{"id":13331,"date":"2022-04-07T08:30:15","date_gmt":"2022-04-07T03:00:15","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=13331"},"modified":"2022-04-07T11:08:50","modified_gmt":"2022-04-07T05:38:50","slug":"big-ideas-math-answers-grade-4-chapter-6","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4-chapter-6\/","title":{"rendered":"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns"},"content":{"rendered":"<p>Get free step-by-step solutions and explanations for all the available questions here. The students who are looking for Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns can download the pdf for free of cost. The BIM 4th Grade Chapter 6 contains all the topics that help the students to score good marks in the exams. The main aim of providing the Big Ideas Math Book 4th Grade Answer Key Chapter 6 Factors, Multiples, and Patterns is to make the students understand the concepts in an easy manner. Learn Big Ideas Grade 4 Math Answer Key with the help of the simple methods.<\/p>\n<h2>Big Ideas 4th Grade Math Book Answer Key Chapter 6 Factors, Multiples, and Patterns<\/h2>\n<p>The advantage of referring to our <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-4\/\">Big Ideas Math Answers Grade 4<\/a> Chapter 6 is you can refer to all the problems and also take practice tests for free of cost. Improve your math skills and score better marks in the exams with the help of the BIM 4th Grade Math Answer Key. Check out the below links for a better understanding of every topic. Just click on the links and grab the depth of knowledge on each topic. Practice real-time problems to gain more knowledge on concepts.<\/p>\n<p><strong>Lesson: 1 Understand Factors<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.1_Understand_Factors\">Lesson 6.1 Understand Factors<\/a><\/li>\n<li><a href=\"#Understand_Factors_Practice_6.1\">Understand Factors Homework &amp; Practice 6.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Factors and Divisibility<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.2_Factors_and_Divisibility\">Lesson 6.2 Factors and Divisibility<\/a><\/li>\n<li><a href=\"#Factors_and_Divisibility_Practice_6.2\">Factors and Divisibility Homework &amp; Practice 6.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Relate Factors and Multiples<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.3_Relate_Factors_and_Multiples\">Lesson 6.3 Relate Factors and Multiples<\/a><\/li>\n<li><a href=\"#Relate_Factors_and_Multiples_Practice_6.3\">Relate Factors and Multiples Homework &amp; Practice 6.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Identify Prime and Composite Numbers<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.4_Identify_Prime_and_Composite_Numbers\">Lesson 6.4 Identify Prime and Composite Numbers<\/a><\/li>\n<li><a href=\"#Identify_Prime_and_Composite_Numbers_Practice_6.4\">Identify Prime and Composite Numbers Homework &amp; Practice 6.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Number Patterns<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.5_Number_Patterns\">Lesson 6.5 Number Patterns<\/a><\/li>\n<li><a href=\"#Number_Patterns_Practice_6.5\">Number Patterns Numbers Homework &amp; Practice 6.5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 6 Shape Patterns<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_6.6_Shape_Patterns\">Lesson 6.6 Shape Patterns<\/a><\/li>\n<li><a href=\"#Shape_Patterns_Practice_6.6\">Shape Patterns Numbers Homework &amp; Practice 6.6<\/a><\/li>\n<\/ul>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Factors,_Multiples,_and_Patterns_Performance_Task\">Factors, Multiples, and Patterns Performance Task<\/a><\/li>\n<li><a href=\"#Factors,_Multiples,_and_Patterns_Activity\">Factors, Multiples, and Patterns Activity<\/a><\/li>\n<li><a href=\"#Factors,_Multiples,_and_Patterns_Chapter_Practice\">Factors, Multiples, and Patterns Chapter Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_6.1_Understand_Factors\"><\/a>Lesson 6.1 Understand Factors<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Draw two different rectangles that each have an area of 24 square units. Label their side lengths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 1\" width=\"429\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-1.png 429w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-1-300x181.png 300w\" sizes=\"(max-width: 429px) 100vw, 429px\" \/><br \/>\nCompare your rectangles to your partner\u2019s rectangles. How are they the same? How are they different?<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6.jpg\" alt=\"\" width=\"100\" height=\"123\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-19975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-1.jpg\" alt=\"\" width=\"162\" height=\"80\" \/><\/p>\n<p>Explanation:<br \/>\nMy rectangle is 6 \u00d7 4 and my partner&#8217;s rectangle is 3 \u00d7 8<br \/>\nWe know that,<br \/>\nArea of rectangle = l \u00d7 b<br \/>\nHence,<br \/>\nAccording to the above formula, the areas of rectangles are the same irrespective of different lengths and different breadths.<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow is each side length related to 24?<\/p>\n<p>Answer:\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-19973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6.jpg\" alt=\"\" width=\"100\" height=\"123\" \/> <img loading=\"lazy\" class=\"alignnone size-full wp-image-19975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-1.jpg\" alt=\"\" width=\"162\" height=\"80\" \/><br \/>\nWe know that,<br \/>\nThe factors of 24 = 4 \u00d7 6, 3 \u00d7 8, 1 \u00d7 24, 2 \u00d7 12<br \/>\nRemember that,<br \/>\na \u00d7 b = b \u00d7 a<br \/>\nSo,<br \/>\n4 \u00d7 6 = 6 \u00d7 4<br \/>\nThis pattern will be applicable to all factor pairs<br \/>\nHence, from the above,<br \/>\nWe can conclude that each side length is related to 24 because of the factor pair.<\/p>\n<p><strong>Think and Grow: Find Factor Pairs<\/strong><\/p>\n<p>You can write whole numbers as products of two factors. The two factors are called a factor pair for the number<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 2\" width=\"221\" height=\"154\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nFind the factor pairs for 20.<br \/>\nFind the side lengths of as many different rectangles with an area of 20 square units as possible.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-2.jpg\" alt=\"\" width=\"596\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-2.jpg 596w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-2-300x113.jpg 300w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><br \/>\nThe side lengths of each rectangle are a factor pair.<br \/>\nSo, the factor pairs for 20 are 12 and 1,\u00a0 10 and 2,\u00a0 and 5 and 4.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nUse the rectangles to find the factor pairs for 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 4\" width=\"233\" height=\"175\" \/><br \/>\nAnswer: Factor pairs of 12 are: 12 and 1, 6 and 2, and 4 and 3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-3.jpg\" alt=\"\" width=\"235\" height=\"168\" \/><br \/>\nThe factor pairs are nothing but the side lengths of a rectangle and the area of a rectangle gives the factor<br \/>\nHence,<br \/>\nThe factor pairs of 12 are: 12 and 1, 6 and 2, and 4 and 3<\/p>\n<p>Question 2.<br \/>\nDraw rectangles to find the factor pairs for 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 5\" width=\"298\" height=\"174\" \/><br \/>\nAnswer: The factor pairs of 16 are: 1 and 16, 2 and 8, 4 and\u00a0 4<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-4.jpg\" alt=\"\" width=\"284\" height=\"40\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-19985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-5.jpg\" alt=\"\" width=\"101\" height=\"89\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-19987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-6.jpg\" alt=\"\" width=\"152\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-6.jpg 152w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-6-150x57.jpg 150w\" sizes=\"(max-width: 152px) 100vw, 152px\" \/><\/p>\n<p>The factor pairs are nothing but the side lengths of a rectangle and the area of a rectangle gives the factor<br \/>\nHence,<br \/>\nThe factor pairs of 16 are: 1 and 16, 2 and 8, 4 and\u00a0 4<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Draw rectangles to find the factor pairs for the number.<\/strong><br \/>\nQuestion 3.<br \/>\n14<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 6\" width=\"329\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-6.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-6-300x154.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Answer: The factor pairs of 14 are: 1 and 14, 2 and 7<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-8.jpg\" alt=\"\" width=\"247\" height=\"47\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-19991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-9.jpg\" alt=\"\" width=\"64\" height=\"134\" \/><\/p>\n<p>Factors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 14 are: 1 and 14, 2 and 7<\/p>\n<p>Question 4.<br \/>\n15<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 7\" width=\"326\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-7.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-7-300x157.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><\/p>\n<p>Answer:\u00a0 The factor pairs of 15 are: 1 and 15, 3 and 5<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-10.jpg\" alt=\"\" width=\"84\" height=\"99\" \/><\/p>\n<p>Factors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 15 are: 1 and 15, 3 and 5<\/p>\n<p>Question 5.<br \/>\n20<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 8\" width=\"329\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-8.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-8-300x154.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><\/p>\n<p>Answer: The factor pairs of 20 are: 1 and 20, 2 and 10, 4 and 5<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-19994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-11.jpg\" alt=\"\" width=\"182\" height=\"45\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-19995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-12.jpg\" alt=\"\" width=\"106\" height=\"90\" \/><br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 15 are: 1 and 15, 3 and 5<\/p>\n<p>Question 6.<br \/>\n36<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 9\" width=\"329\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-9.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-9-300x156.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer: The factor pairs of 36 are: 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-55.jpg\" alt=\"\" width=\"326\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-55.jpg 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-55-300x66.jpg 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-22913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-56.jpg\" alt=\"\" width=\"230\" height=\"85\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-22914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-57.jpg\" alt=\"\" width=\"100\" height=\"176\" \/><br \/>\nFactors are the numbers that divide the number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 36 are: 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6<\/p>\n<p><strong>Find the factor pairs for the number.<\/strong><br \/>\nQuestion 7.<br \/>\n11<br \/>\nAnswer: The factor pairs of 11 are: 1 and 11<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-14.jpg\" alt=\"\" width=\"196\" height=\"33\" \/><br \/>\nFactors are the numbers that divide the original number completely.Hence,<br \/>\nThe factor pairs of 15 are: 1 and 15, 3 and 5<\/p>\n<p>Question 8.<br \/>\n9<br \/>\nAnswer: The factor pairs of 9 are: 1 and 9, and 3 and 3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-15.jpg\" alt=\"\" width=\"77\" height=\"76\" \/><\/p>\n<p>Factors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 15 are: 1 and 15, 3 and 5<\/p>\n<p>Question 9.<br \/>\n4<\/p>\n<p>Answer: The factor pairs of 4 are: 1 and 4, 2 and 2<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 4 are:<br \/>\n1 \u00d7 4, 2 \u00d7 2 ( Since 4 \u00d71 and 1 \u00d7 4 are equal, we will take any 1 factor )<\/p>\n<p>Question 10.<br \/>\n25<br \/>\nAnswer:\u00a0 The factor pairs of 25 are: 1 and 25, 5 and 5<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 25 are:<br \/>\n1 \u00d7 25, 5 \u00d7 5<\/p>\n<p>Question 11.<br \/>\n10<br \/>\nAnswer: The factor pairs of 10 are: 1 and 10, 2 and 5<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 10 are:<br \/>\n1 \u00d7 10, 5 \u00d7 5<\/p>\n<p>Question 12.<br \/>\n40<br \/>\nAnswer: The factor pairs of 40 are: 1 and 40, 2 and 20, 4 and 10, 5 and 8<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 40 are:<br \/>\n1 \u00d7 40, 2 \u00d7 20, 4 \u00d7 10 and 5 \u00d7 8<\/p>\n<p>Question 13.<br \/>\n<strong>Writing<\/strong><br \/>\nUse the word to explain one way that 2 and 6 are related.<br \/>\nAnswer: The factor pair of 6 are: 1 and 6, 2 and 3<\/p>\n<p>Explanation:<br \/>\nThe one way 2 and\u00a0 are related is the &#8220;Factor-pair method&#8221;<br \/>\nAccording to the factor-pair method,<br \/>\nThe factors of 6 are:<br \/>\n1 \u00d7 6 and 2 \u00d7 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that 2 and 6 are related due to the factor-pair method.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou want to organize 30 pictures into a rectangular array on a wall. How many different arrays can you make?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 10\" width=\"600\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-10.png 600w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-10-300x107.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><br \/>\nTo find the number of arrays you can make, find the number of factor pairs for 30.<br \/>\nThere are 3-factor pairs for 30.<br \/>\nYou can use each factor pair to make 30 arrays.<br \/>\nSo, there are 30 \u00d73 = 90 ways to organize the pictures in different arrays.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nA city mayor buys 27 solar panels. She wants to organize the panels into a rectangular array. How many different arrays can she make?<\/p>\n<p>Answer: The different arrays she can make are: 1 \u00d7 27, 3 \u00d7 9, 9 \u00d7 3, and 27 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nGiven that a city mayor buys 27 solar panels and she wants to organize the panels into a rectangular array.<br \/>\nThe &#8220;Array&#8221; is nothing but the number of patterns ( Factor pairs)\u00a0 that we can arrange the given things.<br \/>\nHence,<br \/>\nThe factors of 27 are: 1 and 27, 3 and 9, 9 and 3, and 27 and 1<br \/>\nHence,<br \/>\nThe different arrays she can make in arranging the solar panels are:<br \/>\n1 \u00d7 27, 3 \u00d7 9, 9 \u00d7 3, and 27 \u00d7 1<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA store owner has 42 masks to hang in a rectangular array on a wall. The owner does not have room for more than 10 masks in each row or column. What are the possible numbers of masks the owner should hang in each row?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 11\" width=\"77\" height=\"117\" \/><\/p>\n<p>Answer: The number of possible masks the owner should hang in each row is: 7 masks<\/p>\n<p>Explanation:<br \/>\nGiven that a store owner has 42 masks to hang in a rectangular array on a wall.<br \/>\nSo now,<br \/>\nThe number of arrays ( Factor pairs ) of 42 are:<br \/>\n1 \u00d7 42, 2 \u00d7 21, 3 \u00d7 14, 6 \u00d7 7, 7 \u00d7 6, 14 \u00d7 3, 21 \u00d7 2, and 41 \u00d7 1<br \/>\nIt is also given that the owner does not have enough room for more than 10 masks in each row or column.<br \/>\nSo, from the above factor pairs, we can say that the possible array of masks is: 6 \u00d7 7 and 7 \u00d7 6<br \/>\nHence, from the above,<br \/>\nwe can conclude that the maximum number of masks the owner can put either in rows or columns is: 7 masks<\/p>\n<p>Question 16.<br \/>\nA teacher wants to set up a chair for each of the 48 students in chorus. He wants to set up the chairs in a rectangular array. He can fit no more than 20 rows and no more than 30 chairs in each row in the room. What are the possible numbers of rows that he could set up?<\/p>\n<p>Answer:\u00a0 The possible number of rows that he could set up are: 16 rows<\/p>\n<p>Explanation:<br \/>\nGiven that a teacher wants to set up a chai for each of the 48 students in the chorus and he wants to set up the chairs in a rectangular array.<br \/>\nHence, the number of arrays ( factor pairs) of 48 are:<br \/>\n1 \u00d7 48, 2 \u00d7 24, 3 \u00d7 16, 4 \u00d7 12, 6 \u00d7 8, 8 \u00d7 6, 12 \u00d7 4, 16 \u00d7 3, 24 \u00d7 2, and 48 \u00d7 1<br \/>\nIt is also given that he can fit no more than 20 rows and no more than 30 chairs in each row in the room.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the possible number of rows that he could set up are: 16 rows<\/p>\n<h3><a id=\"Understand_Factors_Practice_6.1\"><\/a>Understand Factors Homework &amp; Practice 6.1<\/h3>\n<p>Question 1.<br \/>\nUse the rectangles to find the factor pairs for 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 12\" width=\"181\" height=\"171\" \/><\/p>\n<p>Answer: The factors of 8 are: 1 and 8, 2 and 4<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-16.jpg\" alt=\"\" width=\"175\" height=\"167\" \/><br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 8 are: 1 \u00d7 8 and 2 \u00d7 4<\/p>\n<p>Question 2.<br \/>\nDraw rectangles to find the factor pairs for 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 13\" width=\"338\" height=\"171\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-13.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-13-300x152.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><\/p>\n<p>Answer: The factor pairs of 21 are: 1 \u00d7 21, 3 \u00d7 7<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-17.jpg\" alt=\"\" width=\"369\" height=\"49\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-17.jpg 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-17-300x40.jpg 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-20014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-18.jpg\" alt=\"\" width=\"83\" height=\"130\" \/><br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 21 are: 1 \u00d7 21, 3 \u00d7 7<\/p>\n<p>Question 3.<br \/>\nDraw rectangles to find the factor pairs for 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 14\" width=\"511\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-14.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-14-300x104.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Answer: The factor pairs of 28 are: 1 \u00d7 28, 2 \u00d7 14, 4 \u00d7 7<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-19.jpg\" alt=\"\" width=\"504\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-19.jpg 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-19-300x39.jpg 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-20017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-20.jpg\" alt=\"\" width=\"252\" height=\"60\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-21.jpg\" alt=\"\" width=\"108\" height=\"135\" \/><br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 28 are: 1 \u00d7 28, 2 \u00d7 14, 4 \u00d7 7<\/p>\n<p><strong>Find the factor pairs for the number.<\/strong><br \/>\nQuestion 4.<br \/>\n13<br \/>\nAnswer: The factor pairs of 13 are: 1 \u00d7 13 and 13 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely. Hence,<br \/>\nThe factor pairs of 13 are:<br \/>\n1 \u00d7 13 and 13 \u00d7 1<\/p>\n<p>Question 5.<br \/>\n5<br \/>\nAnswer: The factor pairs of 5 are: 1 \u00d7 5 and 5 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 5 are:<br \/>\n1 \u00d7 5 and 5 \u00d7 1<\/p>\n<p>Question 6.<br \/>\n35<br \/>\nAnswer: The factor pairs of 35 are: 1 \u00d7 35, 5 \u00d7 7<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 35 are:<br \/>\n1 \u00d7 35, 5 \u00d7 7<\/p>\n<p>Question 7.