{"id":31748,"date":"2022-04-05T20:37:01","date_gmt":"2022-04-05T15:07:01","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=31748"},"modified":"2022-04-07T11:41:12","modified_gmt":"2022-04-07T06:11:12","slug":"big-ideas-math-answers-grade-6-advanced-chapter-1","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6-advanced-chapter-1\/","title":{"rendered":"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors"},"content":{"rendered":"<p>Do you want to become proficient in Math and get a good hold of the Big Ideas Math Book Grade 6 Advanced? If so, this is the one-stop destination for all your needs. You can access the Topicwise BIM Grade 6 Advanced Ch 1 Numerical Expressions and Factors Solutions PDF available as a part of your preparation. Test your knowledge of the concepts by solving from the Big Ideas Math Answers Grade 6 Advanced Chapter 1 and identify the knowledge gap accordingly.<\/p>\n<h2>Big Ideas Math Book 6th Grade Advanced Answer Key Chapter 1 Numerical Expressions and Factors<\/h2>\n<p>Use the ultimate guide over here for all your doubts on Big Ideas Math 6th Grade Advanced Ch 1 Numerical Expressions and Factors Concepts. Big Ideas Math Book 6th Grade Advanced Solutions provided here covers questions from Chapter 1 aligned as per the BIm Textbooks.\u00a0 All you have to do is simply tap on the quick links available to avail the respective topic in no time. Begin your preparation right away taking the help of the Numerical Expressions and Factors Big Ideas Math Grade 6 Solutions and clear the exam with flying colors.<\/p>\n<ul>\n<li><a href=\"#Numerical_Expressions_and_Factors_STEAM_Video\/_Performance_Task\">Numerical Expressions and Factors STEAM Video\/ Performance Task &#8211; Page 1<\/a><\/li>\n<li><a href=\"#Numerical_Expressions_and_Factors_Vocabulary\">Numerical Expressions and Factors Vocabulary &#8211; Page 2<\/a><\/li>\n<li><a href=\"#Section_1.1_Powers_and_Exponents\">Section 1.1 Powers and Exponents &#8211; Page(3-8)<\/a><\/li>\n<li><a href=\"#Lesson_1.1_Powers_and_Exponents\">Lesson 1.1 Powers and Exponents &#8211; Page(4-6)<\/a><\/li>\n<li><a href=\"#Powers_and_Exponents_Practice_1.1\">Powers and Exponents Practice 1.1 &#8211; Page(7-8)<\/a><\/li>\n<li><a href=\"#Section_1.2_Order_of_Operations\">Section 1.2 Order of Operations &#8211; Page(9-14)<\/a><\/li>\n<li><a href=\"#Lesson_1.2_Order_of_Operations\">Lesson 1.2 Order of Operations &#8211; Page(10-12)<\/a><\/li>\n<li><a href=\"#Order_of_Operations_Practice_1.2\">Order of Operations Practice 1.2 &#8211; Page(13-14)<\/a><\/li>\n<li><a href=\"#Section_1.3_Prime_Factorization\">Section 1.3 Prime Factorization &#8211; Page(15-20)<\/a><\/li>\n<li><a href=\"#Lesson_1.3_Prime_Factorization\">Lesson 1.3 Prime Factorization &#8211; Page(16-18)<\/a><\/li>\n<li><a href=\"#Prime_Factorization_Practice_1.3\">Prime Factorization Practice 1.3 &#8211; Page(19-20)<\/a><\/li>\n<li><a href=\"#Section_1.4_Greatest_Common_Factor\">Section 1.4 Greatest Common Factor &#8211; Page(21-26)<\/a><\/li>\n<li><a href=\"#Lesson_1.4_Greatest_Common_Factor\">Lesson 1.4 Greatest Common Factor &#8211; Page(22-24)<\/a><\/li>\n<li><a href=\"#Greatest_Common_Factor_Practice_1.4\">Greatest Common Factor Practice 1.4 &#8211; Page(25-26)<\/a><\/li>\n<li><a href=\"#Section_1.5_Least_Common_Multiple\">Section 1.5 Least Common Multiple &#8211; Page(27-32)<\/a><\/li>\n<li><a href=\"#Lesson_1.5_Least_Common_Multiple\">Lesson 1.5 Least Common Multiple &#8211; Page(28-30)<\/a><\/li>\n<li><a href=\"#Least_Common_Multiple_Practice_1.5\">Least Common Multiple Practice 1.5 &#8211; Page(31-32)<\/a><\/li>\n<li><a href=\"#Numerical_Expressions_and_Factors_Connecting_Concepts\">Numerical Expressions and Factors Connecting Concepts &#8211; Page 33<\/a><\/li>\n<li><a href=\"#Numerical_Expressions_and_Factors_Chapter_Review\">Numerical Expressions and Factors Chapter Review &#8211; Page(34-37)<\/a><\/li>\n<li><a href=\"#Powers_and_Exponents_Homework_&amp;_Practice_1.1\">Powers and Exponents Homework &amp; Practice 1.1 &#8211; Page 35<\/a><\/li>\n<li><a href=\"#Order_of_Operations_Homework_&amp;_Practice_1.2\">Order of Operations Homework &amp; Practice 1.2 &#8211; Page 35<\/a><\/li>\n<li><a href=\"#Prime_Factorization_Homework_&amp;_Practice_1.3\">Prime Factorization Homework &amp; Practice 1.3 &#8211; Page 36<\/a><\/li>\n<li><a href=\"#Greatest_Common_Factor_Homework_&amp;_Practice_1.4\">Greatest Common Factor Homework &amp; Practice 1.4 &#8211; Page 36<\/a><\/li>\n<li><a href=\"#Least_Common_Multiple_Homework_&amp;_Practice_1.5\">Least Common Multiple Homework &amp; Practice 1.5 &#8211; Page 37<\/a><\/li>\n<li><a href=\"#Numerical_Expressions_and_Factors_Practice_Test\">Numerical Expressions and Factors Practice Test &#8211; Page 38<\/a><\/li>\n<li><a href=\"#Numerical_Expressions_and_Factors_Cumulative_Practice\">Numerical Expressions and Factors Cumulative Practice &#8211; Page(39-41)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Numerical_Expressions_and_Factors_STEAM_Video\/_Performance_Task\"><\/a>Numerical Expressions and Factors STEAM Video\/ Performance Task<\/h3>\n<p>STEAM Video<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 1\" width=\"217\" height=\"219\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-1.png 217w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-1-150x150.png 150w\" sizes=\"(max-width: 217px) 100vw, 217px\" \/><\/p>\n<p>Filling Pi\u00f1atas<\/p>\n<p>Common factors can be used to make identical groups of objects. Can you think of any situations in which you would want to separate objects into equal groups? Are there any common factors that may be more useful than others? Can you think of any other ways to use common factors?<\/p>\n<p>Watch the STEAM Video \u201cFilling Pi\u00f1atas.\u201d Then answer the following questions. The table below shows the numbers of party favors that Alex and Enid use to make pi\u00f1atas<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 2\" width=\"388\" height=\"76\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-2.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-2-300x59.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 1.<br \/>\nWhen finding the number of identical pi\u00f1atas that can be made, why is it helpful for Alex and Enid to list the factors of each number given in the table?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nYou raIt to create 6 identical pi\u00f1atas. How can you change the numbers of party favors in the table to make this happen? Can you do this without changing the total number of party favors?<br \/>\nAnswer:<\/p>\n<p>Performance Task<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-33408\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 5\" width=\"263\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-5.png 263w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-5-239x300.png 239w\" sizes=\"(max-width: 263px) 100vw, 263px\" \/><\/p>\n<p>Setting the Table<\/p>\n<p>After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be asked to plan a fundraising event with the items below.<\/p>\n<p>72 chairs<br \/>\n48 balloons<br \/>\n24 flowers<br \/>\n32 candles<\/p>\n<p>You will find the greatest number of identical tables that can be prepared, and what will be in each centerpiece.When making arrangements for a party, should a part planner always use the greatest number of identical tables possible? Explain why or why not.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Getting_Ready_for_Numerical_Expressions_and_Factors\"><\/a>Getting Ready for Numerical Expressions and Factors<\/h3>\n<p>Chapter Exploration<\/p>\n<p>Work with a partner. In Exercises 1 and 2, use the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 3\" width=\"369\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-3.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-3-300x266.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-31750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 4\" width=\"173\" height=\"224\" \/><br \/>\nEratosthenes<br \/>\n(c. 276 &#8211; c. 194 B.c.)<br \/>\nThis table is called the Sieve of Eratosthenes. Eratosthenes was a Greek mathematician who was the chief librarian at theLibrary of Alexandria in Egypt. He was the first person to calculate the circumference of Earth.<\/p>\n<p>Question 1.<br \/>\nCross out the multiples of 2 that are greater than 2. Do the same for 3, 5, and 7.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nThe numbers that are not crossed out are called prime numbers. \u2018The numbers that are crossed out are called composite numbers. In your own words, describe the characteristics of prime numbers and composite numbers.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nWork with a partner. Cicadas are insects that live underground and emerge from the ground after x or x + 4 years. Is it possible that both x and x + 4 are prime? Give some examples.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Numerical_Expressions_and_Factors_Vocabulary\"><\/a>Numerical Expressions and Factors Vocabulary<\/h3>\n<p>The following vocabulary terms are defined in this chapter. think about what each term might rucan and record your thoughts.<br \/>\nexponent\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 common factors\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0common multiples<br \/>\nnumerical expression\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0greatest common factor\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0least common multiple<br \/>\norder of operations<br \/>\nAnswer:<\/p>\n<h3><a id=\"Section_1.1_Powers_and_Exponents\"><\/a>Section 1.1 Powers and Exponents<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Writing Expressions Using Exponents<\/p>\n<p>Work with a partner. Copy and complete the table.<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"208\">Repeated Factors<\/td>\n<td style=\"text-align: center;\" width=\"208\">Using an Exponent<\/td>\n<td style=\"text-align: center;\" width=\"208\">Value<\/td>\n<\/tr>\n<tr>\n<td width=\"208\">a. 10 \u00d7 10<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">b. 4 \u00d7 4<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">c. 6 \u00d7 6<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">d. 10 \u00d7 10 \u00d7 10<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">e. 100 \u00d7 100 \u00d7 100<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">f. 3 \u00d7 3 \u00d7 3 \u00d7 3<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">g. 4 \u00d7 4 \u00d7 4 \u00d7 4 \u00d7 4<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">h. 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p>Math Practice<br \/>\n<strong>Repeat Calculations<\/strong><br \/>\nWhat patterns do you notice in the expressions? How does this help you write exponents?