{"id":24688,"date":"2022-04-05T12:40:05","date_gmt":"2022-04-05T07:10:05","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=24688"},"modified":"2022-04-07T10:58:50","modified_gmt":"2022-04-07T05:28:50","slug":"big-ideas-math-answers-grade-6-chapter-5","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6-chapter-5\/","title":{"rendered":"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties"},"content":{"rendered":"<p>Follow a free step-by-step guide to <strong><em>Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties<\/em><\/strong> available here. There are various topics involved in Big Ideas Math Answers like Properties of Addition and Multiplication, Writing Expressions, Algebraic Expressions, and so on. <a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-6\/\">Big Ideas Math Solutions Grade 6<\/a> Chapter 5 Algebraic Expressions and Properties will aid you to enhance your math skill and problem-solving techniques. Know all the problems and solutions and tips to solve them in an easy manner. Go through the below sections to know the properties and example problems.<\/p>\n<h2>Big Ideas Math Book 6th Grade Answer Key Chapter 5 Algebraic Expressions and Properties<\/h2>\n<p>To ease your learning and make it quick by using <strong>Big Ideas Math Book 6th Grade Solution Key Chapter 5 Algebraic Expressions and Properties pdf<\/strong>. Algebraic Expressions and Properties pdf concepts are explained by proficient math experts. With the help of the Big Ideas Book 6th Grade Answer Key, you can get the solutions to every problem. Just click on the links and start practicing all the problems for the exams and score well in the exam. Follow all the problems and practice them to improve time management skills and accuracy.<\/p>\n<p><strong>Algebraic Expressions and Properties STEAM Video\/Performance<\/strong><\/p>\n<ul>\n<li><a href=\"#Algebraic_Expressions_and_Properties_STEAM_Video\/Performance\">Algebraic Expressions and Properties STEAM Video\/Performance<\/a><\/li>\n<li><a href=\"#Getting_Ready_for_Chapter_5\">Getting Ready for Chapter 5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Algebraic Expressions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.1_Algebraic_Expressions\">Lesson 5.1 Algebraic Expressions<\/a><\/li>\n<li><a href=\"#Algebraic Expressions Homework &amp; Practice 5.1\">Algebraic Expressions Homework &amp; Practice 5.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Writing Expressions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.2_Writing_Expressions\">Lesson 5.2 Writing Expressions<\/a><\/li>\n<li><a href=\"#Writing_Expressions_Homework_&amp;_Practice_5.2\">Writing Expressions Homework &amp; Practice 5.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Properties of Addition and Multiplication<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.3_Properties_of_Addition_and_Multiplication\">Lesson 5.3 Properties of Addition and Multiplication<\/a><\/li>\n<li><a href=\"#Properties_of_Addition_and_Multiplication_Homework_&amp;_Practice_5.3\">Properties of Addition and Multiplication Homework &amp; Practice 5.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 The Distributive Property<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.4_The_Distributive_Property\">Lesson 5.4 The Distributive Property<\/a><\/li>\n<li><a href=\"#The_Distributive_Property_Homework_&amp;_Practice_5.4\">The Distributive Property Homework &amp; Practice 5.4<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 5 Factoring Expressions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.5_Factoring_Expressions\">Lesson 5.5 Factoring Expressions<\/a><\/li>\n<li><a href=\"#Factoring_Expressions_Homework_&amp;_Practice_5.5\">Factoring Expressions Homework &amp; Practice 5.5<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 5 &#8211; Algebraic Expressions and Properties<\/strong><\/p>\n<ul>\n<li><a href=\"#Algebraic_Expressions_and_Properties_Connecting_Concepts\">Algebraic Expressions and Properties Connecting Concepts<\/a><\/li>\n<li><a href=\"#Algebraic_Expressions_and_Properties_Chapter_Review\">Algebraic Expressions and Properties Chapter Review<\/a><\/li>\n<li><a href=\"#Algebraic_Expressions_and_Properties_Practice_Test\">Algebraic Expressions and Properties Practice Test<\/a><\/li>\n<li><a href=\"#Algebraic_Expressions_and_Properties_Cumulative_Practice\">Algebraic Expressions and Properties Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Algebraic_Expressions_and_Properties_STEAM_Video\/Performance\"><\/a>Algebraic Expressions and Properties STEAM Video\/Performance<\/h3>\n<p><strong>Shadow Drawings<\/strong><br \/>\nExpressions can be used to represent the growth of living things over time. Can you think of any other real-life situations in which you would want to use an expression to represent a changing quantity?<br \/>\n<strong>Watch the STEAM Video \u201cShadow Drawings.\u201d Then answer the following questions.<\/strong><\/p>\n<p>Question 1.<br \/>\nTory traces the shadow of a plant each week on the same day of the week and at the same time of day. Why does she need to be so careful about the timing of the drawing?<\/p>\n<p>Answer:<br \/>\nTory traces the shadow of a plant each week on the same day of the week and at the same time of day.<br \/>\nBecause she needs to represent the growth of the plant over time. Thus she needs to be very careful about the timing of the drawing.<\/p>\n<p>Question 2.<br \/>\nThe table shows the height of the plant each week for the \ufb01rst three weeks. About how tall was the plant after 1.5 weeks? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-1.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 1\" width=\"304\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-1.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-1-300x76.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Answer: 10.5 inches<\/p>\n<p>Explanation:<br \/>\nThe above table represents the height of the plant for 3 weeks.<br \/>\n1 week = 7 inches<br \/>\n0.5 week = 7\/2 = 3.5 inches<br \/>\n1.5 week = 7 + 3.5 = 10.5 inches<\/p>\n<p>Question 3.<br \/>\nPredict the height of the plant when Tory makes her next three weekly drawings.<\/p>\n<p>Answer: 42 inches (approx)<\/p>\n<p>Explanation:<br \/>\nThe height of the plant is increased by 7 inches every week.<br \/>\nThe height of the plant is increased to 22 inches for the first three weeks.<br \/>\n7 \u00d7 6 = 42 inches<br \/>\nThus we predict the height of the plant when Tory makes her next three weekly drawings is 42 inches.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Describing Change<\/strong><\/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 given data sets for the following real-life situations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24730\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-2.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 2\" width=\"151\" height=\"126\" \/><br \/>\nYou will be asked to use given data to write expressions and make predictions. Do the expressions provide accurate predictions far into the future?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24731\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-3.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 3\" width=\"287\" height=\"365\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-3.png 287w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-3-236x300.png 236w\" sizes=\"(max-width: 287px) 100vw, 287px\" \/><\/p>\n<h3><a id=\"Getting_Ready_for_Chapter_5\"><\/a>Getting Ready for Chapter 5<\/h3>\n<p>Question 1.<br \/>\nWork with a partner.<br \/>\na. You baby sit for 3 hours. You receive $24. What is your hourly wage?<\/p>\n<ul>\n<li>Write the problem. Underline the important numbers and units you need to solve the problem.<\/li>\n<li>Read the problem carefully a second time. Circle the key phrase for the question.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24732\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-4.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 4\" width=\"529\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-4.png 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-4-300x69.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><\/li>\n<li>Write each important number or phrase, with its units, on a piece of paper. Write +, \u2212, \u00d7, \u00f7, and = on \ufb01ve other pieces of paper.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24733\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-5.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 5\" width=\"497\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-5.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-5-300x71.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/li>\n<li>Arrange the pieces of paper to answer the question, \u201cWhat is your hourly wage?\u201d<\/li>\n<li>Evaluate the expression that represents the hourly wage.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24734\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-6.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 6\" width=\"374\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-6.png 374w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-6-300x73.png 300w\" sizes=\"(max-width: 374px) 100vw, 374px\" \/><\/li>\n<\/ul>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34510\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-6-300x73.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-6\" width=\"300\" height=\"73\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-6-300x73.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-6.jpg 374w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nAccording to the given details, Babysit receives $24 for 3 hours.<br \/>\n3 hours = $24<br \/>\n1 hour = 24\/3 = $8<br \/>\nThus your hourly wage is $8<\/p>\n<p>b. How can you use your hourly wage to \ufb01nd how much you will receive for any number of hours worked?<\/p>\n<p>Answer:<br \/>\nYou can multiply by $8 in given any number of hours worked to get the total receive.<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p>The following vocabulary terms are de\ufb01ned in this chapter. Think about what each term might mean and record your thoughts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24735\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-7.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 7\" width=\"452\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-7.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-7-300x50.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<h3><a id=\"Lesson_5.1_Algebraic_Expressions\"><\/a>Lesson 5.1 Algebraic Expressions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24736\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-8.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 8\" width=\"152\" height=\"169\" \/><br \/>\n<strong>Work with a partner. Identify any missing information that is needed to answer each question. Then choose a reasonable quantity and write an expression for each problem. After you have written the expression, evaluate it using mental math or some other method.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24737\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-9.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 9\" width=\"257\" height=\"184\" \/><br \/>\na. You receive $24 for washing cars. How much do you earn per hour?<\/p>\n<p>Answer:<br \/>\nLet the number of hours 8.<br \/>\n24 \u00f7 8 = 3<br \/>\nThus you earn $3 per hour.<\/p>\n<p>b. You buy 5 silicone baking molds at a craft store. How much do you spend?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24738\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-10.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 10\" width=\"249\" height=\"145\" \/><\/p>\n<p>Answer:<br \/>\nLet the cost of each silicone baking molds is $3<br \/>\n5 \u00d7 $3 = $15<br \/>\nThus you spend $15 to buy 5 silicone baking molds.<br \/>\nc. You are running in a mud race. How much farther do you have to go after running 2000 feet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24739\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-11.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 11\" width=\"240\" height=\"155\" \/><\/p>\n<p>Answer:<br \/>\nYou are running a 4500-foot race.<br \/>\n4500 &#8211; 2000 = 2500 feet<br \/>\nThus you have to run 2500 feet more.<\/p>\n<p>d. A rattlesnake is 25 centimeters long when it hatches. The snake grows at a rate of about 1.6 centimeters per month for several months. What is the length of the rattlesnake?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24740\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-12.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 12\" width=\"239\" height=\"113\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA rattlesnake is 25 centimeters long when it hatches. The snake grows at a rate of about 1.6 centimeters per month for several months.<br \/>\nLet the number of months be m<br \/>\n25 + 1.6m<br \/>\nIf months = 12<br \/>\n1.6 \u00d7 12 = 19.2 cms<br \/>\n25 + 19.2 = 44.2 centimeters<\/p>\n<p><strong>5.1 Lesson<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24741\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-13.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 13\" width=\"207\" height=\"175\" \/><\/p>\n<p>An algebraic expression is an expression that may contain numbers, operations, and one or more variables. A variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24742\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-14.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 14\" width=\"469\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-14.png 469w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-14-300x84.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Identify the terms, coefficients, and constants in the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n12 + 10c<\/p>\n<p>Answer:<br \/>\n12 &#8211; constant<br \/>\n10 &#8211; coefficient<br \/>\nc &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 2.<br \/>\n15 + 3w + \\(\\frac{1}{2}\\)<\/p>\n<p>Answer:<br \/>\n15 and \\(\\frac{1}{2}\\) &#8211; constant<br \/>\n3 &#8211; coefficient<br \/>\nw &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 3.<br \/>\nz<sup>2<\/sup> + 9z<\/p>\n<p>Answer:<br \/>\n2 &#8211; exponent<br \/>\n9 &#8211; coefficient<br \/>\nz &#8211; variable or term<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>write the expression using exponents.<\/p>\n<p>Question 4.<br \/>\nj . j . j . j . j . j<\/p>\n<p>Answer:<br \/>\nj raised to the sixth power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 5.<br \/>\n9 . k . k . k . k . k<\/p>\n<p>Answer:<br \/>\n9 &#8211; constant<br \/>\nk raised to the fifth power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 6.<br \/>\nEvaluate 24 + c when c = 9.<\/p>\n<p>Answer: 33<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n24 + c<br \/>\nand also given c is equal to 9<br \/>\nsubstitute c value in the equation we get<br \/>\n24 + 9 = 33<\/p>\n<p>Question 7.<br \/>\nEvaluate d \u2212 17 when d = 30.<\/p>\n<p>Answer: 13<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\nd &#8211; 17<br \/>\nand also given d is equal to 30<br \/>\nsubstitute d value in the equation we get<br \/>\n30 &#8211; 17 = 13<\/p>\n<p>Question 8.<br \/>\nEvaluate 18 \u00f7 q when q = \\(\\frac{1}{2}\\)<\/p>\n<p>Answer: 36<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n18 \u00f7 q<br \/>\nand also given q is equal to \\(\\frac{1}{2}\\)<br \/>\nsubstitute q value in the equation we get<br \/>\n18 \u00f7 \\(\\frac{1}{2}\\) = 36<\/p>\n<p><strong>Evaluate the expression when p = 24 and q = 8.<\/strong><\/p>\n<p>Question 9.<br \/>\np \u00f7 q<\/p>\n<p>Answer:<br \/>\np = 24<br \/>\nq = 8<br \/>\np \u00f7 q<br \/>\nSubstitute the value of p and q in the expression<br \/>\n24 \u00f7 8 = 3<\/p>\n<p>Question 10.<br \/>\nq + p<\/p>\n<p>Answer:\u00a0 32<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\np = 24<br \/>\nq = 8<br \/>\nq + p<br \/>\nSubstitute the value of p and q in the expression<br \/>\n8 + 24 = 32<br \/>\nHence we get the answer is 32<\/p>\n<p>Question 11.<br \/>\np &#8211; q<\/p>\n<p>Answer: 16<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\np = 24<br \/>\nq = 8<br \/>\np &#8211; q<br \/>\nSubstitute the value of p and q in the expression<br \/>\n24 &#8211; 8 = 16<br \/>\nHence we get the answer is 16<\/p>\n<p>Question 12.<br \/>\np . q<\/p>\n<p>Answer: 192<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\np = 24<br \/>\nq = 8<br \/>\np . q<br \/>\nSubstitute the value of p and q in the expression<br \/>\n24 . 8\u00a0 by multiplying 24 with 8 we get 192<br \/>\nHence\u00a0 the answer is 192<\/p>\n<p><strong>Evaluate the expression when y = 6.<\/strong><\/p>\n<p>Question 13.<br \/>\n5y + 1<\/p>\n<p>Answer: 31<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n5y + 1<br \/>\nand also given y = 6<br \/>\nNow substitute 6 in the given equation<br \/>\n5.6 + 1 is<br \/>\n5 multiply with 6 and then add with 1 we get 30 + 1 is 31<br \/>\nhence answer is 31<\/p>\n<p>Question 14.<br \/>\n30 &#8211; 24 \u00f7 y<\/p>\n<p>Answer: 1<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n30 &#8211; 24 \u00f7 y<br \/>\nand also given y = 6<br \/>\nNow substitute 6 in the given equation<br \/>\n30 &#8211; 24 \u00f7 y is<br \/>\n30 &#8211; 24 \u00f76<br \/>\n6 \u00f7 6<br \/>\nsix divided by six<br \/>\nwe get 1<br \/>\nHence answer is 1<\/p>\n<p>Question 15.<br \/>\ny<sup>2<\/sup> &#8211; 7<\/p>\n<p>Answer: 29<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\ny\u00b2 &#8211; 7<br \/>\nand also given y = 6<br \/>\nNow substitute 6 in the given equation<br \/>\ny2 &#8211; 7<br \/>\n6\u00b2 &#8211; 7<br \/>\n6 \u00d7 6 &#8211; 7<br \/>\n36 &#8211; 7<br \/>\n29<br \/>\nHence answer is 29<\/p>\n<p>Question 16.<br \/>\n1.5 + y<sup>2<\/sup><\/p>\n<p>Answer: 37.5<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n1.5 + y\u00b2<br \/>\nand also given y = 6<br \/>\nNow substitute 6 in the given equation<br \/>\n1.5 + 6\u00b2<br \/>\n1.5 +36<br \/>\n37.5<br \/>\nHence answer is 37.5<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 17.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24743\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-15.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 15\" width=\"359\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-15.png 359w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-15-300x48.png 300w\" sizes=\"(max-width: 359px) 100vw, 359px\" \/><\/p>\n<p>Answer: The expression 3(4) + 5 does not belong to the other three. Because it does not contain any variable in the expression.<\/p>\n<p>Question 18.<br \/>\n<strong>ALGEBRAIC EXPRESSIONS<\/strong><br \/>\nIdentify the terms, coefficients, and constants in the expression 9h + 1.<\/p>\n<p>Answer:<br \/>\n1 &#8211; constant<br \/>\n9 &#8211; coefficient<br \/>\nh &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Evaluate the expression when m = 8.<\/strong><\/p>\n<p>Question 19.<br \/>\nm &#8211; 7<\/p>\n<p>Answer: 1<br \/>\nGiven equation<br \/>\nm &#8211; 7<br \/>\ngiven m value is 8<br \/>\nNow substitute m value 8\u00a0 in the given equation we get<br \/>\nm &#8211; 7<br \/>\n8 &#8211; 7<br \/>\n1<br \/>\nHence the answer is 1<\/p>\n<p>Question 20.<br \/>\n5m + 4<\/p>\n<p>Answer: 44<br \/>\nGiven equation<br \/>\n5m + 4<br \/>\ngiven m value is 8<br \/>\nNow substitute m value 8\u00a0 in the given equation we get<br \/>\n5 . 8 + 4<br \/>\n40 + 4<br \/>\n44<br \/>\nHence the answer is 44<\/p>\n<p>Question 21.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nDoes the value of the expression 20 \u2212 x increase, decrease, or stay the same as x increases? Explain.