<br \/>\n45<br \/>\nAnswer: The factor pairs of 45 are: 1 \u00d7 45, 3 \u00d7 15, 5\u00d7 9<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 45 are:<br \/>\n1 \u00d7 45, 3 \u00d7 15, 5\u00d7 9<\/p>\n<p>Question 8.<br \/>\n18<br \/>\nAnswer: The factor pairs of 18 are: 1 \u00d7 18, 2 \u00d7 9, 3 \u00d7 6<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 18 are:<br \/>\n1 \u00d7 18, 2 \u00d7 9, 3 \u00d7 6<\/p>\n<p>Question 9.<br \/>\n36<br \/>\nAnswer: The factor pairs of 36 are: 1 \u00d7 36, 2 \u00d7 18, 3 \u00d7 12, 4 \u00d7 9, 6 \u00d7 6<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 36 are:<br \/>\n1 \u00d7 36, 2 \u00d7 18, 3 \u00d7 12, 4 \u00d7 9, 6 \u00d7 6<\/p>\n<p>Question 10.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nDescartes says there are 5-factor pairs for 16. Newton says there are 3-factor pairs for 16. Who is correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 15\" width=\"571\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-15.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-15-300x100.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Answer:\u00a0 Newton is correct<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\na \u00d7 b = b \u00d7 a<br \/>\nHence,<br \/>\nThe factor pairs of 16 are:<br \/>\n1 \u00d7 16, 2 \u00d7 8, 4 \u00d7 4, 8 \u00d7 2, 16 \u00d7 1<br \/>\nBut according to the above,<br \/>\nWe don&#8217;t have to consider the factor pairs 8 \u00d7 2 and 16 \u00d7 1<br \/>\nHence,<br \/>\nThere are only 3-factor pairs.<br \/>\nBut, Descartes says that there are 5-factor pairs for 16 while Newton says it three.<br \/>\nHence, from the above,<br \/>\nWe can conclude that Newton is correct.<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA race volunteer has 50 cases of bottled water. He wants to arrange the cases into a rectangular array. How many different arrays can he make?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.1 16\" width=\"183\" height=\"157\" \/><\/p>\n<p>Answer: The number of different arrays he can make is: 6 arrays<\/p>\n<p>Explanation:<br \/>\nGiven that a race volunteer has 50 cases of bottled water and he wants to arrange the cases into a rectangular array.<br \/>\nThe array is nothing but the factor pairs.<br \/>\nHence, the number of arrays of 50 he can make = 1 \u00d7 50, 2 \u00d7 25, 5 \u00d7 10, 10 \u00d7 5, 25 \u00d7 2, 50 \u00d7 1<br \/>\nHence, from the above,<br \/>\nwe can conclude that the number of different arrays to arrange the 50 cases of bottled water are:<br \/>\na) 1 \u00d7 50 b)\u00a0 2 \u00d7 25 c)\u00a0 5 \u00d7 10 d)\u00a0 10 \u00d7 5 e)\u00a0 25 \u00d7 2 f)\u00a0 50 \u00d7 1<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 12.<br \/>\n2 \u00d7 14 = _____<br \/>\nAnswer: 2 \u00d7 14 = 28<\/p>\n<p>Explanation:<br \/>\nAccording to the Distributive Property of Multiplication,<br \/>\n2 \u00d7 14 = ( 10 + 4 ) \u00d7 2<br \/>\n= ( 2 \u00d7 10 ) + ( 2 \u00d7 4 )<br \/>\n= 20 + 8<br \/>\n= 28<br \/>\nHence, 2 \u00d7 14 = 28<\/p>\n<p>Question 13.<br \/>\n22 \u00d7 7 = ______<br \/>\nAnswer: 22 \u00d7 7 = 154<\/p>\n<p>Explanation:<br \/>\nAccording to the Distributive Property of Multiplication,<br \/>\n22 \u00d7 7 = ( 20 + 2 ) \u00d7 7<br \/>\n= ( 20 \u00d7 7 ) + ( 2 \u00d7 7 )<br \/>\n= 140 + 14<br \/>\n= 154<br \/>\nHence, 22 \u00d7 7 = 154<\/p>\n<p>Question 14.<br \/>\n9 \u00d7 27 = ______<br \/>\nAnswer: 27 \u00d7 9 = 243<\/p>\n<p>Explanation:<br \/>\nAccording to the Distributive Property of Multiplication,<br \/>\n27 \u00d7 9 = ( 20 + 7 ) \u00d7 9<br \/>\n= ( 20 \u00d7 9 ) + ( 7 \u00d7 9 )<br \/>\n= 180 + 63<br \/>\n= 243<br \/>\nHence, 27 \u00d7 9 = 243<\/p>\n<h3><a id=\"Lesson_6.2_Factors_and_Divisibility\"><\/a>Lesson 6.2 Factors and Divisibility<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>List any 10 multiples of 3. What do you notice about the sum of the digits in each multiple?<br \/>\nAnswer:<br \/>\nThe 10 multiples of 3 are:<br \/>\n3, 6, 9, 12, 15, 18 ,21, 24, 27, and 30<br \/>\nFrom the sum of the digits in the above multiples,<br \/>\n0 + 3 =3<br \/>\n0 + 6 = 6<br \/>\n0 + 9 = 9<br \/>\n1 + 2 = 3<br \/>\n1 + 5 = 6<br \/>\n2 + 1 = 3<br \/>\n2 + 4= 6<br \/>\n2 + 7 = 9<br \/>\n3 + 0 = 3<br \/>\nHence, from the above sums,<br \/>\nWe can conclude that the sum of the digits in the 10 multiples are also the multiples of 3.<\/p>\n<p>List any 10 multiples of 9. What do you notice about the sum of the digits in each multiple?<br \/>\nAnswer:<br \/>\nThe 10 multiples of 9 are:<br \/>\n9, 18, 27, 36, 45, 54, 63, 72, 81, and 90<br \/>\nFrom the sum of the digits in the above multiples,<br \/>\n0 + 9 = 9<br \/>\n1 + 8 = 9<br \/>\n2 + 7 = 9<br \/>\n3 + 6 = 9<br \/>\n4 + 5 = 9<br \/>\n5 + 4 = 9<br \/>\n6 + 3 = 9<br \/>\n7 + 2 = 9<br \/>\n8 + 1 = 9<br \/>\n9 + 0 = 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the sum of the digits in all the multiples of 9 is equal to 9 only.<\/p>\n<p><strong>Structure<\/strong><br \/>\nHow can you use your observations above to determine whether 3 and 9 are factors of a given number? Explain.<br \/>\nAnswer: The factors of 9 are: 1,3, and 9<\/p>\n<p>Explanation:<br \/>\nThe factor pairs of 9 are:<br \/>\n1 \u00d7 9, 3 \u00d7 3 and 9 \u00d7 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that 3 and 9 are the factors of 9.<\/p>\n<p><strong>Think and Grow: Find Factors and Factor Pairs<\/strong><\/p>\n<p>A number is divisible by another number when a quotient is a whole number and the remainder is 0.<\/p>\n<p>Some numbers have divisibility rules that you can use to determine whether they are factors of other numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13348\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-1.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 1\" width=\"375\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-1.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-1-300x174.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><br \/>\n<strong>Example<\/strong><br \/>\nFind the factor pairs for 48.<br \/>\nUse divisibility rules and division to find the factors of 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-22.jpg\" alt=\"\" width=\"657\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-22.jpg 657w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-22-300x176.jpg 300w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><br \/>\nThe factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.<br \/>\nThe factor pairs for 48 are 6.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Find the factor pairs for the number.<\/strong><br \/>\nQuestion 1.<br \/>\n30<br \/>\nAnswer:<br \/>\nThe factor pairs of 30 are:<br \/>\n1 \u00d7 30, 2 \u00d7 15, 3 \u00d7 10, 5 \u00d7 6, 6 \u00d7 5, 10 \u00d7 3, 15 \u00d7 2, 30 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 30 are:<br \/>\n1 \u00d7 30, 2 \u00d7 15, 3 \u00d7 10, 5 \u00d7 6, 6 \u00d7 5, 10 \u00d7 3, 15 \u00d7 2, 30 \u00d7 1<\/p>\n<p>Question 2.<br \/>\n54<br \/>\nAnswer:<br \/>\nThe factor pairs of 54 are:<br \/>\n1 \u00d7 54, 2 \u00d7 27, 3 \u00d7 18, 6 \u00d7 9, 9 \u00d7 6, 18 \u00d7 3, 27 \u00d7 2, 54 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 54 are:<br \/>\n1 \u00d7 54, 2 \u00d7 27, 3 \u00d7 18, 6 \u00d7 9, 9 \u00d7 6, 18 \u00d7 3, 27 \u00d7 2, 54 \u00d7 1<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Find the factor pairs for the number.<\/strong><br \/>\nQuestion 3.<br \/>\n29<br \/>\nAnswer:<br \/>\nThe factor pairs of 29 are:<br \/>\n1 \u00d7 29 and 29 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original numbers completely.<br \/>\nHence,<br \/>\nThe factor pairs of 29 are:<br \/>\n1 \u00d7 29 and 29 \u00d7 1<\/p>\n<p>Question 4.<br \/>\n50<br \/>\nAnswer:<br \/>\nThe factor pairs of 50 are:<br \/>\n1 \u00d7 50, 2 \u00d7 25, 5 \u00d7 10, 10 \u00d7 5, 25 \u00d7 2, and 50 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original numbers completely.<br \/>\nHence,<br \/>\nThe factor pairs of 50 are:<br \/>\n1 \u00d7 50, 2 \u00d7 25, 5 \u00d7 10, 10 \u00d7 5, 25 \u00d7 2, and 50 \u00d7 1<\/p>\n<p>Question 5.<br \/>\n63<br \/>\nAnswer:<br \/>\nThe factor pairs of 63 are:<br \/>\n1 \u00d7 63, 3 \u00d7 21, 7 \u00d7 9, 9 \u00d7 7, 21 \u00d7 3 and 63 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 63 are:<br \/>\n1 \u00d7 63, 3 \u00d7 21, 7 \u00d7 9, 9 \u00d7 7, 21 \u00d7 3 and 63 \u00d7 1<\/p>\n<p>Question 6.<br \/>\n33<br \/>\nAnswer:<br \/>\nThe factor pairs of 33 are:<br \/>\n1 \u00d7 33, 3 \u00d7 11, 11 \u00d7 3 and 33 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 33 are:<br \/>\n1 \u00d7 33, 3 \u00d7 11, 11 \u00d7 3 and 33 \u00d7 1<\/p>\n<p>Question 7.<br \/>\n60<br \/>\nAnswer:<br \/>\nThe factor pairs of 60 are:<br \/>\n1 \u00d7 60, 2 \u00d7 30, 3 \u00d7 20, 4 \u00d7 15, 5 \u00d7 12, and 6 \u00d7 10<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 60 are:<br \/>\n1 \u00d7 60, 2 \u00d7 30, 3 \u00d7 20, 4 \u00d7 15, 5 \u00d7 12, and 6 \u00d7 10<\/p>\n<p>Question 8.<br \/>\n64<br \/>\nAnswer:<br \/>\nThe factor pairs of 64 are:<br \/>\n1 \u00d7 64, 2 \u00d7 32, 4 \u00d7 16, and 8 \u00d78<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 64 are:<br \/>\n1 \u00d7 64, 2 \u00d7 32, 4 \u00d7 16, and 8 \u00d78<\/p>\n<p><strong>List the factors of the number.<\/strong><br \/>\nQuestion 9.<br \/>\n39<br \/>\nAnswer:<br \/>\nThe factors of 39 are: 1, 3, 13, and 39<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 39 are: 1, 3, 13, and 39<\/p>\n<p>Question 10.<br \/>\n44<br \/>\nAnswer:<br \/>\nThe factors of 44 are: 1, 2, 4, 11, 22, and 44<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 44 are: 1, 2, 4, 11, 22, and 44<\/p>\n<p>Question 11.<br \/>\n72<br \/>\nAnswer:<br \/>\nThe factors of 72 are: 1, 2, 3,4, 6, 8, 9, 12, 18, 24, 36, and 72<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 72 are: 1, 2, 3,4, 6, 8, 9, 12, 18, 24, 36, and 72<\/p>\n<p>Question 12.<br \/>\n67<br \/>\nAnswer:<br \/>\nThe factors of 7 are: 1 and 67<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 7 are: 1 and 67<\/p>\n<p>Question 13.<br \/>\n42<br \/>\nAnswer:<br \/>\nThe factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42<\/p>\n<p>Question 14.<br \/>\n28<br \/>\nAnswer:<br \/>\nThe factors of 28 are:<br \/>\n1, 2, 4, 7, 14, and 28<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally<br \/>\nHence,<br \/>\nThe factors of 28 are:<br \/>\n1, 2, 4, 7, 14, and 28<\/p>\n<p>Question 15.<br \/>\n<strong>Reasoning<\/strong><br \/>\nCan an odd number have an even factor? Explain.<br \/>\nAnswer: No, an odd number doesn&#8217;t have an even factor<\/p>\n<p>Explanation:<br \/>\nLet the number which we want to find the factors is: 15<br \/>\nThe factors of 15 are:<br \/>\n1, 3, 5, and 15<br \/>\nHence, from the above factors,<br \/>\nWe can conclude that an odd number doesn&#8217;t have an even factor.<br \/>\nNote: The &#8220;Odd number&#8221; is the number that can&#8217;t be divisible by 2.<\/p>\n<p>Question 16.<br \/>\n<strong>Writing<\/strong><br \/>\nUse the diagram to explain why you do not have to check whether any numbers greater than 4 are factors of 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-3.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 3\" width=\"177\" height=\"87\" \/><br \/>\nAnswer: We don&#8217;t have to check the numbers greater than 4 are the factors of 12 because the factors of 12 greater than 4 are repeating.<\/p>\n<p>Explanation:<br \/>\nThe given number is 12<br \/>\nThe factors of 12 are:<br \/>\n1, 2, 3, 4, 6, and 12<br \/>\nHence, from the above<br \/>\nWe can conclude that we don&#8217;t have to check the numbers greater than 4 are the factors of 12.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThere are 4 classes going on a field trip. The classes will use 3 buses. Can the teachers have an equal number of students on each bus?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-4.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 4\" width=\"151\" height=\"174\" \/><br \/>\nThink: What do you know? What do you need to find? How will you solve it?<br \/>\nStep 1: Add to find how many students are going on the field trip.<br \/>\n24 + 23 + 25 + 20 = 92<br \/>\n92 students are going on the field trip.<br \/>\nStep 2: Is the total number of students divisible by the number of buses?<br \/>\nFind the sum of the digits of 92. 9 + 2 =11<br \/>\nThe sum of the digits not divisible by 3.<br \/>\nThe teachers don&#8217;t have an equal number of students on each bus.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 17.<br \/>\nA teacher is making a 5-page test with 28 vocabulary problems and 7 reading problems. Can the teacher put an equal number of problems on each page?<br \/>\nAnswer: Yes, the teacher can put an equal number of problems on each page<\/p>\n<p>Explanation:<br \/>\nGiven that a teacher is making a 5- page test.<br \/>\nIt is also given that there are 28 vocabulary problems and 7 reading problems.<br \/>\nSo,<br \/>\nTotal number of problems = 28 + 7 = 35 problems<br \/>\nSo,<br \/>\nThe number of problems that each page contains = 35 \u00f7 5<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n35 \u00f7 5 = ( 30 + 5 ) \u00f7 5<br \/>\n= ( 30 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 6 + 1<br \/>\n= 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the teacher can put an equal number of problems on each page.<\/p>\n<p>Question 18.<br \/>\nA relay race is 39 laps long. Each team member must bike the same number of laps. Could a team have 8, 6, or 3 members? Explain.<br \/>\nAnswer: A team has 3 members.<\/p>\n<p>Explanation:<br \/>\nGiven that a relay race is 39 laps long and each member must bike the same number of laps.<br \/>\nNow,<br \/>\nThe factors of 39 are: 1, 3, 13, and 39<br \/>\nThe factors are the numbers that divide the number originally.<br \/>\nSo, 39 can be divided by 3 only.<br \/>\nHence, from the above,<br \/>\nWe can conclude that each team has only 3 members.<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou have 63 clay figures to display on 7 shelves. Not all of the shelves need to be used and each shelf can hold no more than 25 figures. Each shelf must have the same number of figures. What are all the ways you could arrange the figures?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-5.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 5\" width=\"167\" height=\"205\" \/><br \/>\nAnswer: The number of ways you could arrange the figures is to find the number of factors of 63.<br \/>\nSo,<br \/>\nThe number of factors of 63 is: 1, 3, 7,9 21, and 63<\/p>\n<p>Explanation:<br \/>\nGiven that you have 63 clay figures to display on 7 shelves.<br \/>\nIt is also given that each shelf holds no more than 25 figures.<br \/>\nNow,<br \/>\nThe factors of\u00a0 63 are: 1, 3, 7,9 21, and 63<br \/>\nThe &#8220;Factors&#8221; are the ways to arrange the given clay figures.<br \/>\nSo,<br \/>\nThe number of ways to arrange the clay figures that do not hold more than 25 is: 3, 7, 9, and 21<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of ways to arrange the clay figures in each shelf that do not hold more than 25 figures is: 3, 7, 9, and 21 ways<\/p>\n<h3><a id=\"Factors_and_Divisibility_Practice_6.2\"><\/a>Factors and Divisibility Homework &amp; Practice 6.2<\/h3>\n<p><strong>Find the factor pairs for the number.<\/strong><br \/>\nQuestion 1.<br \/>\n24<br \/>\nAnswer:<br \/>\nThe factor pairs of 24 are:<br \/>\n1 \u00d7 24, 2 \u00d7 12, 3 \u00d7 8, 4 \u00d7 6, 6 \u00d7 4, 8 \u00d7 3, 12 \u00d7 2, and 24 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 24 are:<br \/>\n1 \u00d7 24, 2 \u00d7 12, 3 \u00d7 8, 4 \u00d7 6, 6 \u00d7 4, 8 \u00d7 3, 12 \u00d7 2, and 24 \u00d7 1<\/p>\n<p>Question 2.<br \/>\n48<br \/>\nAnswer:<br \/>\nThe factor pairs of 48 are:<br \/>\n1 \u00d7 48, 2 \u00d7 24, 3 \u00d7 16, 4 \u00d7 12, 6 \u00d7 8<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 48 are:<br \/>\n1 \u00d7 48, 2 \u00d7 24, 3 \u00d7 16, 4 \u00d7 12, 6 \u00d7 8<\/p>\n<p>Question 3.<br \/>\n31<br \/>\nAnswer:<br \/>\nThe factor pairs of 31 are:<br \/>\n1 \u00d7 31 and 31 \u00d7 1<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 31 are:<br \/>\n1 \u00d7 31 and 31 \u00d7 1<\/p>\n<p>Question 4.<br \/>\n99<br \/>\nAnswer:<br \/>\nThe factor pairs of 99 are:<br \/>\n1 \u00d7 99, 3 \u00d7 33, 9 \u00d7 11<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 99 are:<br \/>\n1 \u00d7 99, 3 \u00d7 33, 9 \u00d7 11<\/p>\n<p>Question 5.<br \/>\n45<br \/>\nAnswer:<br \/>\nThe factor pairs of 45 are:<br \/>\n1 \u00d7 45, 3 \u00d7 15, and 5 \u00d7 9<\/p>\n<p>Explanation:<br \/>\nfactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 45 are:<br \/>\n1 \u00d7 45, 3 \u00d7 15, and 5 \u00d7 9<\/p>\n<p>Question 6.<br \/>\n26<br \/>\nAnswer:<br \/>\nThe factor pairs of 26 are:<br \/>\n1 \u00d7 26, 2 \u00d7 13<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factor pairs of 26 are:<br \/>\n1 \u00d7 26, 2 \u00d7 13<\/p>\n<p><strong>List the factors of the number.<\/strong><br \/>\nQuestion 7.<br \/>\n25<br \/>\nAnswer:<br \/>\nThe factors of 25 are: 1, 5, and 25<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the numbers originally.<br \/>\nHence,<br \/>\nThe factors of 25 are: 1, 5, and 25<\/p>\n<p>Question 8.<br \/>\n56<br \/>\nAnswer:<br \/>\nThe factors of 56 are: 1, 2, 4, 7, 8, 14, 28 and 56<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 56 are: 1, 2, 4, 7, 8, 14, 28 and 56<\/p>\n<p>Question 9.<br \/>\n75<br \/>\nAnswer:<br \/>\nThe factors of 75 are: 1, 3, 5, 15, 25, and 75<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 75 are: 1, 3, 5, 15, 25, and 75<\/p>\n<p>Question 10.<br \/>\n80<br \/>\nAnswer:<br \/>\nThe factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20,40 and 80<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the numbers originally.<br \/>\nHence,<br \/>\nThe factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20,40 and 80<\/p>\n<p>Question 11.<br \/>\n93<br \/>\nAnswer:<br \/>\nThe factors of 93 are: 1, 3, 31 and 93<\/p>\n<p>Explanation;<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 93 are: 1, 3, 31 and 93<\/p>\n<p>Question 12.<br \/>\n61<br \/>\nAnswer:<br \/>\nThe factors of 61 are: 1 and 61<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence,<br \/>\nThe factors of 61 are: 1 and 61<\/p>\n<p>Question 13.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWhy does a number that has 9 as a factor also have 3 as a factor?<br \/>\nAnswer: The number that has 9 as a factor also have 3 as a factor because 9 is a multiple of 3<\/p>\n<p>Explanation:<br \/>\nLet the number that has 9 as a factor and that has also 3 as a factor be: 18<br \/>\nNow,<br \/>\nThe factors of 18 are: 1, 2, 3, 6, 9, and 18<br \/>\nHene, from the above,<br \/>\nWe can conclude that the number that has 9 as a factor also have 3 as a factor.<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe number below has 3 as a factor. What could the unknown digit be?<br \/>\n3 _____ 5.<br \/>\nAnswer: The unknown digit could be: 1 or 4 or 7<\/p>\n<p>Explanation:<br \/>\nGiven that the number has 3 as a factor.<br \/>\nTo have 3 as a factor, the sum of the digits in the given number should be a multiple of 3<br \/>\nHence,<br \/>\nThe unknown digit in 3____5 could be: 1 or 4 or 7<\/p>\n<p>Question 15.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich numbers have 5 as a factor?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-6.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 6\" width=\"583\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-6.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-6-300x19.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><br \/>\nAnswer: The numbers which have 5 as a factor are: 50, 25, 1,485 and 100<\/p>\n<p>Explanation:<br \/>\nGiven numbers are: 50, 34, 25, 1,485, 100 and 48<br \/>\nThe numbers that have the factor of 5 must have the last digits 0 or 5<br \/>\nHence,<br \/>\nThe numbers that have 5 as a factor are: 50, 25, 1,485, and 100<\/p>\n<p>Question 16.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYou and a partner are conducting a bottle flipping experiment. You have 3 bottles with different amounts of water in each. You need to flip each bottle 15 times. If you take turns, will you and your partner each get the same number of flips?<br \/>\nAnswer: Yes, you and your partner will each get the same number of flips.