<br \/>\nAnswer:<\/p>\n<p>i. In your own words, describe what the two numbers in the expression 3&lt;sup&gt;5&lt;\/sup&gt; mean.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Using a Calculator to Find a Pattern<\/p>\n<p>Work with a partner. Copy the diagram. Use a calculator to find each value. Write one digit of the value in each box. Describe the pattern in the digits of the values.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-5.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 5\" width=\"391\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-5.png 391w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-5-300x129.png 300w\" sizes=\"(max-width: 391px) 100vw, 391px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_1.1_Powers_and_Exponents\"><\/a>Lesson 1.1 Powers and Exponents<\/h3>\n<p>Try It Write the product as a power.<\/p>\n<p>Question 1.<br \/>\n2 \u00d7 2 \u00d7 2<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n6 \u2022 6 \u2022 6 \u2022 6 \u2022 6 \u2022 6<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n15 \u00d7 15 \u00d7 15 \u00d7 15<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n20 \u2022 20 \u2022 20 \u2022 20 \u2022 20 \u2022 20 \u2022 20<br \/>\nAnswer:<\/p>\n<p>Try It Find the value of the power.<\/p>\n<p>Question 5.<br \/>\n6<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n9<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n3<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n18<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Try It Determine whether the number is a perfect square.<\/p>\n<p>Question 9.<br \/>\n25<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n2<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n99<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n36<br \/>\nAnswer:<\/p>\n<p><strong>FINDING VALUES OF POWERS<\/strong><br \/>\nFind the value of the power.<br \/>\nQuestion 13.<br \/>\n8<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n3<sup>5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n11<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow are exponents and powers different<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIs 10 a perfect square? Is 100 a perfect square? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich one does not belong with the other three? Explain your reasoning.<br \/>\n2<sup>4<\/sup> = 2 \u00d7 2 \u00d7 2 \u00d7 2<br \/>\n3<sup>2<\/sup> = 3 \u00d7 3<br \/>\n3 + 3 + 3 + 3 = 3 \u00d7 4<br \/>\n5 \u2022 5 \u2022 5 = 5<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Self-Assessment for Problem Solving<\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 19.<br \/>\nA square solar panel has an area of 16 square feet. Write the area as a power. Then find the side lengths of the Panel.<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\nThe four-square court shown is a square made up of four identical smaller squares. What is the area of the court?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-6.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 6\" width=\"154\" height=\"141\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nEach face of a number cube is a square with a side length of 16 millimeters. What is the total area of all of the faces of the number cube?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Powers_and_Exponents_Practice_1.1\"><\/a>Powers and Exponents Practice 1.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Multiply<\/p>\n<p>Question 1.<br \/>\n150 \u00d7 2<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n175 \u00d7 8<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n123 \u00d7 3<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n151 \u00d7 9<br \/>\nAnswer:<\/p>\n<p>Write the sentence as a numerical expression.<\/p>\n<p>Question 5.<br \/>\nAdd 5 and 8, then multiply by 4.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nSubtract 7 from 11, then divide by 2.<br \/>\nAnswer:<\/p>\n<p>Round the number to the indicated place value.<\/p>\n<p>Question 7.<br \/>\n4.03785 to the tenths<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n12.89503 to the hundredths<br \/>\nAnswer:<\/p>\n<p>Complete the sentence.<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{10}\\) of 30 is <img loading=\"lazy\" class=\"alignnone size-full wp-image-31925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-7.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 7\" width=\"51\" height=\"41\" \/>.<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n\\(\\frac{4}{5}\\) of 25 is <img loading=\"lazy\" class=\"alignnone size-full wp-image-31925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-7.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 7\" width=\"51\" height=\"41\" \/>.<br \/>\nAnswer:<\/p>\n<p>Concepts, Skills, &amp; Problem Solving<\/p>\n<p><strong>WRITING EXPRESSIONS USING EXPONENTS<\/strong><br \/>\nCopy and complete the table. (See Exploration 1 Page.No 3)<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"208\">Repeated Factors<\/td>\n<td style=\"text-align: center;\" width=\"208\">Using an Exponent<\/td>\n<td style=\"text-align: center;\" width=\"208\">Value<\/td>\n<\/tr>\n<tr>\n<td width=\"208\">11. 8 \u00d7 8<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">12. 4 \u00d7 4 \u00d7 4<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">13. 9 \u00d7 9 \u00d7 9 \u00d7 9<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<tr>\n<td width=\"208\">14. 12 \u00d7 12 \u00d7 12 \u00d7 12 \u00d7 12<\/td>\n<td width=\"208\"><\/td>\n<td width=\"208\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Answer:<\/p>\n<p><strong>WRITING EXPRESSIONS AS POWERS<\/strong><br \/>\nWrite the product as a power.<\/p>\n<p>Question 15.<br \/>\n9 \u00d7 9<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n13 \u00d7 13<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n15 \u00d7 15 \u00d7 15<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n2 \u2022 2 \u2022 2 \u2022 2 \u2022 2<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n14 \u00d7 14 \u00d7 14<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n8 \u2022 8 \u2022 8 \u2022 8<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n11 \u00d7 11 \u00d7 11 \u00d7 11 \u00d7 11<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n7 \u2022 7 \u2022 7 \u2022 7 \u2022 7 \u2022 7<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n16 \u2022 16 \u2022 16 \u2022 16<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n43 \u00d7 43 \u00d7 43 \u00d7 43 \u00d7 43<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n167 \u2022 167 \u2022 167<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n245 \u2022 245 \u2022 245 \u2022 245<br \/>\nAnswer:<\/p>\n<p><strong>FINDING VALUES OF POWERS<\/strong><br \/>\nFind the value of the power.<\/p>\n<p>Question 27.<br \/>\n5<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\n4<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n6<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n1<sup>7<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n0<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\n8<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n2<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\n12<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n7<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\n5<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n2<sup>5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 38.<br \/>\n14<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong><br \/>\nUse a calculator to find the value of the power.<\/p>\n<p>Question 39.<br \/>\n7<sup>6<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 40.<br \/>\n4<sup>8<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n12<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 42.<br \/>\n17<sup>5<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>YOU BE THE TEACLIER<\/strong><br \/>\nYour friend finds the value of 8. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-8.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 8\" width=\"175\" height=\"63\" \/><br \/>\nAnswer:<\/p>\n<p><strong>IDENTIFYING PERFECT SQUARES<\/strong><br \/>\nDetermine whether the number is a perfect square.<\/p>\n<p>Question 44.<br \/>\n8<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n4<br \/>\nAnswer:<\/p>\n<p>Question 46.<br \/>\n81<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n44<br \/>\nAnswer:<\/p>\n<p>Question 48.<br \/>\n49<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n125<br \/>\nAnswer:<\/p>\n<p>Question 50.<br \/>\n150<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n144<br \/>\nAnswer:<\/p>\n<p>Question 52.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nOn each square centimeter of a person\u2019s skin, there are about 39<sup>2<\/sup> bacteria. How many bacteria does this expression represent?<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>MP REPEATED REASONING<\/strong><br \/>\nThe smallest figurine in a gift shop is 2 inches tall. The height of each figurine is twice the height of the previous figurine. What is the height of the tallest figurine?<br \/>\nAnswer:<\/p>\n<p>Question 54.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA square painting measures 2 meters on each side. What is the area of the painting in square centimeters?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-9.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 9\" width=\"376\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-9.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-9-300x246.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>MP NUMBER SENSE<\/strong><br \/>\nWrite three powers that have values greater than 120 and less than 130.<br \/>\nAnswer:<\/p>\n<p>Question 56.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA landscaper has 125 tiles to build a square patio. the patio must have an area of at least 80 square feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-10.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 10\" width=\"132\" height=\"122\" \/><br \/>\na. What arc the Possible arrangements for the patio?<br \/>\nb. How many tiles are not used in each arrangement?<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>MP PATTERNS<\/strong><br \/>\nCopy and complete the table. Describe what happens to the value of the power as the exponent decreases.<br \/>\nUse this pattern to find the value 0f 4<sup>0<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-11.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 11\" width=\"367\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-11.png 367w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-11-300x65.png 300w\" sizes=\"(max-width: 367px) 100vw, 367px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 58.<br \/>\n<strong>MP REPEATED REASONING<\/strong><br \/>\nHow many blocks do you need to add to Square 6 to get Square 7? to Square 9 to get Square 10? to Square 19 to get Square 20? