>\nIn 1 year, the tree grows 1\\(\\frac{5}{6}\\) feet. After 2 years, the tree is 4\\(\\frac{11}{12}\\) feet tall.<br \/>\n4\\(\\frac{11}{12}\\) &#8211; 1\\(\\frac{5}{6}\\)\u00a0 = 3 \\(\\frac{1}{12}\\)<br \/>\n3 \\(\\frac{1}{12}\\) &#8211; 1\\(\\frac{1}{3}\\) = 1 \\(\\frac{3}{4}\\)<br \/>\nThus the growth of the tree in the second year is 1 \\(\\frac{3}{4}\\) feet.<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>Enhance your math skills and performance skills by referring to our Big Ideas Math Grade 5 Answer Key for Chapter 8 Add and Subtract Fractions. Make use of the links to complete your homework and assignments. Practice the given questions number of times to score the highest marks in the exams. Also, keep in touch with our site to get the Solution Key for all Big Ideas Math Grade 5 Chapters from 1 to 14.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions is the best source to learn Add and Subtract Fractions concepts. Get free access to download Big Ideas Math Answers Grade 5 Chapter 8 Add and Subtract Fractions pdf. Learn how to solve a problem in different ways. 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