<\/p>\n<p>Explanation:<br \/>\nGiven that you and your partner are conducting a bottle flipping experiment and you have 3 bottles with different amounts of water in each and you need to flip each bottle 15 times.<br \/>\nSo,<br \/>\nThe number of flips each will get = 15 \u00f7 3<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n15 \u00f7 3 = ( 12 + 3 ) \u00f7 3<br \/>\n= ( 12 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n= 4 + 1<br \/>\n= 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that each bottle will flip 5 times.<\/p>\n<p>Question 17.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA florist has 55 flowers. She wants to put the same number of flowers in each vase without any leftover Should she put 2, 3, or 5 flowers in each vase? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-7.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 7\" width=\"279\" height=\"191\" \/><br \/>\nAnswer: The florist put 5 flowers in each vase.<\/p>\n<p>Explanation:<br \/>\nGiven that a florist has 55 flowers and she wants to put the same number of flowers in each vase without any leftover.<br \/>\nThe number 55 will be divided by to not have any leftover because the last digit is 5.<br \/>\nHence,<br \/>\nThe florist puts 5 flowers in each vase.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Compare.<\/strong><br \/>\nQuestion 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-8.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 8\" width=\"132\" height=\"41\" \/><br \/>\nAnswer: 7,914 is greater than 7,912<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 7,914 and 7,912<br \/>\nHence, from the above,<br \/>\nWe can conclude that 7,914 is greater than 7,912<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-9.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 9\" width=\"153\" height=\"52\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-9.png 153w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-9-150x52.png 150w\" sizes=\"(max-width: 153px) 100vw, 153px\" \/><br \/>\nAnswer: 65,901 is less than 67,904<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 65,901 and 67,904<br \/>\nHence, from the above,<br \/>\nWe can conclude that 65,901 is less than 67,904<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.2-10.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.2 10\" width=\"158\" height=\"43\" \/><br \/>\nAnswer: 839,275 is equal to 839,275<\/p>\n<p>Explanation:<br \/>\nGiven numbers are 839,275 and 839,275<br \/>\nHence, from the above,<br \/>\nWe can conclude that 839,275 is equal to 839,275<\/p>\n<h3><a id=\"Lesson_6.3_Relate_Factors_and_Multiples\"><\/a>Lesson 6.3 Relate Factors and Multiples<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>List all factors of 24.<br \/>\nAnswer:<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the numbers originally.<br \/>\nHence,<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24<\/p>\n<p>List several multiples of each factor. What number appears in each list?<br \/>\nAnswer:<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24<\/p>\n<p>Explanation:<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24<br \/>\nNow,<br \/>\nThere are no other multiples of 1<br \/>\nThe multiples of 2 are: 1, 2<br \/>\nThe multiples of 3 are: 1,3<br \/>\nThe multiples of 4 are: 1, 2, 4<br \/>\nThe multiples of 6 are: 1, 2, 3 and 6<br \/>\nThe multiples of 8 are: 1, 2, 4 and 8<br \/>\nThe multiples of 12 are: 1, 2, 3, 4, 6, and 12<br \/>\nThe multiples of 24 are: 1, 2, 3, 4, 6, 8, 12 and 24<br \/>\nHence, from the above,<br \/>\nWe can conclude that 1 appears in each list<\/p>\n<p><strong>Number Sense<\/strong><br \/>\nHow are factors and multiples related?<br \/>\nAnswer:<br \/>\nFactors are the numbers that can divide the numbers originally.<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<\/p>\n<p><strong>Think and Grow: Identify Multiples<\/strong><\/p>\n<p>A whole number is a multiple of each of its factors.<br \/>\n12 is a multiple of 1, 2, 3, 4, 6, and 12.<br \/>\n1 \u00d7 12 = 12<br \/>\n2 \u00d7 6 = 12<br \/>\n3 \u00d7 4 = 12<br \/>\n4 \u00d7 3 = 12<br \/>\n6 \u00d7 2 = 12<br \/>\n12 \u00d7 1 = 12<\/p>\n<p><strong>Example<\/strong><br \/>\nIs 56 a multiple of 7?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 1\" width=\"141\" height=\"246\" \/><br \/>\nOne Way:<br \/>\nList multiples of 7.<br \/>\n7, 14, 21, 28, 35, 42, 49, 56<br \/>\nSo, 56\u00a0 is a multiple of 7.<br \/>\nAnother Way:<br \/>\nUse division to determine whether 7 is a factor of 56.<br \/>\n56 \u00f7 7 = 8<br \/>\n7 is a factor of 56.<br \/>\nSo, 56 is a multiple of 7.<\/p>\n<p><strong>Example<\/strong><br \/>\nIs 9 a factor of 64?<br \/>\nOne Way:<br \/>\nUse divisibility rules to determine whether 9 is a factor of 64.<br \/>\n9 is not a factor of 64 because 6 + 4 = 10 is not divisible by 9.<br \/>\nAnother Way:<br \/>\nList the multiples of 9.<br \/>\n9, 18, 27, 36, 45, 54, 63, 72<br \/>\n64 is not a multiple of 9.<br \/>\nSo, 9 is not a factor of 64.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nIs 23 a multiple of 3? Explain.<br \/>\nAnswer: 23 is not a multiple of 3<\/p>\n<p>Explanation:<\/p>\n<p>Multiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nThe multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27 and 30<br \/>\nHence, from the above,<br \/>\nWe can conclude that 23 is not a multiple of 3.<\/p>\n<p>Question 2.<br \/>\nIs 8 a factor of 56? Explain.<br \/>\nAnswer: 8 is a factor of 56.<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the numbers originally.<br \/>\nNow,<br \/>\nThe factors of 56 are: 1, 2, 4, 7, 8, 14, 28, and 56<br \/>\nHence, from the above,<br \/>\nWe can conclude that 8 is a factor of 56.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p>Question 3.<br \/>\nIs 65 a multiple of 5? Explain.<br \/>\nAnswer: 65 is a multiple of 5<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nThe multiples of 5 are: 5, 10, 15, 20, 25, 30, 35,40, 45, 50, 55, 60 and 65<br \/>\nHence, fro the above,<br \/>\nWe can conclude that 65 is a multiple of 5.<\/p>\n<p>Question 4.<br \/>\nIs 14 a multiple of 4? Explain.<br \/>\nAnswer: 14 is not a multiple of 4.<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nThe multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, and 40<br \/>\nHence, from the above,<br \/>\nWe can conclude that 14 is not a multiple of 4.<\/p>\n<p>Question 5.<br \/>\nIs 23 a multiple of 2? Explain.<br \/>\nAnswer: 23 is not a multiple of 2<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nThe multiples of 2 are: 2, 4, 6, 8, 10, 1, 14, 16, 18, 20, 22, 24 and 26<br \/>\nHence, from the above,<br \/>\nWe can conclude that 23 is not a multiple of 2.<\/p>\n<p>Question 6.<br \/>\nIs 6 a factor of 96? Explain.<br \/>\nAnswer: 6 is a factor of 96<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nThe factors of 96 are: 1, 2, 3, 4, 6, 8, 12, 16, 28, 32, 48 and 96<br \/>\nHence, from the above,<br \/>\nWe can conclude that 6 is a factor of 96.<\/p>\n<p>Question 7.<br \/>\nIs 3 a factor of 82? Explain.<br \/>\nAnswer: 82 is not a factor of 3<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nThe given number is 82<br \/>\nThe sum of digits of 82 = 8 + 2 = 11<br \/>\nThe number is a multiple of 3 only then the sum of the digits of that number is a multiple of 3.<br \/>\nBut the sum of digits of 82 is not a multiple of 3<br \/>\nHence, from the above,<br \/>\nwe can conclude that 3 is not a factor of 82<\/p>\n<p>Question 8.<br \/>\nIs 9 a factor of 72? Explain.<br \/>\nAnswer: 9 is a factor of 72<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nThe factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72<br \/>\nHence, from the above,<br \/>\nWe can conclude that 9 is a factor of 72.<\/p>\n<p><strong>Tell whether 8 is a multiple or a factor of the number. Write multiple, factor or both.<\/strong><br \/>\nQuestion 9.<br \/>\n4<br \/>\nAnswer: 8 is a multiple of 4.<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nSo,<br \/>\nThe multiples of 4 are: 4, 8, 12, 16, and 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that 8 is a multiple of 4<\/p>\n<p>Question 10.<br \/>\n8<br \/>\nAnswer: 8 is a multiple of 8<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nSo,<br \/>\nThe multiples of 8 are: 8, 16, 24, 32, 0, etc.<br \/>\nHence, from the above,<br \/>\nWe can conclude that 8 is a multiple of 8<\/p>\n<p>Question 11.<br \/>\n32<br \/>\nAnswer: 32 is a multiple of 8<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nSo,<br \/>\nThe multiples of 8 are: 8, 16, 24, 32, 40, 48 etc<br \/>\nHence, from the above,<br \/>\nWe can conclude that 32 is a multiple of 8<\/p>\n<p>Question 12.<br \/>\nWriting<br \/>\nUse numbers 6 and 12 to explain how factors and multiples are related.<br \/>\nAnswer:<br \/>\nThe multiplication Expression using numbers 6 and 12 is:<br \/>\n6 \u00d7 2 = 12<br \/>\nFrom the multiplication Expression,<br \/>\n6 is a factor of 12<br \/>\n12 is a multiple of 6<\/p>\n<p>Explanation:<br \/>\nThe given numbers re 6 and 12<br \/>\nFrom the given numbers, the multiplication Expression is:<br \/>\n6 \u00d7 2 = 12<br \/>\nHence, from the above multiplication Expression,<br \/>\n6 is a factor of 12<br \/>\n12 is a multiple of 6.<\/p>\n<p>Question 13.<br \/>\nComplete the Venn diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-2.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 2\" width=\"267\" height=\"202\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-20523\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-23.jpg\" alt=\"\" width=\"276\" height=\"198\" \/><\/p>\n<p>Explanation:<br \/>\nFrom the given Venn diagram,<br \/>\nThe factors of 40 are: 1, 2, 4, 5, 8, 10, 20, and 40<br \/>\nThe first 10 multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50<br \/>\nHence, from the above,<br \/>\nThe common numbers from both the factors of 4 and the multiples of 5 are:<br \/>\n5, 10, 20 and 40<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou need 96 balloons for a school dance. Balloons come in packs of 4, packs of 6, and packs of 9. Which packs could you buy so you have no leftover balloons?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-3.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 3\" width=\"209\" height=\"149\" \/><br \/>\nUse division to determine whether 96 is a multiple of 4.<br \/>\n4 \u221a96 So, 4\u00a0 is a factor of 96, and 96\u00a0 is a multiple of 4.<br \/>\nUse the divisibility rules to check whether 96 is a multiple of 6.<br \/>\n96 is even and 9 + 6 = 15 divisible by 3. So, 6\u00a0 is a factor of 96 and 96\u00a0 is a multiple of 6.<br \/>\nUse the divisibility rules to check whether 96 is a multiple of 9.<br \/>\n9 + 6 = 15\u00a0 is not\u00a0 divisible by 9. So, 9\u00a0 is not a factor of 96 and<br \/>\n96\u00a0 is not a multiple of 9.<br \/>\nYou could buy packs of 4 balloons or packs of 6 balloons.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nA teacher needs 88 batteries for science experiments. Batteries are sold in packs of 2, packs of 6, and packs of 8. Which packs could the teacher buy so she has no leftover batteries?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-4.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 4\" width=\"178\" height=\"125\" \/><br \/>\nAnswer: The teacher should buy the packs of 2 and packs of 8 so that there will be no leftover batteries.<\/p>\n<p>Explanation:<br \/>\nGiven that a teacher needs 88 batteries for science experiments and that batteries are sold in packs of 2, 6, and 8.<br \/>\nSo,<br \/>\nThe factors of 88 are: 1, 2, 4, 8, 11, 22, 44, and 88<br \/>\nSo, from the factors of 88, we see that there is no 6 as a factor of 88<br \/>\nSo, from this, we can say that we can&#8217;t pack 88 batteries in packs of 6 but in the packs of 2 and 8 ( Since 2 and 8 both are the factors of 88 )<br \/>\nWe know that,<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 88 batteries can be packed in packs of 2 or packs of 8.<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nDescartes buys 2 books for a total of $15. Each book costs a multiple of $3. How much could each book cost?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-5.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 5\" width=\"125\" height=\"147\" \/><\/p>\n<p>Answer: The cost of each book that Descartes bought is: $15<\/p>\n<p>Explanation:<br \/>\nGiven that Descartes bought 3 books for a total of $15 and each book costs a multiple of $3<br \/>\nSo,<br \/>\nThe cost of each book = The total cost of 2 books \u00f7 Total number of books<br \/>\n= 15 \u00f7 2<br \/>\nNow,<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n15 \u00f7 2 = ( 12 + 3 ) \u00f7 2<br \/>\n( 12 \u00f7 2 ) + ( 3 \u00f7 2 )<br \/>\n= 6 + 1.5<br \/>\n= 7.5<br \/>\nHence, from the above,<br \/>\nWe can conclude that the cost of each book is: $7.5 and the cost of each book is also a multiple of $3<\/p>\n<p>Question 16.<br \/>\nNewton buys some boxes of dog treats for $9 each. Descartes buys some bags of cat treats for $6 each. Newton and Descartes spend the same amount of money on treats. What is the least amount of money they could have spent?<\/p>\n<p>Answer: The least amount of money that Newton and Descartes spent on dog treats = $18<\/p>\n<p>Explanation:<br \/>\nGiven that Newton buys some boxes of dog treats for $9 each and Descartes buys some bags of cat treats for $6 each.<br \/>\nIt is also given that Newton and Descartes spend the same amount of money on treats<br \/>\nSo, we have to find the least number that can be a multiple of both 6 and 9.<br \/>\nNow,<br \/>\nthe multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, and 60<br \/>\nThe multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, and 90<br \/>\nFrom the multiples of 6 and 9,<br \/>\nWe can see that the least number that can be the multiple of both 6 and 9 is: 18<br \/>\nHence, from the above,<br \/>\nWe can conclude that the least amount of money that Newton and Descartes spent on dog treats is: $18<\/p>\n<h3><a id=\"Relate_Factors_and_Multiples_Practice_6.3\"><\/a>Relate Factors and Multiples Homework &amp; Practice 6.3<\/h3>\n<p>Question 1.<br \/>\nIs 16 a multiple of 3? Explain.<br \/>\nAnswer: 16 is not a multiple of 3<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nSo,<br \/>\nThe multiples of 16 are 3, 6,9, 12, 15, 18, etc.<br \/>\nHence, from the above,<br \/>\nWe can conclude that 16 is not a multiple of 3.<\/p>\n<p>Question 2.<br \/>\nIs 21 a multiple of 7? Explain.<br \/>\nAnswer: 21 is a multiple of 7<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nSo,<br \/>\nThe multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70<br \/>\nHence, from the above,<br \/>\nWe can conclude that 21 is a multiple of 7<\/p>\n<p>Question 3.<br \/>\nIs 46 a multiple of 2? Explain.<br \/>\nAnswer: 46 is a multiple of 2<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nSo,<br \/>\nFor the multiple of 2, the last digit should be 2, 4, 6, 8, 0<br \/>\nSo,<br \/>\n46 can be said as a multiple of 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that 46 is a multiple of 2.<\/p>\n<p>Question 4.<br \/>\nIs 5 a factor of 71? Explain.<br \/>\nAnswer: 5 is not a factor of 71<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number completely.<br \/>\nSo,<br \/>\nThe factors of 71 are: 1, 71<br \/>\nHence, from the above,<br \/>\nWe can conclude that 5 is not a factor of 71.<\/p>\n<p>Question 5.<br \/>\nIs 8 a factor of 88? Explain.<br \/>\nAnswer: 8 is a factor of 88<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the numbers completely<br \/>\nSo,<br \/>\nThe factors of 88 are: 1, 2, 4, 8, 11, 22, 44, 88<br \/>\nHence, from the above factors,<br \/>\nWe can conclude that 8 is a factor of 88<\/p>\n<p>Question 6.<br \/>\nIs 4 a factor of 80? Explain.<br \/>\nAnswer: 4 is a factor of 80<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number completely.<br \/>\nSo,<br \/>\nThe factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80<br \/>\nHence, from the above factors,<br \/>\nWe can conclude that 4 is a factor of 80.<\/p>\n<p><strong>Tell whether 30 is a multiple or a factor of the number. Write multiple, factor, or both.<\/strong><br \/>\nQuestion 7.<br \/>\n30<br \/>\nAnswer: 30 is a multiple and factor of 30<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nFactors are the numbers that divide the number completely<br \/>\nSo,<br \/>\nThe multiples of 30 are: 30, 60, 90, 120, 150, 180, 210, 240, 270 and 300<br \/>\nThe factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30<br \/>\nHence,<br \/>\nFrom the above,<br \/>\nWe can conclude that 30 is a multiple and factor of 30<\/p>\n<p>Question 8.<br \/>\n90<br \/>\nAnswer: 90 is a multiple of 30<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nSo,<br \/>\nThe multiples of 30 are: 30, 60, 90, 120, 150, 180, 210, 240, 270, 300<br \/>\nHence, from the above multiples,<br \/>\nWe can conclude that 90 is a multiple of 30<\/p>\n<p>Question 9.<br \/>\n10<br \/>\nAnswer: 10 is a factor of 30<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number originally.<br \/>\nSo,<br \/>\nThe factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30<br \/>\nHence, from the above factors,<br \/>\nWe can conclude that 10 is a factor of 30<\/p>\n<p><strong>Tell whether 10 is a multiple or a factor of the number. Write multiple, factor, or both.<\/strong><br \/>\nQuestion 10.<br \/>\n5<br \/>\nAnswer: 5 is a factor of 10<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the number completely.<br \/>\nSo,<br \/>\nThe factors of 10 are: 1, 2, 5, 10<br \/>\nHence, from the above factors,<br \/>\nWe can conclude that 5 is a factor of 10<\/p>\n<p>Question 11.<br \/>\n60<br \/>\nAnswer: 60 is a multiple of 10<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nSo,<br \/>\nThe multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80 , 90, 100<br \/>\nHence, from the above multiples,<br \/>\nWe can conclude that 60 is a multiple of 10<\/p>\n<p>Question 12.<br \/>\n10<br \/>\nAnswer: 10 is a multiple and factor of 10<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nFactors are the numbers that divide the number completely<br \/>\nSo,<br \/>\nThe number of factors of 10 is: 1, 2, 5, 10<br \/>\nThe multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80 , 90, 100<br \/>\nHence, from the above,<br \/>\nWe can conclude that 10 is a factor and a multiple of 10<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nName two numbers that are each a multiple of both 3 and 4. What do you notice about the two multiples?<br \/>\nAnswer: 12 is a multiple of both 3 and 4<\/p>\n<p>Explanation:<br \/>\nWe know that,<br \/>\nIf the number is divisible by 3, then the sum of the digits of that given number must be divisible by 3<br \/>\nIf the number is divisible by 4, then the last 2 digits of that given number must also be divisible by 4<br \/>\nHence,<br \/>\nThe number which is a multiple of both 3 and 4 is: 12<br \/>\n12 will satisfy both the conditions of the number divisible by 3 and 4<br \/>\nHence, from the above,<br \/>\nWe can conclude that 12 is a multiple of both 3 and 4<\/p>\n<p>Question 14.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nIs Newton correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-6.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 6\" width=\"181\" height=\"164\" \/><\/p>\n<p>Answer: Yes, Newton is correct<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nAccording to Newton, all numbers that are multiples of 10 have 2 as a factor.<br \/>\nNow,<br \/>\nThe multiples of 10 are: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100<br \/>\nSo,<br \/>\nLet a multiple of 10 be 20<br \/>\nSo,<br \/>\nThe factors of 20 are: 1, 2, 4, 5, 10, 20<br \/>\nHence, from the above,<br \/>\nWe can conclude that Newton&#8217;s statement is correct<\/p>\n<p>Question 15.<br \/>\n<strong>Logic<\/strong><br \/>\nA quotient is a multiple of 4. The dividend is a multiple of 8. The divisor is a factor of 6. Write one possible equation for the problem.<\/p>\n<p>Answer:<br \/>\nThe possible equation for the problem is:<br \/>\n24 \u00f7 6 = 4<\/p>\n<p>Explanation:<br \/>\nGiven that a quotient is a multiple of 4.