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-12.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 12\" width=\"500\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-12.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-12-300x101.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Section_1.2_Order_of_Operations\"><\/a>Section 1.2 Order of Operations<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Comparing Different Orders<\/p>\n<p>Work with a partner. Find the value of each expression by using different orders of operations. Are your answers the same?<\/p>\n<p>a. Add, then multiply.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Multiply, then add.<br \/>\n3 + 2 \u00d7 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 3 + 2 \u00d7 2<\/p>\n<p>b. Subtract then multiply.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Multiply, then subtract.<br \/>\n18 &#8211; 3 \u2022 3\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a018 &#8211; 3 \u2022 3<\/p>\n<p>c. Multiply, then subtract\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Subtract, then multiply.<br \/>\n8 \u00d7 8 &#8211; 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 8 \u00d7 8 &#8211; 2<\/p>\n<p>d. Multiply, then add.\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Add, then multiply.<br \/>\n6 \u2022 6 + 2\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a06 \u2022 6 + 2<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Determining Order of Operations<\/p>\n<p>Work with a partner.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-31941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-13.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 13\" width=\"252\" height=\"170\" \/><br \/>\na. Scientific calculators use a standard order of operations when evaluating expressions. Why is a standard order of operations needed?<br \/>\nAnswer:<\/p>\n<p>b. Lise a scientific calculator to evaluate each expression in Exploration 1. Enter each expression exactly as written. For each expression, which order of operations is correct?<br \/>\nAnswer:<\/p>\n<p>c. What order of operations should be used to evaluate 3 + 2<sup>2<\/sup>, 18 &#8211; 3<sup>2<\/sup>, 8<sup>2<\/sup> &#8211; 2, and 6<sup>2<\/sup> + 2?<br \/>\nAnswer:<\/p>\n<p>d. Do 18 \u00f7 3 \u2022 3 and 18 \u00f7 3<sup>2<\/sup> have the same value? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>e. How does evaluating powers fit into the order of operations?<br \/>\nAnswer:<\/p>\n<p>Math Practice<br \/>\n<strong>Use Technology to Explore<\/strong><br \/>\nHow does a scientific calculator help you explore order of operations?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_1.2_Order_of_Operations\"><\/a>Lesson 1.2 Order of Operations<\/h3>\n<p>Try It Evaluate the expression.<\/p>\n<p>Question 1.<br \/>\n7 \u2022 5 + 3<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n(28 &#8211; 20) \u00f7 4<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n[6 + (15 &#8211; 10)] \u00d7 5<br \/>\nAnswer:<\/p>\n<p>Try It Evaluate the expression.<\/p>\n<p>Question 4.<br \/>\n6 + 2<sup>4<\/sup> &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n4 \u2022 3<sup>2<\/sup> + 18 &#8211; 9<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n16 + (5<sup>2<\/sup> &#8211; 7) \u00f7 3<br \/>\nAnswer:<\/p>\n<p>Try It Evaluate the expression.<\/p>\n<p>Question 7.<br \/>\n50 + 6(12 \u00f7 4) &#8211; 8<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n5<sup>2<\/sup> &#8211; \\(\\frac{1}{5}\\)(10 &#8211; 5)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{8(2+5)}{7}\\)<br \/>\nAnswer:<\/p>\n<p><strong>USING ORDER OF OPERATIONS<\/strong><br \/>\nEvaluate the expression.<\/p>\n<p>Question 10.<br \/>\n7 + 2 \u2022 4<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n8 \u00f7 4 \u00d7 2<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n3(5 + 1) \u00f7 3<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhy does 12 &#8211; 8 \u00f7 2 = 8, hut(12 &#8211; 8) \u00f7 2 = 2?<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n<strong>MP REASONING<\/strong><br \/>\nDescribe the steps \u00a1n evaluating the expression<br \/>\n8 \u00f7 (6 &#8211; 1) + 3<sup>2<\/sup>.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n5<sup>2<\/sup> &#8211; 8 \u00d7 2<br \/>\n5<sup>2<\/sup> &#8211; (8 \u00d7 2)<br \/>\n5<sup>2<\/sup> &#8211; 2 \u00d7 8<br \/>\n(5<sup>2<\/sup> &#8211; 8) \u00d7 2<br \/>\nAnswer:<\/p>\n<p>Self-Assessment for problem solving<\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 16.<br \/>\nA square plot of land has side lengths of 10 meters. An archaeologist divides the land into 64 equal parts. What is the area of each part?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-14.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 14\" width=\"188\" height=\"174\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nA glass block window is made of two different-sized glass squares. The window has side lengths of 40 inches. The large glass squares have side lengths of 10 inches. Find the total area of the small glass squares.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32238\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-14.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 14\" width=\"188\" height=\"174\" \/><br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA square vegetable garden has side lengths of 12 feel You plant flowers in the center portion as shown. You divide the remaining space into 1 equal sections and plant tomatoes, onions, zucchini, and peppers. What is the area of the onion section?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32237\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-15.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 15\" width=\"152\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Order_of_Operations_Practice_1.2\"><\/a>Order of Operations Practice 1.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Write the product as a power.<\/p>\n<p>Question 1.<br \/>\n11 \u00d7 11 \u00d7 11 \u00d7 11<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n13 \u00d7 13 \u00d7 13 \u00d7 13 \u00d7 13<br \/>\nAnswer:<\/p>\n<p>Find the missing dimension of the rectangular prism.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32236\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-16.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 16\" width=\"110\" height=\"145\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32235\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-17.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 17\" width=\"107\" height=\"145\" \/><br \/>\nAnswer:<\/p>\n<p>Tell whether the number is prime or composite.<\/p>\n<p>Question 5.<br \/>\n9<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n11<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n23<br \/>\nAnswer:<\/p>\n<p>Concepts, skills, &amp; Problem Solving<\/p>\n<p><strong>COMPARING DIFFERENT ORDERS<\/strong><br \/>\nFind the value of the expression by using different orders of operations. Are your answers the saine? (See Exploration 1 Page.No 9)<\/p>\n<p>Question 8.<br \/>\nAdd, then multiply. Multiply, then add.<br \/>\n4 + 6 \u00d7 6 4 + 6 \u00d7 6<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nSubtract, then multiply. MuItiply then subtract.<br \/>\n5 \u00d7 5 &#8211; 3 5 \u00d7 5 &#8211; 3<br \/>\nAnswer:<\/p>\n<p><strong>USING ORDER OF OPERATIONS<\/strong><br \/>\nEvaluate the expression.<\/p>\n<p>Question 10.<br \/>\n5 + 8 \u00f7 6<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n(11 &#8211; 3) \u00f7 2 + 1<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n45 \u00f7 9 \u00d7 12<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n6<sup>2<\/sup> &#8211; 3 \u2022 4<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n42 \u00f7 (15 &#8211; 2<sup>3<\/sup>)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n4<sup>2<\/sup> \u2022 2 + 8 \u2022 7<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n(5<sup>2<\/sup> &#8211; 2) \u00d7 1<sup>5<\/sup> + 4<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n4 + 2 \u00d7 3<sup>2<\/sup> &#8211; 9<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n8 \u00f7 2 \u00d7 3 + 4<sup>2<\/sup> \u00f7 4<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n3<sup>2<\/sup> + 12 \u00f7 (6 &#8211; 3) \u00d7 8<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n(10 + 4) \u00f7 (26 &#8211; 19)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n(5<sup>2<\/sup> &#8211; 4) \u2022 2 &#8211; 18<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n2 \u00d7 [(16 &#8211; 8) \u00d7 2]<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n12 + 8 \u00d7 3<sup>2<\/sup> &#8211; 24<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n6<sup>2<\/sup> \u00f7 [(2 + 4) \u00d7 2<sup>3<\/sup>]<br \/>\nAnswer:<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend evaluates the expression. Is your friend correct? Explain your reasoning.<br \/>\nQuestion 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32234\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-18.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 18\" width=\"201\" height=\"94\" \/><br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32233\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-19.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 19\" width=\"198\" height=\"93\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>MP PROBLEM SOLVING<\/strong><br \/>\nYou need to read 20 poems in 5 days for an English project. Each poem is 2 pages long. Evaluate the expression 20 \u00d7 2 \u00f7 5 to find how many pages you need to read each day.<br \/>\nAnswer:<\/p>\n<p><strong>USING ORDER OF OPERATIONS<\/strong><br \/>\nEvaluate the expression.<\/p>\n<p>Question 28.<br \/>\n12 &#8211; 2(7 &#8211; 4)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n4(3 + 5) &#8211; 3(6 &#8211; 2)<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n6 + \\(\\frac{1}{4}\\) (12 &#8211; 8)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n9<sup>2<\/sup> &#8211; 8(6 + 2)<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\n4(3 &#8211; 1)<sup>3<\/sup> + 7(6) &#8211; 5<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n\\(8\\left[\\left(1 \\frac{1}{6}+\\frac{5}{6}\\right) \\div 4\\right]\\)<br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\n7<sup>2<\/sup> &#8211; 2\\(\\left(\\frac{11}{8}-\\frac{3}{8}\\right)\\)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n8(7.3 + 3.7 &#8211; 8) \u00f7 2<br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\n2<sup>4<\/sup>(5.2 &#8211; 3.2) \u00f7 4<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n\\(\\frac{6^{2}(3+5)}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 38.