<\/p>\n<p>Answer:<br \/>\nWhen the value of x increases, the value of 20 &#8211; x decreases. And when the value of x does not change, 20 &#8211; x remains the same. When greater values of x are subtracted from 20, you will have a lower value left. Therefore, as x increases, the value of the expression 20 &#8211; x will decrease.<\/p>\n<p>Question 22.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite an algebraic expression using more than one operation. When you evaluate the expression, how do you know which operation to perform \ufb01rst?<\/p>\n<p>Answer:<br \/>\nExample\u00a0 40 \u2013 2(6 \u2013 4)\u00b2<br \/>\n40 &#8211; 2 (2)\u00b2<br \/>\n40 &#8211; 2(4)<br \/>\n40 &#8211; 8<br \/>\n32<\/p>\n<p>When evaluating an expression, proceed in this order:<\/p>\n<p>parentheses are done first.<br \/>\nexponents are done next.<br \/>\nmultiplication and division are done as they are encountered from left to right.<br \/>\naddition and subtraction are done as they are encountered from left to right.<\/p>\n<p>Question 23.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nIs the expression 8.2 \u00f7 m . m . m . m the same as the expression 8.2 \u00f7 m<sup>4<\/sup>? Explain your reasoning.<\/p>\n<p>Answer: Yes<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nHence the expression 8.2 \u00f7 m . m . m . m the same as the expression 8.2 \u00f7 m\u2074<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 24.<br \/>\nThe expression 12.25m + 29.99 gives the cost (in dollars) of a gym membership for m months. You have $180 to spend on a membership. Can you buy a one-year membership?<\/p>\n<p>Answer: Yes.<br \/>\nGiven<br \/>\nThe expression 12.25m + 29.99<br \/>\ngym membership for m months<br \/>\nYou have $180 to spend on a membership<br \/>\nLet&#8217;s solve your equation step-by-step.<br \/>\n12.25m+29.99=180<br \/>\nStep 1: Subtract 29.99 from both sides.<br \/>\n12.25m+29.99\u221229.99=180\u221229.99<br \/>\n12.25m=150.01<br \/>\nStep 2: Divide both sides by 12.25.<br \/>\n12.25m\/12.25=150.01\/12.25<br \/>\nm=12.245714<br \/>\nThe expression 12.25m + 29.99= 12.25(12.24)+29.99 = 179.93<\/p>\n<p>Question 25.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe expression p \u221215 gives the amount (in dollars) you pay after using the coupon when the original amount of a purchase is p dollars. The expression 30 + 6n gives the amount of money (in dollars) you save after n weeks. A jacket costs $78. Can you buy the jacket after 6 weeks? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24744\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-16.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 16\" width=\"168\" height=\"109\" \/><\/p>\n<p>Answer:<br \/>\nThe amount you pay using coupon = p (purchase) -15<br \/>\nso we simply plug in our value into this equation<br \/>\n$78- $15 = $63<br \/>\nso $63 is the amount you pay after using the coupon on an original purchase of $78<br \/>\nn = 6 weeks<br \/>\n30 + 6n<br \/>\n30 + 6(6)<br \/>\n30 + 36 = 66<br \/>\nNo, you cannot buy the jacket after 6 weeks.<\/p>\n<h3><a id=\"Algebraic Expressions Homework &amp; Practice 5.1\"><\/a>Algebraic Expressions Homework &amp; Practice 5.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>You ask 40 students which of three items from the cafeteria they like the best. You record the results on the piece of paper shown.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-500.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 500\" width=\"291\" height=\"172\" \/><\/p>\n<p>Question 1.<br \/>\nWhat percent of students answered salad?<\/p>\n<p>Answer: 25%<\/p>\n<p>Explanation:<br \/>\nTotal number of students = 40<br \/>\nThe number of students who like a salad in the Cafeteria food is 10 students<br \/>\n40\/10 = 4<br \/>\nThe percentage of the students is<br \/>\n(10\/40) \u00d7 100 = 25%<br \/>\nThus the percentage of students who answered salad is 25%.<\/p>\n<p>Question 2.<br \/>\nHow many students answered pizza?<\/p>\n<p>Answer: 12 students<\/p>\n<p>Explanation:<br \/>\nTotal number of students = 40<br \/>\nThe number of students who like a salad in the Cafeteria food is 10 students<br \/>\nThe number of students who answered pasta is 18<br \/>\n40 &#8211; 18 &#8211; 10 = 12<br \/>\nThus the number of students who answered pizza is 12.<\/p>\n<p>Question 3.<br \/>\nWhat percent of students answered pasta?<\/p>\n<p>Answer: 45%<\/p>\n<p>Explanation:<br \/>\nTotal number of students = 40<br \/>\nThe number of students who answered pasta is 18<br \/>\n(18\/40) \u00d7 100 = 45<br \/>\nThus the percentage of students who answered pasta is 45%<\/p>\n<p>Find the missing quantity in the double number line.<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24745\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-17.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 17\" width=\"249\" height=\"81\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34422\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-17.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-17\" width=\"249\" height=\"81\" \/><br \/>\nThe ratio of 2 and 10 is 1:5<br \/>\nThe equivalent ratio of 1:5 is 6:30<br \/>\nSo, the missing quantity is 6.<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24746\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-18.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 18\" width=\"255\" height=\"107\" \/><\/p>\n<p>Answer:<br \/>\nBased on the ratios we can find the missing quantity.<br \/>\nThe cost of 1 pastry is $2.5<br \/>\nThe cost of 9 pastries is $22.5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34427\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-18.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-18\" width=\"255\" height=\"107\" \/><\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 6.<br \/>\n1\\(\\frac{3}{8}\\) \u00f7 \\(\\frac{3}{4}\\)<\/p>\n<p>Answer: \\(\\frac{1}{2}\\)<br \/>\nTo simplify a fraction, divide the top and bottom by the highest number that<br \/>\ncan divide into both numbers exactly.<br \/>\nSimplifying (or reducing) fractions means making the fraction as simple as possible<\/p>\n<p>Question 7.<br \/>\n2\\(\\frac{7}{9}\\) \u00f7 2<\/p>\n<p>Answer: \\(\\frac{7}{9}\\)<br \/>\nTo simplify a fraction, divide the top and bottom by the highest number that<br \/>\ncan divide into both numbers exactly.<br \/>\nSimplifying (or reducing) fractions means making the fraction as simple as possible<\/p>\n<p>Question 8.<br \/>\n4 \u00f7 4\\(\\frac{2}{5}\\)<\/p>\n<p>Answer: \\(\\frac{5}{2}\\)<br \/>\nTo simplify a fraction, divide the top and bottom by the highest number that<br \/>\ncan divide into both numbers exactly.<br \/>\nSimplifying (or reducing) fractions means making the fraction as simple as possible<\/p>\n<p>Question 9.<br \/>\n3\\(\\frac{2}{3}\\) \u00f7 1\\(\\frac{2}{7}\\)<\/p>\n<p>Answer: latex]\\frac{14}{3}[\/latex]<br \/>\nTo simplify a fraction, divide the top and bottom by the highest number that<br \/>\ncan divide into both numbers exactly.<br \/>\nSimplifying (or reducing) fractions means making the fraction as simple as possible<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Write and evaluate an expression for the problem.<\/strong> (See Exploration 1, p. 201.)<\/p>\n<p>Question 10.<br \/>\nThe scores on your \ufb01rst two history tests are 82 and 95. By how many points did you improve on your second test?<\/p>\n<p>Answer: 13<\/p>\n<p>Explanation:<br \/>\nThe scores on your \ufb01rst two history tests are 82 and 95.<br \/>\n95 &#8211; 82 = 13<br \/>\nThus you have to improve 13 points on your second test.<\/p>\n<p>Question 11.<br \/>\nYou buy a hat for $12 and give the cashier a $20 bill. How much change do you receive?<\/p>\n<p>Answer: $8<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou buy a hat for $12 and give the cashier a $20 bill.<br \/>\n20 &#8211; 12 = 8<br \/>\nThus you receive $8 change.<\/p>\n<p>Question 12.<br \/>\nYou receive $8 for raking leaves for 2 hours. What is your hourly wage?<\/p>\n<p>Answer: $4<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nYou receive $8 for raking leaves for 2 hours.<br \/>\n2 hour = $8<br \/>\n1 hour = ?<br \/>\n8\/2 = 4<br \/>\nThus the hourly wage is $4.<\/p>\n<p>Question 13.<br \/>\nMusic lessons cost $20 per week. How much do 6 weeks of lessons cost?<\/p>\n<p>Answer: $120<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nMusic lessons cost $20 per week.<br \/>\n1 week = $20<br \/>\n$20 \u00d7 6 = $120<br \/>\nThus the cost of 6 weeks is $120.<\/p>\n<p><strong>ALGEBRAIC EXPRESSIONS<\/strong><br \/>\n<strong>Identify the terms, coefficients, and constants in the expression.<\/strong><\/p>\n<p>Question 14.<br \/>\n7h + 3<\/p>\n<p>Answer:<br \/>\n3 &#8211; constant<br \/>\n7 &#8211; coefficient<br \/>\nh &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 15.<br \/>\ng + 12 + 9g<\/p>\n<p>Answer:<br \/>\n12 &#8211; constant<br \/>\n9 &#8211; coefficient<br \/>\ng &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 16.<br \/>\n5c<sup>2<\/sup> + 7d<\/p>\n<p>Answer:<br \/>\n2 &#8211; exponent<br \/>\n5 and 7 &#8211; coefficient<br \/>\nc and d &#8211; variable or term<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 17.<br \/>\n2m<sup>2<\/sup> + 15 + 2p<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\n15 &#8211; constant<br \/>\n2 &#8211; exponent<br \/>\n2 &#8211; coefficient<br \/>\nm and p &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 18.<br \/>\n6 + n<sup>2<\/sup> + \\(\\frac{1}{2}\\)d<\/p>\n<p>Answer:<br \/>\n6 &#8211; constant<br \/>\n\\(\\frac{1}{2}\\)&#8211; exponent<br \/>\n2 &#8211; coefficient<br \/>\nn and d &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24747\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-19.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 19\" width=\"76\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\n2 &#8211; exponent<br \/>\n8 and \\(\\frac{1}{3}\\)&#8211; coefficient<br \/>\nx &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 20.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the terms, coefficients, and constants in the algebraic expression 2x<sup>2<\/sup>y. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24748\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-20.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 20\" width=\"191\" height=\"121\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34646\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-20-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-20\" width=\"191\" height=\"121\" \/><br \/>\nA term without a variable is called a constant.<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 21.<br \/>\n<strong>PERIMETER<\/strong><br \/>\nYou can use the expression 2\u2113 + 2w to \ufb01nd the perimeter of a rectangle, where \u2113 is the length and w is the width.<br \/>\na. Identify the terms, coefficients, and constants in the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24749\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-21.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 21\" width=\"187\" height=\"125\" \/><\/p>\n<p>Answer:<br \/>\nGiven Expression 2\u2113 + 2w<br \/>\nThe coefficients of the expression are 2.<br \/>\nterms &#8211; l, w<br \/>\nb. Interpret the coefficients of the terms.<\/p>\n<p>Answer: The coefficients of the terms are 2, 2<br \/>\n2 + 2 = 4<\/p>\n<p><strong>USING EXPONENTS<\/strong><br \/>\n<strong>Write the expression using exponents.<\/strong><\/p>\n<p>Question 22.<br \/>\nb . b . b<\/p>\n<p>Answer:<br \/>\nb raised to the third power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 23.<br \/>\ng . g . g . g . g<\/p>\n<p>Answer:<br \/>\ng raised to the fifth power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 24.<br \/>\n8 . w . w . w . w<\/p>\n<p>Answer:<br \/>\n8 &#8211; constant<br \/>\nw raised to the fourth power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 25.<br \/>\n5 . 2 . y . y . y<\/p>\n<p>Answer:<br \/>\n5 and 2 &#8211; constant<br \/>\ny raised to the third power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 26.<br \/>\na . a . c . c<\/p>\n<p>Answer:<br \/>\na and c\u00a0 raised to the two power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 27.<br \/>\n2 . 1 . x . z . z .z . z<\/p>\n<p>Answer:<br \/>\n2 and 1 &#8211; constant<br \/>\nx raised to the 1 power<br \/>\nz raised to the fourth power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 28.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend writes the product using exponents. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24750\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-22.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 22\" width=\"194\" height=\"94\" \/><\/p>\n<p>Answer: correct<br \/>\n5\u00a0 &#8211; constant<br \/>\nn\u00a0 raised to the fourth power<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<\/p>\n<p>Question 29.<br \/>\n<strong>AREA<\/strong><br \/>\nWrite an expression using exponents that represents the area of the square.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24751\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-23.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 23\" width=\"137\" height=\"111\" \/><\/p>\n<p>Answer:<br \/>\nSide = 5d<br \/>\nArea of the square = s \u00d7 s<br \/>\nA = 5d \u00d7 5d<br \/>\nA = 25d\u00b2<\/p>\n<p>Question 30.<br \/>\n<strong>REASONING<\/strong><br \/>\nSuppose the man in the St. Ives poem has x wives, each wife has x sacks, each sack has x cats, and each cat has x kits. Write an expression using exponents that represent the total number of kits, cats, sacks, and wives.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24752\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-24.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 24\" width=\"317\" height=\"194\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-24.png 317w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-24-300x184.png 300w\" sizes=\"(max-width: 317px) 100vw, 317px\" \/><\/p>\n<p>Answer:<br \/>\nSuppose the man in the St. Ives poem has x wives, each wife has x sacks, each sack has x cats, and each cat has x kits.<br \/>\nx = 7<br \/>\n7 \u00d7 7 \u00d7 7 \u00d7 7<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Evaluate the expression when a = 3, b = 2, and c = 12.<\/strong><\/p>\n<p>Question 31.<br \/>\n6 + a<\/p>\n<p>Answer: 9<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n6 + a<br \/>\ngiven data<br \/>\na = 3<br \/>\nnow substitute given data in the equation we get<br \/>\n6 + 3 = 9<br \/>\nhence the answer is 9<\/p>\n<p>Question 32.<br \/>\nb.5<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\nb.5<br \/>\ngiven data<br \/>\nb = 2<br \/>\nnow substitute given data in the equation we get<br \/>\n2 . 5= 10 (2 multiply by 5)<br \/>\nhence the answer is 10<\/p>\n<p>Question 33.<br \/>\nc &#8211; 1<\/p>\n<p>Answer: 11<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\nc &#8211; 1<br \/>\ngiven data<br \/>\nc = 12<br \/>\nnow substitute given data in the equation we get<br \/>\n12 &#8211; 1 = 11<br \/>\nhence the answer is 11<\/p>\n<p>Question 34.<br \/>\n27 \u00f7 a<\/p>\n<p>Answer: 9<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n27 \u00f7a<br \/>\ngiven data<br \/>\na = 3<br \/>\nnow substitute given data in the equation we get<br \/>\n27 \u00f7 3 = 9<br \/>\nHence the answer is 9<\/p>\n<p>Question 35.<br \/>\n12 &#8211; b<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n12 -b<br \/>\ngiven data<br \/>\nb = 2<br \/>\nnow substitute given data in the equation we get<br \/>\n12 &#8211; 2 = 10<br \/>\nHence the answer is 10<\/p>\n<p>Question 36.<br \/>\nc + 5<\/p>\n<p>Answer: 17<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\nc + 5<br \/>\ngiven data<br \/>\nc = 12<br \/>\nnow substitute given data in the equation we get<br \/>\n12+ 5 = 17<br \/>\nHence the answer is 17<\/p>\n<p>Question 37.<br \/>\n2a<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n2a<br \/>\ngiven data<br \/>\na = 3<br \/>\nnow substitute given data in the equation we get<br \/>\n2(3) = 6<br \/>\nHence the answer is 6<\/p>\n<p>Question 38.<br \/>\nc \u00f7 6<\/p>\n<p>Answer: 2<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\nc \u00f7 6<br \/>\ngiven data<br \/>\nc = 12<br \/>\nnow substitute given data in the equation we get<br \/>\n12 \u00f7 6 = 2<br \/>\nHence the answer is 2<\/p>\n<p>Question 39.<br \/>\na + b<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\na + b<br \/>\ngiven data<br \/>\na = 3, b = 2<br \/>\nnow substitute given data in equation we get<br \/>\n3 + 2 = 5<br \/>\nhence the answer is 5<\/p>\n<p>Question 40.<br \/>\nc + a<\/p>\n<p>Answer: 15<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\na + b<br \/>\ngiven data<br \/>\na = 3, b = 2<br \/>\nnow substitute given data in equation we get<br \/>\n3 + 2 = 5<br \/>\nhence the answer is 5<\/p>\n<p>Question 41.<br \/>\nc &#8211; a<\/p>\n<p>Answer: 11<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\nc &#8211; a<br \/>\ngiven data<br \/>\na = 3, c = 12<br \/>\nnow substitute given data in equation we get<br \/>\n12 &#8211; 3 = 11<br \/>\nhence the answer is 11<\/p>\n<p>Question 42.<br \/>\na &#8211; b<\/p>\n<p>Answer: 1<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\na &#8211; b<br \/>\ngiven data<br \/>\na = 3, b = 2<br \/>\nnow substitute given data in equation we get<br \/>\n3 &#8211; 2 = 1<br \/>\nhence the answer is 1<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{c}{a}\\)<\/p>\n<p>Answer: 4<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n\\(\\frac{c}{a}\\)<br \/>\ngiven data<br \/>\na = 3, c = 12<br \/>\nnow substitute given data in equation we get<br \/>\n\\(\\frac{12}{3}\\) = 4<br \/>\nhence the answer is 4<\/p>\n<p>Question 44.<br \/>\n\\(\\frac{c}{b}\\)<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\n\\(\\frac{c}{b}\\)<br \/>\ngiven data<br \/>\nb = 2, c = 12<br \/>\nnow substitute given data in equation we get<br \/>\n\\(\\frac{12}{2}\\) = 6<br \/>\nhence the answer is 6<\/p>\n<p>Question 45.<br \/>\nb.c<\/p>\n<p>Answer: 24<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\nb . a<br \/>\ngiven data<br \/>\nb = 2, c = 12<br \/>\nnow substitute given data in equation we get<br \/>\n2(12) = 24<br \/>\nhence the answer is 24<\/p>\n<p>Question 46.<br \/>\nc(a)<\/p>\n<p>Answer: 36<\/p>\n<p>Explanation:<br \/>\nGiven equation<br \/>\nc(a)<br \/>\ngiven data<br \/>\na = 3, c = 12<br \/>\nnow substitute given data in equation we get<br \/>\n12(3) = 36<br \/>\nhence the answer is 36<\/p>\n<p>Question 47.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou earn 15n dollars for mowing n lawns. How much do you earn for mowing 1 lawn? 7 lawns?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nYou earn 15n dollars for mowing n lawns.<br \/>\nn = 1<br \/>\n15 \u00d7 1 = 15<br \/>\nn = 7<br \/>\n15 \u00d7 7 = 105<br \/>\nThus you earn $15 for mowing 1 lawn and $105 for mowing 7 lawns.<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Copy and complete the table.<\/strong><\/p>\n<p>Question 48.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24753\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-25.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 25\" width=\"170\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34656\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-25-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-25\" width=\"170\" height=\"79\" \/><br \/>\nExplanation:<br \/>\nGiven data from the table<br \/>\nx = 3 ,6, and 9<br \/>\nsubstitute x values in the given equation x . 8<br \/>\n3(8) = 24<br \/>\n6(8) = 48<br \/>\n9(8) = 72<\/p>\n<p>Question 49.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24754\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-26.