<br \/>\nIt is also given that the dividend is a multiple of 8 and the divisor is a factor of 6.<br \/>\nSo,<br \/>\nThe possible Equation for the given problem is:<br \/>\n24 \u00f7 6 = 4<br \/>\nWhere,<br \/>\n24 is a dividend<br \/>\n6 is a divisor<br \/>\n4 is a quotient<br \/>\nHence, from the above,<br \/>\nWe can conclude that the possible\u00a0 equation according to the given conditions is:<br \/>\n24 \u00f7 6 = 4<\/p>\n<p>Question 16.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour friend needs our friend needs t0 50 US state capitals. She wants to memorize the same number of capitals each day. Which numbers of capitals can she memorize each day: 2, 3, 4, or 5?<\/p>\n<p>Answer: The number of capitals she can memorize each day in packs of 2 and 5<\/p>\n<p>Explanation:<br \/>\nGiven that your friend needs 50 US state capitals and she wants to memorize the same number of capitals each day.<br \/>\nIt is also given that the number of capitals she had to memorize in the packs of 2, 3, 4, or 5<br \/>\nSo,<br \/>\nIf the number has to be divided by 5, the last digit of that given number should be 5 (or) 0<br \/>\nSo,<br \/>\nThe factors of 50 are: 1, 2, 5,\u00a0 10, 25, 50<br \/>\nHence, from the above,<br \/>\nWe can conclude that 50 US capitals she had to memorize is in the packs of 2 or packs of 5<\/p>\n<p>Question 17.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nZookeepers plan an enrichment day for the animals every 7 days and bathe the elephants every 2 days. You want to go to the zoo when both events are happening. What other dates in May will this happen?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-7.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 7\" width=\"283\" height=\"207\" \/><\/p>\n<p>Answer: The events of both Enrichment day and Elephant Day come in the month of May other than 14 May is:<br \/>\n21 May and 28 May<\/p>\n<p>Explanation:<br \/>\nGiven that Zookeepers plan an enrichment day for the animals every 7 days<br \/>\nIt is also given that the Elephant bathing takes place every 2 days.<br \/>\nSo, other than 14 May,<br \/>\nThe other days that these two events will take place on May are: 21 May and 28 May with 7 days gap from 14 May<br \/>\nHence, from the above,<br \/>\nWe can conclude that\u00a0 both the events are happening on 21 and 28 May<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Estimate the sum or difference.<\/strong><br \/>\nQuestion 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-8.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 8\" width=\"80\" height=\"69\" \/><br \/>\nAnswer: 71,606 &#8211; 49,641 = 21,965<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-9.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 9\" width=\"83\" height=\"71\" \/><br \/>\nAnswer: 75,294 + 36,043 = 111,337<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.3-10.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.3 10\" width=\"77\" height=\"74\" \/><br \/>\nAnswer: 93,294 &#8211; 40,293 = 53,001<\/p>\n<h3><a id=\"Lesson_6.4_Identify_Prime_and_Composite_Numbers\"><\/a>Lesson 6.4 Identify Prime and Composite Numbers<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Draw as many different rectangles as possible that each has the given area. Label their side lengths.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-1.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.4 1\" width=\"463\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-1.png 463w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-1-300x215.png 300w\" sizes=\"(max-width: 463px) 100vw, 463px\" \/><br \/>\nCompare the numbers of factors of 32 and 13.<\/p>\n<p>Answer: <img loading=\"lazy\" class=\"alignnone size-full wp-image-20573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-24.jpg\" alt=\"\" width=\"305\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-24.jpg 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-24-267x300.jpg 267w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-20574\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-25.jpg\" alt=\"\" width=\"305\" height=\"271\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-25.jpg 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-25-300x267.jpg 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nThe factors of 32 are: 1, 2, 4, 8, 16, 32<br \/>\nThe factors of 13 are: 1, 13<br \/>\nOn comparison of the factors of 32 and 13, we can say that 13 has less number of factors than 32<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nCan a whole number have fewer than two factors? exactly two factors? more than two factors?<\/p>\n<p>Answer: Yes, a whole number has exactly 2 factors and more than 2 factors but not less than 2 factors.<\/p>\n<p>Explanation:<br \/>\nA whole number will be divided into 2 types based on the number of factors. They are:<br \/>\nA) Composite numbers:<br \/>\nThe numbers that have more than 2 factors are called &#8220;Composite numbers&#8221;<br \/>\nB) Prime numbers:<br \/>\nThe numbers that have exactly 2 factors are called &#8220;Prime numbers&#8221;<br \/>\nThere will no less than 2 factors for any number.<\/p>\n<p><strong>Think and Grow: Identify Prime and Composite Numbers<br \/>\n<\/strong>A prime number is a whole number greater than 1 with exactly two factors, 1 and itself. A composite number is a whole number greater than 1 with more than two factors.<\/p>\n<p>Example<br \/>\nTell whether 27 is a prime composite<br \/>\nUse divisibility rules.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-2.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.4 2\" width=\"191\" height=\"232\" \/><br \/>\n\u2022 27 is odd, so it is not divisible by 2 or any other even number.<br \/>\n\u2022 2 + 7 = 9 is divisible by 3,<br \/>\nso 27 is divisible by 3.<br \/>\n27 has factors in addition to 1 and itself.<br \/>\nSo, 27 is a Composite number.<\/p>\n<p><strong>Example<\/strong><br \/>\nTell whether 11 is a prime composite<br \/>\nUse divisibility rules.<br \/>\n\u2022 11 is odd, so it is not divisible by 2 or any other even number.<br \/>\n\u2022 1 + 1 = 2 is not divisible by 3 or 9,<br \/>\nso 11 is not divisible by 3 or 9.<br \/>\n\u2022 The ones digit is not 0 or 5,<br \/>\nso 11 is not divisible by 5.<br \/>\n11 has exactly two factors, 1 and itself.<br \/>\nSo, 11 is a prime number.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Tell whether the number is prime or composite. Explain.<br \/>\nQuestion 1.<br \/>\n7<br \/>\nAnswer: 7 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime number:<br \/>\nThe numbers which have exactly 2 factors 1 and itself is called &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 7 are: 1, 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that 7 is a prime number<\/p>\n<p>Question 2.<br \/>\n12<br \/>\nAnswer: 12 is a Composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are called &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 12 are: 1, 2, 3, 4, 6, 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that 12 is a Composite number<\/p>\n<p>Question 3.<br \/>\n2<br \/>\nAnswer: 2 is a prime number.<\/p>\n<p>Explanation:<br \/>\nPrime number:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are called &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 2 are: 1, 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that 2 is a prime number<\/p>\n<p>Question 4.<br \/>\n19<br \/>\nAnswer: 19 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime number:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are called &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 19 are: 1, 19<br \/>\nHence, from the above,<br \/>\nwe can conclude that 19 is a prime number<\/p>\n<p>Question5.<br \/>\n45<br \/>\nAnswer: 45 is a Composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are called &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 45 are: 1, 3, 5, 9, 15, 45<br \/>\nHence, from the above,<br \/>\nwe can conclude that 45 is a Composite number<\/p>\n<p>Question 6.<br \/>\n54<br \/>\nAnswer 54 is a\u00a0 Composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are called &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 54 are: 1, 2. 3. 6, 9, 18, 27, 54<br \/>\nHence, from the above,<br \/>\nWe can conclude that 54 is a Composite number<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Tell whether the number is prime or composite. Explain.<\/strong><br \/>\nQuestion 7.<br \/>\n35<br \/>\nAnswer:35 is a Composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are called &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 35 are: 1, 5, 7, 35<br \/>\nHence, from the above,<br \/>\nWe can conclude that 35 is a Composite number<\/p>\n<p>Question 8.<br \/>\n5<br \/>\nAnswer: 5 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are called &#8220;prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 5 are: 1, 5<br \/>\nHence, from the above,<br \/>\nwe can conclude that 5 is a prime number<\/p>\n<p>Question 9.<br \/>\n23<br \/>\nAnswer: 23 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are called &#8221; Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 23 are: 1, 23<br \/>\nHence, from the above,<br \/>\nWe can conclude that 23 is a prime number<\/p>\n<p>Question 10.<br \/>\n40<br \/>\nAnswer: 40 is a Composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are called &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40<br \/>\nHence, from the above,<br \/>\nWe can conclude that 40 is a Composite number<\/p>\n<p>Question 11.<br \/>\n41<br \/>\nAnswer: 41 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are called &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 41 are: 1, 41<br \/>\nHence, from the above,<br \/>\nwe can conclude that 41 is a prime number<\/p>\n<p>Question 12.<br \/>\n81<br \/>\nAnswer: 81 is a Composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are called &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 81 are: 1, 3, 9, 27, 81<br \/>\nhence, from the above,<br \/>\nwe can conclude that 81 is a Composite number<\/p>\n<p>Question 13.<br \/>\n<strong>Structure<\/strong><br \/>\nTo create a list of the prime numbers that are less than 100, do the following.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-3.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.4 3\" width=\"354\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-3.png 354w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-3-300x296.png 300w\" sizes=\"(max-width: 354px) 100vw, 354px\" \/><\/p>\n<ul>\n<li>Place a square around 1. It is neither prime nor composite.<\/li>\n<li>Circle 2 and cross out all other multiples of 2.<\/li>\n<li>Circle 3 and cross out all other multiples of 3.<\/li>\n<li>Circle 5 and cross out all other multiples of 5.<\/li>\n<li>Circle the next number that is not crossed out. This number is prime. Cross out all other multiples of this number.<\/li>\n<li>Continue until every number is either circled or crossed out.<\/li>\n<\/ul>\n<p>What are the prime numbers that are less than 100? Explain why these numbers not were crossed out on the chart.<br \/>\nAnswer:<br \/>\nThe prime numbers below 100 are:<br \/>\n2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 73, 79, 83, 87, 89, 93, and 97<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA museum volunteer has 76 shark teeth to display. Can the volunteer arrange the teeth into a rectangular array with more than 1 row and more than 1 tooth in each row? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-4.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.4 4\" width=\"309\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-4.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-4-300x231.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nUse divisibility rules to determine whether 76 is prime or composite.<br \/>\n76 is even, so it is divisible by 2.<br \/>\n76 has factors in addition to 1 and itself.<br \/>\nSo, 76 is the Composite number.<br \/>\nSo,<br \/>\nThe volunteer will arrange the teeth into a rectangular array with more than 1 row and more than 1 tooth in each row.<br \/>\n<strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nA teacher has 29 students in class. Can the teacher separate the students into equal groups? Explain.<br \/>\nAnswer: No, the teacher can&#8217;t separate the students into equal groups.<\/p>\n<p>Explanation:<br \/>\nGiven that a teacher has 29 students in the class<br \/>\nNow,<br \/>\nLet find whether 29 is Prime or Composite<br \/>\nNow,<br \/>\nFactors of 29 are: 1, 29<br \/>\nHence, from the above factors,<br \/>\nWe can conclude that 29 is a prime number<br \/>\nHence,<br \/>\nThe teacher can&#8217;t divide 29 students into equal groups.<\/p>\n<p>Question 15.<br \/>\nA band instructor wants to have several ways to organize band members into rectangular arrays on the field for a performance.Should the instructor have 89 members or 99 members on the field? Explain.<br \/>\nAnswer: The Instructor should have 99 members on the field so that he can arrange the band members into rectangular arrays.<\/p>\n<p>Explanation:<br \/>\nGiven that a band instructor wants to organize band members into rectangular arrays on the field for a performance.<br \/>\nIt is also given that the instructor wants to arrange into an array of whether 89 members or 99 members<br \/>\nNow,<br \/>\nFactors of 89 are: 1, 89<br \/>\nFactors of 99 are: 1, 3, 9, 11, 33, 99<br \/>\nHence, from the above,<br \/>\nSince the 99 members can be arranged into different arrays,<br \/>\nWe can conclude that the instructor can arrange the participants into an array of 99 members.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA paramedic is arranging bandages into 4 bins. An equal number of bandages are in each bin. Did the paramedic arrange a prime number or a composite number of bandages? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-5.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.4 5\" width=\"222\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-5.png 222w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-5-150x150.png 150w\" sizes=\"(max-width: 222px) 100vw, 222px\" \/><br \/>\nAnswer: The paramedic has to arrange a composite number of bandages.<\/p>\n<p>Explanation:<br \/>\nGien that a paramedic is arranging bandages into 4 bins.<br \/>\nIt is also given that there is an equal number of bandages in each bin.<br \/>\nNow,<br \/>\nGiven there are 4 bins and 4 is a Composite number<br \/>\nSo, 4 can divide only a Composite number but not a prime number.<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly only 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are &#8220;Composite numbers&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that the paramedic has to arrange a Composite number of bandages.<\/p>\n<h3><a id=\"Identify_Prime_and_Composite_Numbers_Practice_6.4\"><\/a>Identify Prime and Composite Numbers Homework &amp; Practice 6.4<\/h3>\n<p><strong>Tell whether the number is prime or composite. Explain.<\/strong><br \/>\nQuestion 1.<br \/>\n3<br \/>\nAnswer: 3 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 3 are: 1, 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that 3 is a prime number<\/p>\n<p>Question 2.<br \/>\n27<br \/>\nAnswer: 27 is a composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 27 are: 1, 3, 9, 27<br \/>\nHence, from the above,<br \/>\nWe can conclude that 27 is a composite number<\/p>\n<p>Question 3.<br \/>\n46<br \/>\nAnswer: 46 is a composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 46 are: 1, 2, 23, 46<br \/>\nHence, from the above,<br \/>\nWe can conclude that 46 is a composite number<\/p>\n<p>Question 4.<br \/>\n17<br \/>\nAnswer: 17 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 17 are: 1, 17<br \/>\nHence, from the above,<br \/>\nWe can conclude that 17 is a prime number<\/p>\n<p>Question 5.<br \/>\n53<br \/>\nAnswer: 53 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 53 are: 1, 53<br \/>\nHence, from the above,<br \/>\nwe can conclude that 53 is a prime number<\/p>\n<p>Question 6.<br \/>\n63<br \/>\nAnswer: 63 is a composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 63 are: 1, 3, 7, 9, 21, 63<br \/>\nHence, from the above,<br \/>\nWe can conclude that 63 is a composite number<\/p>\n<p>Question 7.<br \/>\n29<br \/>\nAnswer: 29 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 29 are: 1, 29<br \/>\nHence, from the above,<br \/>\nWe can conclude that 29 is a prime number<\/p>\n<p>Question 8.<br \/>\n31<br \/>\nAnswer: 31 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 31 are: 1, 31<br \/>\nHence, from the above,<br \/>\nWe can conclude that 31 is a prime number<\/p>\n<p>Question 9.<br \/>\n75<br \/>\nAnswer: 75 is a composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are &#8220;Composite numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 75 are: 1, 3, 5, 15, 25, 75<br \/>\nHence, from the above,<br \/>\nWe can conclude that 75 is a composite number<\/p>\n<p>Question 10.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nCan a number be both prime and composite? Explain.<br \/>\nAnswer: No, a number can&#8217;t be both prime and composite<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are &#8220;Composite numbers&#8221;<br \/>\nHence, from the number of factors,<br \/>\nWe can say a number can&#8217;t be both prime and composite at the same time<\/p>\n<p>Question 11.<br \/>\n<strong>Logic<\/strong><br \/>\nYour friend is thinking of a prime number between 60 and 80. The tens digit is one less than the ones digit. What is the number?<br \/>\nAnswer: The number is 67<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nSo,<br \/>\nThe prime numbers between 60 and 80 are: 61, 67, 73, 79<br \/>\nIt is also given that the tens digit is one less than the ones digit<br \/>\nSo,<br \/>\nTens position value &#8211; 1 = ones position value<br \/>\nHence, from the above,<br \/>\nWe can conclude that 67 is the number.<\/p>\n<p><strong>Number Sense<\/strong><br \/>\n<strong>Write true or false for the statement. If false, provide an example to support your answer.<\/strong><br \/>\nQuestion 12.<br \/>\nAll odd numbers are prime. _______<br \/>\nAnswer: False<\/p>\n<p>Explanation:<br \/>\nGiven that all odd numbers are prime.<br \/>\nPrime numbers:<br \/>\nThe number of factors which have exactly 2 factors 1 and itself is &#8220;Prime numbers&#8221;<br \/>\nSo, let take the off numbers from 1 to 10<br \/>\nThe odd numbers from 1 to 10 are: 1, 3, 5, 7, 9<br \/>\nSo, from 1 to 10,<br \/>\nThe prime numbers are: 3, 5, 7<br \/>\nSo, from the above<br \/>\n9 is an odd number but it is not prime.<br \/>\nHence, from the above,<br \/>\nWe can conclude that all odd numbers are not prime<\/p>\n<p>Question 13.<br \/>\nAll even numbers, except 2, are composite. _______<br \/>\nAnswer: True<\/p>\n<p>Explanation:<br \/>\nGiven that all even numbers except 2 are composite numbers<br \/>\nNow,<br \/>\nThe even numbers from 1 to 0 are: 2, 4, 6, 8<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are &#8220;Composite numbers&#8221;<br \/>\nSo,<br \/>\nThe composite numbers from 1 to 10 are: 4, 6, 8<br \/>\nNote: 2 is an even prime number<br \/>\nHence, from the above,<br \/>\nWE can conclude that all even numbers except\u00a0 are composite numbers<br \/>\nQuestion 14.<br \/>\nA composite number cannot have exactly three factors. _______<br \/>\nAnswer: True<\/p>\n<p>Explanation:<br \/>\nGiven that a composite number has exactly 3 factors<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are &#8220;Composite numbers&#8221;<br \/>\nLet the number be 63<br \/>\nNow,<br \/>\nThe factors of 63 are: 1, 3, 7, 9, 21, 63<br \/>\nHence, from the above,<br \/>\nWe can conclude that a composite number don&#8217;t have exactly 3 factors<\/p>\n<p>Question 15.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThere are 43 students trying out for a basketball team. Can the coach separate the students into equal groups? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13373\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-6.