<br \/>\n\\(\\frac{12^{2}-4(6)+1}{11^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n\\(\\frac{26 \\div 2+5}{3^{2}-3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 40.<br \/>\n<strong>MP PROBLEM SOLVING<\/strong><br \/>\nBefore a show, there arc 8 people in a theater. Five groups of 4 people enter; and then three groups of 2 PeoPle leave. Evaluate the expression 8 5(4) &#8211; 3(2) to find how many people arc in the theater.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe front door of a house is painted white and blue. Each window is a square with a side length of 7 inches. What is the area of the door that is painted blue?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32232\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-20.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 21\" width=\"107\" height=\"218\" \/><br \/>\nAnswer:<\/p>\n<p>Question 42.<br \/>\n<strong>MP PROBLEM SOLVING<\/strong><br \/>\nYou buy 6 notebooks, 10 folders, 1 pack of pencils, and 1 lunch box for school. After using a $10 gift card, how much do you owe? Explain how you solved the problem.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32231\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-21.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 21\" width=\"214\" height=\"173\" \/><br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nUse all four operations and at least one exponent to write an expression that has a value of 100.<br \/>\nAnswer:<\/p>\n<p>Question 44.<br \/>\n<strong>MP REPEATED REASONING<\/strong><br \/>\nA Petri dish contains 35 cells. Every day, each cell in the Petri dish divides into 2 cells in a process called mitosis. How many cells are there after 11 days? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>MP REASONING<\/strong><br \/>\nTwo groups collect litter along the<br \/>\nside of a road. It takes each group 5 minutes to clean up a 200-yard section. 1 low long does it take both groups working together to clean up 2 miles? Explain how you solved the problem.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32230\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-22.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 22\" width=\"230\" height=\"175\" \/><br \/>\nAnswer:<\/p>\n<p>Question 46.<br \/>\n<strong>MP NUMBER SENSE<\/strong><br \/>\nCopy each statement Insert +, -, \u00d7, or \u00f7 symbols to make each statement true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32229\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-23.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 23\" width=\"624\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-23.png 624w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-23-300x38.png 300w\" sizes=\"(max-width: 624px) 100vw, 624px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Section_1.3_Prime_Factorization\"><\/a>Section 1.3 Prime Factorization<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Rewriting Numbers as Products of Factors<\/p>\n<p>Work with a partner. Two students use factor trees to write 108 as a product of factors, as shown below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-24.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 24\" width=\"457\" height=\"292\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-24.png 457w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-24-300x192.png 300w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><\/p>\n<p>a. Without using 1 as a factor, can you write 108 as a product with more factors than each student used? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>b. Use factor trees to Write 80, 162, and 300 as products of as many factors as possible. Do not use 1 as a factor.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-25.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 25\" width=\"289\" height=\"238\" \/><br \/>\nAnswer:<\/p>\n<p>c. Compare your results in parts (a) and (b) with other groups. For each number, identify the product with the greatest number of factors. What do these factors have in common?<br \/>\nAnswer:<\/p>\n<p>Math Practice<br \/>\n<strong>Interpret Results<\/strong><br \/>\nHow do you know your answer makes sense?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_1.3_Prime_Factorization\"><\/a>Lesson 1.3 Prime Factorization<\/h3>\n<p>Try It List the factor pairs of the number.<\/p>\n<p>Question 1.<br \/>\n18<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n24<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n51<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe woodwinds section of the marching hand has 38 members. Which has more possible arrangements, the brass section or the woodwinds section? Explain.<br \/>\nAnswer:<\/p>\n<p>Try It Write the prime factorization of the number.<\/p>\n<p>Question 5.<br \/>\n20<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n88<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n90<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n462<br \/>\nAnswer:<\/p>\n<p>Self-Assessment for Concepts &amp; Skills<\/p>\n<p>Solve each exercise. Then rare your understanding of the success criteria in your journal.<\/p>\n<p><strong>WRITING A PRIME FACTORIZATION<\/strong><br \/>\nWrite the prime factorization of the number.<br \/>\nQuestion 9.<br \/>\n14<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n86<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n10<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n516<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain the difference between prime numbers and composite numbers.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n<strong>MP STRUCTURE<\/strong><br \/>\nYour friend lists the following factor pairs and concludes that there arc 6 factor pairs of 12. Explain why your friend incorrect.<br \/>\n1,12\u00a0 \u00a02,6\u00a0 \u00a0 \u00a03,4<br \/>\n12,1\u00a0 \u00a06,2\u00a0 \u00a0 \u00a04,3<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich factor pair does not belong with the other three? Explain your reasoning.<br \/>\n2, 28\u00a0 \u00a04, 14\u00a0 \u00a0 6, 9\u00a0 \u00a07, 8<br \/>\nAnswer:<\/p>\n<p>Self-Assessment for Problem Solving<\/p>\n<p>Solve each exercise. Then rate your understanding of the Success criteria in your journal<\/p>\n<p>Question 16.<br \/>\nA group of 20 friends plays a card game. \u2018The game can be played with 2 or more teams of equal size. Each team must have at least 2 members. List the possible numbers and sizes of teams.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-26.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 26\" width=\"233\" height=\"147\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nYou arrange 150 chairs in rows for a school play. You want each row to have the same number of chairs. how many possible arrangements arc there? Are all of the possible arrangements appropriate for the play? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nWhat is the least perfect square that is a factor of 4536? What is the greatest perfect square that is a factor of 4536?<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe prime factorization of a number is 2<sup>4<\/sup> \u00d7 3<sup>4<\/sup> \u00d7 5<sup>4<\/sup> \u00d7 7<sup>2<\/sup> Is the number a Perfect square? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Prime_Factorization_Practice_1.3\"><\/a>Prime Factorization Practice 1.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Evaluate the expression.<\/p>\n<p>Question 1.<br \/>\n2 + 4<sup>2<\/sup> (5 &#8211; 3)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n2<sup>3<\/sup> + 4 \u00d7 3<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n9 \u00d7 5 &#8211; 2<sup>4<\/sup>\\(\\left(\\frac{5}{2}-\\frac{1}{2}\\right)\\)<br \/>\nAnswer:<\/p>\n<p>Plot the points in a coordinate plane. Draw a line segment connecting the points.<\/p>\n<p>Question 4.<br \/>\n(1, 1) and (4, 3)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n(2, 3) and (5, 9)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n(2, 5) and (4, 8)<br \/>\nAnswer:<\/p>\n<p>Use the Distributive Property to find the quotient. Justify your answer.<\/p>\n<p>Question 7.<br \/>\n408 \u00f7 4<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n628 \u00f7 2<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n969 \u00f7 3<br \/>\nAnswer:<\/p>\n<p>Classify the triangle in as many ways as possible.<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-27.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 27\" width=\"110\" height=\"95\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-28.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 28\" width=\"126\" height=\"108\" \/><br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-29.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 29\" width=\"113\" height=\"112\" \/><br \/>\nAnswer:<\/p>\n<p>Concepts, Skills, &amp; Problem Solving<\/p>\n<p><strong>REWRITING A NUMBER<\/strong><br \/>\nWrite the number as a product of as many factors as possible. (See Exploration 1 Page.No 15)<br \/>\nQuestion 13.<br \/>\n60<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n63<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n120<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n150<br \/>\nAnswer:<\/p>\n<p><strong>FINDING FACTOR PAIRS<\/strong><br \/>\nList the factor pairs of the number.<br \/>\nQuestion 17.<br \/>\n15<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n22<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n31<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n39<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n45<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n54<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n59<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n61<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n100<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n58<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n25<br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\n76<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n52<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n88<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n71<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\n91<br \/>\nAnswer:<\/p>\n<p><strong>WRITING A PRIME FACTORIZATION<\/strong><br \/>\nWrite the prime factorization of the number.<br \/>\nQuestion 33.<br \/>\n16<br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\n25<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n30<br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\n26<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n84<br \/>\nAnswer:<\/p>\n<p>Question 38.<br \/>\n54<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n65<br \/>\nAnswer:<\/p>\n<p>Question 40.<br \/>\n77<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n46<br \/>\nAnswer:<\/p>\n<p>Question 42.<br \/>\n39<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n99<br \/>\nAnswer:<\/p>\n<p>Question 44.