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 26\" width=\"184\" height=\"73\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-34658\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-26-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-26\" width=\"184\" height=\"73\" \/><br \/>\nExplanation:<br \/>\nGiven data from the table<br \/>\nx = 2 ,4, and 8<br \/>\nsubstitute x values in the given equation 64 \u00f7 x = 24<br \/>\n64 \u00f7 2 = 32<br \/>\n64 \u00f7 4 = 16<br \/>\n64 \u00f7 8 = 8<\/p>\n<p>Question 50.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nDue to gravity, an object falls 16t<sup>2<\/sup> feet in t seconds. You drop a rock from a bridge that is 75 feet above the water. Will the rock hit the water in 2 seconds? Explain.<\/p>\n<p>Answer:\u00a0 No<br \/>\nGiven<br \/>\nDue to gravity, an object falls 16t2 feet in t seconds. You drop a rock from a bridge that is 75 feet above the water<br \/>\nd = 16t\u00b2 (d in ft, t in sec)<br \/>\nSet d = 75 ft and solve for t.<br \/>\n75 = 16t\u00b2<br \/>\nt = \u221a(75\/16) sec \u2245 2.17 sec<br \/>\nIt hits the water in 2.17 sec.<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Evaluate the expression when a = 10, b = 9, and c = 4.<\/strong><\/p>\n<p>Question 51.<br \/>\n2a + 3<\/p>\n<p>Answer: 23<br \/>\nGiven equation<br \/>\n2a + 3<br \/>\ngiven data<br \/>\na = 10,<br \/>\nnow substitute given data in equation we get<br \/>\n2(10)+3<br \/>\n= 20 + 3<br \/>\n= 23<br \/>\nhence the answer is 23<\/p>\n<p>Question 52.<br \/>\n4c &#8211; 7.8<\/p>\n<p>Answer:<br \/>\nGiven equation<br \/>\n4c &#8211; 7.8<br \/>\ngiven data<br \/>\na = 10,<br \/>\nnow substitute given data in equation we get<br \/>\n4(4) &#8211; 7.8<br \/>\n= 16 &#8211; 7.8<br \/>\n= 8.2<br \/>\nHence the answer is 8.2<\/p>\n<p>Question 53.<br \/>\n\\(\\frac{a}{4}\\) + \\(\\frac{1}{3}\\)<\/p>\n<p>Answer: \\(\\frac{17}{6}\\) or 2.83<br \/>\nGiven equation<br \/>\n\\(\\frac{a}{4}\\) + \\(\\frac{1}{3}\\)<br \/>\ngiven data<br \/>\na = 10,<br \/>\nnow substitute given data in equation we get<br \/>\n\\(\\frac{10}{4}\\) + \\(\\frac{1}{3}\\)<br \/>\n= \\(\\frac{17}{6}\\)<br \/>\n= 2.83<br \/>\nhence the answer is \\(\\frac{17}{6}\\) or 2.83<\/p>\n<p>Question 54.<br \/>\n\\(\\frac{24}{b}\\) + 8<\/p>\n<p>Answer:<br \/>\n\\(\\frac{32}{3}\\) or 10.66<br \/>\nGiven equation<br \/>\n\\(\\frac{24}{b}\\) + 8<br \/>\ngiven data<br \/>\nb = 9,<br \/>\nnow substitute given data in equation we get<br \/>\n\\(\\frac{24}{9}\\) + 8<br \/>\n= \\(\\frac{8}{3}\\) + 8<br \/>\n= \\(\\frac{32}{3}\\)<br \/>\n= 10.66<br \/>\nHence the answer is \\(\\frac{32}{3}\\) or 10.66<\/p>\n<p>Question 55.<br \/>\nc<sup>2<\/sup> + 6<\/p>\n<p>Answer: 22<br \/>\nGiven equation<br \/>\nc\u00b2 + 6<br \/>\ngiven data<br \/>\nc = 4,<br \/>\nnow substitute given data in equation we get<br \/>\nc\u00b2 + 6<br \/>\n= 4\u00b2 + 6<br \/>\n= (4 \u00d7 4) + 6<br \/>\n= 16 + 6<br \/>\n= 22<br \/>\nHence the answer is 22<\/p>\n<p>Question 56.<br \/>\na<sup>2<\/sup> &#8211; 18<\/p>\n<p>Answer: 82<br \/>\nGiven equation<br \/>\na\u00b2 &#8211; 18<br \/>\ngiven data<br \/>\na = 10,<br \/>\nnow substitute given data in equation we get<br \/>\na\u00b2 &#8211; 18<br \/>\n= 10\u00b2 &#8211; 18<br \/>\n= (10 \u00d7 10) &#8211; 18<br \/>\n= 100 &#8211; 18<br \/>\n= 82<br \/>\nHence the answer is 82<\/p>\n<p>Question 57.<br \/>\na + 9c<\/p>\n<p>Answer: 40<br \/>\nGiven equation<br \/>\na\u00a0 + 9c<br \/>\ngiven data<br \/>\na = 10, c = 4<br \/>\nnow substitute given data in equation we get<br \/>\n10 + 9(4)<br \/>\n= 10 + 36<br \/>\n= 46<br \/>\nHence the answer is 46<\/p>\n<p>Question 58.<br \/>\nbc + 12.3<\/p>\n<p>Answer: 48.3<br \/>\nbc + 12.3<br \/>\ngiven data<br \/>\nb = 9, c = 4<br \/>\nnow substitute given data in equation we get<br \/>\n9(4) + 12.3<br \/>\n= 36 + 12.3<br \/>\n= 48.3<br \/>\nHence the answer is 48.3<\/p>\n<p>Question 59.<br \/>\n3a + 2b &#8211; 6c<\/p>\n<p>Answer: 24<br \/>\n3a + 2b &#8211; 6c<br \/>\ngiven data<br \/>\na = 10, b = 9, c = 4<br \/>\nnow substitute given data in equation we get<br \/>\n3(10) + 2(9) &#8211; 6(4)<br \/>\n= 30 + 18 &#8211; 24<br \/>\n= 24<br \/>\nHence the answer is 24<\/p>\n<p>Question 60.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend evaluates the expression when m = 8. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24755\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-27.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 27\" width=\"189\" height=\"121\" \/><\/p>\n<p>Answer:\u00a0 incorrect.<\/p>\n<p>Explanation:<br \/>\nGiven the expression 5m + 3<br \/>\nm = 8<br \/>\n5 \u00d7 8 + 3<br \/>\n40 + 3 = 43<br \/>\nBy this we can say that your friend is incorrect.<\/p>\n<p>Question 61.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nAfter m months, the height of a plant is (10 + 3m) millimeters. How tall is the plant after 8 months? 3 years?<\/p>\n<p>Answer:<br \/>\n8 months = 34 millimeters<br \/>\nEXPLANATION:<br \/>\nYou have to plug in the number 8 as \u201cm\u201d in the equation then solve. 10 + 3(8)<br \/>\n3 years = 118 millimeters<br \/>\n3 years converted to months would be 12&#215;3 which equals 36. Then put it into the equation 10 + 3(36) and you do the multiplication first.<\/p>\n<p>Question 62.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nYou use a video streaming service to rent x new releases and y standard rentals. Which expression tells you how much money you will need?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24756\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-28.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 28\" width=\"294\" height=\"51\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24757\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-29.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 29\" width=\"248\" height=\"357\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-29.png 248w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-29-208x300.png 208w\" sizes=\"(max-width: 248px) 100vw, 248px\" \/><\/p>\n<p>Answer:<br \/>\n4x+3y<\/p>\n<p>Explanation:<br \/>\nIt is given that,<br \/>\nThe number of new releases are represented by &#8216;x&#8217; and number of standard rentals are represented by &#8216;y&#8217;.<br \/>\nAlso, the cost for one new release = $4 and the cost of one standard rental = $3.<br \/>\nThus, the cost of &#8216;x&#8217; new releases = $4x and the cost of &#8216;y&#8217; new releases = $3y.<br \/>\nSo, the total cost = cost of &#8216;x&#8217; new releases + cost of &#8216;y&#8217; standard rentals.<br \/>\ni.e. Total cost = 4x + 3y in dollars.<br \/>\nThus, the expression to tell the money required is 4x+3y.<\/p>\n<p>Question 63.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nYou \ufb02oat 2000 feet along a lazy river water ride. The ride takes less than 10 minutes. Give two examples of possible times and speeds.<\/p>\n<p>Answer:<br \/>\nif you travel at 200 feet per minute you can make in ten minutes<\/p>\n<p>Question 64.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe expression 20a + 13c is the cost (in dollars) for a adults and c students to enter a science center.<br \/>\na. How much does it cost for an adult? a student? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nIt costs $20 per adult. If this is a cost function,<br \/>\nwhich it is because the wording is &#8220;the cost (in dollars) for adults and c students&#8221;, the adult is the cost for 1 adult, 1a, is 20.<br \/>\nThat relates the number of adults to the cost of 1 adult.<br \/>\nIt costs $13 per student. Again, this is a cost function, so since the student is c,<br \/>\nthe cost for 1 student, 1c, is 13. That relates the number of students to the cost of 1 student.<\/p>\n<p>b. Find the total cost for 4 adults and 24 students.<\/p>\n<p>Answer:<br \/>\nThe total cost for 4 adult and 24 students looks like this:<br \/>\n20(4) + 13(24) which is 80 + 312 = $392<\/p>\n<p>c. You \ufb01nd the cost for a group. Then the numbers of adults and students in the group both double. Does the cost double? Explain your answer using an example.<\/p>\n<p>Answer:<br \/>\nIf you have 3 adults and 3 students in your group, the cost is 20(3) + 13(3) which is $99.<br \/>\nIf you double the number of each, let&#8217;s see if the cost doubles.<br \/>\nWe will &#8220;up&#8221; the numbers to 6 each. 20(6) + 13(6) = $198. Is $198 the double of $99.<br \/>\nYes it is. Let&#8217;s do it again to check. Let&#8217;s double the 6.<br \/>\n20(12) + 13(12) = $396, and $198 doubled does in fact equal $396<\/p>\n<p>d. In part(b), the number of adults is cut in half, but the number of students doubles. Is the cost the same? Explain your answer.<\/p>\n<p>Answer:<br \/>\n20(12) + 13(12) = $396, and $198 doubled does in fact equal $396.<\/p>\n<p>Question 65.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe volume of the cube (in cubic inches) is equal to four times the area of one of its faces (in square inches). What is the volume of the cube?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24758\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-30.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 30\" width=\"126\" height=\"147\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThe volume of the cube (in cubic inches) is equal to four times the area of one of its faces (in square inches).<br \/>\nWe know that,<br \/>\nThe volume of a cube = x\u00b3<br \/>\nMultiply 3 sides = x \u00d7 x \u00d7 x = x\u00b3<\/p>\n<h3><a id=\"Lesson_5.2_Writing_Expressions\"><\/a>Lesson 5.2 Writing Expressions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Writing Expressions<\/strong><br \/>\n<strong>Work with a partner. You use a $20 bill to buy lunch at a caf\u00e9. You order a sandwich from the menu board shown.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24759\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-31.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 31\" width=\"365\" height=\"290\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-31.png 365w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-31-300x238.png 300w\" sizes=\"(max-width: 365px) 100vw, 365px\" \/><br \/>\na. Complete the table. In the last column, write a numerical expression for the amount of change you receive.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24761\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 32\" width=\"351\" height=\"188\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32.png 351w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32-300x161.png 300w\" sizes=\"(max-width: 351px) 100vw, 351px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-34675\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32-1-300x161.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32\" width=\"300\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32-1-300x161.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32-1.png 351w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. Write an algebraic expression that represents the amount of change you receive when you order any sandwich from the menu board.<\/p>\n<p>Answer:<br \/>\nYou have only $20 for lunch, so if you order any sandwich from the menu<br \/>\nthe board then the amount will be change<br \/>\nif you ordered chicken salad then your changing amount is<br \/>\nprice = $ 4.95<br \/>\nchange Received = $20 &#8211; $4.95 = $15.05<br \/>\nchange Received = $15.05<\/p>\n<p>c. The expression 20 \u2212 4.65 represents the amount of change one customer receives after ordering from the menu board. Explain what each part of the expression represents. Do you know what the customer ordered? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24760\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-32.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 32.1\" width=\"156\" height=\"175\" \/><\/p>\n<p>Answer:<br \/>\ncalculated changing amount for chicken salad in part (b),<br \/>\nso comparison between chicken salad expression and beef expression<br \/>\nFor Chicken salad<br \/>\nPrice = $4.95<br \/>\nchange Recived = $20 &#8211; $4.95 = $15.05<br \/>\nchange Recieved = $15.05<br \/>\nFor Roast Beef<br \/>\nprice = $6.75<br \/>\nChange Recived = $20 &#8211; $6.75 = $13.25<br \/>\nchange Recived = $13.25<\/p>\n<p><strong>5.2 Lesson<\/strong><\/p>\n<p>Some words can imply math operations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24762\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-33.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 33\" width=\"572\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-33.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-33-300x103.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Write the phrase as an expression.<\/strong><\/p>\n<p>Question 1.<br \/>\nthe sum of 18 and 35<\/p>\n<p>Answer: 53<br \/>\nGiven<br \/>\nthe sum of 18 and 35<br \/>\nso by add 18 with 35<br \/>\nwe get 18+35<br \/>\n=53<br \/>\nSo the answer is 53<\/p>\n<p>Question 2.<br \/>\n6 times 50<\/p>\n<p>Answer: 300<br \/>\ngiven<br \/>\n6 times 50<br \/>\nso multiply 6 with 50 we get<br \/>\n300<br \/>\nHence the answer is 300<\/p>\n<p><strong>Write the phrase as an expression.<\/strong><\/p>\n<p>Question 3.<br \/>\n25 less than a number b<\/p>\n<p>Answer: b &#8211; 25<\/p>\n<p>Question 4.<br \/>\na number x divided by 4<\/p>\n<p>Answer:\u00a0 \\(\\frac{x}{4}\\)<\/p>\n<p>Question 5.<br \/>\nthe total of a number t and 11<\/p>\n<p>Answer: t + 11<\/p>\n<p>Question 6.<br \/>\n100 decreased by a number k.<\/p>\n<p>Answer: 100 &#8211; k<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 7.<br \/>\nYour friend has 5 more than twice as many game tokens as you. Let t be the number of game tokens you have. Write an expression for the number of game tokens your friend has.<\/p>\n<p>Answer: 5+2t<br \/>\ngiven<br \/>\nYour friend has 5 more than twice as many game tokens as you<br \/>\n5+2t because 5 more then is adding 5 and twice as many is doubling or multiplying by 2<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>WRITING EXPRESSIONS<\/strong><br \/>\n<strong>Write the phrase as an expression.<\/strong><\/p>\n<p>Question 8.<br \/>\nthe sum of 7 and 11<\/p>\n<p>Answer: 7 + 11 we get 18<\/p>\n<p>Question 9.<br \/>\n5 subtracted from 9<\/p>\n<p>Answer: 9 &#8211; 5 we get 4<\/p>\n<p>Question 10.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Write \u201cboth\u201d expressions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24763\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-34.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 34\" width=\"346\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-34.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-34-300x80.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Answer: 12 more than x and x increased by 12 has different words but the question is same.<\/p>\n<p>Question 11.<br \/>\n<strong>PRECISION<\/strong><br \/>\nYour friend says that the phrases below have the same meaning. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24764\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-35.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 35\" width=\"284\" height=\"90\" \/><\/p>\n<p>Answer: No your friend is incorrect.<br \/>\n&#8220;the difference of number x and 12&#8221; is x &#8211; 12<br \/>\n&#8220;the diffrence of 12 and number x&#8221; is 12 &#8211; x<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 12.<br \/>\nA company rents paddleboards by charging a rental fee plus an hourly rate. Write an expression that represents the cost (in dollars) of renting a paddleboard for h hours. How much does an eight-hour rental cost?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24765\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-36.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 36\" width=\"218\" height=\"244\" \/><\/p>\n<p>Answer:<br \/>\nThe independent variable is that whose values do not take into account the values of other variables.<br \/>\nThat is the time in hours for this item. Then, for the dependent variable, the answer would be the cost of renting.<br \/>\nThe value of the dependent variable is based on the changes done in the values of the independent variable.<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA county fair charges an entry fee of $7 and $0.75 for each ride token. You have $15. Write an expression that represents the amount (in dollars) you have left after entering the fair and purchasing n tokens. How many tokens can you purchase? How much money do you have left after purchasing 6 tokens?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24766\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-37.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 37\" width=\"150\" height=\"154\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA county fair charges an entry fee of $7 and $0.75 for each ride token.<br \/>\nYou have $15.<br \/>\n15.00 &#8211; 7.00 = 8.00<br \/>\n6 x .75 = 4.50<br \/>\n8.00- 4.5 = 3.50<\/p>\n<h3><a id=\"Writing_Expressions_Homework_&amp;_Practice_5.2\"><\/a>Writing Expressions Homework &amp; Practice 5.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Identify the terms, coefficients, and constants in the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n4f + 8<\/p>\n<p>Answer:<br \/>\n8 &#8211; constant<br \/>\n4 &#8211; coefficient<br \/>\nf- variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{4}{5}\\) + 3s + 2<\/p>\n<p>Answer:<br \/>\n\\(\\frac{4}{5}\\) and 2 &#8211; constant<br \/>\n3 &#8211; coefficient<br \/>\ns- variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 3.<br \/>\n9h<sup>2<\/sup> + \\(\\frac{8}{9}\\)p + 1<\/p>\n<p>Answer:<br \/>\n1 &#8211; constant<br \/>\n2 &#8211; exponent<br \/>\n9 and \\(\\frac{8}{9}\\) \u00a0&#8211; coefficient<br \/>\nh and p &#8211; variable or term<br \/>\nAn exponent is a number or letter written above and to the right of a mathematical expression called the base<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p><strong>Copy and complete the statement.<\/strong><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24767\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-38.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 38\" width=\"125\" height=\"55\" \/><\/p>\n<p>Answer: 7.5 gallon per hour<\/p>\n<p>Explanation:<br \/>\nConvert from cup per minute to gallon per hour<br \/>\n1 Cup per minute = 3.75 gallon per hour<br \/>\n2 cup per minute = 2 \u00d7 3.75 = 7.5 gallon per hour<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24768\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-39.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 39\" width=\"112\" height=\"56\" \/><\/p>\n<p>Answer: 2362.2 feet per minute<\/p>\n<p>Explanation:<br \/>\nConvert from meter per second to feet per minute<br \/>\n1 meter per second = 196.85 feet per minute<br \/>\n12 minute per second = 2362.2 feet per minute<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24769\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-40.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 40\" width=\"119\" height=\"64\" \/><\/p>\n<p>Answer: 4898.79 kg per hour<\/p>\n<p>Explanation:<br \/>\nConvert from lb per second to kg per hour<br \/>\n1 lb per second = 1632.93 kg per hour<br \/>\n3 lb per second = 4898.79 kg per hour<\/p>\n<p><strong>Divide. Write the answer in simplest form.<\/strong><\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24770\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-41.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 41\" width=\"55\" height=\"50\" \/><\/p>\n<p>Answer:\u00a0 \\(\\frac{8}{9}\\) or 0.533<\/p>\n<p>Explanation:<br \/>\nby dividing \\(\\frac{1}{2}\\) with \\(\\frac{5}{8}\\)<br \/>\nwe get \\(\\frac{1}{2}\\) \u00f7 \\(\\frac{5}{8}\\)<br \/>\n\\(\\frac{8}{9}\\)<br \/>\n0.533<\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-42.