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.4 6\" width=\"142\" height=\"138\" \/><br \/>\nAnswer: No, the coach can&#8217;t separate the students into equal groups<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nNow,<br \/>\nThe factors of 43 are: 1, 43<br \/>\nHence, from the above,<br \/>\nWe can conclude that the coach can&#8217;t separate the students into equal groups since 43 is a prime number<\/p>\n<p>Question 16.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nWhich planet not does have a prime number of rings?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-7.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.4 7\" width=\"371\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-7.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-7-300x193.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><br \/>\nAnswer: Saturn does not have a prime number of rings.<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n1 full circle = 2 rings<br \/>\nSo,<br \/>\n1 half circle = 1 ring<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-7.png\" alt=\"Big Ideas Math Solutions Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.4 7\" width=\"371\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-7.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.4-7-300x193.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><br \/>\nSo, from the above table,<br \/>\nThe number of rings of Jupiter is: 3<br \/>\nThe number of rings of Saturn is: 9<br \/>\nThe number of rings of Uranus is: 13<br \/>\nThe number of rings of Neptune is: 5<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are &#8220;Prime numbers&#8221;<br \/>\nHence, from the above,<br \/>\nWe can conclude that Saturn does not have a prime number of rings ( Because 9 is a composite number )<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Use properties to find the product. Explain your reasoning<\/strong><br \/>\nQuestion 17.<br \/>\n4 \u00d7 9 \u00d7 25<br \/>\nAnswer: 4 \u00d7 9 \u00d7 25 = 900<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of multiplication,<br \/>\n4 \u00d7 9 \u00d7 25 = 4 \u00d7 9 \u00d7 ( 20 + 5 )<br \/>\n= 36 \u00d7 ( 20 + 5 )<br \/>\n= ( 36 \u00d7 20 ) + ( 36 \u00d7 5 )<br \/>\n= 720 + 180<br \/>\n= 900<br \/>\nHence, 4 \u00d7 9 \u00d7 25 = 900<\/p>\n<p>Question 18.<br \/>\n405 \u00d7 3<br \/>\nAnswer: 403 \u00d7 3 = 1,215<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of Multiplication,<br \/>\n405 \u00d7 3 = ( 400 + 5 ) \u00d7 3<br \/>\n= ( 400 \u00d7 3 ) + ( 5 \u00d7 3 )<br \/>\n= 1,200 + 15<br \/>\n= 1,215<br \/>\nHence, 405 \u00d7 3 = 1,215<\/p>\n<p>Question 19.<br \/>\n698 \u00d7 7<br \/>\nAnswer: 698 \u00d7 7 = 4,886<\/p>\n<p>Explanation:<br \/>\nUsing the Distributive Property of Multiplication,<br \/>\n698 \u00d7 7 = ( 600 + 90 + 8 ) \u00d7 7<br \/>\n= ( 600 \u00d7 7 ) + ( 90 \u00d7 7 ) + ( 8 \u00d7 7 )<br \/>\n= 4,200 + 630 + 56<br \/>\n= 4,886<br \/>\nHence, 698 \u00d7 7 = 4,886<\/p>\n<h3><a id=\"Lesson_6.5_Number_Patterns\"><\/a>Lesson 6.5 Number Patterns<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Shade every third square in the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.5-1.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.5 1\" width=\"381\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.5-1.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.5-1-300x188.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\nWrite the shaded numbers. What patterns do you see?<\/p>\n<p>What other patterns do you see in the table?<\/p>\n<p>Answer:<br \/>\nThe shaded numbers are:<br \/>\n3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60<br \/>\nFrom the shaded numbers, we can see that each third square is a multiple of 3<br \/>\nThe other patterns we can observe in the given table is:<br \/>\na) If we first shaded the second square and then shaded each second square, then we get the multiples of 2<br \/>\nb) The same pattern will have to be applied for the fourth square<br \/>\nThere will also be other patterns by shading 5th square, 6th square, etc.<\/p>\n<p><strong>Structure<\/strong><br \/>\nCircle every fourth square in the table. Write the circled numbers. What patterns do you see?<br \/>\nAnswer:<br \/>\nThe circled numbers are:<br \/>\n4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60<br \/>\nFrom the circled numbers of every fourth square, we can see that every fourth square is a multiple of 4.<\/p>\n<p><strong>Think and Grow: Create Number Patterns<\/strong><\/p>\n<p>A rule tells how numbers or shapes in a pattern are related.<br \/>\nExample<br \/>\nUse the rule \u201cAdd 3.\u201d to create a number pattern. The first number in the pattern is 3. Then describe another feature of the pattern.<br \/>\nCreate a pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-26.jpg\" alt=\"\" width=\"305\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-26.jpg 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-26-300x69.jpg 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nSo,<br \/>\nThe numbers in the pattern are multiples of 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.5-3.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.5 3\" width=\"234\" height=\"266\" \/><\/p>\n<p><strong>Example<\/strong><br \/>\nUse the rule \u201cMultiply by 2.\u201d to create a number pattern. The first number in the pattern is 10. Then describe another feature of the pattern.<br \/>\nCreate a pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-27.jpg\" alt=\"\" width=\"315\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-27.jpg 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-27-300x64.jpg 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><br \/>\nSo,<br \/>\nThe one&#8217;s digit of each number in the pattern is 0.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Write the first six numbers in the pattern. Then describe another feature of the pattern.<\/strong><br \/>\nQuestion 1.<br \/>\nRule: Add 5.<br \/>\nFirst number: 1<br \/>\n1, ____, _____, _____, _____, _____<br \/>\nAnswer: The first 6 numbers are: 1, 6, 11, 16, 21 and 26<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nThe given rules are:<br \/>\nRule 1 : Add 5<br \/>\nRule 2: Add 5<br \/>\nHence,<br \/>\nThe given pattern is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-28.jpg\" alt=\"\" width=\"305\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-28.jpg 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-28-300x69.jpg 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 2.<br \/>\nRule: Multiply by 3.<br \/>\nFirst number: 3<br \/>\n3, _____, _____, ____, _____, _____<br \/>\nAnswer: The first 6 numbers are: 3, 9, 27, 81, 243, 729<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule 1: Multiply by 3<br \/>\nRule 2: First number: 3<br \/>\nHence,<br \/>\nThe given pattern is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-29.jpg\" alt=\"\" width=\"315\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-29.jpg 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-29-300x64.jpg 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p>Question 3.<br \/>\nRule: Subtract 2.<br \/>\nFirst number: 20<br \/>\nAnswer: The first 6 numbers are: 20, 18, 16, 14, 12, 10<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule 1: Subtract 20<br \/>\nRule 2: First number: 20<br \/>\nHence,<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-30.jpg\" alt=\"\" width=\"305\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-30.jpg 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-30-300x69.jpg 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 4.<br \/>\nRule: Divide by 2.<br \/>\nFirst number: 256<br \/>\nAnswer: The first 6 numbers are: 256, 128, 64, 32, 16, 8<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule 1: Divide by 2<br \/>\nRule 2: First number: 256<br \/>\nHence,<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-31.jpg\" alt=\"\" width=\"315\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-31.jpg 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-31-300x64.jpg 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Write the first six numbers in the pattern. Then describe another feature of the pattern.<\/strong><br \/>\nQuestion 5.<br \/>\nRule: Add 11.<br \/>\nFirst number: 11<br \/>\nAnswer: The first 6 numbers are: 11, 22, 33, 44, 55, 66<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Add 11<br \/>\nFirst number: 11<br \/>\nHence,<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-32.jpg\" alt=\"\" width=\"314\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-32.jpg 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-32-300x58.jpg 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<p>Question 6.<br \/>\nRule: Multiply by 4.<br \/>\nFirst number: 4<br \/>\nAnswer: The first 6 numbers are: 4, 16, 64, 256, 1024, 4096<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule 1: Multiply by 4<br \/>\nFirst number: 4<br \/>\nHence,<br \/>\nThe given pattern is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-33.jpg\" alt=\"\" width=\"311\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-33.jpg 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-33-300x61.jpg 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p>Question 7.<br \/>\nRule: Subtract 3.<br \/>\nFirst number: 21<br \/>\nAnswer: The first 6 numbers are: 21, 18, 15, 12, 9, 6<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Subtract 3<br \/>\nFirst number: 21<br \/>\nHence,<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-34.jpg\" alt=\"\" width=\"309\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-34.jpg 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-34-300x69.jpg 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Question 8.<br \/>\nRule: Divide by 3.<br \/>\nFirst number: 729<br \/>\nAnswer: The first 6 numbers are: 729, 243, 81, 27, 9, 3<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule 1: Divide by 3<br \/>\nFirst number: 729<br \/>\nHence,<br \/>\nThe given pattern is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-35.jpg\" alt=\"\" width=\"318\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-35.jpg 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-35-300x63.jpg 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/p>\n<p>Question 9.<br \/>\nRule: Add 9.<br \/>\nFirst number: 8<br \/>\nAnswer: The first\u00a0 numbers are: 8, 17, 26, 35, 44, 53<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule 1: Add 9<br \/>\nFirst number: 8<br \/>\nHence,<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-36.jpg\" alt=\"\" width=\"314\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-36.jpg 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-36-300x58.jpg 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<p>Question 10.<br \/>\nRule: Multiply by 5.<br \/>\nFirst number: 5<br \/>\nAnswer: The first 6 numbers are: 5, 25, 125, 625, 3125, 15,625<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule 1: Multiply by 5<br \/>\nFirst number: 5<br \/>\nHence,<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-37.jpg\" alt=\"\" width=\"311\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-37.jpg 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-37-300x61.jpg 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p><strong>Open-Ended<\/strong><br \/>\n<strong>Use the rule to generate a pattern of four numbers.<\/strong><br \/>\nQuestion 11.<br \/>\nRule: Multiply by 2.<br \/>\nAnswer:<br \/>\nLet the first number be 2.<br \/>\nHence,<br \/>\nThe pattern of four numbers is: 2, 4, 8, 16<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Multiply by 2<br \/>\nLet the first number be: 2<br \/>\nHence,<br \/>\nThe obtained pattern will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-38.jpg\" alt=\"\" width=\"311\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-38.jpg 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-38-300x61.jpg 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p>Question 12.<br \/>\nRule: Subtract 9.<br \/>\nAnswer:<br \/>\nLet the first number be 36<br \/>\nHence,<br \/>\nThe pattern of four numbers is: 36, 27, 18, 9<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Subtract 9<br \/>\nLet the first number be 36<br \/>\nHence,<br \/>\nThe obtained pattern will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-39.jpg\" alt=\"\" width=\"309\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-39.jpg 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-39-300x69.jpg 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Question 13.<br \/>\nRule: Divide by 4.<br \/>\nAnswer:<br \/>\nLet the first number be 16<br \/>\nHence,<br \/>\nThe pattern of 4 numbers are: 16, 12, 8, 4<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Divide by 4<br \/>\nLet the first number be 16<br \/>\nHence,<br \/>\nThe obtained pattern will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-40.jpg\" alt=\"\" width=\"318\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-40.jpg 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-40-300x63.jpg 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><\/p>\n<p>Question 14.<br \/>\nRule: Add 7.<br \/>\nAnswer:<br \/>\nLet the first number be 7<br \/>\nHence,<br \/>\nThe pattern of the four numbers are: 7, 14, 21, 28<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Add 7<br \/>\nLet the first number be 7<br \/>\nHence,<br \/>\nThe obtained pattern will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-41.jpg\" alt=\"\" width=\"314\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-41.jpg 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-41-300x58.jpg 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<p>Question 15.<br \/>\n<strong>Patterns<\/strong><br \/>\nWrite a rule for the pattern below. Then write a different pattern that follows the same rule.<br \/>\n3, 6, 12, 24, 48<br \/>\nAnswer:\u00a0 The rule for the given pattern is: Multiply by 2<\/p>\n<p>Explanation:<br \/>\nGiven numbers are: 3, 6, 12, 24, 48<br \/>\nSo, from the given numbers,<br \/>\nWe can say that the given pattern follows the &#8220;Multiply by 2&#8221; rule<\/p>\n<p>Question 16.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWhat is the missing number in the pattern? Explain.<br \/>\n39, 37, 35, _____, 31, 29<br \/>\nAnswer: The missing number in the pattern is: 33<\/p>\n<p>Explanation:<br \/>\nThe given numbers are: 39, 37, 35, 31, 29<br \/>\nFrom the given pattern,<br \/>\nthe numbers that are following the rule is &#8220;Subtract by 2&#8221;<br \/>\nHence, from the above,<br \/>\nThe missing number will be: 35 &#8211; 2 = 33<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA presidential election is held every 4 years. There was a presidential election in 2016. How many presidential elections will occur between 2017 and 2030?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.5-5.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.5 5\" width=\"206\" height=\"183\" \/><br \/>\nThe rule is to add 4 years to each presidential election year. Start with 2016. Then count the years in the pattern that is between 2017 and 2030.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-42.jpg\" alt=\"\" width=\"241\" height=\"64\" \/><br \/>\nSo,<br \/>\n3 presidential elections will occur between 2017 and 2030.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 17.<br \/>\nThe pattern of animals on a Chinese calendar repeats every 12 years. The year 2000 was the year of the dragon. How many times will the year of the dragon occur between 2001 and 2100?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.5-7.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.5 7\" width=\"177\" height=\"179\" \/><br \/>\nAnswer: The number of times the dragon will appear between 2001 and 2100 is: 8<\/p>\n<p>Explanation:<br \/>\nGiven that the pattern of animals on a Chinese calendar repeats every 12 years<br \/>\nIt is also given that the year 2000 was the year of the dragon<br \/>\nNow, between the year 2001 and 2100, there are 99 years<br \/>\nSo,<br \/>\nThe number of times the dragon will appear = The difference between the years 2001 and 2100 \u00f7 The number of years the pattern will change<br \/>\n= 99 \u00f7 12<br \/>\nNow,<br \/>\n99 \u00f7 12 = 8 R 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the dragon will appear 8 times between the years 2001 and 2021<\/p>\n<p>Question 18.<br \/>\nA robotics team raised $25 the first month of school. Each month of school, the team wants to raise 2 times as much money as the month before. How much money should they raise in the fifth month of school?<br \/>\nAnswer: The money should they raise in the fifth month of school is: $400<\/p>\n<p>Explanation:<br \/>\nGiven that a robotics team raised $25 for the first month of the school and each month of the school, the team wants to raise 2 times as much money as the month before.<br \/>\nHence,<br \/>\nThe rule followed here is: Multiply by 2<br \/>\nThe given first number is: $25<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-21874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-43.jpg\" alt=\"\" width=\"308\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-43.jpg 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-43-300x56.jpg 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\nHence, from the above,<br \/>\nWe can conclude that the money they should raise in the fifth month is: $400<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou start with 128 pictures on your tablet. You take 6 pictures and delete 3 pictures each day. How many pictures do you have on your tablet after 6 days?<br \/>\nAnswer: The pictures you have on your tablet after 6 days is: 110 pictures<\/p>\n<p>Explanation:<br \/>\nGiven that you have 128 pictures on your tablet and you take 6 pictures and delete 3 pictures each day.<br \/>\nSo,<br \/>\nThe number of pictures you have each day = 6 &#8211; 3 = 3 pictures<br \/>\nSo,<br \/>\nThe total number of pictures in 6 days = 6 \u00d7 3 = 18 pictures<br \/>\nSo,<br \/>\nThe total number of pictures you have in 6 days = Total number of pictures &#8211; Total number f pictures in 6 days<br \/>\n= 128 &#8211; 18<br \/>\n= 110 pictures<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 110 pictures you have in 6 days.<\/p>\n<h3><a id=\"Number_Patterns_Practice_6.5\"><\/a>Number Patterns Numbers Homework &amp; Practice 6.5<\/h3>\n<p><strong>Write the first six numbers in the pattern. Then describe another feature of the pattern.<\/strong><br \/>\nQuestion 1.<br \/>\nRule: Subtract 8.<br \/>\nFirst number: 88<br \/>\n88, ____, ____, ____, _____, _____<br \/>\nAnswer:<br \/>\nThe first 6 numbers in the given pattern are: 88, 80, 72, 64, 56, 48<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Subtract 8<br \/>\nFirst number: 88<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22440\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-44.jpg\" alt=\"\" width=\"305\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-44.jpg 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-44-300x61.jpg 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 2.<br \/>\nRule: Multiply by 10.<br \/>\nFirst number: 2<br \/>\n2, _____, _____, _____, ____, ____<br \/>\nAnswer:<br \/>\nThe first 6 numbers of the given pattern are: 2, 20, 200, 2,000, 20,000, 200,000<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Multiply by 10<br \/>\nFirst number: 2<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22455\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-45.jpg\" alt=\"\" width=\"323\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-45.jpg 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-45-300x66.jpg 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Question 3.<br \/>\nRule: Add 9.<br \/>\nFirst number: 17<br \/>\nAnswer:<br \/>\nThe first 6 numbers for the given pattern is: 17, 26, 35, 44, 53, 62<\/p>\n<p>Explanation:<br \/>\nFor the formation,<br \/>\nthe given rules are:<br \/>\nRule: Add 9<br \/>\nFirst number: 17<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-46.jpg\" alt=\"\" width=\"301\" height=\"74\" \/><\/p>\n<p>Question 4.<br \/>\nRule: Divide by 2.