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n315<br \/>\nAnswer:<\/p>\n<p>Question 46.<br \/>\n190<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n110<br \/>\nAnswer:<\/p>\n<p>Question 48.<br \/>\n640<br \/>\nAnswer:<\/p>\n<p><strong>USING A PRIME FACTORIZATION<\/strong><br \/>\nFind the number represented by the prime factorization.<br \/>\nQuestion 49.<br \/>\n2<sup>2<\/sup> \u2022 3<sup>2<\/sup> \u2022 5<br \/>\nAnswer:<\/p>\n<p>Question 50.<br \/>\n3<sup>2<\/sup> \u2022 5<sup>2<\/sup> \u2022 7<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n2<sup>3<\/sup> \u2022 11<sup>2<\/sup> \u2022 13<br \/>\nAnswer:<\/p>\n<p>Question 52.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the prime factorization of 72. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-30.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 30\" width=\"276\" height=\"138\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING A PRIME FACTORIZATION<\/strong><br \/>\nFind the greatest perfect square that is a factor of the number.<br \/>\nQuestion 53.<br \/>\n250<br \/>\nAnswer:<\/p>\n<p>Question 54.<br \/>\n275<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n392<br \/>\nAnswer:<\/p>\n<p>Question 56.<br \/>\n338<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n244<br \/>\nAnswer:<\/p>\n<p>Question 58.<br \/>\n650<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n756<br \/>\nAnswer:<\/p>\n<p>Question 60.<br \/>\n1290<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n2205<br \/>\nAnswer:<\/p>\n<p>Question 62.<br \/>\n1890<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n495<br \/>\nAnswer:<\/p>\n<p>Question 64.<br \/>\n4725<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nA botanist separates plants into equal groups of 5 for an experiment. Is the total number of plants in the experiment prime or composite? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-31.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 31\" width=\"183\" height=\"248\" \/><br \/>\nAnswer:<\/p>\n<p>Question 66.<br \/>\n<strong>MP REASONING<\/strong><br \/>\nA teacher divides 36 students into equal groups for a scavenger hunt. Each group should have at least 1 students hut no more than 8 students. What are the possible group sizes?<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs 2 the only even prime number? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 68.<br \/>\n<strong>MP LOGIC<\/strong><br \/>\nOne topic at a back saic has 75 cookies. Another table has 60 cupcakes. Which table allows for more rectangular arrangements? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<strong>PERFECT NUMBERS<\/strong><br \/>\nA perfect number is a number that equals the sum of its factors, not including itself. \u00cbor example, the factors of 28 arc 1, 2, 1, 7, 14, and 28. Because 1 + 2 + 4 + 7 + 14 = 28, 28 is a perfect number. What are the perfect numbers between 1 and 27?<br \/>\nAnswer:<\/p>\n<p>Question 70.<br \/>\n<strong>MP REPEATED REASONING<\/strong><br \/>\nChoose any two perfect squares and find their product. \u2018Then multiply your answer by another perfect square. Continue this process. Are any of the products perfect squares? What can you conclude?<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n<strong>MP PROBLEM SOLVING<\/strong><br \/>\nThe stage manager of a school play creates a rectangular stage that has whole number dimensions and an area of 42 square yards. String lights will outline the stage. What is the least number of yards of string lights needed to enclose the stage?<br \/>\nAnswer:<\/p>\n<p>Question 72.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nConsider the rectangular prism shown. Using only whole number dimensions, how many different prisms are possible? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-32.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 32\" width=\"176\" height=\"126\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Section_1.4_Greatest_Common_Factor\"><\/a>Section 1.4 Greatest Common Factor<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Identifying Common Factors<\/p>\n<p>Work with a partner. in parts (a) &#8211; (d), create a Venn diagram that represents the factors of each number and identify any common factors.<br \/>\na. 36 and 18<br \/>\nb. 16 and 56<br \/>\nc. 30 and 75<br \/>\nd. 54 and 90<br \/>\ne. Look at the Venn diagrams in parts (a) &#8211; (d). Explain how to identify the greatest common factor of each pair of numbers. Then circle it in each diagram.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Using Prime Factors<\/p>\n<p>Work with a partner.<\/p>\n<p>a. Each Venn diagram represents the prime factorizations of two numbers. Identify each pair of numbers. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32487\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-33.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 33\" width=\"458\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-33.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-33-300x91.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><br \/>\nAnswer:<\/p>\n<p>b. Create a Venn diagram that represents the prime factorizations of 36 and 18.<br \/>\nAnswer:<\/p>\n<p>c. Repeat part (b) for the remaining number pairs in Exploration 1.<br \/>\nAnswer:<\/p>\n<p>d. <strong>MP STRUCTURE<\/strong><br \/>\nMake a conjecture about the relationship between the greatest common factors you found in Exploration 1 and the numbers in the overlaps of the Venn diagrams you just created.<br \/>\nAnswer:<\/p>\n<p>Math Practice<br \/>\n<strong>Interpret a Solution<\/strong><br \/>\nWhat does the diagram representing the prime factorizations mean?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_1.4_Greatest_Common_Factor\"><\/a>Lesson 1.4 Greatest Common Factor<\/h3>\n<p>Try It Find the GCF of the numbers using lists of factors.<\/p>\n<p>Question 1.<br \/>\n8, 36<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n18, 72<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n14, 28, 49<br \/>\nAnswer:<\/p>\n<p>Try It Find the GCF of the numbers using prime factorizations.<\/p>\n<p>Question 4.<br \/>\n20, 15<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n32, 90<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n45, 75, 120<br \/>\nAnswer:<\/p>\n<p>Try It<\/p>\n<p>Question 7.<br \/>\nWrite a pair of numbers whose greatest common factor is 10.<br \/>\nAnswer:<\/p>\n<p>Self-Assessment for concept &amp; Skills<\/p>\n<p>Solve each exercise. \u2018Then rate your understanding of the success criteria in your journal.<br \/>\n<strong>FINDING THE GCF<\/strong><br \/>\nFind the GCF of the numbers.<br \/>\nQuestion 8.<br \/>\n16, 40<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n35, 63<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n18, 72, 141<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>MULTIPLE CHOICE<\/strong><br \/>\nWhich number is not a factor of 10? Explain.<br \/>\nA. 1<br \/>\nB. 2<br \/>\nC. 4<br \/>\nD. 5<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find &#8220;both\u201d answers.<br \/>\nWhat is the greatest common factor of 24 and 32?<br \/>\nWhat is the greatest common divisor of 24 and 32?<br \/>\nWhat is the greatest common prime factor of 24 and 32?<br \/>\nWhat is the product of the common prime factors of 24 and 32?<br \/>\nAnswer:<\/p>\n<p>Self-Assessment for Problem Solving<\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 13.<br \/>\nYou usc 30 sandwiches and 42 granola bars to make identical picnic baskets. You make thc greatest number of picnic baskets with no food left over. How many sandwiches and how many granola bars are in each basket?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32486\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-34.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 34\" width=\"192\" height=\"141\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nYou fill bags with cookies to give to your friends. You bake 45 chocolate chip cookies, 30 peanut butter cookies, and<br \/>\n15 oatmeal cookies. You want identical groups of cookies in each hag with no cookies left over. What is the greatest number of bags you can make?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Greatest_Common_Factor_Practice_1.4\"><\/a>Greatest Common Factor Practice 1.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>List the factor pairs of the number.<br \/>\nQuestion 1.<br \/>\n20<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n16<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n56<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n87<br \/>\nAnswer:<\/p>\n<p>Tell whether the statement is always, sometimes, or sever true.<\/p>\n<p>Question 5.<br \/>\nA rectangle is a rhombus.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nA rhombus is a square.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nA square is a rectangle.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nA trapezoid is a parallelogram.<br \/>\nAnswer:<\/p>\n<p>Concepts, Skills, &amp; Problem Solving<\/p>\n<p><strong>USING A VENN DIAGRAM<\/strong><br \/>\nUse a Venn diagram to find the greatest common factor of the numbers. (See Exploration 1 Page.No 21)<\/p>\n<p>Question 9.<br \/>\n12, 30<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n32, 54<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n24, 108<br \/>\nAnswer:<\/p>\n<p><strong>FINDING THE GCF<\/strong><br \/>\nFind the GCF of the numbers using lists of factors<br \/>\nQuestion 12.<br \/>\n6, 15<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n14, 84<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n45, 76<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n39, 65<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n51, 85<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n40, 63<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n12, 48<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n24, 52<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n30, 58<br \/>\nAnswer:<\/p>\n<p><strong>FINDING THE GCF<\/strong><br \/>\nFind the GCF of the numbers using lists of factors prime factorizations.<\/p>\n<p>Question 21.<br \/>\n45, 60<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n27, 63<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n36, 81<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n72, 84<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n61, 73<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n38, 95<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n60, 75<br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\n42, 60<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n42, 63<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n24, 96<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n189, 200<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\n90, 108<br \/>\nAnswer:<\/p>\n<p><strong>OPEN-ENDED<\/strong><br \/>\nwrite a pair of numbers with the indicated GCF.