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 42\" width=\"64\" height=\"57\" \/><\/p>\n<p>Answer: \\(\\frac{4}{9}\\)<\/p>\n<p>Explanation:<br \/>\nby dividing \\(\\frac{1}{3}\\) with \\(\\frac{3}{4}\\)<br \/>\nwe get \\(\\frac{1}{3}\\) \u00f7 \\(\\frac{3}{4}\\)<br \/>\n\\(\\frac{4}{9}\\)<br \/>\n0.44<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-43.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 43\" width=\"49\" height=\"56\" \/><\/p>\n<p>Answer: \\(\\frac{2}{15}\\) or 0.133<\/p>\n<p>Explanation:<br \/>\nby dividing \\(\\frac{2}{5}\\) with \\(\\frac{3}{1}\\)<br \/>\nwe get \\(\\frac{2}{5}\\) \u00f7 \\(\\frac{3}{1}\\)<br \/>\n\\(\\frac{2}{15}\\)<br \/>\n0.133<\/p>\n<p>Question 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-44.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 44\" width=\"56\" height=\"58\" \/><\/p>\n<p>Answer: \\(\\frac{7}{2}\\) or 3.5<\/p>\n<p>Explanation:<br \/>\nby dividing \\(\\frac{3}{1}\\) with \\(\\frac{6}{7}\\)<br \/>\nwe get \\(\\frac{3}{1}\\) \u00f7 \\(\\frac{6}{7}\\)<br \/>\n\\(\\frac{7}{2}\\)<br \/>\n3.5<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>STRUCTURE<\/strong><br \/>\n<strong>The expression represents the amount of change you receive after buying n sandwiches. Explain what each part of the expression represents.<\/strong> (See Exploration 1, p. 209.)<\/p>\n<p>Question 11.<br \/>\n10 &#8211; 5.25n<\/p>\n<p>Answer:<br \/>\nLet us assume that you buy 1 sandwich.<br \/>\n10 &#8211; 5.25(1)<br \/>\n= 10 &#8211; 5.25<br \/>\n= 4.75<\/p>\n<p>Question 12.<br \/>\n20 &#8211; 4.95n<\/p>\n<p>Answer:<br \/>\nLet us assume that you buy 2 sandwiches.<br \/>\n20 &#8211; 4.95(2)<br \/>\n20 &#8211; 9.9 = 10.1<\/p>\n<p>Question 3.<br \/>\n100 &#8211; 6.75n<\/p>\n<p>Answer:<br \/>\nLet us assume that you buy 6 sandwiches.<br \/>\n100 &#8211; 6.75(6)<br \/>\n= 100 &#8211; 40.50<br \/>\n= 59.50<\/p>\n<p><strong>WRITING EXPRESSIONS<\/strong><br \/>\n<strong>Write the phrase as an expression.<\/strong><\/p>\n<p>Question 14.<br \/>\n5 less than 8<\/p>\n<p>Answer: 5 &lt; 8<\/p>\n<p>Explanation:<br \/>\nThe phrase &#8220;less than&#8221; indicates &lt; symbol.<br \/>\nSo, the expression is 5 &lt; 8<\/p>\n<p>Question 15.<br \/>\nthe product of 3 and 12<\/p>\n<p>Answer: 3 \u00d7 12<\/p>\n<p>Explanation:<br \/>\nThe phrase &#8220;product&#8221; indicates multiplication.<br \/>\nSo, the expression is 3 \u00d7 12<\/p>\n<p>Question 16.<br \/>\n28 divided by 7<\/p>\n<p>Answer: 28 \u00f7 7<\/p>\n<p>Explanation:<br \/>\nThe phrase &#8220;divided by&#8221; indicates \u00f7 symbol<br \/>\nSo, the expression is 28 \u00f7 7<\/p>\n<p>Question 17.<br \/>\nthe total of 6 and 10<\/p>\n<p>Answer: 6 + 10 = 16<\/p>\n<p>Explanation:<br \/>\nThe phrase &#8220;total&#8221; indicates &#8216;+&#8217; symbol.<br \/>\nSo, the expression is 6 + 10 = 16<\/p>\n<p>Question 18.<br \/>\n3 fewer than 18<\/p>\n<p>Answer: 18 &#8211; 3<\/p>\n<p>Explanation:<br \/>\nThe phrase fewer than indicates &#8216;subtraction&#8217;<br \/>\nSo, the expression is 18 &#8211; 3<\/p>\n<p>Question 19.<br \/>\n17 added to 15<\/p>\n<p>Answer: 17 + 15<\/p>\n<p>Explanation:<br \/>\nGiven 17 added to 15<br \/>\nso add 17 with 15<\/p>\n<p>Question 20.<br \/>\n13 subtracted from a number x<\/p>\n<p>Answer: 13 &#8211; x<\/p>\n<p>Explanation:<br \/>\nThe number represents the variable x<br \/>\nSo here we have to subtract number x from 13<br \/>\nThat gives the expression 13 &#8211; x<\/p>\n<p>Question 21.<br \/>\n5 times a number d<\/p>\n<p>Answer: 5d<\/p>\n<p>Explanation:<br \/>\nThe number represents variable d.<br \/>\nThe word &#8220;times&#8221; represents \u00d7<br \/>\nSo the expression is 5d<\/p>\n<p>Question 22.<br \/>\nthe quotient of 18 and a number a<\/p>\n<p>Answer: 18 \u00f7 a<\/p>\n<p>Explanation:<br \/>\na represents the number<br \/>\nSo, the expression would be 18 \u00f7 a<\/p>\n<p>Question 23.<br \/>\nthe difference of a number s and 6<\/p>\n<p>Answer: s &#8211; 6<\/p>\n<p>Question 24.<br \/>\n7 increased by a number w<\/p>\n<p>Answer: 7 + w<\/p>\n<p>Question 25.<br \/>\na number t cubed<\/p>\n<p>Answer: t\u00b3<\/p>\n<p><strong>YOU BE THE TEACHER<\/strong><br \/>\n<strong>Your friend writes the phrase as an expression. Is your friend correct? Explain your reasoning.<\/strong><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-45.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 45\" width=\"195\" height=\"86\" \/><\/p>\n<p>Answer: incorrect<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe quotient of 8 and a number is y is 8 \u00f7 y<br \/>\nBy this, we can say that your friend is incorrect.<\/p>\n<p>Question 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-46.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 46\" width=\"201\" height=\"94\" \/><\/p>\n<p>Answer: correct<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n16 decreased by a number x<br \/>\nIt means we have to subtract x from 16.<br \/>\nThus the expression is 16 &#8211; x.<\/p>\n<p>Question 28.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nFive friends share the cost of a dinner equally.<br \/>\na. Write an expression that represents the cost (in dollars) per person.<\/p>\n<p>Answer: 600 \u00f7 p<\/p>\n<p>b. Make up a reasonable total cost and test your expression.<\/p>\n<p>Answer:<br \/>\nThe total cost of dinner is $600.<br \/>\nNow divide the cost per person.<br \/>\nThere are 5 friends.<br \/>\nThe expression is 600 \u00f7 p<br \/>\np = 5<br \/>\n600 \u00f7 5 = 12<br \/>\nThe cost per person is $120<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA biologist analyzes 15 bacteria samples each day.<br \/>\na. Copy and complete the table.<br \/>\nb. Write an expression that represents the total number of samples analyzed after n days.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-47.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 47\" width=\"309\" height=\"79\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-47.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-47-300x77.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-37594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-47-300x77.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-47\" width=\"300\" height=\"77\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-47-300x77.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-47.jpg 309w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe expression that represents the total number of samples analyzed after n days is 15n<\/p>\n<p>Question 30.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nTo rent a moving truck for the day, it costs $33 plus $1 for each mile driven.<br \/>\na. Write an expression that represents the cost (in dollars) to rent the truck.<\/p>\n<p>Answer: 33 + d<br \/>\nb. You drive the truck 300 miles. How much do you pay?<\/p>\n<p>Answer:<br \/>\nUse the expression 33 + d to find how much do you pay.<br \/>\n33 + 300 = 333<br \/>\nThus you pay $333 for 300 miles.<\/p>\n<p><strong>WRITING PHRASES<\/strong><br \/>\nGive two ways to write the expression as a phrase.<\/p>\n<p>Question 31.<br \/>\nn + 6<\/p>\n<p>Answer:<br \/>\nAccording to the given details, we can write the expression in two ways<br \/>\na number n more than 6<br \/>\nthe sum of a number n and 6<\/p>\n<p>Question 32.<br \/>\n4w<\/p>\n<p>Answer:<br \/>\nAccording to the given details, we can write the expression in two ways<br \/>\na number w is four times<br \/>\nThe product of 4 and a number w<\/p>\n<p>Question 33.<br \/>\n15 &#8211; b<\/p>\n<p>Answer:<br \/>\nAccording to the given details we can write the expression in two ways.<br \/>\n15 decreased by a number d<br \/>\nThe difference of 15 and a number b<\/p>\n<p>Question 34.<br \/>\n14 &#8211; 3z<\/p>\n<p>Answer:<br \/>\nAccording to the given details, we can write the expression in two ways.<br \/>\nThe product of 3 and z subtracted from 14.<br \/>\nThe difference of 14 and product of 3 and a number z.<\/p>\n<p><strong>EVALUATING EXPRESSIONS<\/strong><br \/>\n<strong>Write the phrase as an expression. Then evaluate the expression when x = 5 and y = 20.<\/strong><\/p>\n<p>Question 35.<br \/>\n3 less than the quotient of a number y and 4<\/p>\n<p>Answer:<br \/>\ngiven 3 less than the quotient of a number y and 4<br \/>\nThe quotient of a number y and 4<br \/>\nNow we are given that 3 less than the quotient of a number y and 4<br \/>\nSo, \\(\\frac{y}{4}\\) &#8211; 3<br \/>\nHence the expression becomes \\(\\frac{y}{4}\\) &#8211; 3<\/p>\n<p>Question 36.<br \/>\nthe sum of a number x and 4, all divided by 3<\/p>\n<p>Answer:<br \/>\ngiven<br \/>\na sum, x and 4, so that becomes x + 4<br \/>\nAll divided by denotes that we need to do the addition before division, so we need to put it in parentheses:<br \/>\n(x + 4)<br \/>\nAnd it is divided by 3.<br \/>\nSo you can write the answer down in a few different ways:<br \/>\n(x + 4) \u00f7 3<br \/>\n(x + 4) \/ 3<br \/>\n\\(\\frac{x + 4}{3}\\)<\/p>\n<p>Question 37.<br \/>\n6 more than the product of 8 and a number x<\/p>\n<p>Answer:<br \/>\nA Product is an answer to a multiplication.<br \/>\nThe product of 8 and a number is 8\u00d7n=8n<br \/>\n6 more than that means to add on 6<br \/>\nSo the expression &#8220;6 more than the product of 8 and a number&#8221; is<br \/>\n8n+6<\/p>\n<p>Question 38.<br \/>\nthe quotient of 40 and the difference of a number y and 16<\/p>\n<p>Answer:<br \/>\nas we know that<br \/>\nThe expression &#8221; the quotient of and the difference of a number y and &#8221; is equivalent to the algebraic equation<br \/>\n\\(\\frac{40}{y-16}\\)<br \/>\nFor\u00a0 y = 20\u00a0 given problem<br \/>\nsubstitute the value of y in the equation<br \/>\n\\(\\frac{40}{20-16}\\)\u00a0 = \\(\\frac{40}{4}\\) = 10<\/p>\n<p>Question 39.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nIt costs $3 to bowl a game and $2 for shoe rental.<br \/>\na. Write an expression that represents the total cost (in dollars) of g games.<br \/>\nb. Use your expression to \ufb01nd the total cost of 8 games.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-48.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 48\" width=\"221\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\na. If shoes are for all games in row, P=2+3g<br \/>\nb. If not, P=5g, with g the number of games<br \/>\nExplanation:<br \/>\nThe price depends if shoes are included for the whole games, you just have to pay them once and then you have to pay g games, so P(g)=2+3g<br \/>\nElse, you have to pay for g shoes and g bowl party, so P(g)=2g+3g\u21d4P(g)=5g<\/p>\n<p>Question 40.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nFlorida has 8 less than 5 times the number of counties in Arizona. Georgia has 25 more than twice the number of counties in Florida.<br \/>\na. Write an expression that represents the number of counties in Florida.<br \/>\nb. Write an expression that represents the number of counties in Georgia.<br \/>\nc. Arizona has 15 counties. How many do Florida and Georgia have?<\/p>\n<p>Answer:<br \/>\nNumber of countries in Florida=5\u00d7a-8<br \/>\nNumber of countries in Georgia=2\u00d7f+25<br \/>\nExplanation:<br \/>\nGiven that the number of countries in Florida is denoted by f,<br \/>\nThe number of countries in Arizona is given by a and the number of countries in Georgia is given by g.<br \/>\nas Florida has 8 less than five times the number of countries in Arizona<br \/>\nSo f=5\u00d7a-8<br \/>\nGeorgia has 25 more than twice the number of countries in Florida<br \/>\nSo g=2\u00d7f+25<br \/>\nNow it is given that Arizona has 15 countries i.e. a=15<br \/>\nSo f=5\u00d715-8<br \/>\nf=67<br \/>\ng=2\u00d767+25<br \/>\ng=159<br \/>\nHence, the number of countries in Florida is:67<br \/>\nnumber of countries in Georgia is:159<\/p>\n<p>Question 41.<br \/>\n<strong>PATTERNS<\/strong><br \/>\nThere are 140 people in a singing competition. The graph shows the results for the \ufb01rst \ufb01ve rounds.<br \/>\na. Write an expression that represents the number of people after each round.<br \/>\nb. Assuming this pattern continues, how many people compete in the ninth round? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 49\" width=\"290\" height=\"198\" \/><\/p>\n<p>Answer:<br \/>\na) The expression is y = 140 &#8211; 15 x<br \/>\nb ) There are 5 participants in the 9th round<\/p>\n<p>Step-by-step explanation:<br \/>\nStep 1 :<br \/>\nFrom the graph we can see that,<br \/>\nNumber of people in the singing competition = 140<br \/>\nNumber of people in the first round = 125<br \/>\nNumber of people in the second round = 110<br \/>\nNumber of people in the third round = 95<br \/>\nNumber of people in the fourth round = 80<br \/>\nNumber of people in the fifth round = 65<br \/>\nStep 2 :<br \/>\nFrom the given data, We can get that the difference between the number of people participating in each round is 15 less than the previous round .<br \/>\nThe first round has 15 people less than the total number of 140<br \/>\nLet x represent the number of the round and y represent the number of people participating in each round .<br \/>\nThen the expression to represent this would be<br \/>\ny = 140 &#8211; 15 x<br \/>\nStep 3 :<br \/>\nTo find the number of participants in the 9th round given the same pattern continues.<br \/>\nFor the 9th round x = 9, as x represents the number of the round<br \/>\nSubstituting this in the equation obtained in step 2, we get<br \/>\ny = 140 -15 (9) = 140 &#8211; 135 = 5<br \/>\nThere are 5 participants in the 9th round<\/p>\n<p>Question 42.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nThe difference between two numbers is 8. The lesser number is a. Write an expression that represents the greater number.<\/p>\n<p>Answer:<br \/>\nGiven The difference between the two numbers is 8. The lesser number is a.<br \/>\nb-a=8<br \/>\nb is the greater number; b&gt;a<br \/>\nSo, b=a+8<\/p>\n<p>Question 43.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nOne number is four times another. The greater number is x. Write an expression that represents the lesser number<\/p>\n<p>Answer: y = x\/4<\/p>\n<p>Let us assume the smaller number y.<br \/>\nWe know that four times the smaller number is equal to x. So, four times y is equal to x.<br \/>\nTurning this into an expression, you get 4y = x.<br \/>\nThis means, to get y on its own, we need to divide by 4 on both sides, giving us the answer of y = x\/4<\/p>\n<h3><a id=\"Lesson_5.3_Properties_of_Addition_and_Multiplication\"><\/a>Lesson 5.3 Properties of Addition and Multiplication<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p><strong>Identifying Equivalent Expressions<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Choose four values for a variable x. Then evaluate each expression for each value of x. Are any of the expressions equivalent? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 49.1\" width=\"507\" height=\"282\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.1.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.1-300x167.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-37597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.1-300x167.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.1\" width=\"300\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.1-300x167.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-49.1.jpg 507w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe equation x + 8, 4 + 4 + x, x + 4 + 4 are equal.<br \/>\nThe equation 16x, 4.(x.4), (4.x).x are equal.<br \/>\nb. You have used the following properties in a previous course. Use the examples to explain the meaning of each property.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-50.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 50\" width=\"498\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-50.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-50-300x93.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-51.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 51\" width=\"155\" height=\"183\" \/><br \/>\nAre these properties true for algebraic expressions? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\n<strong>Commutative property of addition:<\/strong> The commutative property of addition says that changing the order of addends does not change the sum. Here&#8217;s an example: 5 + 2 = 7 or 2 + 5 = 7<br \/>\n<strong>Commutative property of multiplication:<\/strong> The commutative property of multiplication tells us that we can multiply a string of numbers in any order. Basically: 2 x 3 x 5 will create the same answer as 3 x 5 x 2, or 2 x 5 x 3<br \/>\n<strong>Associative property of addition:<\/strong> The associative property of addition says that changing the grouping of the addends does not change the sum.<br \/>\nExample: 2 + (7 + 5) = (2 + 7) + 5<br \/>\n<strong>Associative Property of Multiplication:<\/strong> The associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.<br \/>\nExample: 2 \u00d7 (7 \u00d7 5) = (2 \u00d7 7) \u00d7 5<\/p>\n<p><strong>5.3 Lesson<\/strong><\/p>\n<p>Expressions that result in the same number for any value of each variable are equivalent expressions. You can use the Commutative and Associative Properties to write equivalent expressions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-52.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 52\" width=\"206\" height=\"93\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Simplify the expression. Explain each step.<\/p>\n<p>Question 1.<br \/>\n10 + (a + 9)<\/p>\n<p>Answer: a+19<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n10+(a+9)=10+a+9<br \/>\nStep 2:Add the numbers<br \/>\nStep 3: Rearrange terms<br \/>\na+19<\/p>\n<p>Question 2.<br \/>\n(c + \\(\\frac{2}{3}\\)) + \\(\\frac{1}{2}\\)<\/p>\n<p>Answer: c + \\(\\frac{7}{6}\\)<br \/>\n(c + \\(\\frac{2}{3}\\)) + \\(\\frac{1}{2}\\)<br \/>\nc+ \\(\\frac{7}{6}\\)<\/p>\n<p>Question 3.<br \/>\n5(4n)<\/p>\n<p>Answer: 20n<br \/>\nMultiply 5 with 4n<br \/>\nwe get 20n<\/p>\n<p><strong>Simplify the expression. Explain each step.<\/strong><\/p>\n<p>Question 4.<br \/>\n12.b.0<\/p>\n<p>Answer: 0<br \/>\nstep 1<br \/>\n12 multiply with a number b<br \/>\nand then multiply with 0<br \/>\nwe get 0<\/p>\n<p>Question 5.<br \/>\n1.m.24<\/p>\n<p>Answer: 24m<br \/>\nstep 1<br \/>\n1 multiply with a number m<br \/>\nand then multiply with 24<br \/>\nwe get 24m<\/p>\n<p>Question 6.<br \/>\n(t + 15) + 0<\/p>\n<p>Answer: t + 15<br \/>\nstep 1<br \/>\nAdd t + 15 with 0<br \/>\nand then<br \/>\nwe get t + 15<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p><strong>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/strong><\/p>\n<p><strong>USING PROPERTIES<\/strong><br \/>\n<strong>Simplify the expression. Explain each step.<\/strong><\/p>\n<p>Question 7.<br \/>\n(7 + c) + 4<\/p>\n<p>Answer:<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n4+(7+c)= 4+7+c<br \/>\nStep 2:Add the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n11 + c<\/p>\n<p>Question 8.<br \/>\n4(b.6)<\/p>\n<p>Answer: 24b<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n4 \u00d7 b\u00d7 6 = 4 \u00d7 6\u00d7 b<br \/>\nmultiply 4 with 6 we get 24 and then with b<br \/>\nso we get 24b<\/p>\n<p>Question 9.<br \/>\n0.b.9<\/p>\n<p>Answer: 0<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n0 \u00d7 b\u00d7 9 = 0 \u00d7 9\u00d7 b<br \/>\nmultiply 0 with 9 we get 0 and then with b<br \/>\nso we get 0<\/p>\n<p>Question 10.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain what it means for expressions to be equivalent. Then give an example of equivalent expressions.<\/p>\n<p>Answer:<br \/>\nequivalent expressions are algebraic expressions that, although they look different, turn out to really be the same.<\/p>\n<p>Example:<br \/>\nLet&#8217;s consider this algebraic expression: 2(x^2 + x). If we substitute 1 for the variable, the expression equals 4. But what about the expression<br \/>\n2x^2 + 2x? If, again, we substitute 1 for the variable x, we still get 4. How does this happen?