<br \/>\nFirst number: 1,600<br \/>\nAnswer:<br \/>\nThe first 6 numbers of the given pattern are: 1,600, 800, 400, 200, 100, 50<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Divide by 2<br \/>\nFirst number: 1,600<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-47.jpg\" alt=\"\" width=\"315\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-47.jpg 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-47-300x71.jpg 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p><strong>Open-Ended Use the rule to generate a pattern of four numbers.<\/strong><br \/>\nQuestion 5.<br \/>\nRule: Divide by 5.<br \/>\nAnswer:<br \/>\nLet the first number be: 625<br \/>\nHence,<br \/>\nThe\u00a0 four numbers of the given pattern will be: 625, 125, 25, 5<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Divide by 5<br \/>\nLet the first number be: 625<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-48.jpg\" alt=\"\" width=\"315\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-48.jpg 315w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-48-300x71.jpg 300w\" sizes=\"(max-width: 315px) 100vw, 315px\" \/><\/p>\n<p>Question 6.<br \/>\nRule: Add 8.<br \/>\nAnswer:<br \/>\nLet the first number be 8<br \/>\nHence,<br \/>\nThe four numbers of the given pattern are: 8, 16, 24, 32<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Add 8<br \/>\nLet the first number be 8<br \/>\nHence,<br \/>\nThe pattern we will obtain will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-49.jpg\" alt=\"\" width=\"301\" height=\"74\" \/><\/p>\n<p>Question 7.<br \/>\nRule: Multiply by 9.<br \/>\nAnswer:<br \/>\nLet the first number be 9<br \/>\nHence,<br \/>\nThe four numbers of the pattern will be: 9, 81, 729, 6551<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Multiply 9<br \/>\nLet the first number be 9<br \/>\nHence,<br \/>\nThe pattern we obtain will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-50.jpg\" alt=\"\" width=\"323\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-50.jpg 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-50-300x66.jpg 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><\/p>\n<p>Question 8.<br \/>\nRule: Subtract 3.<br \/>\nAnswer:<br \/>\nLet the first number be 27<br \/>\nHence,<br \/>\nThe four numbers of the given pattern will be: 27, 24, 21, 18<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Subtract 3<br \/>\nLet the first number be 27<br \/>\nHence,<br \/>\nThe pattern we obtain will be:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-22604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-51.jpg\" alt=\"\" width=\"305\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-51.jpg 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-51-300x61.jpg 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 9.<br \/>\n<strong>Structure<\/strong><br \/>\nList the first ten multiples of 9. What patterns do you notice with the digits in the one&#8217;s place? in the tens place?<br \/>\nDoes this pattern continue beyond the tenth number in the pattern?<br \/>\nAnswer: The first 10 multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90<\/p>\n<p>Explanation:<br \/>\nThe first 10 multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90<br \/>\nSo,<br \/>\nfrom the above 10 multiples of 9,<br \/>\nThe pattern we can observe in the one&#8217;s place is: Decreasing of numbers from 9 to 0 i.e., 9, 8, 7, &#8230;&#8230;&#8230;..0<br \/>\nThe pattern we can observe in the ten&#8217;s place is: Increasing of numbers from 0 to 9 i.e., 0, 1, 2 &#8230;&#8230;&#8230;&#8230;..9<br \/>\nThe above 2 patterns will continue beyond the first 10 multiples of 9<br \/>\nHence, from the above,<br \/>\nWe can conclude that the patterns we observed are:<br \/>\nThe pattern we can observe in the one&#8217;s place is: Decreasing of numbers from 9 to 0 i.e., 9, 8, 7, &#8230;&#8230;&#8230;..0<br \/>\nThe pattern we can observe in the ten&#8217;s place is: Increasing of numbers from 0 to 9 i.e., 0, 1, 2 &#8230;&#8230;&#8230;&#8230;..9<\/p>\n<p>Question 10.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nIt takes the moon about 28 days to orbit Earth. How many times will the moon orbit Earth in 1 year?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-6.5-8.png\" alt=\"Big Ideas Math Answer Key Grade 4 Chapter 6 Factors, Multiples, and Patterns 6.5 8\" width=\"197\" height=\"147\" \/><br \/>\nAnswer: The moon will orbit the earth 10,220 times in 1 year<\/p>\n<p>Explanation:<br \/>\nGiven that it takes the moon about 28 days to orbit the earth.<br \/>\nWe know that,<br \/>\n1 year = 365 days<br \/>\nSo,<br \/>\nThe number of times the moon will orbit around the earth in 1 year = 365 \u00d7 28<br \/>\nNow,<br \/>\nBy using the partial products method,<br \/>\n365 \u00d7 28\u00a0 = ( 300 + 65 ) \u00d7\u00a0 ( 20 + 8 )<br \/>\n= ( 300 \u00d7\u00a0 20 ) + ( 300 \u00d7\u00a0 8 ) + ( 65 \u00d7\u00a0 20 ) + ( 65 \u00d7\u00a0 8 )<br \/>\n= 6,000 + 2,400 + 1,300 + 520<br \/>\n= 10,220 times<br \/>\nHence, from the above,<br \/>\nWe can conclude that the moon will orbit around the Earth 10,220 times<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nIn each level of a video game, you can earn up to 10 points and lose up to 3 points. Your friend earns 9 points in the first level. If he earns and loses the maximum number of points at each level, how many total points will he have after level 6?<br \/>\nAnswer: The total points your friend will have is: 44 points<\/p>\n<p>Explanation:<br \/>\nGiven that in each level of a video game, you can earn up to 10 points and lose up to 3 points<br \/>\nSo,<br \/>\nThe maximum number of points you can get = 10 &#8211; 3 = 7 points<br \/>\nIt is also given that your friend earns 9 points in the first level<br \/>\nSo,<br \/>\nThe number of points he will have at level 6 = The number of points he has at the first level + 5 \u00d7 ( The maximum number of points he can get )<br \/>\n= 9 + ( 5 \u00d7\u00a0 7 )<br \/>\n= 9 + 35<br \/>\n= 44 points<br \/>\nHence, from the above,<br \/>\nWe can conclude that he will have 44 points at the sixth level.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 12.<br \/>\n14 \u00d7 23 = _____<br \/>\nAnswer: 14 \u00d7\u00a0 23 = 322<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n14 \u00d7\u00a0 23 = ( 10 + 4 ) \u00d7 ( 20 + 3 )<br \/>\n= ( 10 \u00d7\u00a0 20 ) + ( 10 \u00d7\u00a0 3 ) + ( 4 \u00d7\u00a0 20 ) + ( 4 \u00d7\u00a0 3 )<br \/>\n= 200 + 30 + 80 + 12<br \/>\n= 322<br \/>\nHnece, 14 \u00d7 23 = 322<\/p>\n<p>Question 13.<br \/>\n48 \u00d7 60 = _____<br \/>\nAnswer: 48 \u00d7 60 = 2,880<\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property of Multiplication,<br \/>\n48 \u00d7\u00a0 60 = ( 40 + 8 ) \u00d7 60<br \/>\n= ( 40 \u00d7\u00a0 60 ) + ( 8 \u00d7\u00a0 60 )<br \/>\n= 2,400 + 480<br \/>\n= 2,880<br \/>\nHence, 48 \u00d7 60 = 2,880<\/p>\n<p>Question 14.<br \/>\n55 \u00d7 31 = _____<br \/>\nAnswer: 55 \u00d7\u00a0 31 = 1,705<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n55 \u00d7 31 = ( 50 + 5 ) \u00d7\u00a0 ( 30 + 1 )<br \/>\n= ( 50 \u00d7\u00a0 30 ) + ( 50 \u00d7\u00a0 1 ) + ( 5 \u00d7\u00a0 30 ) + ( 5 \u00d7\u00a0 1 )<br \/>\n= 1,500 + 50 + 150 + 5<br \/>\n= 1,705<br \/>\nHence, 55 \u00d7\u00a0 31 = 1,705<\/p>\n<h3><a id=\"Lesson_6.6_Shape_Patterns\"><\/a>Lesson 6.6 Shape Patterns<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Create a rule using 3 different shapes. Draw the first six shapes in the pattern.<\/p>\n<p>What is the next shape in the pattern?<\/p>\n<p>What is the 9th shape in the pattern? Explain.<\/p>\n<p>What is the 99th shape? 1,000th shape? Explain?<\/p>\n<p>Answer:\u00a0 <img loading=\"lazy\" class=\"alignnone size-full wp-image-22608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-54.jpg\" alt=\"\" width=\"322\" height=\"126\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-54.jpg 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-54-300x117.jpg 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\nFrom the above 3 shapes,<br \/>\nThe rule we can create is: Add 1<br \/>\nSo,<br \/>\nWe can say the above pattern will repeat after every 3 shapes.<br \/>\nSo,<br \/>\nThe 9th shape will be: Pentagon<br \/>\nThe 99th shape will be: 99 \/ 3\u00a0 =\u00a0 33 R 0<br \/>\nSo, The 99th shape will be: Pentagon<br \/>\nThe 100th shape will be: Triangle (Because the remainder will be 1 i.e., the shapes will completely repeat 99 times and for the 100th time, it will start from 1st shape)<\/p>\n<p><strong>Structure<\/strong><br \/>\nYou want to show the first 40 shapes in the pattern above. Without modeling, how many of each shape do you think you will need?<br \/>\nAnswer:<br \/>\nThe number of times each shape will appear in the first 40 shapes is:<br \/>\nTriangle: 14 times<br \/>\nSquare: 13 times<br \/>\nPentagon: 13 times<\/p>\n<p>Explanation:<br \/>\nIn the above pattern, the shapes are: Triangle, Square, Pentagon<br \/>\nThe rule we obtained by using these 3 shapes is: Add 1<br \/>\nSo,<br \/>\nThe pattern for the first 40 shapes will be: 40 \u00f7 3<br \/>\nNow,<br \/>\nBy using the Distributive Property of Division,<br \/>\n40 \u00f7 3 = ( 36 + 3 ) \u00f7 3<br \/>\n= ( 36 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n= 12 + 1<br \/>\n= 13 R 1<br \/>\nHence, the 3 shapes will appear 39 times<br \/>\nSo,<br \/>\nThe number of times each shape will appear = 13 times<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of times the shape will appear is:<br \/>\nTriangle: 14 times ( 13 + 1. This 1 is because 40th time, the triangle will repeat again )<br \/>\nSquare: 13 times<br \/>\nPentagon: 13 times<\/p>\n<p><strong>Think and Grow: Create Shape Patterns<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nCreate a shape pattern by repeating the rule \u201ctriangle, hexagon, square, rhombus.\u201dWhat is the 42nd shape in the pattern?<br \/>\nCreate a pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-1.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 1\" width=\"550\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-1.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-1-300x33.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><br \/>\n42 \u00f7 4 is 10 R2, so when the pattern repeats 10 times, the 40th shape is a rhombus So, the 41st shape is a Triangle and the 42nd shape is a hexagon.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-2.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 2\" width=\"180\" height=\"249\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-3.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 3\" width=\"482\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-3.png 482w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-3-300x57.png 300w\" sizes=\"(max-width: 482px) 100vw, 482px\" \/><br \/>\nFigure 1 has 1 column of 4 dots, so it has 1 \u00d7 4 = 4 dots.<br \/>\nFigure 2 has 2 columns of 4 dots, so it has 2 \u00d7 4 = 8 dots.<br \/>\nFigure 3 has 3 columns of 4 dots, so it has 3 \u00d7 4 = 12 dots.<br \/>\nSo,<br \/>\nThe 25th figure has 1 column of 4 dots, ( Because the 3 figures will be repeated 24 times and the first figure will appear again 25th time)<br \/>\nSo, it has 1 \u00d7 4 =4 dots.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nExtend the pattern of shapes by repeating the rule \u201csquare, trapezoid, triangle, hexagon, triangle.\u201dWhat is the 108th shape in the pattern?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-4.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 4\" width=\"521\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-4.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-4-300x36.png 300w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><br \/>\nAnswer: The 108th shape in the pattern will be: Triangle<\/p>\n<p>Explanation:<br \/>\nThe given pattern is: Square, trapezoid, triangle, hexagon, triangle<br \/>\nSo, there is a total of 5 shapes.<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\n108 \u00f7 5 = ( 100 + 5 ) \u00f7 5<br \/>\n= ( 100 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 20 + 1<br \/>\n= 21 R 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 108th shape will be the triangle.<\/p>\n<p>Question 2.<br \/>\nDescribe the dot pattern. How many dots are in the 76th figure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-5.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 5\" width=\"210\" height=\"81\" \/><br \/>\nAnswer: The number of dots in the 76th figure is: 3 dots<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-5.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 5\" width=\"210\" height=\"81\" \/><br \/>\nFrom the above pattern,<br \/>\nIn figure 1, the number of dots = 1 \u00d7 3 = 3 dots<br \/>\nIn figure 2, the number of dots = 2 \u00d7 3 =\u00a0 dots<br \/>\nIn figure 3, the number of dots = 3 \u00d7 3 = 9 dots<br \/>\nSo,<br \/>\nThe total number of patterns is: 3<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n76 \u00f7 3 = ( 66 +9 ) \u00f7 3<br \/>\n= ( 66 \u00f7 3 ) + ( 9 \u00f7 3 )<br \/>\n= 22 + 3<br \/>\n= 25 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 3 dots in the 76th figure.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><br \/>\nQuestion 3.<br \/>\nExtend the pattern of shapes by repeating the rule \u201coval, triangle.\u201dWhat is the 55th shape?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-6.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 6\" width=\"567\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-6.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-6-300x34.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><br \/>\nAnswer: The 55th shape is: Oval<\/p>\n<p>Explanation:<br \/>\nThe given pattern of shapes is: Oval, Triangle<br \/>\nSo,<br \/>\nThe total number of patterns is: 2<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n55 \u00f7 2 = ( 50 + 4 ) \u00f7 2<br \/>\n= ( 50 \u00f7 2 ) + ( 4 \u00f7 2 )<br \/>\n= 25 + 2<br \/>\n= 27 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 55th shape is: Oval<\/p>\n<p>Question 4.<br \/>\nExtend the pattern of symbols by repeating the rule \u201cadd, subtract, multiply, divide.\u201dWhat is the 103rd symbol?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-7.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 7\" width=\"540\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-7.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-7-300x41.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nAnswer: The 103rd symbol is: Multiply<\/p>\n<p>Explanation:<br \/>\nThe given patterns are: Add, Subtract, Multiply, Divide<br \/>\nSo,<br \/>\nThe total number of patterns is: 4<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n103 \u00f7 4 = ( 80 + 20 ) \u00f7 4<br \/>\n= ( 80 \u00f7 4 ) + ( 20 \u00f7 4 )<br \/>\n= 20 + 5<br \/>\n= 25 R 3<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 103rd shape is: Multiply<\/p>\n<p>Question 5.<br \/>\nDescribe the pattern. How many squares are in the 24th figure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-8.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 8\" width=\"219\" height=\"103\" \/><br \/>\nAnswer: The number of squares in the 24th figure is: 4 squares<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-8.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 8\" width=\"219\" height=\"103\" \/><br \/>\nIn figure 1, the number of squares is: 2<br \/>\nIn figure 2, the number of squares is: 3<br \/>\nIn figure 3, the number of squares is: 4<br \/>\nSo,<br \/>\nTotal number of figures = 3<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n24 \u00f7 3 = ( 21 + 3 ) \u00f7 3<br \/>\n= ( 21 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n= 7 + 1<br \/>\n= 8 R 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that\u00a0 in the 24th figure, the number of squares is: 4<\/p>\n<p>Question 6.<br \/>\nDescribe the pattern of the small triangles. How many small triangles are in the 10th figure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-9.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 9\" width=\"261\" height=\"107\" \/><br \/>\nAnswer: The small triangles in the 10th figure is: 1<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-9.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 9\" width=\"261\" height=\"107\" \/><br \/>\nFrom the given figure,<br \/>\nIn fig 1, the number of triangles is: 1<br \/>\nIn fig 2, the number of triangles is: 2<br \/>\nIn fig 3, the number of triangles is: 4<br \/>\nSo,<br \/>\nTotal number of figures = 3<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n10 \u00f7 3 = ( 3 + 6 ) \u00f7 9<br \/>\n= ( 3 \u00f7 3 ) + ( 6 \u00f7 3 )<br \/>\n= 1 + 2<br \/>\n= 3 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 10th figure has 1 triangle<\/p>\n<p>Question 7.<br \/>\n<strong>Structure<\/strong><br \/>\nMake a shape pattern that uses twice as many squares as triangles.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich shape patterns have a heart as the 12th shape?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-10.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 10\" width=\"328\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-10.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-10-300x122.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<br \/>\nLet the patterns be named as A), B), C) and D)<br \/>\nSo,<br \/>\nThe shape patterns that have a heart as the 12th shape is: A), B) and D)<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-10.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 10\" width=\"328\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-10.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-10-300x122.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nLet the patterns be named as A), B), C) and D)<br \/>\nA) In pattern A,<br \/>\nThe total number of figures = 2<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\n12 \u00f7 2 = 6<br \/>\nHence, A) will have a heart as the 12th shape<br \/>\nB) In pattern B,<br \/>\nThe total number of figures = 4<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\n12 \u00f7 4 = 3<br \/>\nHence, B) will have a heart as the 12th shape<br \/>\nC) In pattern C,<br \/>\nThe total number of figures = 2<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\n12 \u00f7 2 = 6<br \/>\nBut, the 12th shape in C) will be a circle<br \/>\nD) In pattern D,<br \/>\nThe total number of figures = 3<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\n12 \u00f7 3 = 4<br \/>\nHence, C) will have a heart as the 12th shape<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nYou make a necklace with a cube, hexagon, and star beads. You string the beads in a pattern. You use the rule \u201ccube, star, cube, hexagon.\u201dIt takes 64 beads to complete the necklace. How many times do you repeat the pattern?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-11.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 11\" width=\"140\" height=\"133\" \/><br \/>\nDivide the number of beads it takes to complete the necklace by the number of beads in the rule. There are 4 beads in the rule.<br \/>\nSo,<br \/>\n4\u221a64 = 64 \u00f7 4<br \/>\nBy using the Distributive Property of division,<br \/>\n64 \u00f7 4 = ( 60 + 4 ) \u00f7 4<br \/>\n= ( 60 \u00f7 4 ) + ( 4 \u00f7 4 )<br \/>\n= 15 + 1<br \/>\n= 16<br \/>\nHence,<br \/>\nYou repeat the pattern 16 times<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 9.<br \/>\nThe path on a board game uses the rule \u201cred, green, pink, yellow, blue.\u201dThere are 55 spaces on the game board. How many times does the pattern repeat?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-12.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 12\" width=\"401\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-12.png 401w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-12-300x127.png 300w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><br \/>\nAnswer: The number of times the pattern will repeat is: 11 times<\/p>\n<p>Explanation:<br \/>\nGiven that the path on a board game uses the rule &#8221; red, green, pink, yellow, blue &#8221;<br \/>\nIt is also given that there are 55 spaces on the game board<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the Distributive Property of division,<br \/>\n55 \u00f7 5 = ( 50 + 5 ) \u00f7 5<br \/>\n= ( 50 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 10 + 1<br \/>\n= 11<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of times the patterns repeat is: 11 times<\/p>\n<p>Question 10.