<\/p>\n<p>Question 33.<br \/>\n5<br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\n12<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n37<br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA teacher is making identical activity packets using 92 crayons and 23 sheets of paper. What is the greatest number of packets the teacher can make with no items left over?<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou arc making balloon arrangements for a birthday party. \u2018there are 16 white balloons and 24 red balloons Each arrangement must he identical. What is the greatest number of arrangements you can make using every balloon?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32485\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-35.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 35\" width=\"118\" height=\"277\" \/><br \/>\nAnswer:<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the CCI of the two numbers. Is your friend correct? Explain your reasoning.<\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32484\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-36.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 36\" width=\"168\" height=\"104\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32483\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-37.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 37\" width=\"184\" height=\"107\" \/><br \/>\nAnswer:<\/p>\n<p><strong>FINDING THE GCF<\/strong><br \/>\nFind the GCF of the numbers.<br \/>\nQuestion 40.<br \/>\n35, 56, 63<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n30, 60, 78<br \/>\nAnswer:<\/p>\n<p>Question 42.<br \/>\n42, 70, 84<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n40, 55, 72<br \/>\nAnswer:<\/p>\n<p>Question 44.<br \/>\n18, 54, 90<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n16, 18, 88<br \/>\nAnswer:<\/p>\n<p>Question 46.<br \/>\n52, 78, 101<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n96, 120, 156<br \/>\nAnswer:<\/p>\n<p>Question 48.<br \/>\n280, 300, 380<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite three numbers that have a GCF of 16. What method did you use to find your answer?<br \/>\nAnswer:<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\nTell whether the statement \u00a1s always, someUmes, or never true. Explain your reasoning.<br \/>\nQuestion 50.<br \/>\nThe GCF of two even numbers is 2.<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nThe GCF of two prime numbers is 1.<br \/>\nAnswer:<\/p>\n<p>Question 52.<br \/>\nWhen one number is a multiple of another, the GCF of the numbers is the greater of the numbers.<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA science museum makes gift bags for students using 168 magnets, 48 robot figurines, and 24 packs of freeze-dried ice cream. What is the greatest number of gift bags that can be made using all of the items? How many of each item are in each gift bag?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32482\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-38.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 38\" width=\"193\" height=\"285\" \/><br \/>\nAnswer:<\/p>\n<p>Question 54.<br \/>\n<strong>VENN DIAGRAM<\/strong><br \/>\nConsider the numbers 252, 270, and 300.<br \/>\na. Create a Venn diagram using the prime factors of the numbers.<br \/>\nAnswer:<\/p>\n<p>b. Use the Venn diagram to find the GCF of 252, 270, and 300.<br \/>\nAnswer:<\/p>\n<p>c. What is the GCF of 252 and 270? 252 and 300? 270 and 300? Explain how you found your answers.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>MP REASONING<\/strong><br \/>\nYou are making fruit baskets using 54 apples, 36 oranges, and 73 bananas.<br \/>\na. Explain why you cannot make identical fruit baskets without leftover fruit.<br \/>\nAnswer:<\/p>\n<p>b. What is the greatest number of identical fruit baskets you can make with the least amount of fruit left over? Explain how you found your answer<br \/>\nAnswer:<\/p>\n<p>Question 56.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTwo rectangular, adjacent rooms share a wall. One-foot-by-one-foot tiles cover the floor of each room. Describe how the greatest possible length of the adjoining wall is related to the total number of tiles in each room. Draw a diagram that represents one possibility.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32481\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-39.png\" alt=\"Big Ideas Math Answer Key Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 39\" width=\"200\" height=\"100\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Section_1.5_Least_Common_Multiple\"><\/a>Section 1.5 Least Common Multiple<\/h3>\n<p><strong>Exploration 1<\/strong><\/p>\n<p>Identifying Common Multiples<\/p>\n<p>Work with a partner. In paris (a) &#8211; (d), create a Venn diagram that represents the first several multiples of each number and identify any common multiples.<br \/>\na. 8 and 12<br \/>\nAnswer:<\/p>\n<p>b. 4 and 14<br \/>\nAnswer:<\/p>\n<p>c. 10 and 15<br \/>\nAnswer:<\/p>\n<p>d. 20 and 35<br \/>\nAnswer:<\/p>\n<p>e. Look at the Venn diagrams in parts (a) &#8211; (d). Explain how to identify the least common multiple of each pair of numbers. Then circle it in each diagram.<br \/>\nAnswer:<\/p>\n<p><strong>Exploration 2<\/strong><\/p>\n<p>Using Prime Factors<\/p>\n<p>Work with a partner.<\/p>\n<p>a. Create a Venn diagram that represents the prime factorizations of 8 and 12.<\/p>\n<p>b. Repeat part (a) for the remaining number pairs in Exploration 1.<\/p>\n<p>c. <strong>MP STRUCTURE<\/strong><br \/>\nMake a conjecture about the relationship between the least common multiples you found in Exploration 1 and the numbers in the Venn diagrams you just created.<\/p>\n<p>d. The Venn diagram shows the prime factors of two numbers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32508\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-40.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 40\" width=\"193\" height=\"126\" \/><br \/>\nUse the diagram to complete the following tasks.<\/p>\n<ul>\n<li>Identify the two numbers.<\/li>\n<li>Find the greatest common factor.<\/li>\n<li>Find the least common multiple.<\/li>\n<\/ul>\n<p>Answer:<\/p>\n<p>Math Practice.<br \/>\n<strong>Analyze Conjectures<\/strong><br \/>\nHow can you test your conjecture in part (c)?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_1.5_Least_Common_Multiple\"><\/a>Lesson 1.5 Least Common Multiple<\/h3>\n<p>Try It Find the LCM of the numbers using lists of multiples.<br \/>\nQuestion 1.<br \/>\n3, 8<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n9, 12<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n6, 10<br \/>\nAnswer:<\/p>\n<p>Try It Find the LCM of the numbers using prime factorizations.<\/p>\n<p>Question 4.<br \/>\n14, 18<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n28, 36<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n24, 90<br \/>\nAnswer:<\/p>\n<p>Try It Find the LCM of the numbers.<br \/>\nQuestion 7.<br \/>\n2, 5, 8<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n6, 10, 12<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nWrite three numbers that have a least common multiple of 100.<br \/>\nAnswer:<\/p>\n<p>Self-Assessment for Concepts &amp; Skills<\/p>\n<p>Solve each exercise. Then rare your understanding of the success criteria in your journal<\/p>\n<p><strong>FINDING THE LCM<\/strong><br \/>\nFind the LCM of the numbers.<\/p>\n<p>Question 10.<br \/>\n6, 9<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n30, 10<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n5, 11<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>MP REASONING<\/strong><br \/>\nWrite two numbers such that 18 and 30 are multiples of the numbers. justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n<strong>MP REASONING<\/strong><br \/>\nYou need to find the LCM of 13 and 14. Would you rather list their multiples or use their prime factorizations? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<strong>MP CHOOSE TOOLS<\/strong><br \/>\nA student writes the prime factorizations of 8 and 12 in a table as shown. She claims she can use the table to find the greatest common factor and the least common multiple 8 and 12. How is this possible?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32506\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-42.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 42\" width=\"202\" height=\"168\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32507\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-41.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 41\" width=\"335\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-41.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-41-300x64.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nHow can you use least common multiples to add or subtract fractions with different denominators?<br \/>\nAnswer:<\/p>\n<p>Self-Assessment for Problem Solving<\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 17.<br \/>\nA geyser erupts every fourth day. Another geyser erupts every sixth day. Today both geysers erupted. In how many days will b0th geysers erupt on the same day again?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32505\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-43.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 43\" width=\"176\" height=\"249\" \/><br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nA water park has two large buckets that slowly fill with water. One bucket dumps water every 12 minutes. The other bucket dumps water every 10 minutes. Five minutes ago, b0th buckets dumped water. When will both buckets dump water at the same time again?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32505\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-43.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 43\" width=\"176\" height=\"249\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou purchase disposable plates, cups, and forks for a cookout. Plates are sold in packages of 24, cups in packages of 32, and forks in packages of 18. What are the least numbers of packages you should buy in order to have the same number of plates, cups, and forks?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Least_Common_Multiple_Practice_1.5\"><\/a>Least Common Multiple Practice 1.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Find the GCF of the numbers.<\/p>\n<p>Question 1.<br \/>\n18, 42<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n72, 96<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n38, 76, 111<br \/>\nAnswer:<\/p>\n<p>Divide.<br \/>\nQuestion 4.