<br \/>\nWhat we really did was simplify the original expression by distributing the 2 into the part in parentheses. So we really haven&#8217;t changed the expression at all &#8211; all we&#8217;ve done is rewrite it in a different form.<br \/>\nBecause these two expressions are really the same, no matter what number we substitute for x, the results will always be identical. If we use 0, both expressions come out to 0. If we use 10, both expressions come out to 220. If we use 100, both expressions come out to 20,200. We get the same result no matter how large or small the number we use for x.<\/p>\n<p>Question 11.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite an algebraic expression that can be simpli\ufb01ed using the Associative Property of Multiplication and the Multiplication Property of One.<\/p>\n<p>Answer:<br \/>\nLet us consider an expression 4 \u00d7 30.<br \/>\nWe can simplify the expression by using the Associative Property of Multiplication<br \/>\n4 \u00d7 30 = 4 \u00d7 (5 \u00d7 6)<br \/>\n(4 \u00d7 5) \u00d7 6 = 4 \u00d7 (5 \u00d7 6)<br \/>\n20 \u00d7 6 = 4 \u00d7 30<br \/>\n120 = 120<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 12.<br \/>\nYou and \ufb01ve friends form a team for an outdoor adventure race. Your team needs to raise money to pay for $130 of travel fees, x dollars for each team member\u2019s entry fee, and $85.50 for food. Use an algebraic expression to \ufb01nd the total amount your team needs to raise when the entry fee is $25.50 per person.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-53.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 53\" width=\"188\" height=\"257\" \/><\/p>\n<p>Answer: (130+85)+25.5p=total amount<\/p>\n<p>Step-by-step explanation:<br \/>\n130+85 is how much you&#8217;d need just for the fees and food, for the entry fee its per person<br \/>\nso it would be $25.5 for every person that is part of your team.<\/p>\n<p>Question 13.<br \/>\nYou have $50 and a $15 gift card to spend online. You purchase a pair of headphones for $34.99 and 8 songs for x dollars each. Use an algebraic expression to \ufb01nd the amount you have left when each song costs $1.10.<\/p>\n<p>Answer: $21.21<br \/>\nGiven<br \/>\nYou have $50 and a $15 gift card to spend online<br \/>\npurchase a pair of headphones for $34.99 and 8 songs for x dollars each.<br \/>\nUse an algebraic expression to \ufb01nd the amount you have left when each song costs $1.10.<br \/>\nso<br \/>\n50 + 15 -34.99 &#8211; 8x<br \/>\n65 &#8211; 34.99 &#8211; 8(1.10)<br \/>\n30.01 &#8211; 8.8<br \/>\n$21.21<\/p>\n<h3><a id=\"Properties_of_Addition_and_Multiplication_Homework_&amp;_Practice_5.3\"><\/a>Properties of Addition and Multiplication Homework &amp; Practice 5.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write the phrase as an expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n10 added to a number p<\/p>\n<p>Answer:\u00a0 p + 10<br \/>\nFirst consider the expression for<br \/>\n10 added to a number p<br \/>\nwe get p + 10<br \/>\nAn algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.<br \/>\nA variable is a letter that can represent one or more numbers.<\/p>\n<p>Question 2.<br \/>\nthe product of 6 and a number m<\/p>\n<p>Answer: 6m<br \/>\nFirst consider the expression for<br \/>\nthe product of 6 and a number m<br \/>\nso multiply 6 with m<br \/>\nwe get 6m<br \/>\nAn algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.<br \/>\nA variable is a letter that can represent one or more numbers.<\/p>\n<p>Question 3.<br \/>\nthe quotient of a number b and 15<\/p>\n<p>Answer: \\(\\frac{b}{15}\\)<br \/>\nFirst consider the expression for<br \/>\nthe quotient of a number b and 15<br \/>\nso divide b by 15<br \/>\nwe get \\(\\frac{b}{15}\\)<br \/>\nAn algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.<br \/>\nA variable is a letter that can represent one or more numbers.<\/p>\n<p>Question 4.<br \/>\n7 fewer than a number s<\/p>\n<p>Answer:\u00a0 s &#8211; 7<br \/>\nFirst consider the expression for<br \/>\n7 fewer than a number s<br \/>\nso subtract a number s with 7<br \/>\nwe get s &#8211; 7<br \/>\nAn algebraic expression is a mathematical phrase that contains a combination of numbers, variables and operational symbols.<br \/>\nA variable is a letter that can represent one or more numbers.<\/p>\n<p><strong>Write the prime factorization of the number.<\/strong><\/p>\n<p>Question 5.<br \/>\n36<\/p>\n<p>Answer:<br \/>\nThe number 36 can be written as a product of primes as<br \/>\n36 = 2\u00b2 x 3\u00b2.<br \/>\nThe expression 2\u00b2 x 3\u00b2 is said to be the prime factorization of 36<\/p>\n<p>Question 6.<br \/>\n144<\/p>\n<p>Answer:<br \/>\nThe prime factor of the 144 is 24 x 32.<br \/>\n144 = 2 x 2 x 2 x 2 x 3 x 3<\/p>\n<p>Question 7.<br \/>\n147<\/p>\n<p>Answer:<br \/>\nFactors of 147: 1, 3, 7, 21, 49, 147.<br \/>\nPrime factorization: 147 = 3 x 7 x 7,<br \/>\nwhich can also be written<br \/>\n147 = 3 x (7\u00b2)<\/p>\n<p>Question 8.<br \/>\n205<\/p>\n<p>Answer:<br \/>\nthe prime factors of the number 205.<br \/>\nIf we put all of it together we have the factors 5 x 41 = 205.<br \/>\nit can also be written in exponential form as 5\u00b9 x 41\u00b9.<\/p>\n<p><strong>Evaluate the expression.<\/strong><\/p>\n<p>Question 9.<br \/>\n8.092 + 3.5<\/p>\n<p>Answer: 11.592<br \/>\nGiven expression 8.092 + 3.5<br \/>\nnow add 8.092 with 3.5 we get<br \/>\n11.592<\/p>\n<p>Question 10.<br \/>\n16.78 &#8211; 12.237<\/p>\n<p>Answer: 4.543<br \/>\nGiven expression 16.78 &#8211; 12.237<br \/>\nnow subtract\u00a0 16.75 with 12.237\u00a0 we get<br \/>\n4.543<\/p>\n<p>Question 11.<br \/>\n9.17 + 1.83 + 2.641<\/p>\n<p>Answer:\u00a0 13.641<br \/>\nGiven expression 9.17 + 1.83 + 2.641<br \/>\nnow add 9.17\u00a0 with 1.83\u00a0 we get\u00a0 11 then add with 2.641<br \/>\nwe get 13.641<\/p>\n<p>Question 12.<br \/>\n8.43 &#8211; 6.218 + 4.2<\/p>\n<p>Answer:<br \/>\nGiven expression 8.43 &#8211; 6.218 + 4.2<br \/>\nnow subtract\u00a0 8.43 with 6.218 \u00a0we get 2.212\u00a0 then add with 4.2<br \/>\nwe get\u00a0 6.412<\/p>\n<p><strong>Represent the ratio relationship using a graph.<\/strong><\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-54.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 54\" width=\"242\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-37611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-Answers-img_1-300x262.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 5 Algebraic Expressions and Properties Answers img_1\" width=\"300\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-Answers-img_1-300x262.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-Answers-img_1.jpg 542w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-55.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 55\" width=\"211\" height=\"79\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-37618\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-Answers-img_2-300x262.jpg\" alt=\"Big Ideas Math Grade 6 Chapter 5 Algebraic Expressions and Properties Answers img_2\" width=\"300\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-Answers-img_2-300x262.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-Answers-img_2.jpg 542w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>MATCHING<\/strong><br \/>\n<strong>Match the expression with an equivalent expression.<\/strong> (See Exploration 1, p. 215.)<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-56.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 56\" width=\"86\" height=\"58\" \/><\/p>\n<p>Answer: B<\/p>\n<p>Explanation:<br \/>\n3 + 3 + y is equivalent to y + 3 + 3<br \/>\nSo, the correct answer is option B<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-5-Algebraic-Expressions-and-Properties-57.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 5 Algebraic Expressions and Properties 57\" width=\"99\" height=\"61\" \/><\/p>\n<p>Answer: C<\/p>\n<p>Explanation:<br \/>\n(y.y).3 = y(3 . y)<br \/>\nSo, the correct answer is option C.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-5-Algebraic-Expressions-and-Properties-58.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 5 Algebraic Expressions and Properties 58\" width=\"89\" height=\"61\" \/><\/p>\n<p>Answer: A<\/p>\n<p>Explanation:<br \/>\n3 . 1 . y = y . 3<br \/>\nSo, the correct answer is option A.<\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-6th-Grade-Chapter-5-Algebraic-Expressions-and-Properties-59.png\" alt=\"Big Ideas Math Answers 6th Grade Chapter 5 Algebraic Expressions and Properties 59\" width=\"135\" height=\"73\" \/><\/p>\n<p>Answer: D<\/p>\n<p>Explanation:<br \/>\n(3 + 0) + (y + y)<br \/>\n(3 + y) + y<br \/>\nSo, the correct answer is option D.<\/p>\n<p><strong>IDENTIFYING PROPERTIES<\/strong><br \/>\n<strong>Tell which property the statement illustrates.<\/strong><\/p>\n<p>Question 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-60.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 60\" width=\"94\" height=\"27\" \/><\/p>\n<p>Answer: commutative property of multiplication<\/p>\n<p>Explanation:<br \/>\nThe commutative property of multiplication tells us that we can multiply a string of numbers in any order.<br \/>\n5 . p = p . 5<\/p>\n<p>Question 20.<br \/>\n2 + (12 + r) = (2 + 12) + r<\/p>\n<p>Answer: associative property of addition<\/p>\n<p>Explanation:<br \/>\nAssociative property of addition: Changing the grouping of addends does not change the sum.<br \/>\n2 + (12 + r) = (2 + 12) + r<\/p>\n<p>Question 21.<br \/>\n4 . (x . 10) = (4 . x) . 10<\/p>\n<p>Answer: associative property of multiplication<\/p>\n<p>Explanation:<br \/>\nThe associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.<\/p>\n<p>Question 22.<br \/>\nx + 7.5 = 7.5 + x<\/p>\n<p>Answer: commutative property of addition<\/p>\n<p>Explanation:<br \/>\nThe commutative property of addition says that changing the order of addends does not change the sum.<\/p>\n<p>Question 23.<br \/>\n(c + 2) + 0 = c + 2<\/p>\n<p>Answer: Additive Identity<\/p>\n<p>Explanation:<br \/>\nAdditive identity is a number, which when added to any number, gives the sum as the number itself. It means that additive identity is \u201c0\u201d as adding 0 to any number, gives the sum as the number itself.<\/p>\n<p>Question 24.<br \/>\na . 1 = a<\/p>\n<p>Answer: Multiplicative Identity<\/p>\n<p>Explanation:<br \/>\nAccording to the multiplicative identity property of 1, any number multiplied by 1, gives the same result as the number itself. It is also called the Identity property of multiplication because the identity of the number remains the same.<\/p>\n<p>Question 25.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend states the property that the statement illustrates. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-61.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 61\" width=\"257\" height=\"89\" \/><\/p>\n<p>Answer: correct<\/p>\n<p>Explanation:<br \/>\nAssociative property of addition: Changing the grouping of addends does not change the sum.<br \/>\n(7 + x) + 3 = (x + 7) + 3<br \/>\nThus we can say that your friend is correct.<\/p>\n<p><strong>USING PROPERTIES<\/strong><br \/>\n<strong>Simplify the expression. Explain each step.<\/strong><\/p>\n<p>Question 26.<br \/>\n6 + (5 + x)<\/p>\n<p>Answer: 11 + x<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n6 + (5 + x) = 6+5+x<br \/>\nStep 2:Add the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n11 + x<\/p>\n<p>Question 27.<br \/>\n(14 + y) + 3<\/p>\n<p>Answer: 17 + y<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n(14 + y) + 3 = 14 + 3 + y<br \/>\nStep 2:Add the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n17 + y<\/p>\n<p>Question 28.<br \/>\n6(2b)<\/p>\n<p>Answer: 12b<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n6(2b) = 6 \u00d7 2 \u00d7b<br \/>\nStep 2:multiply\u00a0 the numbers<br \/>\nStep 3: Rearrange terms<br \/>\nwe get 12b<\/p>\n<p>Question 29.<br \/>\n7(9w)<\/p>\n<p>Answer: 63w<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n7(9w) = 7 \u00d7\u00a0 \u00d7w<br \/>\nStep 2:multiply\u00a0 the numbers<br \/>\nStep 3: Rearrange terms<br \/>\nwe get 63w<\/p>\n<p>Question 30.<br \/>\n3.2 + (x + 5.1)<\/p>\n<p>Answer: 8.3 + x<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n3.2 + (x + 5.1) = 3.2 + 5.1 + x<br \/>\nStep 2:Add the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n8.3 + x<\/p>\n<p>Question 31.<br \/>\n(0 + a) + 8<\/p>\n<p>Answer: 8 + a<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n(0 + a) + 8 = 0 + 8 +a<br \/>\nStep 2:Add the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n8 + a<\/p>\n<p>Question 32.<br \/>\n9 . c . 4<\/p>\n<p>Answer: 36c<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n9 . c . 4 = 9 . 4 . c<br \/>\nStep 2: multiply the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n36c<\/p>\n<p>Question 33.<br \/>\n(18.6 . d) . 1<\/p>\n<p>Answer: 18.6 d<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n(18.6 . d) . 1 = (18.6 . 1) d<br \/>\nStep 2: multiply the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n18.6 d<\/p>\n<p>Question 34.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-62.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 62\" width=\"121\" height=\"52\" \/><\/p>\n<p>Answer:<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-62.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 62\" width=\"121\" height=\"52\" \/> = 3k + (4\\(\\frac{1}{5}\\) + 8\\(\\frac{3}{5}\\))<br \/>\nStep 2: add the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n3k + 12\\(\\frac{4}{5}\\)<\/p>\n<p>Question 35.<br \/>\n(2.4 + 4n) + 9<\/p>\n<p>Answer:<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n(2.4 + 4n) + 9 = 2.4 + 9 + 4n<br \/>\nStep 2:Add the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n11.4 + 4n<\/p>\n<p>Question 36.<br \/>\n(3s) . 8<\/p>\n<p>Answer: 24s<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\n(3s) . 8 = (3 . 8) s<br \/>\nStep 2: multiply the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n24s<\/p>\n<p>Question 37.<br \/>\nz . 0 . 12<\/p>\n<p>Answer: 0<br \/>\nStep 1: Eliminate redundant parentheses<br \/>\nz . 0 . 12 = z \u00d7 0 \u00d7 12<br \/>\nStep 2: multiply the numbers<br \/>\nStep 3: Rearrange terms<br \/>\n0<\/p>\n<p>Question 38.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe expression 12 + x + 4 represents the perimeter of a triangle. Simplify the expression.<\/p>\n<p>Answer: x+16<\/p>\n<p>Explanation:<br \/>\nyour simplifying so you only combine like terms.<br \/>\n12 and 4 dont have any variables following them so you add the two.<br \/>\n12+4=16<br \/>\nthere is only 1 x in the expression so just add it on.<br \/>\n16+x<\/p>\n<p>Question 39.<br \/>\n<strong>PRECISION<\/strong><br \/>\nA case of scout cookies has 10 cartons. A carton has 12 boxes. The amount you earn on a whole case is 10(12x) dollars.<br \/>\na. What does x represent?<br \/>\nb. Simplify the expression.<\/p>\n<p>Answer:<br \/>\nGiven<br \/>\nA case of scout cookies has 10 cartons. A carton has 12 boxes<br \/>\nA. x represents the money made per box<br \/>\nB. 10(12x) = 120x<\/p>\n<p>Question 40.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA government estimates the cost to design new radar technology over a period of m months. The government estimates $840,000 for equipment, $15,000 for software,and $40,000 per month for wages. Use an algebraic expression to \ufb01nd the total cost the government estimates when the project takes 16 months to complete.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-63.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 63\" width=\"214\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-63.png 214w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-63-150x150.png 150w\" sizes=\"(max-width: 214px) 100vw, 214px\" \/><\/p>\n<p>Answer: $1,495,000.<\/p>\n<p>Explanation:<br \/>\nThe cost that is affected by the number of months mm is the wages while the first two costs are fixed. Hence, you multiply $40,000 by the number of months so that<br \/>\n840,000+15,000+40,000m<br \/>\n840,000+15,000+40,000m<br \/>\nFor m=16m=16 (16 months),<br \/>\n=840,000+15,000+40,000(16)<br \/>\n=840,000+15,000+40,000(16)<br \/>\n=840,000+15,000+640,000<br \/>\n=840,000+15,000+640,000<br \/>\n=1,495,000<br \/>\n=1,495,000<br \/>\nSo, the total cost is $1,495,000.<\/p>\n<p><strong>WRITING EXPRESSIONS<\/strong><br \/>\n<strong>Write the phrase as an expression. Then simplify the expression.<\/strong><\/p>\n<p>Question 41.<br \/>\n7 plus the sum of a number x and 5<\/p>\n<p>Answer:<br \/>\n7+(x+5)\u00a0 sum means addition and it says x and 5. then it says 7 plus that so you put 7.<br \/>\nIn reality, you wouldn&#8217;t need parenthesis,<br \/>\nbut if you want it to match the phrase, you can put it in parenthesis.<\/p>\n<p>Question 42.<br \/>\nthe product of 8 and a number y, multiplied by 9<\/p>\n<p>Answer: 8y x 9 \u21d2 72y<br \/>\nGiven<br \/>\nthe product of 8 and a number y \u21d2 8 \u00d7 y = 8y<br \/>\nand also given multiplied by 9 \u21d2 8y \u00d7 9<br \/>\nso we get 72 y<\/p>\n<p><strong>USING PROPERTIES<\/strong><br \/>\n<strong>Copy and complete the statement using the speci\ufb01ed property.<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-64.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 64\" width=\"550\" height=\"215\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-64.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-64-300x117.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-37633\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-64-300x117.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-64\" width=\"300\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-64-300x117.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-64.jpg 550w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nFive identical triangles form the trapezoid shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-65.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 65\" width=\"172\" height=\"99\" \/><br \/>\na. What is the perimeter of the trapezoid?<\/p>\n<p>Answer:<br \/>\nThe perimeter of the trapezoid is a + b + c + d<br \/>\nP = sum of four sides<br \/>\nP = 3x + 7 + 7 + 2x<br \/>\nP = 5x + 14<br \/>\nThus the perimeter of the trapezoid is 5x + 14<br \/>\nb. How can you use some or all of the triangles to form a new trapezoid with a perimeter of 3x +14? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nYou can reduce the size of the triangle to form a new trapezoid with a perimeter of 3x +14<br \/>\nThe perimeter of the trapezoid is a + b + c + d<br \/>\nP = sum of four sides<br \/>\nP = 2x + 7 + 7 + 1x<br \/>\nP = 3x + 14<\/p>\n<p>Question 49.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou and a friend sell hats at a fair booth. You sell 16 hats on the \ufb01rst shift and 21 hats on the third shift. Your friend sells x hats on the second shift.<br \/>\na. The expression 37(14) + 10x represents the amount (in dollars) that you both earn. How can you tell that your friend is selling the hats for a lower price?<br \/>\nb. You earn more money than your friend. What can you say about the value of x?<\/p>\n<p>Answer:<br \/>\n37+x<\/p>\n<p>Explanation:<br \/>\n1st shift: 16 hats were sold<br \/>\n2nd shift: x hats were sold<br \/>\n3rd shift: 21 hats were sold<br \/>\nThe total is<br \/>\n16+x+21<br \/>\nSimplifying<br \/>\n37+x<br \/>\nanother step<br \/>\n16 + 21 + x = y<br \/>\ny = the number of hats sold<br \/>\n16 = hats sold on first shift<br \/>\n21 = hats on the third shift<br \/>\nx = hats on the second shift<\/p>\n<h3><a id=\"Lesson_5.4_The_Distributive_Property\"><\/a>Lesson 5.4 The Distributive Property<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Using Models to Simplify Expressions<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Use the models to simplify the expressions. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 66\" width=\"403\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66-150x150.png 150w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-37698\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66-300x300.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66-150x150.jpg 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-66.jpg 403w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nb. In part(a), check that the original expressions are equivalent to the simpli\ufb01ed expressions.<br \/>\nc. You used the Distributive Property in a previous course. Use the example to explain the meaning of the property.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-67.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 67\" width=\"162\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-67.png 162w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-67-150x150.png 150w\" sizes=\"(max-width: 162px) 100vw, 162px\" \/><br \/>\nDistributive Property: 6(20 + 3) = 6(20) + 6(3)<br \/>\nIs this property true for algebraic expressions? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nThe distributive property of multiplication over addition can be used when you multiply a number by a sum.<br \/>\n6(20 + 3) = 6(20) + 6(3)<br \/>\n6(23) = 120 + 18<br \/>\n138 = 138<br \/>\nYes this property true for algebraic expressions<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Use the Distributive Property to simplify the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n7(a + 2)<\/p>\n<p>Answer: 7(a) + 7(2)<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe distributive property of multiplication over addition can be used when you multiply a number by a sum.<br \/>\n7(a + 2) = (7 \u00d7 a) + (7 \u00d7 2)<br \/>\n7a + 14<br \/>\nThus 7(a + 2) = 7a + 14<\/p>\n<p>Question 2.<br \/>\n3(d &#8211; 11)<\/p>\n<p>Answer: 3(d) &#8211; 3(11)<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe distributive property of multiplication over addition can be used when you multiply a number by a sum.<br \/>\n3(d &#8211; 11) = (3 \u00d7 d) &#8211; (3 \u00d7 11)<br \/>\n3d &#8211; 33<br \/>\nThus 3(d &#8211; 11) = 3d &#8211; 33<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-68.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 68\" width=\"92\" height=\"57\" \/><\/p>\n<p>Answer: 12a + 12\\(\\frac{2}{3}\\)b<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe distributive property of multiplication over addition can be used when you multiply a number by a sum.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-68.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 68\" width=\"92\" height=\"57\" \/>= (12 \u00d7 a) + (12 \u00d7 \\(\\frac{2}{3}\\)b)<br \/>\n= 12a + 12\\(\\frac{2}{3}\\)b<br \/>\nThus <img loading=\"lazy\" class=\"alignnone size-full wp-image-24796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-68.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 68\" width=\"92\" height=\"57\" \/>= 12a + 12\\(\\frac{2}{3}\\)b<\/p>\n<p>Question 4.<br \/>\n7(2 + 6 &#8211; 4d)<\/p>\n<p>Answer: 7(2) + 7(6) &#8211; 7(4d)<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe distributive property of multiplication over addition can be used when you multiply a number by a sum.<br \/>\n7(2 + 6 &#8211; 4d) = 7(8 &#8211; 4d)<br \/>\n56 &#8211; 28d<br \/>\nThus 7(2 + 6 &#8211; 4d) = 56 &#8211; 28d<\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 5.<br \/>\n8 + 3z &#8211; z<\/p>\n<p>Answer: 8 + 2z<\/p>\n<p>Explanation:<br \/>\nCombine the like terms and simplify the expression.<br \/>\n8 + 3z &#8211; z<br \/>\n8 + z(3 &#8211; 1)<br \/>\n8 + 2z<br \/>\nSo, 8 + 3z &#8211; z = 8 + 2z<\/p>\n<p>Question 6.<br \/>\n3(b + 5) + b + 2<\/p>\n<p>Answer: 4b + 17<\/p>\n<p>Explanation:<br \/>\nCombine the like terms and simplify the expression.<br \/>\n3(b + 5) + b + 2<br \/>\n= 3b + 15 + b + 2<br \/>\n= 3b + b + 15 + 2<br \/>\n= 4b + 17<br \/>\nThus 3(b + 5) + b + 2 = 4b + 17<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\n<strong>WRITING<\/strong><br \/>\nOne meaning of the word distribute is to give something to each member of a group. How can this help you remember the Distributive Property?<\/p>\n<p>Answer:<br \/>\nYou must distribute or give the number outside the parenthesis to all the numbers inside the parenthesis<\/p>\n<p><strong>SIMPLIFYING EXPRESSIONS<\/strong><br \/>\n<strong>Use the Distributive Property to simplify the expression.<\/strong><\/p>\n<p>Question 8.<br \/>\n3(x + 10)<\/p>\n<p>Answer: 3(x) + 3(10)<\/p>\n<p>Explanation:<br \/>\nWe can simplify the expression by using the Distributive Property<br \/>\nThe distributive property of multiplication over addition can be used when you multiply a number by a sum.<br \/>\n3(x + 10) = (3 \u00d7 x) + (3 \u00d7 10)<br \/>\n= 3x + 30<br \/>\nSo, 3(x + 10) = 3x + 30<\/p>\n<p>Question 9.<br \/>\n15(4n &#8211; 2)<\/p>\n<p>Answer: 15(4n) &#8211; 15(2)<\/p>\n<p>Explanation:<br \/>\nWe can simplify the expression by using the Distributive Property<br \/>\nThe distributive property of multiplication over addition can be used when you multiply a number by a sum.<br \/>\n15(4n &#8211; 2) = (15 \u00d7 4n) &#8211; (15 \u00d7 2)<br \/>\n= 60n &#8211; 30<br \/>\nSo, 15(4n &#8211; 2) = 60n &#8211; 30<\/p>\n<p>Question 10.<br \/>\n2w + 4 + 13w + 1<\/p>\n<p>Answer:15w + 5 = 5(3w + 1)<\/p>\n<p>Explanation:<br \/>\nWe can simplify the expression by using the Distributive Property<br \/>\nThe distributive property of multiplication over addition can be used when you multiply a number by a sum.<br \/>\n2w + 4 + 13w + 1<br \/>\nCombine the like terms<br \/>\n=2w + 13w + 4 + 1<br \/>\n=15w + 5<br \/>\n=5(3w + 1)<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 11.<br \/>\nYou purchase a remote-controlled drone for d dollars. Your friend purchases a drone that costs $35 more than your drone. Your brother purchases a drone that costs three times as much as your friend\u2019s drone. Write and simplify an expression that represents the cost (in dollars) of your brother\u2019s drone.<\/p>\n<p>Answer:<br \/>\nBrother = 105+3d<\/p>\n<p>Explanation:<br \/>\nGiven<br \/>\nDrone = d<br \/>\nFriend = $35 more expensive than yours.<br \/>\nBrother = 3 times as much as your friend<br \/>\nRequired<br \/>\nWrite an expression for the cost of your brother&#8217;s drone<br \/>\nI&#8217;ll solve by analyzing the question one sentence after the other<br \/>\nYou: Drone = d<\/p>\n<p>Your friend:<br \/>\nFriend = $35 more expensive than yours.<br \/>\nThis means<br \/>\nBrother = 3 \u00d7 Friend<br \/>\nSubstitute 35 + d for Friend<br \/>\nBrother = 3 \u00d7 (35+d)<br \/>\nOpen bracket<br \/>\nBrother = 3\u00d735+3\u00d7d<br \/>\nBrother=105+3d<\/p>\n<p>Question 12.<br \/>\nWrite and simplify an expression that represents the total cost (in dollars) of buying the items shown for each member of a baseball team.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-68.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 68.1\" width=\"188\" height=\"159\" \/><\/p>\n<p>Answer: 9(10 + x)<\/p>\n<p>Explanation:<br \/>\nNumber of members in the baseball team = 9<br \/>\nCost of the pant = $10<br \/>\nCost of a belt = $x<br \/>\nThe expression that represents the total cost (in dollars) of buying the items shown for each member of a baseball team is 9(10 + x)<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nOne molecule of caffeine contains x oxygen atoms, twice as many nitrogen atoms as oxygen atoms, 4 more carbon atoms than nitrogen atoms, and 1.25 times as many hydrogen atoms as carbon atoms. Write and simplify an expression that represents the number of hydrogen atoms in one molecule of caffeine.<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nOne molecule of caffeine contains x oxygen atoms, twice as many nitrogen atoms as oxygen atoms, 4 more carbon atoms than nitrogen atoms, and 1.25 times as many hydrogen atoms as carbon atoms.<br \/>\nOne molecule of caffeine contains x oxygen atoms = x<br \/>\ntwice as many nitrogen atoms as oxygen atoms = 2 . x<br \/>\n4 more carbon atoms than nitrogen atoms = 4 . x<br \/>\n1.25 times as many hydrogen atoms as carbon atoms = 1.25 \u00d7 x<br \/>\nx + 2x + 6x + 1.25(6x)<\/p>\n<h3><a id=\"The_Distributive_Property_Homework_&amp;_Practice_5.4\"><\/a>The Distributive Property Homework &amp; Practice 5.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Simplify the expression. Explain each step.<\/strong><\/p>\n<p>Question 1.<br \/>\n(s + 4) + 8<\/p>\n<p>Answer: s + 12<\/p>\n<p>Explanation:<br \/>\nAccording to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.<br \/>\n(s + 4) + 8<br \/>\n= s + 4 + 8<br \/>\n= s + 12<\/p>\n<p>Question 2.<br \/>\n(12 + x) + 2<\/p>\n<p>Answer: 14 + x<\/p>\n<p>Explanation:<br \/>\nAccording to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.<br \/>\n12 + x + 2<br \/>\nx + 12 + 2<br \/>\nx + 14<\/p>\n<p>Question 3.<br \/>\n3(4n)<\/p>\n<p>Answer: 12n<\/p>\n<p>Explanation:<br \/>\nAccording to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.<br \/>\n3 \u00d7 4n = 12n<\/p>\n<p><strong>You are given the difference of the numbers of boys and girls in a class and the ratio of boys to girls. How many boys and how many girls are in the class?<\/strong><\/p>\n<p>Question 4.<br \/>\n3 more boys; 5 for every 4<\/p>\n<p>Answer:<br \/>\nLet the total number of boys in the class be x.<br \/>\nThe ratio of boys and girls is 5 : 4<br \/>\nNumber of boys = 5x<br \/>\nNumber of girls = 4x<br \/>\n5x &#8211; 4x = 3<br \/>\nx = 3<br \/>\nNumber of boys = 5(3) = 15<br \/>\n15 + 3 = 18<br \/>\nNumber of girls = 4(3) = 12<br \/>\nTo find the total number of boys and girls in the class we have to add them<br \/>\n18 + 12 = 30<br \/>\nThus there are 30 boys and girls in the class.<\/p>\n<p>Question 5.<br \/>\n8 more girls; 3 for every 2<\/p>\n<p>Answer:<br \/>\nLet the total number of boys in the class be x.<br \/>\nThe ratio of boys and girls is 3 : 2<br \/>\nNumber of boys = 3x<br \/>\nNumber of girls = 2x<br \/>\n3x &#8211; 2x = 8<br \/>\nx = 8<br \/>\nNumber of boys = 3x = 3(8) = 24<br \/>\nNumber of girls = 2x = 2(8) = 16<br \/>\nMore number of girls = 16 + 8 = 24<br \/>\nTo find the total number of boys and girls in the class we have to add them<br \/>\n24 + 24 = 48<br \/>\nThus there are 48 boys and girls in the class.<\/p>\n<p>Question 6.<br \/>\n4 more girls; 9 for every 13<\/p>\n<p>Answer:<br \/>\nLet the total number of boys in the class be x.<br \/>\nThe ratio of girls and boys is 13 : 9<br \/>\nNumber of boys = 9x<br \/>\nNumber of girls = 13x<br \/>\n13x &#8211; 9x = 4<br \/>\n4x = 4<br \/>\nx = 1<br \/>\nNumber of boys = 9x = 9(1) = 9<br \/>\nNumber of girls = 13x = 13(1) = 13<br \/>\n13 + 4 = 17<br \/>\nTo find the total number of boys and girls in the class we have to add them<br \/>\n9 + 17 = 26<br \/>\nThus there are 26 boys and girls in the class.<\/p>\n<p>Question 7.<br \/>\n6 more boys; 7 for every 4<\/p>\n<p>Answer:<br \/>\nLet the total number of boys in the class be x.<br \/>\nThe ratio of girls and boys is 7 : 4<br \/>\nNumber of boys = 7x<br \/>\nNumber of girls = 4x<br \/>\n7x &#8211; 4x = 6<br \/>\n3x = 6<br \/>\nx = 2<br \/>\nNumber of boys = 7(2) = 14<br \/>\nNumber of girls = 4(2) = 8<br \/>\n15 + 6 = 21<br \/>\nTo find the total number of boys and girls in the class we have to add them<br \/>\n21 + 8 = 29<br \/>\nThus there are 29 boys and girls in the class.<\/p>\n<p><strong>Divide.<\/strong><\/p>\n<p>Question 8.<br \/>\n301 \u00f7 7<\/p>\n<p>Answer: 43<br \/>\nSo divide 301 with 7<br \/>\nthen we get 43<\/p>\n<p>Question 9.<br \/>\n1722 \u00f7 14<\/p>\n<p>Answer: 123<br \/>\nSo divide 1722 with 14<br \/>\nthen we get 123<\/p>\n<p>Question 10.<br \/>\n629 \u00f7 12<\/p>\n<p>Answer: 52.41<br \/>\nSo divide 629 with 12<br \/>\nthen we get 52.14<\/p>\n<p>Question 11.<br \/>\n8068 \u00f7 31<\/p>\n<p>Answer: 260.25<br \/>\nSo divide 8068 with 31<br \/>\nthen we get 260.25<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>USING MODELS<\/strong><br \/>\n<strong>Use the model to simplify the expression. Explain your reasoning.<\/strong> (See Exploration 1, p. 221.)<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-69.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 69\" width=\"180\" height=\"165\" \/><\/p>\n<p>Answer: 5z + 30<\/p>\n<p>Explanation:<br \/>\nThe shape of the above figure is a rectangle.<br \/>\nArea of the rectangle = l \u00d7 b<br \/>\nA = (z + 6) \u00d7 5<br \/>\nA = 5z + 30<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-70.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 70\" width=\"187\" height=\"125\" \/><\/p>\n<p>Answer: 6s<\/p>\n<p>Explanation:<br \/>\nCombine the like terms<br \/>\nThere are 4s in the first block<br \/>\nThere are 2s in the second block<br \/>\n4s + 2s = 6s<\/p>\n<p><strong>SIMPLIFYING EXPRESSIONS<\/strong><br \/>\n<strong>Use the Distributive Property to simplify the expression.<\/strong><\/p>\n<p>Question 14.<br \/>\n3(x + 4)<\/p>\n<p>Answer: 3x + 12<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n3(x + 4) = (3 \u00d7 x) + (3 \u00d7 4)<br \/>\n= 3x + 12<\/p>\n<p>Question 15.<br \/>\n10(b &#8211; 6)<\/p>\n<p>Answer: 10b &#8211; 60<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n10(b &#8211; 6) = (10 \u00d7 b) &#8211; (10 \u00d7 6)<br \/>\n= 10b &#8211; 60<\/p>\n<p>Question 16.<br \/>\n6(s &#8211; 9)<\/p>\n<p>Answer: 6s &#8211; 54<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n6(s &#8211; 9) = (6 \u00d7 s) &#8211; (6 \u00d7 9)<br \/>\n= 6s &#8211; 54<\/p>\n<p>Question 17.<br \/>\n7(8 + y )<\/p>\n<p>Answer: 56 + 7y<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n7(8 + y) = (7 \u00d7 8) + (7 \u00d7 y)<br \/>\n= 56 + 7y<\/p>\n<p>Question 18.<br \/>\n8(12 + a)<\/p>\n<p>Answer: 96 + 8a<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n8(12 + a) = (8 \u00d7 12) + (8 \u00d7 a)<br \/>\n= 96 + 8a<\/p>\n<p>Question 19.<br \/>\n9(2n + 1)<\/p>\n<p>Answer: 18n + 9<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n9(2n + 1) = (9 \u00d7 2n) + (9 \u00d7 1)<br \/>\n= 18n + 9<\/p>\n<p>Question 20.<br \/>\n12(6 &#8211; k)<\/p>\n<p>Answer: 72 &#8211; 12k<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n12(6 &#8211; k) = (12 \u00d7 6) &#8211; (12 \u00d7 k)<br \/>\n= 72 &#8211; 12k<\/p>\n<p>Question 21.<br \/>\n18(5 &#8211; 3w)<\/p>\n<p>Answer: 90 &#8211; 54w<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n18(5 &#8211; 3w) = (18 \u00d7 5) &#8211; (18 \u00d7 3w)<br \/>\n= 90 &#8211; 54w<\/p>\n<p>Question 22.<br \/>\n9(3 + c + 4)<\/p>\n<p>Answer: 63 + 9c<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n9(3 + c + 4) = 9(7 + c)<br \/>\n(9 \u00d7 7) + ( 9 \u00d7 c)<br \/>\n63 + 9c<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-71.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 71\" width=\"93\" height=\"47\" \/><\/p>\n<p>Answer: 3 + x\/4<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n1\/4(8 + x + 4) = 1\/4(12 + x)<br \/>\n= 3 + x\/4<\/p>\n<p>Question 24.<br \/>\n8(5g + 5 &#8211; 2)<\/p>\n<p>Answer: 40g + 24<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n8(5g + 5 &#8211; 2) = 8(5g) + 8(5) &#8211; 8(2)<br \/>\n40g + 40 &#8211; 16<br \/>\n40g + 24<\/p>\n<p>Question 25.<br \/>\n6(10 + z + 3)<\/p>\n<p>Answer: 78 + 6z<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n6(10 + z + 3) = 6(10) + 6(z) + 6(3)<br \/>\n= 60 + 6z + 18<br \/>\n= 78 + 6z<\/p>\n<p>Question 26.<br \/>\n4(x + y)<\/p>\n<p>Answer: 4x + 4y<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n4(x + y) = (4 \u00d7 x) + (4 \u00d7 y)<br \/>\n= 4x + 4y<\/p>\n<p>Question 27.<br \/>\n25(x &#8211; y)<\/p>\n<p>Answer: 25x &#8211; 25y<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n25(x &#8211; y) = (25 \u00d7 x) &#8211; (25 \u00d7 y)<br \/>\n= 25x &#8211; 25y<\/p>\n<p>Question 28.<br \/>\n7(p + q + 9)<\/p>\n<p>Answer: 7p + 7q + 63<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n7(p + q + 9) = (7 \u00d7 p) + (7 \u00d7 q) + (7 \u00d7 9)<br \/>\n= 7p + 7q + 63<\/p>\n<p>Question 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-72.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 72\" width=\"126\" height=\"51\" \/><\/p>\n<p>Answer: n + 3m + 2<\/p>\n<p>Explanation:<br \/>\nWe can use the distributive property to simplify the expression.<br \/>\n1\/2 (2n + 4 + 6m) = 1\/2 (2n) + 1\/2 (4) + 1\/2 (6m)<br \/>\n= n + 2 + 3m<\/p>\n<p><strong>MATCHING<\/strong><br \/>\n<strong>Match the expression with an equivalent expression.<\/strong><\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-73.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 73\" width=\"110\" height=\"57\" \/><\/p>\n<p>Answer: C<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n6(n + 4) = 6n + 24<br \/>\nNow take 3 as common factor<br \/>\n3(2n + 8)<br \/>\nThus the equivalent expression is option C.<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-74.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 74\" width=\"85\" height=\"55\" \/><\/p>\n<p>Answer: A<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n2(3n + 9) = 6n + 18<br \/>\nNow take 3 as common factor<br \/>\n6n + 18 = 3(2n + 6)<br \/>\nThus the equivalent expression is option A.<\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-75.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 75\" width=\"101\" height=\"63\" \/><\/p>\n<p>Answer: D<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n6(n + 2) = 6n + 12<br \/>\nThus the equivalent expression is option D.<\/p>\n<p>Question 33.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-76.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 76\" width=\"97\" height=\"64\" \/><\/p>\n<p>Answer: B<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n3(2n + 3) = 6n + 9<br \/>\nThus the equivalent expression is option B.<\/p>\n<p>Question 34.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nEach day, you run on a treadmill for r minutes and lift weights for 15 minutes. Which expressions can you use to \ufb01nd how many minutes of exercise you do in 5 days? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-77.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 77\" width=\"437\" height=\"45\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-77.png 437w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-77-300x31.png 300w\" sizes=\"(max-width: 437px) 100vw, 437px\" \/><\/p>\n<p>Answer: 5(r + 15)<\/p>\n<p>Explanation:<br \/>\nEach day, you run on a treadmill for r minutes and lift weights for 15 minutes.<br \/>\nThey are both expressions with r as the variable.<br \/>\nThey are not equivalent expressions.<br \/>\nThey are equivalent expressions.<br \/>\nBoth expressions contain the terms 5, r, and 15.<br \/>\n5(15 + r) = 5(15) + 5(r)<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA cheetah can run 103 feet per second. A zebra can run x feet per second. Write and simplify an expression that represents how many feet farther the cheetah can run in 10 seconds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-78.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 78\" width=\"280\" height=\"222\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA cheetah can run 103 feet per second. A zebra can run x feet per second.<br \/>\nWe are given that the rate of cheetah Rc is:<br \/>\nRc = 103 ft \/ sec<br \/>\nAnd the rate of zebra Rz is:<br \/>\nRz = x ft \/ sec<br \/>\nWe are to find the distance between the two after 10 seconds, that is:<br \/>\ndistance = (103 \u2013 x) 10<br \/>\ndistance = 1030 \u2013 10 x<\/p>\n<p><strong>COMBINING LIKE TERMS<\/strong><br \/>\n<strong>Simplify the expression.<\/strong><\/p>\n<p>Question 36.<br \/>\n6(x + 4) + 1<\/p>\n<p>Answer: 6x + 25<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n6(x + 4) + 1<br \/>\n= (6 \u00d7 x) + (6 \u00d7 4) + 1<br \/>\n= 6x + 24 + 1<br \/>\n= 6x + 25<br \/>\nThus, 6(x + 4) + 1 = 6x + 25<\/p>\n<p>Question 37.