<br \/>\nYou make a walkway in a garden using different-shaped stepping stones. You use the rule \u201csquare, circle, square, hexagon.\u201dYou use 24 square stepping stones. How many circle and hexagon stepping stones do you use altogether? How many stones do you use in all?<br \/>\nAnswer:<br \/>\nThe Total number of stones used are: 24<br \/>\nThe number of\u00a0 circle and hexagon stepping stones use are: 12<\/p>\n<p>Explanation:<br \/>\nGiven that there is a walkway in a garden using different-shaped stepping stones.<br \/>\nThe rule used here is: Square, circle, square, hexagon<br \/>\nIt is also given that there are 24 stepping stones you used<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the Distributive Property of division,<br \/>\n24 \u00f7 4 = ( 20 + 4 ) \u00f7 4<br \/>\n= ( 20 \u00f7 4 ) + ( 4 \u00f7 4 )<br \/>\n= 5 + 1<br \/>\n= 6<br \/>\nSo,<br \/>\nThe number of stones used each time is: 6 times<br \/>\nSo,<br \/>\nThe number of\u00a0 circle and hexagon stepping stones used altogether is: 6 + 6 = 12<br \/>\nHence, from the above,<br \/>\nWe can conclude that circle and hexagon stepping stones you used altogether is: 12<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou make a rectangular picture frame using square tiles. The picture frame is 12 tiles long and 8 tiles wide. You arrange the tiles in a pattern. You use the rule \u201cred, orange, yellow.\u201d How many of each color tile do you use?<br \/>\nAnswer: The number of each color tiles do you use is: 32<\/p>\n<p>Explanation:<br \/>\nGiven that you make a rectangular picture frame using square tiles and it is also given that the picture frame is 12 tiles long and 8 tiles wide.<br \/>\nSo,<br \/>\nThe area of a rectangular picture frame = 12 \u00d7 8 = 96 square- meters<br \/>\nThe rule used is: red, orange, yellow<br \/>\nSo,<br \/>\nThe total number of colors is: 3<br \/>\nSo,<br \/>\nThe number of each color tile you used = Area of rectangular picture frame \u00f7 Total number of colors<br \/>\n= 96 \u00f7 3<br \/>\nNow,<br \/>\nBy using the Distributive Property of division,<br \/>\n96 \u00f7 3 = ( 90 + 6 ) \u00f7 3<br \/>\n= ( 90 \u00f7 3 ) + ( 6 \u00f7 3 )<br \/>\n= 30 + 2<br \/>\n= 32<br \/>\nHence, from the above,<br \/>\nwe can conclude that each number of color tile used is: 32<\/p>\n<h3><a id=\"Shape_Patterns_Practice_6.6\"><\/a>Shape Patterns Numbers Homework &amp; Practice 6.6<\/h3>\n<p>Question 1.<br \/>\nExtend the pattern of shapes by repeating the rule \u201cup, right, down, left.\u201dWhat is the 48th shape in the pattern?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-13.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 13\" width=\"501\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-13.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-13-300x41.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\nAnswer: The 48th shape in the pattern is: Left<\/p>\n<p>Explanation:<br \/>\nGiven pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-13.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 13\" width=\"501\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-13.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-13-300x41.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\nThe rule for the given pattern is: up, right, down, left<br \/>\nSo,<br \/>\nThe total number of patterns is: 4<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n48 \u00f7 4 = ( 40 + 8 ) \u00f7 4<br \/>\n= ( 40 \u00f7 4 ) + ( 8 \u00f7 4 )<br \/>\n= 10 + 2<br \/>\n= 12 R 0<br \/>\nHence, from the above<br \/>\nWe can conclude that the 48th figure in the given pattern is: Left<\/p>\n<p>Question 2.<br \/>\nExtend the pattern of shapes by repeating the rule \u201csmall circle, medium circle, large circle.\u201dWhat is the 86th shape in the pattern?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-14.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 14\" width=\"534\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-14.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-14-300x43.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><br \/>\nAnswer: The 86th shape in the pattern is: Medium circle<\/p>\n<p>Explanation:<br \/>\nGiven pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-14.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 14\" width=\"534\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-14.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-14-300x43.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><br \/>\nThe rule for the pattern is: Small circle, Medium circle, large circle<br \/>\nSo,<br \/>\nThe total number of patterns = 3<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n86 \u00f7 3 = ( 75 + 9 ) \u00f7 3<br \/>\n= ( 75 \u00f7 3 ) + ( 9 \u00f7 3 )<br \/>\n= 25 + 3<br \/>\n= 28 R 2<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 86th shape in the pattern is: Medium circle<\/p>\n<p>Question 3.<br \/>\nDescribe the dot pattern. How many dots are in the 113th figure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-15.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 15\" width=\"211\" height=\"83\" \/><br \/>\nAnswer: The number of dots in the 113th figure is: 4 dots<\/p>\n<p>Explanation:<br \/>\nGiven pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-15.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 15\" width=\"211\" height=\"83\" \/><br \/>\nSo,<br \/>\nIn fig 1, the number of dots = 2<br \/>\nIn fig 2, the number of dots = 4<br \/>\nIn fig 3, the number of dots = 6<br \/>\nSo,<br \/>\nThe total number of figures = 3<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n113 \u00f7 3 = ( 99 + 12 ) \u00f7 3<br \/>\n= ( 99 \u00f7 3 ) + ( 12 \u00f7 3 )<br \/>\n= 33 + 4<br \/>\n= 37 R 2<br \/>\nHence, from the above,<br \/>\nwe can conclude that the number of dots in the 113th figure is: 4 dots<\/p>\n<p>Question 4.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYou and your friend each create a shape pattern with 100 shapes. Your friend says both patterns will have the same number of circles. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-16.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 16\" width=\"255\" height=\"178\" \/><br \/>\nAnswer: Yes, both patterns will have the same number of circles.<\/p>\n<p>Explanation:<br \/>\nGiven patterns are:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-16.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 16\" width=\"255\" height=\"178\" \/><br \/>\nThe pattern of the friend is: Star, circle<br \/>\nThe pattern of you si: Heart, circle, pentagon, circle<br \/>\nIt is also given that,<br \/>\nThe total number of figures = 100<br \/>\nSo,<br \/>\nThe total number of figures for your friend = 2<br \/>\nThe total number of figures for you = 4<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo<br \/>\nFor your friend,<br \/>\nBy using the partial quotients method,<br \/>\n100 \u00f7 2 = ( 50 + 50 ) \u00f7 2<br \/>\n= ( 50 \u00f7 2 ) + ( 50 \u00f7 2 )<br \/>\n= 25 + 25<br \/>\n= 50<br \/>\nHence,<br \/>\nThe number of circles = 50<br \/>\nThe number of stars = 50<br \/>\nFor you,<br \/>\nBy using the partial quotients method,<br \/>\n100 \u00f7 4 = ( 80 + 20 ) \u00f7 4<br \/>\n= ( 80 \u00f7 4 ) + ( 20 \u00f7 4 )<br \/>\n= 20 + 5<br \/>\n= 25<br \/>\nHence,<br \/>\nThe number of circles altogether = 25 + 25 = 50<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are equal number of circles in both the patterns<\/p>\n<p>Question 5.<br \/>\n<strong>Structure<\/strong><br \/>\nDraw the missing figure in the pattern. Explain the pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13399\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-17.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 17\" width=\"455\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-17.png 455w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-17-300x75.png 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n<strong>Reasoning<\/strong><br \/>\nNewton uses the rule \u201cbone, bone, paw print\u201d to make a shape pattern. He wants the pattern to repeat 8 times. How many bones will be in Newton\u2019s pattern?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-18.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 18\" width=\"245\" height=\"67\" \/><br \/>\nAnswer: The number of bones in Newton&#8217;s pattern is: 16<\/p>\n<p>Explanation:<br \/>\nGiven pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13400\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-4th-Grade-Chapter-6-Factors-Multiples-and-Patterns-6.6-18.png\" alt=\"Big Ideas Math Answers 4th Grade Chapter 6 Factors, Multiples, and Patterns 6.6 18\" width=\"245\" height=\"67\" \/><br \/>\nThe rule followed in the pattern is: Bone, Bone, pawprint<br \/>\nSo,<br \/>\nThe total number of figures in the given pattern = 3<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nIt is also given that the pattern repeated 8 times.<br \/>\nSo,<br \/>\nThe total number of figures when the pattern repeated 8 times = 8 \u00d7 3 = 24 figures<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n24 \u00f7 3 = ( 21 + 3 ) \u00f7 3<br \/>\n= ( 21 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n= 7 + 1<br \/>\n= 8<br \/>\nSo,<br \/>\nThe number of each figure in a pattern = 8<br \/>\nFrom the pattern, we can say there are 2 bones<br \/>\nSo,<br \/>\nThe total number of bones when the pattern repeated 8 times = 2 \u00d7 8 = 16<br \/>\nHence, from the above,<br \/>\nWe can conclude that there are 16 bones in the pattern when the pattern repeated 8 times<\/p>\n<p>Question 7.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThe black keys on a piano follow the pattern \u201ctwo black keys, three black keys.\u201d There are 36 black keys on a standard piano. How many times does this entire pattern repeat?<br \/>\nAnswer: The entire pattern repeat 12 times<\/p>\n<p>Explanation:<br \/>\nGiven that the black keys on a pattern follow the pattern<br \/>\nThe given pattern is: two black keys, three black keys<br \/>\nSo,<br \/>\nThe total number of patterns = 2<br \/>\nIt is also given that there are 36 black keys on a standard piano.<br \/>\nSo,<br \/>\nThe total number of black keys on a piano = 36<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n36 \u00f7 2 = ( 30 + 6 ) \u00f7 2<br \/>\n= ( 30 \u00f7 2 ) + ( 6 \u00f7 2 )<br \/>\n= 15 + 3<br \/>\n= 18<br \/>\nHence, from the above,<br \/>\nWe can conclude that the entire pattern will repeat 18 times.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the quotient.<\/strong><br \/>\nQuestion 8.<br \/>\n30 \u00f7 5 = _____<br \/>\nAnswer: 30 \u00f7 5 = 6<\/p>\n<p>Explanation:<br \/>\nBy using the partial products method,<br \/>\n30 \u00f7 5 = ( 25 + 5 ) \u00f7 5<br \/>\n= ( 25 \u00f7 5 ) + ( 5 \u00f7 5 )<br \/>\n= 5 + 1<br \/>\n= 6<br \/>\nHence, 30 \u00f7 5 = 6<\/p>\n<p>Question 9.<br \/>\n360 \u00f7 9 = ______<br \/>\nAnswer: 360 \u00f7 9 = 40<\/p>\n<p>Explanation:<br \/>\nBy using the partial quotients method,<br \/>\n360 \u00f7 9 = ( 270 + 90 ) \u00f7 9<br \/>\n= ( 270 \u00f7 9 ) + ( 90 \u00f7 9 )<br \/>\n= 30 + 10<br \/>\n= 40<br \/>\nHence, 360 \u00f7 9 = 40<\/p>\n<p>Question 10.<br \/>\n6,400 \u00f7 8 = _____<br \/>\nAnswer: 6,400 \u00f7 8 = 800<\/p>\n<p>Explanation:<br \/>\nBy using the place -value method,<br \/>\n6,400 \u00f7 8 = 64 hundreds \u00f7 8<br \/>\n= 8 hundred<br \/>\n= 8 \u00d7 100<br \/>\n= 800<br \/>\nHence, 6,400 \u00f7 8 = 800<\/p>\n<p>Question 11.<br \/>\n140 \u00f7 2 = _____<br \/>\nAnswer: 140 \u00f7 2 = 70<\/p>\n<p>Explanation:<br \/>\nBy using the place-value method,<br \/>\n140 \u00f7 2 = 14 tens \u00f7 2<br \/>\n= 7 tens<br \/>\n= 7 \u00d7 10<br \/>\n= 70<br \/>\nHence, 140 \u00f7 2 = 70<\/p>\n<p>Question 12.<br \/>\n4,200 \u00f7 7 = _____<br \/>\nAnswer: 4,200 \u00f7 7 = 600<\/p>\n<p>Explanation:<br \/>\nBy using the place-value method,<br \/>\n4,200 \u00f7 7 = 42 hundreds \u00f7 7<br \/>\n= 6 hundred<br \/>\n= 6 \u00d7 100<br \/>\n= 600<br \/>\nHence, 4,200 \u00f7 7 = 600<\/p>\n<p>Question 13.<br \/>\n40 \u00f7 2 = _____<br \/>\nAnswer: 40 \u00f7 2 = 20<\/p>\n<p>Explanation:<br \/>\nBy using the place-value method,<br \/>\n40 \u00f7 2 = 4 tens \u00f7 2<br \/>\n= 2 tens<br \/>\n= 2 \u00d7 10<br \/>\n= 20<br \/>\nHence, 40 \u00f7 2 = 20<\/p>\n<h3><a id=\"Factors,_Multiples,_and_Patterns_Performance_Task\"><\/a>Factors, Multiples, and Patterns Performance Task<\/h3>\n<p>You play basketball in a youth basketball program.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13401\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 1\" width=\"144\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-1.png 144w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-1-123x300.png 123w\" sizes=\"(max-width: 144px) 100vw, 144px\" \/><br \/>\nQuestion 1.<br \/>\nThere are 72 players in the program. Each team needs an equal number of players and must have at least 5 players. What are two different ways the teams can be made?<br \/>\nAnswer: The different ways the teams can be made and to have at least 5 members are: 8 \u00d7 9 and 9 \u00d7 8<\/p>\n<p>Explanation:<br \/>\nGiven that there are 72 players in the program and each team needs an equal number of players.<br \/>\nIt is also given that each team must have at least 5 players.<br \/>\nNow,<br \/>\nTo find the different ways the teams can be made, we have to find the factors of 72<br \/>\nNow,<br \/>\nThe factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72<br \/>\nNow, to make an equal number of players and to have at least 5 players,<br \/>\nThe different ways the teams can be made is: 8 \u00d7 9, 9 \u00d7 8<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 2 different ways the teams can be made are: 8 \u00d7 9 and 9 \u00d7 8<\/p>\n<p>Question 2.<br \/>\nThe width of a basketball court is 42 feet and the length is 74 feet. You run around the perimeter of the court 4 times to warm up. How many feet do you run?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13402\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-2.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 2\" width=\"254\" height=\"153\" \/><br \/>\nAnswer: The number of feet you run is: 464 feet<\/p>\n<p>Explanation:<br \/>\nGiven that the width of a basketball court is 42 feet high and the length is 74 feet<br \/>\nSo,<br \/>\nThe perimeter of the basketball court = 42 + 74 = 116 feet<br \/>\nIt is also given that you run around the perimeter of the basketball court 4 times to warm up.<br \/>\nSo,<br \/>\nThe number of feet you run to warm up = The perimeter of the basketball court \u00d7 4<br \/>\n= 116 \u00d7 4<br \/>\nNow,<br \/>\nBy using the partial products method,<br \/>\n116 \u00d7 4 = ( 100 + 16 ) \u00d7 4<br \/>\n= ( 100 \u00d7 4 ) + ( 16 \u00d7 4 )<br \/>\n= 400 + 64<br \/>\n= 464 feet<br \/>\nHence, from the above,<br \/>\nWe can conclude that you will run up 464 feet to warm up your body.<\/p>\n<p>Question 3.<br \/>\nYou and your friend are on the same team. You played your first game last week.<br \/>\na. Your team scored 4 more points than the other team. The total number of points scored by both teams was 58. How many points did your team score?<br \/>\nb. You and your friend scored the same number of points. You made 2-point shots and your friend made 3-point shots. What could be the greatest number of points you and your friend each scored?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nYour team uses the pattern below to decide which jersey color to wear to each game. Which color jersey will your team wear on the 20th game?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-3.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 3\" width=\"280\" height=\"117\" \/><br \/>\nAnswer: The color of jersey your team will wear on the 20th game is: Game 4<\/p>\n<p>Explanation:<br \/>\nGiven that your team uses the following pattern:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13403\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-3.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 3\" width=\"280\" height=\"117\" \/><br \/>\nFrom the above pattern,<br \/>\nThe total number of shirts is: 4<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n20 \u00f7 4 = 5 R 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the color of the shirt your team will wear on the 20th game is: Game 4<\/p>\n<h3><a id=\"Factors,_Multiples,_and_Patterns_Activity\"><\/a>Factors, Multiples, and Patterns Activity<\/h3>\n<p><strong>Multiple Lineup<\/strong><br \/>\n<strong>Directions:<\/strong><br \/>\n1. Players take turns rolling a die.<br \/>\n2. On your turn, place a counter on a multiple of the number of your roll. If there is not a multiple of the number of your roll, you lose your turn.<br \/>\n3. The first player to create a line of 5 in a row, horizontally, vertically, or diagonally, wins!<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13404\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-4.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns 4\" width=\"697\" height=\"746\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-4.png 697w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-4-280x300.png 280w\" sizes=\"(max-width: 697px) 100vw, 697px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Factors,_Multiples,_and_Patterns_Chapter_Practice\"><\/a>Factors, Multiples, and Patterns Chapter Practice<\/h3>\n<p><strong>6.1 Understand Factors<\/strong><\/p>\n<p>Question 1.<br \/>\nUse the rectangles to find the factor pairs for 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13405\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-1.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 1\" width=\"190\" height=\"170\" \/><br \/>\nAnswer: The factor pairs of 6 are: 1 and 6, 2 and 3<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23432\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-58.jpg\" alt=\"\" width=\"183\" height=\"173\" \/><br \/>\nThe factor pairs are nothing but the side lengths of a rectangle and the area of a rectangle gives the factor<br \/>\nHence,<br \/>\nThe factor pairs of 6 are: 1 and 6, 2 and 3<\/p>\n<p>Question 2.<br \/>\nDraw rectangles to find the factor pairs for 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13406\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-2.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 2\" width=\"266\" height=\"171\" \/><br \/>\nAnswer: The factor pairs of 12 are: 1 and 12, 2 and 6, 3 and 4<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-59.jpg\" alt=\"\" width=\"225\" height=\"46\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-23434\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-60.jpg\" alt=\"\" width=\"139\" height=\"65\" \/><img loading=\"lazy\" class=\"alignnone size-full wp-image-23436\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-61.jpg\" alt=\"\" width=\"99\" height=\"77\" \/><br \/>\nThe factor pairs are nothing but the side lengths of a rectangle and the area of a rectangle gives the factor<br \/>\nHence,<br \/>\nThe factor pairs of 12 are: 1 and 12, 2 and 6, 3 and 4<\/p>\n<p><strong>Find the factor pairs for the number.<\/strong><br \/>\nQuestion 3.<br \/>\n17<br \/>\nAnswer: The factor pairs of 17 are: 1 and 17<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original completely.<br \/>\nHence,<br \/>\nThe factor pairs of 17 are: 1 \u00d7 17<\/p>\n<p>Question 4.<br \/>\n10<br \/>\nAnswer: The factor pairs of 10 are: 1 and 10, 2 and 5<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 10 are: 1 \u00d7 10, 2 \u00d7 5<\/p>\n<p>Question 5.<br \/>\n21<br \/>\nAnswer: The factor pairs of 21 are: 1 and 21, 3 and 7<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 21 are: 1 \u00d7 21, 3 \u00d7 7<\/p>\n<p>Question 6.<br \/>\n20<br \/>\nAnswer: The factor pairs of 20 are: 1 and 20, 2 and 10, 4 and 5<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 20 are: 1 \u00d7 20, 2 \u00d7 10, 5 \u00d7 4<\/p>\n<p>Question 7.<br \/>\n36<br \/>\nAnswer: The factor pairs of 36 are: 1 and 36, 2 and 18, 3 and 12, 4 and 9, 6 and 6<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 36 are: 1 \u00d7 36, 2 \u00d7 18, 3 \u00d7 12, 4 \u00d7 9, 6 \u00d7 6<\/p>\n<p>Question 8.