<br \/>\n900 \u00f7 6<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n1941 \u00f7 9<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n672 \u00f7 12<br \/>\nAnswer:<\/p>\n<p>Write an ordered pair that corresponds to the point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32504\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-44.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 44\" width=\"227\" height=\"222\" \/><\/p>\n<p>Question 7.<br \/>\nPoint A<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nPoint B<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nPoint C<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nPoint D<br \/>\nAnswer:<\/p>\n<p>Concepts, Skills, &amp; Problem Solving<\/p>\n<p><strong>USING A VENN DIAGRAM<\/strong><br \/>\nUse a Venn diagram to find the least common multiple of the numbers. (See Exploration 1 Page.No 27)<br \/>\nQuestion 11.<br \/>\n3, 7<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n6, 8<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n1, 5<br \/>\nAnswer:<\/p>\n<p><strong>FINDING THE LCM<\/strong><br \/>\nFind the LCM of the numbers using lists of multiplies.<br \/>\nQuestion 14.<br \/>\n1, 5<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n2, 6<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n2, 3<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n2, 9<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n3, 4<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n8, 9<br \/>\nAnswer:<\/p>\n<p>20.<br \/>\n5, 8<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n11, 12<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n12, 18<br \/>\nAnswer:<\/p>\n<p><strong>FINDING THE LCM<\/strong><br \/>\nFind the LCM of the numbers using prime factorizations.<br \/>\nQuestion 23.<br \/>\n7, 12<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n5, 9<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n4, 11<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n9, 10<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n12, 27<br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\n18, 45<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n22, 33<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\n36, 60<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n35, 50<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the LCM of 6 and 9. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32503\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-45.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 45\" width=\"216\" height=\"89\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou have diving lessons every fifth day and swimming lessons every third day. Today you have both lessons. In how many days will you have both lessons on the same day again?<br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\n<strong>MP REASONING<\/strong><br \/>\nWhich model represents an LCM that is different from the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32502\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-46.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 46\" width=\"569\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-46.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-46-300x82.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>FINDING THE LCM<\/strong><br \/>\nFind the LCM of the numbers.<br \/>\nQuestion 35.<br \/>\n2, 3, 7<br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\n3, 5, 11<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n4, 9, 12<br \/>\nAnswer:<\/p>\n<p>Question 38.<br \/>\n6, 8, 15<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n7, 18, 21<br \/>\nAnswer:<\/p>\n<p>Question 40.<br \/>\n9, 10, 28<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>MP PROBLEM SOLVING<\/strong><br \/>\nAt Union Station, you notice that three subway lines just arrived at the same time. How long must you wait until all three lines arrive at Union Station at the same time again?<\/p>\n<table border=\"2\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"90\">Subway Line<\/td>\n<td style=\"text-align: center;\" width=\"96\">Arrival Time<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">A<\/td>\n<td width=\"96\">Every 10 min<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">B<\/td>\n<td width=\"96\">Every 12 min<\/td>\n<\/tr>\n<tr>\n<td width=\"90\">C<\/td>\n<td width=\"96\">Every 15 min<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32501\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-47.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 47\" width=\"164\" height=\"216\" \/><br \/>\nAnswer:<\/p>\n<p>Question 42.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA radio station gives away $15 to every 15th caller, $25 to every 25th caller, and a free concert ticket to every 100th caller. When will the station first give away all three prizes to one caller? When this happens, how much money and how many tickets are given away?<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>MP LOGIC<\/strong><br \/>\nYou and a friend are running on treadmills. You run 0.5 mile every 3 minutes, and your friend runs 2 miles every 14 minutes. You both start and stop running at the same time and run a whole number of miles. What are the least possible numbers of miles you and your friend can run?<br \/>\nAnswer:<\/p>\n<p>Question 44.<br \/>\n<strong>VENN DIAGRAM<\/strong><br \/>\nRefer to the Venn diagram.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32500\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-48.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 48\" width=\"220\" height=\"122\" \/><br \/>\na. Copy and complete the Venn diagram.<br \/>\nAnswer:<\/p>\n<p>b. What is the LCM of 16, 24, and 40?<br \/>\nAnswer:<\/p>\n<p>c. What is the LCM of 16 and 40? 24 and 40? 16 and 21? Explain how you found your answers.<br \/>\nAnswer:<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\nTell whether the statement is always, sometimes, or never true. Explain your reasoning.<br \/>\nQuestion 45.<br \/>\nThe LCM of two different prime numbers is their Product.<br \/>\nAnswer:<\/p>\n<p>Question 46.<br \/>\nThe LCM of a set of numbers is equal to one of the numbers in the set.<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\nThe GCF of two different numbers is the LCM of the numbers.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Numerical_Expressions_and_Factors_Connecting_Concepts\"><\/a>Numerical Expressions and Factors Connecting Concepts<\/h3>\n<p>Using the Problem-Solving Plan<\/p>\n<p>Question 1.<br \/>\nA sports team gives away shirts at the stadium. There arc 60 large shirts, 1.6 times as many small shirts as large shirts, and 1.5 times as many medium shirts as small shirts. The team wants to divide the shirts into identical groups to he distributed throughout the stadium. What is the greatest number of groups that can be formed using every shirt?<\/p>\n<p>Understand the problem: You know the number of large shirts and two relationships among the numbers of small, medium, and large shirts. You are asked to find the greatest number of identical groups that can be formed using every shirt.<\/p>\n<p>Make a plan: Break the problem into parts. First use multiplication to find the number of each size shirt. Then find the GCF of these numbers.<\/p>\n<p>Solve and check: Lise the plan to solve the problem. Then check your solution.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nAn escape artist fills the tank shown with water. Find the number of cubic feet of water needed to fill the tank. Then find the number of cubic yards of water that are needed to fill the tank. justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32520\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-49.png\" alt=\"Big Ideas Math Answers 6th Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 49\" width=\"131\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Numerical_Expressions_and_Factors_Chapter_Review\"><\/a>Numerical Expressions and Factors Chapter Review<\/h3>\n<h3><a id=\"Powers_and_Exponents_Homework_&amp;_Practice_1.1\"><\/a>Powers and Exponents Homework &amp; Practice 1.1<\/h3>\n<p>Write the product as a power.<\/p>\n<p>Question 1.<br \/>\n3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n5 \u00d7 5 \u00d7 5<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n17 \u2022 17 \u2022 17 \u2022 17 \u2022 17<br \/>\nAnswer:<\/p>\n<p>Find the value of the power.<br \/>\nQuestion 4.<br \/>\n3<sup>3<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n2<sup>6<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n4<sup>4<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nWrite a power that has a value greater than 2<sup>3<\/sup> and less than 3<sup>3<\/sup>.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nWithout evaluating, determine whether 2<sup>5<\/sup> or 2<sup>2<\/sup> is greater. Explain.<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nThe bases on a softball field arc square. What is the area of each base?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32540\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-50.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 50\" width=\"375\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-50.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-50-300x194.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-51.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 51\" width=\"115\" height=\"96\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Order_of_Operations_Homework_&amp;_Practice_1.2\"><\/a>Order of Operations Homework &amp; Practice 1.2<\/h3>\n<p>Evaluate the expression.<\/p>\n<p>Question 10.<br \/>\n3 \u00d7 6 &#8211; 12 \u00f7 6<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n30 \u00f7(14 &#8211; 2<sup>2<\/sup>) \u00d7 5<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n\\(\\frac{5(2.3+3.7)}{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n4<sup>3<\/sup> &#8211; \\(\\frac{1}{2}\\)(7<sup>2<\/sup> + 5)<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n20 \u00d7 (3<sup>2<\/sup> &#8211; 4) \u00f7 50<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n5 + 3 (4<sup>2<\/sup> &#8211; 2) \u00f7 6<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nUse grouping symbols and at least one exponent to write a numerical expression that has a value of 80.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Prime_Factorization_Homework_&amp;_Practice_1.3\"><\/a>Prime Factorization Homework &amp; Practice 1.3<\/h3>\n<p>List the factor Pairs of the number.<\/p>\n<p>Question 17.<br \/>\n28<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n44<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n96<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\nThere arc 36 graduated cylinders to put away on a shelf after science class. The shelf can fit a maximum of 20 cylinders across and 4 cylinders deep. The teacher wants each row to have the same number of cylinders. List the possible arrangements of the graduated cylinders on the shelf.