<br \/>\n5 + 8(3 + x)<\/p>\n<p>Answer: 29 + 8x<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n5 + 8(3 + x)<br \/>\n= 5 + (8 \u00d7 3) + (8 \u00d7 x)<br \/>\n= 5 + 24 + 8x<br \/>\n= 29 + 8x<br \/>\nThus 5 + 8(3 + x) = 29 + 8x<\/p>\n<p>Question 38.<br \/>\nx + 3 + 5x<\/p>\n<p>Answer: 6x + 3<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\nx + 3 + 5x<br \/>\nCombine the like terms<br \/>\nx + 5x + 3<br \/>\n6x + 3<br \/>\nSo, x + 3 + 5x = 6x + 3<\/p>\n<p>Question 39.<br \/>\n7y + 6 &#8211; 1 + 12y<\/p>\n<p>Answer: 19y + 5<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n7y + 6 &#8211; 1 + 12y<br \/>\nCombine the like terms<br \/>\n7y + 12y + 6 &#8211; 1<br \/>\n= 19y + 5<br \/>\nSo, 7y + 6 &#8211; 1 + 12y = 19y + 5<\/p>\n<p>Question 40.<br \/>\n4d + 9 &#8211; d &#8211; 8<\/p>\n<p>Answer: 3d + 1<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n4d + 9 &#8211; d &#8211; 8<br \/>\nCombine the like terms<br \/>\n4d &#8211; d + 9 &#8211; 8<br \/>\n3d + 1<br \/>\nSo, 4d + 9 &#8211; d &#8211; 8 = 3d + 1<\/p>\n<p>Question 41.<br \/>\nn + 3(n &#8211; 1)<\/p>\n<p>Answer: 4n &#8211; 3<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\nn + 3(n &#8211; 1)<br \/>\nn + (3 \u00d7 n) &#8211; (3 \u00d7 1)<br \/>\nn + 3n &#8211; 3<br \/>\n4n &#8211; 3<br \/>\nSo, n + 3(n &#8211; 1) = 4n &#8211; 3<\/p>\n<p>Question 42.<br \/>\n2v + 8v &#8211; 5v<\/p>\n<p>Answer: 5v<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n2v + 8v &#8211; 5v<br \/>\nCombine the like terms<br \/>\nv(2 + 8 &#8211; 5)<br \/>\nv(5) = 5v<br \/>\nThus 2v + 8v &#8211; 5v = 5v<\/p>\n<p>Question 43.<br \/>\n5(z + 4) + 5(2 &#8211; z)<\/p>\n<p>Answer: 30<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n5(z + 4) + 5(2 &#8211; z)<br \/>\n= (5 \u00d7 z) + (5 \u00d7 4) + (5 \u00d7 2) &#8211; (5 \u00d7 z)<br \/>\n= 5z + 20 + 10 &#8211; 5z<br \/>\nNow combine the like terms<br \/>\n5z + 20 + 10 &#8211; 5z = 30<\/p>\n<p>Question 44.<br \/>\n2.7(w &#8211; 5.2)<\/p>\n<p>Answer: 2.7w &#8211; 14.04<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n2.7(w &#8211; 5.2)<br \/>\n= (2.7 \u00d7 w) &#8211; (2.7 \u00d7 5.2)<br \/>\n= 2.7w &#8211; 14.04<br \/>\nThus 2.7(w &#8211; 5.2) = 2.7w &#8211; 14.04<\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-79.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 79\" width=\"104\" height=\"52\" \/><\/p>\n<p>Answer:1 \\(\\frac{1}{2}\\)y<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n\\(\\frac{2}{3}\\)y + \\(\\frac{1}{6}\\)y + y<br \/>\ny(\\(\\frac{2}{3}\\) + \\(\\frac{1}{6}\\) + 1)<br \/>\n= 1 \\(\\frac{1}{2}\\)y<br \/>\nSo, <img loading=\"lazy\" class=\"alignnone size-full wp-image-24835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-79.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 79\" width=\"104\" height=\"52\" \/> = 1 \\(\\frac{1}{2}\\)y<\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-80.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 80\" width=\"106\" height=\"56\" \/><\/p>\n<p>Answer: 2\\(\\frac{3}{4}\\)z + \\(\\frac{3}{10}\\)<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-80.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 80\" width=\"106\" height=\"56\" \/><br \/>\n\\(\\frac{3}{4}\\)z + \\(\\frac{3}{10}\\) + 2z<br \/>\n2\\(\\frac{3}{4}\\)z + \\(\\frac{3}{10}\\)<\/p>\n<p>Question 47.<br \/>\n7(x + y) &#8211; 7x<\/p>\n<p>Answer: 7y<\/p>\n<p>Explanation:<br \/>\nGiven the expression<br \/>\n7(x + y) &#8211; 7x<br \/>\n= (7 \u00d7 x) + (7 \u00d7 y) &#8211; 7x<br \/>\n= 7x + 7y &#8211; 7x<br \/>\n= 7y<br \/>\nSo, 7(x + y) &#8211; 7x = 7y<\/p>\n<p>Question 48.<br \/>\n4x + 9y + 3(x + y)<\/p>\n<p>Answer: 7x + 12y<\/p>\n<p><span style=\"font-size: 16px;\">Explanation:<br \/>\n<\/span>Given the expression<br \/>\n4x + 9y + 3(x + y)<br \/>\n=4x + 9y + 3x + 3y<br \/>\n=4x + 3x + 9y + 3y<br \/>\n=7x + 12y<br \/>\nThus 4x + 9y + 3(x + y) = 7x + 12y<\/p>\n<p>Question 49.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend simpli\ufb01es the expression. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-81.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 81\" width=\"218\" height=\"126\" \/><\/p>\n<p>Answer: your friend is incorrect<\/p>\n<p>Explanation:<br \/>\n8x &#8211; 2x + 5x<br \/>\n= 6x + 5x<br \/>\n= 11x<br \/>\nBy this we can say that your friend is incorrect.<\/p>\n<p>Question 50.<br \/>\n<strong>REASONING<\/strong><br \/>\nEvaluate each expression by(1) using the Distributive Property and (2) evaluating inside the parentheses \ufb01rst. Which method do you prefer? Is your preference the same for both expressions? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-82.png\" alt=\"Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties 82\" width=\"311\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-82.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-82-300x54.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><\/p>\n<p>Answer:<br \/>\na. 2(3.22 &#8211; 0.12)<br \/>\nWe can solve this by using the Distributive Property<br \/>\n= 2(3.22) &#8211; 2(0.12)<br \/>\n= 6.44 &#8211; 0.24<br \/>\n= 6.20<br \/>\n2(3.22 &#8211; 0.12) = 6.20<br \/>\nb. 12(\\(\\frac{1}{2}\\) + \\(\\frac{2}{3}\\))<br \/>\nWe can solve this by using the Distributive Property<br \/>\n(12 \u00d7 \\(\\frac{1}{2}\\)) + (12 \u00d7 \\(\\frac{2}{3}\\))<br \/>\n= 6 + 8<br \/>\n= 14<br \/>\n12(\\(\\frac{1}{2}\\) + \\(\\frac{2}{3}\\)) = 14<\/p>\n<p>Question 51.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAn art club sells 42 large candles and 56 small candles.<br \/>\na. Write and simplify an expression that represents the pro\ufb01t.<br \/>\nb. A large candle costs $5, and a small candle costs $3. What is the club\u2019s pro\ufb01t?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-83.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 83\" width=\"251\" height=\"244\" \/><\/p>\n<p>Answer:<br \/>\nFor large candles, the selling price is $10 and its making cost is $x.<br \/>\nSo, by selling a large candle the profit is $(10 &#8211; x)<br \/>\nAgain for small candles, the selling price is $5 and its making cost is $y.<br \/>\nSo, by selling a small candle the profit is $(5 &#8211; y)<br \/>\nTherefore, in a sale of 42 large candles and 56 small candles, the total profit will be, P = 42 (10 &#8211; x) + 56 (5 &#8211; y)<br \/>\nP = 420 &#8211; 42x + 280 &#8211; 56y<br \/>\nP = $(700 &#8211; 42x &#8211; 56y<\/p>\n<p>Question 52.<br \/>\n<strong>REASONING<\/strong><br \/>\nFind the difference between the perimeters of the rectangle and the hexagon. Interpret your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-84.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 84\" width=\"346\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-84.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-84-300x134.png 300w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><\/p>\n<p>Answer:<br \/>\nRectangle:<br \/>\nPerimeter of the Rectangle = 2l + 2w<br \/>\nP = 2(2x + 7) + 2(2x)<br \/>\nP = 4x + 14 + 4x<br \/>\nP = 8x + 14<br \/>\nHexagon:<br \/>\nPerimeter of the Hexagon = 6a<br \/>\nP = x + x + 2x + 2x + x + 6 + x + 8<br \/>\nP = 8x + 14<br \/>\nThe difference between the perimeters of the rectangle and the hexagon is (8x + 14) &#8211; (8x + 14) = 0<\/p>\n<p>Question 53.<br \/>\n<strong>PUZZLE<\/strong><br \/>\nAdd one set of parentheses to the expression 7 . x + 3 + 8 . x + 3 . x + 8 \u2212 9 so that it is equivalent to 2(9x + 10).<\/p>\n<p>Answer:<br \/>\n7\u00d7(X+3)+8\u00d7X+3\u00d7X+8-9<br \/>\n=7\u00d7(X+3)+11\u00d7X-1<br \/>\n=7\u00d7X+21+11\u00d7X-1<br \/>\n=18\u00d7X+20<br \/>\n=2(9X+10)<\/p>\n<h3><a id=\"Lesson_5.5_Factoring_Expressions\"><\/a>Lesson 5.5 Factoring Expressions<\/h3>\n<p><strong>EXPLORATION 1<\/strong><br \/>\n<strong>Finding Dimensions<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. The models show the area (in square units) of each part of a rectangle. Use the models to \ufb01nd missing values that complete the expressions. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-85.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 85\" width=\"691\" height=\"412\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-85.png 691w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-85-300x179.png 300w\" sizes=\"(max-width: 691px) 100vw, 691px\" \/><br \/>\nb. In part(a), check that the original expressions are equivalent to the expressions you wrote. Explain your reasoning.<br \/>\nc. Explain how you can use the Distributive Property to rewrite a sum of two whole numbers with a common factor.<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-37810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-85-300x179.jpg\" alt=\"Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-85\" width=\"300\" height=\"179\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-85-300x179.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-85.jpg 691w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Factor the expression using the GCF.<\/p>\n<p>Question 1.<br \/>\n9 + 15<\/p>\n<p>Answer: 3<\/p>\n<p>Explanation:<br \/>\nThe factors of 9 are: 1, 3, 9<br \/>\nThe factors of 15 are: 1, 3, 5, 15<br \/>\nThe number does not contain any common variable factors.<br \/>\nThen the greatest common factor is 3.<\/p>\n<p>Question 2.<br \/>\n60 + 45<\/p>\n<p>Answer: 15<\/p>\n<p>Explanation:<br \/>\nThe factors of 45 are: 1, 3, 5, 9, 15, 45<br \/>\nThe factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60<br \/>\nThe number does not contain any common variable factors.<br \/>\nThen the greatest common factor is 15.<\/p>\n<p>Question 3.<br \/>\n30 &#8211; 20<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nThe factors of 20 are: 1, 2, 4, 5, 10, 20<br \/>\nThe factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30<br \/>\nThen the greatest common factor is 10.<\/p>\n<p><strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 4.<br \/>\n7x + 49<\/p>\n<p>Answer: 7<\/p>\n<p>Explanation:<br \/>\nSince 7x, 49 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 7 are: 1, 7<br \/>\nThe factors of 49 are: 1, 7, 49<br \/>\nThen the greatest common factor is 7.<\/p>\n<p>Question 5.<br \/>\n8y &#8211; 44<\/p>\n<p>Answer: 4<\/p>\n<p>Explanation:<br \/>\nSince 8y, 44 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 8 are: 1, 2, 4, 8<br \/>\nThe factors of 44 are: 1, 2, 4, 11, 22, 44<br \/>\nThen the greatest common factor is 4.<\/p>\n<p>Question 6.<br \/>\n25a + 10b<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nSince 25a, 10b contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 10 are: 1, 2, 5, 10<br \/>\nThe factors of 25 are: 1, 5, 25<br \/>\nThen the greatest common factor is 5.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>FACTORING EXPRESSIONS<\/strong><br \/>\n<strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 7.<br \/>\n16 + 24<\/p>\n<p>Answer: 8<\/p>\n<p>Explanation:<br \/>\nThe factors of 16 are: 1, 2, 4, 8, 16<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThen the greatest common factor is 8.<\/p>\n<p>Question 8.<br \/>\n49 &#8211; 28<\/p>\n<p>Answer: 7<\/p>\n<p>Explanation:<br \/>\nThe factors of 28 are: 1, 2, 4, 7, 14, 28<br \/>\nThe factors of 49 are: 1, 7, 49<br \/>\nThen the greatest common factor is 7.<\/p>\n<p>Question 9.<br \/>\n8y + 14<\/p>\n<p>Answer: 2<\/p>\n<p>Explanation:<br \/>\nSince 8y, 14 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 8 are: 1, 2, 4, 8<br \/>\nThe factors of 14 are: 1, 2, 7, 14<br \/>\nThen the greatest common factor is 2.<\/p>\n<p>Question 10.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-86.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 86\" width=\"472\" height=\"47\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-86.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-86-300x30.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Answer: 6(4n + 3)<\/p>\n<p>Explanation:<br \/>\ni. 3(8n + 12)<br \/>\n= 24n + 36<br \/>\nii. 4(6n + 9)<br \/>\n24n + 36<br \/>\niii. 6(4n + 3)<br \/>\n24n + 18<br \/>\niv. 12(2n + 3)<br \/>\n24n + 36<br \/>\nThus the third expression does not belong to the other three.<\/p>\n<p>Question 11.<br \/>\n<strong>REASONING<\/strong><br \/>\nUse what you know about factoring to explain how you can factor the expression 18x + 30y + 9z. Then factor the expression.<\/p>\n<p>Answer: 3 (6x + 10y + 3z)<\/p>\n<p>Explanation:<br \/>\nFactoring is a mathematical representation of the expression with the help of common factors.<br \/>\nIn this expression, we have given terms and their coefficients. Since we cannot factorize the terms, they will be intact in the process.<br \/>\nWe can factorize this expression with the help of prime numbers:<br \/>\n2 \u00d7 3 \u00d7 3 \u00d7 x + 2 \u00d7 3 \u00d7 5 \u00d7 y + 3 \u00d7 3 \u00d7 z<br \/>\nAnd finally, we will be able to obtain common factor from this expression:<br \/>\n3 ( 6x + 10y + 3z)<\/p>\n<p>Question 12.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIdentify the GCF of the terms (x . x) and (4 . x). Explain your reasoning. Then use the GCF to factor the expression x<sup>2<\/sup> + 4x.<\/p>\n<p>Answer:<br \/>\nx<sup>2<\/sup> + 4x<br \/>\n= x(x + 4)<br \/>\nThe factors of 1 are: 1<br \/>\nThe factors of 4 are: 1, 2, 4<br \/>\nThen the greatest common factor is 1.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 13.<br \/>\nA youth club receives a discount on each pizza purchased for a party. The original price of each pizza is x dollars. The club leader purchases 8 pizzas for a total of (8x \u2212 32) dollars. Factor the expression. What can you conclude about the discount?<\/p>\n<p>Answer:<br \/>\nGiven that,<br \/>\nA youth club receives a discount on each pizza purchased for a party.<br \/>\nThe original price of each pizza is x dollars.<br \/>\nThe club leader purchases 8 pizzas for a total of (8x \u2212 32) dollars.<\/p>\n<p>Question 14.<br \/>\nThree crates of food are packed on a shuttle departing for the Moon. Each crate weighs x pounds. On the Moon, the combined weight of the crates is (3x \u2212 81) pounds. What can you conclude about the weight of each crate on the Moon?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-87.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 87\" width=\"204\" height=\"282\" \/><\/p>\n<p>Answer:<br \/>\nThree crates of food are packed on a shuttle departing for the Moon.<br \/>\nEach crate weighs x pounds. On the Moon, the combined weight of the crates is (3x \u2212 81) pounds.<br \/>\nThe factors of 3 are: 1, 3<br \/>\nThe factors of 81 are: 1, 3, 9, 27, 81<br \/>\nThen the greatest common factor is 3.<\/p>\n<h3><a id=\"Factoring_Expressions_Homework_&amp;_Practice_5.5\"><\/a>Factoring Expressions Homework &amp; Practice 5.5<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Use the Distributive Property to simplify the expression.<\/p>\n<p>Question 1.<br \/>\n2(n + 8)<\/p>\n<p>Answer: 2n + 16<\/p>\n<p>Explanation:<br \/>\nGiven the expression 2(n + 8)<br \/>\nThe distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\n(2 \u00d7 n) + (2 \u00d7 8)<br \/>\n= 2n + 16<\/p>\n<p>Question 2.<br \/>\n3(4 + m)<\/p>\n<p>Answer: 12 + 3m<\/p>\n<p>Explanation:<br \/>\nThe distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\n3(4 + m)<br \/>\n= (3 \u00d7 4) + (3 \u00d7 m)<br \/>\n= 12 + 3m<\/p>\n<p>Question 3.<br \/>\n7(b &#8211; 3)<\/p>\n<p>Answer: 7b &#8211; 21<\/p>\n<p>Explanation:<br \/>\nThe distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\n7(b &#8211; 3)<br \/>\n= (7 \u00d7 b) &#8211; (7 \u00d7 3)<br \/>\n= 7b &#8211; 21<\/p>\n<p>Question 4.<br \/>\n10(4 &#8211; w)<\/p>\n<p>Answer: 40 &#8211; 10w<\/p>\n<p>Explanation:<br \/>\nThe distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\n10 (4 &#8211; w)<br \/>\n= (10 \u00d7 4) &#8211; (10 \u00d7 w)<br \/>\n= 40 &#8211; 10w<\/p>\n<p>Write the phrase as an expression.<\/p>\n<p>Question 5.<br \/>\n5 plus a number p<\/p>\n<p>Answer: 5 + p<\/p>\n<p>Explanation:<br \/>\nThe phrase plus indicates addition.<br \/>\nThe Express would be 5 + p<\/p>\n<p>Question 6.<br \/>\n18 less than a number r<\/p>\n<p>Answer: 18 &lt; r<\/p>\n<p>Explanation:<br \/>\nThe phrase less than indicates &lt; symbol.<br \/>\nSo the expression would be 18 &lt; r<\/p>\n<p>Question 7.<br \/>\n11 times a number d<\/p>\n<p>Answer: 11d<\/p>\n<p>Explanation:<br \/>\nThe phrase times indicates \u00d7 symbol.<br \/>\nSo, the expression would be 11d<\/p>\n<p>Question 8.<br \/>\na number c divided by 25<\/p>\n<p>Answer: c \u00f7 25<\/p>\n<p>Explanation:<br \/>\nThe phrase divided by indicates \u00f7<br \/>\nSo, the expression would be c \u00f7 25<\/p>\n<p><strong>Decide whether the rates are equivalent.<\/strong><\/p>\n<p>Question 9.<br \/>\n84 feet in 12 seconds<br \/>\n217 feet in 31 seconds<\/p>\n<p>Answer: The rates are equivalent<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n84 feet in 12 seconds<br \/>\n217 feet in 31 seconds<br \/>\nHere we have to check whether the rates are equivalent or not.<br \/>\n84 feet in 12 seconds = 7 : 1<br \/>\n217 feet in 31 seconds = 7 : 1<br \/>\nThus the rates are equivalent.<\/p>\n<p>Question 10.<br \/>\n12 cups of soda for every 54 cups of juice<br \/>\n8 cups of soda for every 36 cups of juice<\/p>\n<p>Answer: the rates are equivalent<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\n12 cups of soda for every 54 cups of juice<br \/>\n8 cups of soda for every 36 cups of juice<br \/>\nHere we have to check whether the rates are equivalent or not.<br \/>\n12 cups of soda for every 54 cups of juice = 2 : 9<br \/>\n8 cups of soda for every 36 cups of juice = 2 : 9<br \/>\nThus the rates are equivalent.<\/p>\n<p>Match the decimal with its equivalent percent.<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-88.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 88\" width=\"85\" height=\"65\" \/><\/p>\n<p>Answer: C<\/p>\n<p>Explanation:<br \/>\nThe fraction form of the decimal 0.36 is \\(\\frac{36}{100}\\)<br \/>\n\\(\\frac{36}{100}\\) \u00d7 100 = 36%<br \/>\nThus the equivalent percent is option C.<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-89.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 89\" width=\"82\" height=\"61\" \/><\/p>\n<p>Answer: B<\/p>\n<p>Explanation:<br \/>\nThe fraction form of the decimal 3.6 is \\(\\frac{36}{10}\\)<br \/>\n\\(\\frac{36}{10}\\) \u00d7 100 = 36 \u00d7 10 = 360%<br \/>\nThus the equivalent percent is option B.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-90.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 90\" width=\"72\" height=\"57\" \/><\/p>\n<p>Answer: A<\/p>\n<p>Explanation:<br \/>\nThe fraction form of the decimal 0.0036 is \\(\\frac{36}{10000}\\)<br \/>\n\\(\\frac{36}{10000}\\) \u00d7 100 = \\(\\frac{36}{100}\\) = 0.36%<br \/>\nThus the equivalent percent is option A.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-91.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 91\" width=\"75\" height=\"61\" \/><\/p>\n<p>Answer: B<\/p>\n<p>Explanation:<br \/>\nExplanation:<br \/>\nThe fraction form of the decimal 0.0036 is \\(\\frac{36}{1000}\\)<br \/>\n\\(\\frac{36}{1000}\\) \u00d7 100 = \\(\\frac{36}{10}\\) =3.6%<br \/>\nThus the equivalent percent is option D.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><br \/>\n<strong>FINDING DIMENSIONS<\/strong><br \/>\n<strong>The model shows the area (in square units) of each part of a rectangle. Use the model to \ufb01nd missing values that complete the expression. Explain your reasoning.<\/strong> (See Exploration 1, p. 227.)<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-92.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 92\" width=\"211\" height=\"146\" \/><\/p>\n<p>Answer:4(3 + 4)<\/p>\n<p>Explanation:<br \/>\nWe can find the area of the rectangle by using the distributive property.<br \/>\nLet us take 4 as the common factor<br \/>\n(12 + 16) = 4(3 + 4)<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-93.