<br \/>\n50<br \/>\nAnswer: The factor pairs of 50 are: 1 and 50, 2 and 25, 5 and 10<\/p>\n<p>Explanation:<br \/>\nfactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 50 are: 1 \u00d7 50, 2 \u00d7 25, 5 \u00d7 10<\/p>\n<p><strong>6.2 Factors and Divisibility<\/strong><\/p>\n<p><strong>Find the factor pairs for the number.<\/strong><br \/>\nQuestion 9.<br \/>\n16<br \/>\nAnswer: The factor pairs of 16 are: 1 and 16, 2 and 8, 4 and 4<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 16 are: 1 \u00d7 16, 2 \u00d7 8, 4 \u00d7 4<\/p>\n<p>Question 10.<br \/>\n24<br \/>\nAnswer: The factor pairs of 24 are: 1 and 24, 2 and 12, 3 and 8, 4 and 6<\/p>\n<p>Explanation:<br \/>\nfactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 24 are: 1 \u00d7 24, 2 \u00d7 12, 3 \u00d7 8, 4 \u00d7 6<\/p>\n<p>Question 11.<br \/>\n56<br \/>\nAnswer: The factor pairs of 56 are: 1 and 56, 2 and 28, 4 and 14, 7 and 8<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factor pairs of 56 are: 1 \u00d7 56, 2 \u00d7 28, 4 \u00d7 14, 7 \u00d7 8<\/p>\n<p><strong>List the factors of the number.<\/strong><br \/>\nQuestion 12.<br \/>\n25<br \/>\nAnswer: The factors of 25 are: 1, 5, 25<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factors of 25 are: 1, 5, 25<\/p>\n<p>Question 13.<br \/>\n60<br \/>\nAnswer: The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60<\/p>\n<p>Question 14.<br \/>\n72<br \/>\nAnswer: The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nHence,<br \/>\nThe factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72<\/p>\n<p>Question 15.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich numbers have 3 as a factor?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13407\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-15.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 15\" width=\"574\" height=\"35\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-15.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-15-300x18.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\nAnswer: The numbers which have 3 as a factor are: 21, 36, 48, 93<\/p>\n<p>Explanation:<br \/>\nGiven numbers are: 56, 21, 3, 48, 93, 71<br \/>\nFor the given number to have 3 as a factor, the sum of the digits of the given number must be a multiple of 3<br \/>\nSo,<br \/>\nThe sum of digits of:<br \/>\n56: 5 + 6 = 11: 1 + 1 = 2<br \/>\n21: 2 + 1 = 3<br \/>\n36: 3 + 6 = 9<br \/>\n48: 4 + 8 = 12: 1 + 2 = 3<br \/>\n93: 9 + 3 = 12: 1 + 2 = 3<br \/>\n71: 7 + 1 = 8<br \/>\nHence, from the above,<br \/>\nwe can conclude that the numbers which have 3 as a factor are: 21, 36, 48, 93<\/p>\n<p><strong>6.3 Relate Factors and Multiples<\/strong><\/p>\n<p>Question 16.<br \/>\nIs 54 a multiple of 3? Explain.<br \/>\nAnswer: 54 is a multiple of 3<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nThe multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33<br \/>\nTo be a multiple of 3, the sum of the digits of the given number should also be a multiple of 3.<br \/>\nSo,<br \/>\n54: 5 + 4 = 9 ( Divisible by 3 )<br \/>\nHence, from the above,<br \/>\nwe can conclude that 54 is a multiple of 3<\/p>\n<p>Question 17.<br \/>\nIs 45 a multiple of 7? Explain.<br \/>\nAnswer: 45 is not a multiple of 7<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nThe multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70<br \/>\nHence, from the above,<br \/>\nwe can conclude that 45 is not a multiple of 7<\/p>\n<p>Question 18.<br \/>\nIs 2 a factor of 97? Explain.<br \/>\nAnswer: 2 is not a factor of 97<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nThe factors of 97 are: 1, 97<br \/>\nHence, from the above,<br \/>\nWe can conclude that 2 is not a factor of 97<\/p>\n<p>Question 19.<br \/>\nIs 5 a factor of 60? Explain.<br \/>\nAnswer: 5 is a factor of 60<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nThe factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60<br \/>\nHence, from the above,<br \/>\nWe can conclude that 5 is a factor of 60<\/p>\n<p><strong>Tell whether 20 is a multiple or a factor of the number. Write multiple, factor, or both.<\/strong><br \/>\nQuestion 20.<br \/>\n60<br \/>\nAnswer: 20 is a factor of 60<\/p>\n<p>Explanation:<br \/>\nFactors are the numbers that divide the original number completely.<br \/>\nThe factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60<br \/>\nHence, from the above,<br \/>\nWe can conclude that 20 is a factor of 60<\/p>\n<p>Question 21.<br \/>\n4<br \/>\nAnswer: 20 is a multiple of 4<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nThe multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40<br \/>\nHence, from the above,<br \/>\nWe can conclude that 20 is a multiple of 4<\/p>\n<p>Question 22.<br \/>\n20<br \/>\nAnswer: 20 is a multiple and factor of 20<\/p>\n<p>Explanation:<br \/>\nMultiples are the numbers that can be divided by another number a certain number of times without any remainder.<br \/>\nFactors are the numbers that divide the original number completely<br \/>\nNow,<br \/>\nFactors of 20 are: 1, 2, 4, 5, 10, 20<br \/>\nMultiples of 20 are: 20, 40, 60, 80, 100<br \/>\nHence, from the above,<br \/>\nwe can conclude that 20 is a multiple and factor of 20<\/p>\n<p>Question 23.<br \/>\n<strong>Number Sense<\/strong><br \/>\nName two numbers that are each a multiple of both 5 and 2. What do you notice about the two multiples?<br \/>\nAnswer: The 2 numbers that are each a multiple of both 5 and 2 are: 10 and 20<\/p>\n<p>Explanation;<br \/>\nMultiples of 2 are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20<br \/>\nMultiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50<br \/>\nSo,<br \/>\nFrom the multiples of both 2 and 5,<br \/>\nThe numbers which have common multiples of both 5 and 2 are: 10, 20<br \/>\nThe multiples of 2 have the one&#8217;s digit as 2 or 4 or 6 or 8 or 0<br \/>\nThe multiples of 5 have the one&#8217;s digit as 5 or 0<\/p>\n<p>Question 24.<br \/>\n<strong>Logic<\/strong><br \/>\nA quotient is a multiple of 5. The dividend is a multiple of 4. The divisor is a factor of 8. Write one possible equation for the problem.<br \/>\nAnswer: The possible equation is:<br \/>\n80 \u00f7 8 = 10<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nQuotient: Multiple of 5<br \/>\nDividend: Multiple of 4<br \/>\nDivisor: Factor of 8<br \/>\nHence, from the above,<br \/>\nwe can conclude that the possible equation for the problem is:<br \/>\n80 \u00f7 8 = 10<\/p>\n<p><strong>6.4 Identify Prime and Composite Numbers<\/strong><\/p>\n<p><strong>Tell whether the number is prime or composite. Explain.<\/strong><br \/>\nQuestion 25.<br \/>\n5<br \/>\nAnswer: 5 is a prime number<\/p>\n<p>Explanation;<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are \u201cPrime numbers\u201d<br \/>\nNow,<br \/>\nThe factors of 5 are: 1, 5<br \/>\nHence, from the above,<br \/>\nWe can conclude that 5 is a prime number<\/p>\n<p>Question 26.<br \/>\n25<br \/>\nAnswer: 25 is a composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are \u201cComposite numbers\u201d<br \/>\nNow,<br \/>\nThe factors of 25 are: 1, 5, 25<br \/>\nHence, from the above,<br \/>\nWe can conclude that 25 is a composite number<\/p>\n<p>Question 27.<br \/>\n51<br \/>\nAnswer: 51 is a composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are \u201cComposite numbers\u201d<br \/>\nNow,<br \/>\nThe factors of 51 are: 1, 3, 17, 51<br \/>\nHence, from the above,<br \/>\nWe can conclude that 51 is a composite number<\/p>\n<p>Question 28.<br \/>\n21<br \/>\nAnswer: 21 is a composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are \u201cComposite numbers\u201d<br \/>\nNow,<br \/>\nThe factors of 21 are: 1, 3, 7, 21<br \/>\nHence, from the above,<br \/>\nWe can conclude that 21 is a composite number<\/p>\n<p>Question 29.<br \/>\n50<br \/>\nAnswer: 50 is a composite number<\/p>\n<p>Explanation:<br \/>\nComposite numbers:<br \/>\nThe numbers which have more than 2 factors are \u201cComposite numbers\u201d<br \/>\nNow,<br \/>\nThe factors of 50 are: 1, 2, 5, 10, 25, 50<br \/>\nHence, from the above,<br \/>\nWe can conclude that 50 is a composite number<\/p>\n<p>Question 30.<br \/>\n83<br \/>\nAnswer: 83 is a prime number<\/p>\n<p>Explanation:<br \/>\nPrime numbers:<br \/>\nThe numbers which have exactly 2 factors 1 and itself are \u201cPrime numbers\u201d<br \/>\nNow,<br \/>\nThe factors of 83 are: 1, 83<br \/>\nHence, from the above,<br \/>\nWe can conclude that 83 is a prime number<\/p>\n<p>Question 31.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA prime number of students have which type of fingerprint?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-31.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 31\" width=\"587\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-31.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-31-300x90.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Answer: A prime number of students have Whorl fingerprint<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-31.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 31\" width=\"587\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-31.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-31-300x90.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><br \/>\nFrom the given figure,<br \/>\nEach half-circle = 1 student<br \/>\nThe number of fingerprints of loop-type fingerprint: 9<br \/>\nThe number of fingerprints of Arch-type fingerprint: 12<br \/>\nThe number of fingerprints on Whorl-type fingerprint: 7<br \/>\nHence, from the above,<br \/>\nWe can conclude that the prime number of students has Whorl-type fingerprint<\/p>\n<p><strong>6.5 Number Patterns<\/strong><\/p>\n<p><strong>Write the first six numbers in the pattern. Then describe another feature of the pattern.<\/strong><br \/>\nQuestion 32.<br \/>\nRule: Subtract 11.<br \/>\nFirst number: 99<br \/>\n99, ___, _____, _____, _____, _____<br \/>\nAnswer:<br \/>\nThe first 6 numbers in the given pattern are: 99, 88, 77, 66, 55, 44<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Subtract 11<br \/>\nFirst number: 99<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23476\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-62.jpg\" alt=\"\" width=\"307\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-62.jpg 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-62-300x69.jpg 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 33.<br \/>\nRule: Multiply by 5.<br \/>\nFirst number: 10<br \/>\n10, _____, _____, ____, _____, _____<br \/>\nAnswer:<br \/>\nThe first 6 numbers of the given pattern is: 10, 50, 250, 1,250, 6,250, 31,250<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Multiply by 5<br \/>\nFirst number: 10<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23477\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-63.jpg\" alt=\"\" width=\"312\" height=\"72\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-63.jpg 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-63-300x69.jpg 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Question 34.<br \/>\nRule: Add 8.<br \/>\nFirst number: 15<br \/>\nAnswer:<br \/>\nThe first 6 numbers of the given pattern are: 15, 23, 31, 39, 47, 55<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe rules are:<br \/>\nRule: Add 8<br \/>\nFirst number: 15<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23479\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-64.jpg\" alt=\"\" width=\"304\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-64.jpg 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-64-300x67.jpg 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Question 35.<br \/>\nRule: Divide by 4.<br \/>\nFirst number: 4,096<br \/>\nAnswer:<br \/>\nThe first 6 numbers in the given pattern is: 4,096, 1,024, 256, 64, 16, 4<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Divide by\u00a0 4<br \/>\nFirst number: 4,096<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23480\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-65.jpg\" alt=\"\" width=\"314\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-65.jpg 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-65-300x60.jpg 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><\/p>\n<p><strong>Open-Ended<\/strong><br \/>\n<strong>Use the rule to generate a pattern of four numbers.<\/strong><br \/>\nQuestion 36.<br \/>\nRule: Divide by 2.<br \/>\nAnswer:<br \/>\nLet the first number be 16<br \/>\nHence,<br \/>\nThe first 4 numbers of the given pattern are: 16, 8, 4, 2<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Divide by 2<br \/>\nLet the first number be 16<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-66.jpg\" alt=\"\" width=\"187\" height=\"72\" \/><\/p>\n<p>Question 37.<br \/>\nRule: Add 3.<br \/>\nAnswer:<br \/>\nLet the first number be 3<br \/>\nHence,<br \/>\nThe first four numbers of the given pattern are: 3, 6, 9, 12<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Add 3<br \/>\nLet the first number be 3<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-67.jpg\" alt=\"\" width=\"169\" height=\"68\" \/><\/p>\n<p>Question 38.<br \/>\nRule: Multiply by10.<br \/>\nAnswer:<br \/>\nLet the first number be 10<br \/>\nHence,<br \/>\nThe first\u00a0 4 numbers of the given pattern are: 10, 100, 1,000, 10,000<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Multiply by 10<br \/>\nLet the first number be 10<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-68.jpg\" alt=\"\" width=\"177\" height=\"74\" \/><\/p>\n<p>Question 39.<br \/>\nRule: Subtract 6.<br \/>\nAnswer:<br \/>\nLet the first number be 36<br \/>\nHence,<br \/>\nThe first 4 numbers of the given pattern are: 36, 30, 24, 18<\/p>\n<p>Explanation:<br \/>\nFor the formation of the pattern,<br \/>\nthe given rules are:<br \/>\nRule: Subtract 6<br \/>\nLet the first number be 36<br \/>\nHence,<br \/>\nThe pattern we will obtain is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-23484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-69.jpg\" alt=\"\" width=\"185\" height=\"65\" \/><\/p>\n<p><strong>6.6 Shape Patterns<\/strong><\/p>\n<p>Question 40.<br \/>\nExtend the pattern of shapes by repeating the rule \u201ctrapezoid, circle.\u201d What is the 57th shape in the pattern?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-40.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 40\" width=\"614\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-40.png 614w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-40-300x37.png 300w\" sizes=\"(max-width: 614px) 100vw, 614px\" \/><br \/>\nAnswer: The 57th shape in the pattern is: Trapezoid<\/p>\n<p>Explanation:<br \/>\nGiven pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13409\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-40.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 40\" width=\"614\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-40.png 614w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-40-300x37.png 300w\" sizes=\"(max-width: 614px) 100vw, 614px\" \/><br \/>\nThe rule given for the pattern is: trapezoid, circle<br \/>\nSo,<br \/>\nThe total number of figures in the given pattern is: 2<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotient method,<br \/>\n57 \u00f7 2 = ( 40 + 16 ) \u00f7 2<br \/>\n= ( 40 \u00f7 2 ) + ( 16 \u00f7 2 )<br \/>\n= 20 + 8<br \/>\n= 28 R 1<br \/>\nHence, from the above,<br \/>\nwe can conclude that the 57th shape in the pattern is: Trapezoid<\/p>\n<p>Question 41.<br \/>\nExtend the pattern of shapes by repeating the rule \u201ctop left, top right, bottom right, bottom left.\u201d What is the 102nd shape in the pattern?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-41.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 41\" width=\"575\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-41.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-41-300x33.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\nAnswer: The 102nd shape in the pattern is: Bottom left<\/p>\n<p>Explanation:<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13410\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-41.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 41\" width=\"575\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-41.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-41-300x33.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\nThe rule given for the pattern is: top left, top right, bottom right, bottom left<br \/>\nSo,<br \/>\nThe total number of figures in the given pattern is: 4<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n102 \u00f7 3 = ( 99 + 3 ) \u00f7 3<br \/>\n= ( 99 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n= 33 + 1<br \/>\n= 34 R 0<br \/>\nHence, from the above,<br \/>\nWe can conclude that the 102nd shape in the pattern is: Bottom left<\/p>\n<p>Question 42.<br \/>\nDescribe the pattern. How many squares are in the 61st figure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-42.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 42\" width=\"329\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-42.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-42-300x82.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer: The number of squares in the 61st figure is: 3<\/p>\n<p>Explanation:<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13411\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-42.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 42\" width=\"329\" height=\"90\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-42.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-42-300x82.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nIn figure 1, the total number of squares = 3<br \/>\nIn figure 2, the total number of squares = 6<br \/>\nIn figure 3, the total number of squares = 9<br \/>\nSo,<br \/>\nThe total number of figures = 3<br \/>\nSo,<br \/>\nfor this, when we divide any number by the total number of patterns, the value of the quotient will be a total repetition of the patterns and the remainder will be the counting of the pattern from the 1st figure.<br \/>\nSo,<br \/>\nBy using the partial quotients method,<br \/>\n61 \u00f7 3 = ( 57 + 3 ) \u00f7 3<br \/>\n= ( 57 \u00f7 3 ) + ( 3 \u00f7 3 )<br \/>\n= 19 + 1<br \/>\n= 20 R 1<br \/>\nHence, from the above,<br \/>\nWe can conclude that the number of squares in the\u00a0 61st figure in the pattern is: 4<\/p>\n<p>Question 43.<br \/>\nStructure<br \/>\nDraw the missing figure in the pattern. Explain the pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-43.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 43\" width=\"485\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-43.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-43-300x87.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nAnswer: The missing figure has: 7 squares<\/p>\n<p>Explanation:<br \/>\nThe given pattern is:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-13412\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-43.png\" alt=\"Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns chp 43\" width=\"485\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-43.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-4-Chapter-6-Factors-Multiples-and-Patterns-chp-43-300x87.png 300w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\nThe rule-following in the given pattern is: Add 2<br \/>\nThe first number: 1<br \/>\nAccording to the rule,<br \/>\nThe number of squares in the pattern will be like 1, 3, 5, 7, 9<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>We hope the details mentioned in the Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns are helpful for you to finish your homework in time. Learn the concepts in depth so that you can solve any kind of problem easily. If you have any queries you can post your comments in the below section.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Get free step-by-step solutions and explanations for all the available questions here. The students who are looking for Big Ideas Math Answers Grade 4 Chapter 6 Factors, Multiples, and Patterns can download the pdf for free of cost. 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