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32538\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-52.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 52\" width=\"229\" height=\"157\" \/><br \/>\nAnswer:<\/p>\n<p>Write the prime factorization of the number.<\/p>\n<p>Question 21.<br \/>\n12<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n50<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n66<br \/>\nAnswer:<\/p>\n<h3><a id=\"Greatest_Common_Factor_Homework_&amp;_Practice_1.4\"><\/a>Greatest Common Factor Homework &amp; Practice 1.4<\/h3>\n<p>Find the GCF of the numbers using lists of factors.<br \/>\nQuestion 24.<br \/>\n27, 45<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n30, 48<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n28, 48<br \/>\nAnswer:<\/p>\n<p>Find the GCF of the numbers using prime factorizations.<br \/>\nQuestion 27.<br \/>\n24, 80<br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\n52, 68<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n32, 56<br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\nWrite a pair of numbers that have a GCF of 20.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nWhat is the greatest number of friends you can invite to an arcade using the coupon such that the tokens and slices of pizza are equally split between you and your friends with none left over? How many slices of pizza and tokens will each person receive?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32537\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-53.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 53\" width=\"254\" height=\"188\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Least_Common_Multiple_Homework_&amp;_Practice_1.5\"><\/a>Least Common Multiple Homework &amp; Practice 1.5<\/h3>\n<p>Find the LCM of the numbers using lists of multiples.<br \/>\nQuestion 32.<br \/>\n4, 14<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n6, 20<br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\n12, 28<br \/>\nAnswer:<\/p>\n<p>Find the LCM of the numbers using prime factorbations.<br \/>\nQuestion 35.<br \/>\n6, 15<br \/>\nAnswer:<\/p>\n<p>Question 36.<br \/>\n10, 12<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n18, 27<br \/>\nAnswer:<\/p>\n<p>Question 38.<br \/>\nFind the LCM of 8, 12, and 18.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nWrite a pair of numbers that have an LCM of 84.<br \/>\nAnswer:<\/p>\n<p>Question 40.<br \/>\nWrite three numbers that have an LCM of 45.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nYou water your roses every sixth day and your hydrangeas every fifth day. Today you water both plants. In how man days will you water both plants on the same day again<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32536\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-54.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 54\" width=\"207\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p>Question 42.<br \/>\nHamburgers are sold in packages of 20, while buns are sold in packages of 12. What are the least numbers of packages you should buy in order to have the same number of hamburgers and buns?<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nA science museum is giving away a magnetic liquid kit to every 50th guest and a plasma ball to every 35th guest until someone receives both prizes.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-55.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 55\" width=\"124\" height=\"184\" \/><br \/>\na. Which numbered guest will receive both a magnetic liquid kit and a plasma ball?<br \/>\nAnswer:<\/p>\n<p>b. How many people will receive a plasma ball?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Numerical_Expressions_and_Factors_Practice_Test\"><\/a>Numerical Expressions and Factors Practice Test<\/h3>\n<p>Question 1.<br \/>\nFind the value of 2<sup>3<\/sup>.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nEvaluate \\(\\frac{5+4(12-2)}{3^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nWrite 261 \u2022 264 \u2022 264 as a power.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nList the factor pairs of 66.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWrite the prime factorization of 56.<br \/>\nAnswer:<\/p>\n<p>Find the GCF of the numbers.<br \/>\nQuestion 6.<br \/>\n24, 54<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n16, 32, 72<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n52, 65<br \/>\nAnswer:<\/p>\n<p>Find the LCM of the numbers.<br \/>\nQuestion 9.<br \/>\n9, 24<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n26, 39<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n6, 12, 11<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nYou have 16 yellow beads, 20 red heads, and 21 orange beads to make identical bracelets. What is the greatest number of bracelets that you can make using all of the beads?<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nA bag contains equal numbers of green marbles and blue marbles. You can divide all of the green marbles into groups of 12 and all the blue marbles into groups of 16. What is the least number of each color of marble that can be in the bag?<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nThe ages of the members of a family are 65, 58, 27, 25, 5, and 2 years old. What is the total admission price for the family to visit the zoo?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32634\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-56.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 56\" width=\"195\" height=\"139\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nA competition awards prizes for fourth, third, second, and first place. The fourth place winner receives $5. Each place above that receives a prize that is five times the amount of the previous prize. How much prize money is awarded?<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nYou buy tealight candles and mints as party favors for a baby shower. The tealight candles come in packs of 12 for $3.50. The mints come in packs of 50 for $6.25. What is the least amount of money you can spend to buy the same number of candles and mints?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-57.png\" alt=\"Big Ideas Math Answers Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 57\" width=\"267\" height=\"143\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Numerical_Expressions_and_Factors_Cumulative_Practice\"><\/a>Numerical Expressions and Factors Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nWhat is the value of 8 \u00d7 135?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nWhich number is equivalent to the expression below?<br \/>\n3 \u2022 2<sup>3<\/sup> &#8211; 8 \u00f7 4<br \/>\nA. 0<br \/>\nB. 4<br \/>\nC. 22<br \/>\nD. 214<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nThe top of an end table is a square with a side length of 16 inches. What is the area of the tabletop?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-59.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 59\" width=\"212\" height=\"201\" \/><br \/>\nF. 16 in.<sup>2<\/sup><br \/>\nG. 32 in.<sup>2<\/sup><br \/>\nH. 64 in.<sup>2<\/sup><br \/>\nI. 256 in.<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nYou are filling baskets using 18 green eggs, 36 red eggs, and 54 blue eggs. What is the greatest number of baskets that you can fill so that the baskets are identical and there are no eggs left over?<br \/>\nA. 3<br \/>\nB. 6<br \/>\nC. 9<br \/>\nD. 18<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWhat is the value of 2<sup>2<\/sup> \u2022 3<sup>2<\/sup> \u2022 5?<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nYou hang the two strands of decorative lights shown below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32655\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-60.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 60\" width=\"209\" height=\"72\" \/><br \/>\nStrand 1: changes between red and blue every 15 seconds<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32654\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-61.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 61\" width=\"204\" height=\"67\" \/><br \/>\nStrand 2: changes between green and gold every 18 seconds<br \/>\nBoth strands just changed color. After how many seconds will the strands change color at the same time again?<br \/>\nF. 3 seconds<br \/>\nG. 30 seconds<br \/>\nH. 90 seconds<br \/>\nI. 270 seconds<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nPoint p is plotted in the coordinate plane below.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32653\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-62.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 62\" width=\"148\" height=\"152\" \/><br \/>\nWhat arc the coordinates of Point p?<br \/>\nA. (5, 3)<br \/>\nB. (4, 3)<br \/>\nC. (3, 5)<br \/>\nD. (3, 4)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nWhat is the prime factorization 1100?<br \/>\nF. 2 \u00d7 5 \u00d7 11<br \/>\nG. 2<sup>2<\/sup> \u00d7 5<sup>2<\/sup> \u00d7 11<br \/>\nH. 4 \u00d7 5<sup>2<\/sup> \u00d7 11<br \/>\nI. 2<sup>2<\/sup> \u00d7 5 \u00d7 55<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nWhat is the least common multiple of 3, 8, and 10?<br \/>\nA. 21<br \/>\nB. 30<br \/>\nC. 80<br \/>\nD. 120<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nWhat is the area of the shaded region of the figure below?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32652\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Advanced-Chapter-1-Numerical-Expressions-and-Factors-63.png\" alt=\"Big Ideas Math Solutions Grade 6 Advanced Chapter 1 Numerical Expressions and Factors 63\" width=\"188\" height=\"177\" \/><br \/>\nF. 16yd<sup>2<\/sup><br \/>\nG. 65yd<sup>2<\/sup><br \/>\nH. 81 yd<sup>2<\/sup><br \/>\nI. 97 yd<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nWhich expression represents a prime factorization?<br \/>\nA. 4 \u00d7 4 \u00d7 7<br \/>\nB. 2<sup>2<\/sup> \u00d7 21 \u00d7 23<br \/>\nC. 3<sup>4<\/sup> \u00d7 5 \u00d7 7<br \/>\nD. 5 \u00d7 5 \u00d7 9 \u00d7 11<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nFind the greatest common factor for each pair of numbers.<br \/>\nThink<br \/>\nSolve<br \/>\nExplain<br \/>\n10 and 15\u00a0 \u00a0 \u00a0 10 and 21\u00a0 \u00a0 \u00a015 and 21<br \/>\nWhat can you conclude about the greatest common factor of 10, 15, and 21?<br \/>\nExplain your reasoning.<br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Do you want to become proficient in Math and get a good hold of the Big Ideas Math Book Grade 6 Advanced? 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