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 93\" width=\"215\" height=\"159\" \/><\/p>\n<p>Answer: 8(6 + 4)<\/p>\n<p>Explanation:<br \/>\nWe can find the area of the rectangle by using the distributive property.<br \/>\nLet us take 8 as a common factor<br \/>\n48 + 32 = 8 (6 + 4)<\/p>\n<p><strong>FACTORING NUMERICAL EXPRESSIONS<\/strong><br \/>\n<strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 17.<br \/>\n7 + 14<\/p>\n<p>Answer: 7<\/p>\n<p>Explanation:<br \/>\nThe factors of 7 are: 1, 7<br \/>\nThe factors of 14 are: 1, 2, 7, 14<br \/>\nThen the greatest common factor is 7.<\/p>\n<p>Question 18.<br \/>\n12 + 42<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nThe factors of 12 are: 1, 2, 3, 4, 6, 12<br \/>\nThe factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42<br \/>\nThen the greatest common factor is 6.<\/p>\n<p>Question 19.<br \/>\n22 + 11<\/p>\n<p>Answer: 11<\/p>\n<p>Explanation:<br \/>\nThe factors of 11 are: 1, 11<br \/>\nThe factors of 22 are: 1, 2, 11, 22<br \/>\nThen the greatest common factor is 11.<\/p>\n<p>Question 20.<br \/>\n70 + 95<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nThe factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70<br \/>\nThe factors of 95 are: 1, 5, 19, 95<br \/>\nThen the greatest common factor is 5.<\/p>\n<p>Question 21.<br \/>\n60 &#8211; 36<\/p>\n<p>Answer: 12<\/p>\n<p>Explanation:<br \/>\nThe factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36<br \/>\nThe factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60<br \/>\nThen the greatest common factor is 12.<\/p>\n<p>Question 22.<br \/>\n100 &#8211; 80<\/p>\n<p>Answer: 20<\/p>\n<p>Explanation:<br \/>\nThe factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80<br \/>\nThe factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100<br \/>\nThen the greatest common factor is 20.<\/p>\n<p>Question 23.<br \/>\n84 + 28<\/p>\n<p>Answer: 28<\/p>\n<p>Explanation:<br \/>\nThe factors of 28 are: 1, 2, 4, 7, 14, 28<br \/>\nThe factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84<br \/>\nThen the greatest common factor is 28.<\/p>\n<p>Question 24.<br \/>\n48 + 80<\/p>\n<p>Answer: 16<\/p>\n<p>Explanation:<br \/>\nThe factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48<br \/>\nThe factors of 80 are: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80<br \/>\nThen the greatest common factor is 16.<\/p>\n<p>Question 25.<br \/>\n19 + 95<\/p>\n<p>Answer: 19<\/p>\n<p>Explanation:<br \/>\nThe factors of 19 are: 1, 19<br \/>\nThe factors of 95 are: 1, 5, 19, 95<br \/>\nThen the greatest common factor is 19.<\/p>\n<p>Question 26.<br \/>\n44 &#8211; 11<\/p>\n<p>Answer: 11<\/p>\n<p>Explanation:<br \/>\nThe factors of 11 are: 1, 11<br \/>\nThe factors of 44 are: 1, 2, 4, 11, 22, 44<br \/>\nThen the greatest common factor is 11.<\/p>\n<p>Question 27.<br \/>\n18 &#8211; 12<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nThe factors of 12 are: 1, 2, 3, 4, 6, 12<br \/>\nThe factors of 18 are: 1, 2, 3, 6, 9, 18<br \/>\nThen the greatest common factor is 6.<\/p>\n<p>Question 28.<br \/>\n48 + 16<\/p>\n<p>Answer: 16<\/p>\n<p>Explanation:<br \/>\nThe factors of 16 are: 1, 2, 4, 8, 16<br \/>\nThe factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48<br \/>\nThen the greatest common factor is 16.<\/p>\n<p>Question 29.<br \/>\n98 &#8211; 70<\/p>\n<p>Answer: 14<\/p>\n<p>Explanation:<br \/>\nThe factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70<br \/>\nThe factors of 98 are: 1, 2, 7, 14, 49, 98<br \/>\nThen the greatest common factor is 14.<\/p>\n<p>Question 30.<br \/>\n58 + 28<\/p>\n<p>Answer: 2<\/p>\n<p>Explanation:<br \/>\nThe factors of 28 are: 1, 2, 4, 7, 14, 28<br \/>\nThe factors of 58 are: 1, 2, 29, 58<br \/>\nThen the greatest common factor is 2.<\/p>\n<p>Question 31.<br \/>\n72 &#8211; 39<\/p>\n<p>Answer: 3<\/p>\n<p>Explanation:<br \/>\nThe factors of 39 are: 1, 3, 13, 39<br \/>\nThe factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72<br \/>\nThen the greatest common factor is 3.<\/p>\n<p>Question 32.<br \/>\n69 + 84<\/p>\n<p>Answer: 3<\/p>\n<p>Explanation:<br \/>\nThe factors of 69 are: 1, 3, 23, 69<br \/>\nThe factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84<br \/>\nThen the greatest common factor is 3.<\/p>\n<p>Question 33.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe whole numbers a and b are divisible by c, where b is greater than a. Is a + b divisible by c ? Is b \u2212 a divisible by c ? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nLet the whole numbers a and b be 12 and 54<br \/>\nLet c be 6.<br \/>\nIn this case b is greater than a.<br \/>\nNow let us check whether and b are divisible by c.<br \/>\na + b \u00f7 c:<br \/>\n12 + 54 \u00f7 6<br \/>\n66 \u00f7 6 = 11<br \/>\nb &#8211; a \u00f7 c:<br \/>\n54 &#8211; 12 \u00f7 6<br \/>\n42 \u00f7 6 = 7<\/p>\n<p>Question 34.<br \/>\n<strong>MULTIPLE CHOICE<\/strong><br \/>\nWhich expression is not equivalent to 81x + 54?<br \/>\nA. 27(3x + 2)<br \/>\nB. 3(37x + 18)<br \/>\nC. 9(9x + 6)<br \/>\nD. 6(13x + 9)<\/p>\n<p>Answer: B. 3(37x + 18), D. 6(13x + 9)<\/p>\n<p>Explanation:<br \/>\nGiven the expression 81x + 54<br \/>\nA. 27(3x + 2)<br \/>\n= (27 \u00d7 3x) + (27 \u00d7 2)<br \/>\n= 81x + 54<br \/>\nB. 3(37x + 18)<br \/>\n= 111x + 54<br \/>\nC. 9(9x + 6)<br \/>\n= 81x + 54<br \/>\nD. 6(13x + 9)<br \/>\n78x + 54<br \/>\nThus the expression is not equivalent to 81x + 54 are option B and D.<\/p>\n<p><strong>FACTORING ALGEBRAIC EXPRESSIONS<br \/>\n<\/strong><strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 35.<br \/>\n2x + 10<\/p>\n<p>Answer: 2<\/p>\n<p>Explanation:<br \/>\nSince 2x, 10 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 2 are: 1, 2<br \/>\nThe factors of 10 are: 1, 2, 5, 10<br \/>\nThen the greatest common factor is 2.<\/p>\n<p>Question 36.<br \/>\n15x + 6<\/p>\n<p>Answer: 3<\/p>\n<p>Explanation:<br \/>\nSince 15x, 6 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 6 are: 1, 2, 3, 6<br \/>\nThe factors of 15 are: 1, 3, 5, 15<br \/>\nThen the greatest common factor is 3.<\/p>\n<p>Question 37.<br \/>\n26x &#8211; 13<\/p>\n<p>Answer: 13<\/p>\n<p>Explanation:<br \/>\nSince 26x, 13 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 13 are: 1, 13<br \/>\nThe factors of 26 are: 1, 2, 13, 26<br \/>\nThen the greatest common factor is 13<\/p>\n<p>Question 38.<br \/>\n50x &#8211; 60<\/p>\n<p>Answer: 10<\/p>\n<p>Explanation:<br \/>\nSince 50x, 60 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 50 are: 1, 2, 5, 10, 25, 50<br \/>\nThe factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60<br \/>\nThen the greatest common factor is 10.<\/p>\n<p>Question 39.<br \/>\n36x + 9<\/p>\n<p>Answer: 9<\/p>\n<p>Explanation:<br \/>\nSince 36x, 9 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 9 are: 1, 3, 9<br \/>\nThe factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36<br \/>\nThen the greatest common factor is 9<\/p>\n<p>Question 40.<br \/>\n14x &#8211; 98<\/p>\n<p>Answer: 14<\/p>\n<p>Explanation:<br \/>\nSince 14x, 98 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 14 are: 1, 2, 7, 14<br \/>\nThe factors of 98 are: 1, 2, 7, 14, 49, 98<br \/>\nThen the greatest common factor is 14.<\/p>\n<p>Question 41.<br \/>\n18p + 26<\/p>\n<p>Answer: 2<\/p>\n<p>Explanation:<br \/>\nSince 18p, 26 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 18 are: 1, 2, 3, 6, 9, 18<br \/>\nThe factors of 26 are: 1, 2, 13, 26<br \/>\nThen the greatest common factor is 2.<\/p>\n<p>Question 42.<br \/>\n16m + 40<\/p>\n<p>Answer: 8<\/p>\n<p>Explanation:<br \/>\nSince 16m, 40 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 16 are: 1, 2, 4, 8, 16<br \/>\nThe factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40<br \/>\nThen the greatest common factor is 8.<\/p>\n<p>Question 43.<br \/>\n24 + 72n<\/p>\n<p>Answer: 24<\/p>\n<p>Explanation:<br \/>\nSince 24, 72n contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThe factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72<br \/>\nThen the greatest common factor is 24.<\/p>\n<p>Question 44.<br \/>\n50 + 65h<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nSince 50, 65h contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 50 are: 1, 2, 5, 10, 25, 50<br \/>\nThe factors of 65 are: 1, 5, 13, 65<br \/>\nThen the greatest common factor is 5.<\/p>\n<p>Question 45.<br \/>\n76d &#8211; 24<\/p>\n<p>Answer: 4<\/p>\n<p>Explanation:<br \/>\nSince 76d, 24 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThe factors of 76 are: 1, 2, 4, 19, 38, 76<br \/>\nThen the greatest common factor is 4.<\/p>\n<p>Question 46.<br \/>\n27 &#8211; 45c<\/p>\n<p>Answer: 9<\/p>\n<p>Explanation:<br \/>\nSince 27, 45c contains both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 27 are: 1, 3, 9, 27<br \/>\nThe factors of 45 are: 1, 3, 5, 9, 15, 45<br \/>\nThen the greatest common factor is 9.<\/p>\n<p>Question 47.<br \/>\n18t + 38x<\/p>\n<p>Answer: 2<\/p>\n<p>Explanation:<br \/>\nSince 18t, 38x contains both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 18 are: 1, 2, 3, 6, 9, 18<br \/>\nThe factors of 38 are: 1, 2, 19, 38<br \/>\nThen the greatest common factor is 2.<\/p>\n<p>Question 48.<br \/>\n90y + 65z<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nSince 90y, 65z contains both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 65 are: 1, 5, 13, 65<br \/>\nThe factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90<br \/>\nThen the greatest common factor is 5.<\/p>\n<p>Question 49.<br \/>\n10x &#8211; 25y<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nSince 10x, 25y contains both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 10 are: 1, 2, 5, 10<br \/>\nThe factors of 25 are: 1, 5, 25<br \/>\nThen the greatest common factor is 5.<\/p>\n<p>Question 50.<br \/>\n24y + 88x<\/p>\n<p>Answer: 8<\/p>\n<p>Explanation:<br \/>\nSince 24y, 88x contains both numbers and variables, there are two steps to find the GCF.<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThe factors of 88 are: 1, 2, 4, 8, 11, 22, 44, 88<br \/>\nThen the greatest common factor is 8.<\/p>\n<p>Question 51.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nUse the Distributive Property to write two expressions that are equivalent to 8x + 16.<\/p>\n<p>Answer: 8(x + 2), 4(2x + 4)<\/p>\n<p>Explanation:<br \/>\nBy using the Distributive Property we can write 8x + 16 in two ways.<br \/>\n8x + 16<br \/>\nTake 8 as a common factor<br \/>\n8(x + 2)<br \/>\nNext take 4 as a common factor<br \/>\n4(2x + 4)<br \/>\nThe expressions 8(x + 2) and 4(2x + 4) are equivalent to 8x + 16<\/p>\n<p><strong>MATCHING<\/strong><br \/>\n<strong>Match the expression with an equivalent expression.<\/strong><\/p>\n<p>Question 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-94.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 94\" width=\"107\" height=\"66\" \/><\/p>\n<p>Answer: C<\/p>\n<p>Explanation:<br \/>\nGiven the expression 8x + 16y<br \/>\nLet us take 4 as a common factor.<br \/>\n4(2x + 4y)<br \/>\nThus the equivalent expression is option C.<\/p>\n<p>Question 53.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-95.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 95\" width=\"108\" height=\"67\" \/><\/p>\n<p>Answer: B<\/p>\n<p>Explanation:<br \/>\nGiven the expression 4x + 8y<br \/>\nLet us take 2 as a common factor.<br \/>\n4x + 8y = 2(4y + 2x)<br \/>\nThus the equivalent expression is option B.<\/p>\n<p>Question 54.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-96.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 96\" width=\"110\" height=\"68\" \/><\/p>\n<p>Answer: D<\/p>\n<p>Explanation:<br \/>\nGiven the expression 16x + 8y<br \/>\nLet us take 8 as a common factor.<br \/>\n16x + 8y = 8(2x + y)<br \/>\nThis can also be written as 8(y + 2x)<br \/>\nThus the equivalent expression is option D.<\/p>\n<p>Question 55.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-97.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 97\" width=\"99\" height=\"79\" \/><\/p>\n<p>Answer: A<\/p>\n<p>Explanation:<br \/>\nGiven the expression 8x + 4y<br \/>\nLet us take 4 as a common factor.<br \/>\n8x + 4y = 4(2x + y)<br \/>\nThus the equivalent expression is option A.<\/p>\n<p>Question 56.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend factors the expression 24x + 56. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-98.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 98\" width=\"255\" height=\"112\" \/><\/p>\n<p>Answer: your friend is incorrect<\/p>\n<p>Explanation:<br \/>\nGiven the expression 24x + 56<br \/>\nTake 8 as the common factor from the expression.<br \/>\n24x + 56 = 8(3x + 7)<br \/>\nBy this, we can say that your friend is incorrect.<\/p>\n<p>Question 57.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou sell soup mixes for a fundraiser. For each soup mix you sell, the company that makes the soup receives x dollars, and you receive the remaining amount. You sell 16 soup mixes for a total of (16x + 96) dollars. How much money do you receive for each soup mix that you sell?<\/p>\n<p>Answer: $6<\/p>\n<p>Explanation:<br \/>\nHere, the cost price of each soup = x dollars<br \/>\nThe cost price of 16 soup = 16 x<br \/>\nThe selling price of 16 soup = 16 x + 96<br \/>\nSince, the total money received for 16 soup = The selling price of 16 soup &#8211; The cost price of 16 soup<br \/>\n= 16 x + 96 &#8211; 16 x<br \/>\n= 96<br \/>\nThus, the total money received for 16 soup = 96 dollars<br \/>\n\u21d2 The total money received for 1 soup = 96\/16 dollars<br \/>\n\u21d2 The total money received for 1 soup = 6 dollars<br \/>\nHence, for each soup 6 dollars is received.<\/p>\n<p>Question 58.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA clothing store is having a sale on holiday socks. Each pair of socks costs x dollars. You leave the store with 6 pairs of socks and spend a total of (6x \u2212 14) dollars. You pay with $40. How much change do you receive? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-99.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 99\" width=\"207\" height=\"196\" \/><\/p>\n<p>Answer: $14<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA clothing store is having a sale on holiday socks. Each pair of socks costs x dollars.<br \/>\nYou leave the store with 6 pairs of socks and spend a total of (6x \u2212 14) dollars.<br \/>\nYou pay with $40.<br \/>\nSince, the cost of 1 pair of socks = x<br \/>\nThe cost of 6 pair of socks = 6 x<br \/>\nTotal amount spend = $ 40<br \/>\nAccording to the question,<br \/>\n6 x &#8211; 14 = 40<br \/>\n6 x = 40 + 14<br \/>\n6 x = 54<br \/>\nx = 9<br \/>\nThus, the original price of one pair of socks = $ 9<br \/>\nThe original price of 6 pairs of socks = $ 54<br \/>\nHence, the total change = original price of socks &#8211; the price of socks in the sale = 54 &#8211; 40 = $ 14<\/p>\n<p>Question 59.<br \/>\n<strong>STRUCTURE<\/strong><br \/>\nYou buy 37 concert tickets for $8 each, and then sell all 37 tickets for $11 each. The work below shows two ways you can determine your pro\ufb01t. Describe each solution method. Which do you prefer? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-100.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 100\" width=\"428\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-100.png 428w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-100-300x87.png 300w\" sizes=\"(max-width: 428px) 100vw, 428px\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nYou buy 37 concert tickets for $8 each, and then sell all 37 tickets for $11 each.<br \/>\nI prefer the second method which is simplified using the distributive property.<br \/>\nNumber of concert tickets = 37<br \/>\nActual price = $8<br \/>\nselling price = $11<br \/>\nProfit = Number of tickets (selling price &#8211; cost price)<br \/>\nP = 37 (11 &#8211; 8)<br \/>\nP = 37(3)<br \/>\nP = $111<\/p>\n<p>Question 60.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nThe prime factorizations of two numbers are shown, where a and b represent prime numbers. Write the sum of the two numbers as an expression of the form <img loading=\"lazy\" class=\"alignnone size-full wp-image-24821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-101.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 101\" width=\"116\" height=\"38\" \/>. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-101.1.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 101.1\" width=\"390\" height=\"43\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-101.1.png 390w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-101.1-300x33.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>Answer:<br \/>\nLet us consider a and b are 2 and 5<br \/>\nNumber 1:<br \/>\n2 \u00d7 11 \u00d7 5 \u00d7 a<br \/>\nNumber 2:<br \/>\n7 \u00d7 b \u00d7 3 \u00d7 3<br \/>\n14 (2 + 5) = 140<\/p>\n<h3><a id=\"Algebraic_Expressions_and_Properties_Connecting_Concepts\"><\/a>Algebraic Expressions and Properties Connecting Concepts<\/h3>\n<p><strong>Connecting Concepts<\/strong><br \/>\n<strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nA store sells 18 pairs of the wireless earbuds shown. Customers saved a total of $882 on the earbuds. Find the original price of the earbuds.<br \/>\n<strong>Understand the problem.<\/strong><br \/>\nYou know the percent discount on a pair of wireless earbuds, the number of pairs of earbuds sold, and the total amount of money that customers saved. You are asked to \ufb01nd the original price of the earbuds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-102.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 102\" width=\"171\" height=\"182\" \/><br \/>\n<strong>Make a plan<\/strong><br \/>\nFirst, write an expression that represents the total amount of money that customers pay for the earbuds. Then factor the expression to \ufb01nd the discount (in dollars) on each pair of earbuds. Finally, solve a percent problem to \ufb01nd the original price.<br \/>\n<strong>Solve and check.<\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<br \/>\nNumber of pairs = 18<br \/>\nAmount saved = $882<br \/>\nLet d be the cost of the wireless earbuds<br \/>\nSo, the expression would be 18d + 882<\/p>\n<p>Question 2.<br \/>\nAll of the weight plates in a gym are labeled in kilograms. You want to convert the weights to pounds. Write an expression to \ufb01nd the number of pounds in z kilograms. Then \ufb01nd the weight in pounds of a plate that weighs 20.4 kilograms.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-103.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 103\" width=\"242\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\nAll of the weight plates in a gym are labeled in kilograms. You want to convert the weights to pounds<br \/>\nConvert from kilograms to pounds<br \/>\n1 kg = 2.20 pounds<br \/>\nThe expression would be 2.20z<br \/>\nNow we have to find the weight of 20.4 kilograms to pounds.<br \/>\n20.4kg = 2.20 \u00d7 20.4<br \/>\n= 44.97 pounds<\/p>\n<p>Question 3.<br \/>\nYou buy apple chips and banana chips in the ratio of 2 : 7.<br \/>\na. How many ounces of banana chips do you buy when you buy n ounces of apple chips? Explain.<\/p>\n<p>Answer:<br \/>\nThe ratio of apple chips and banana chips = 2 : 7<br \/>\nApple chips = 2<br \/>\nBanana chips = 7<br \/>\n2 + 7 = 9<br \/>\nn\/2 = 9<br \/>\nn = 18<br \/>\n18 ounces of apple chips<br \/>\nn\/7 = 9<br \/>\nn = 9 \u00d7 7<br \/>\nn = 63<br \/>\n63 ounces of banana chips for 18 ounces of apple chips.<br \/>\nb. You buy 12 ounces of apple chips. How many ounces of banana chips do you buy?<\/p>\n<p>Answer:<br \/>\nYou buy 12 ounces of apple chips.<br \/>\nThe ratio of apple chips and banana chips = 2 : 7<br \/>\nApple chips = 2x<br \/>\nBanana chips = 7x<br \/>\n2 + 7 = 9<br \/>\nn = 12<br \/>\nFor 12 ounces of apple chips you buy 42 ounces of banana chips<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Describing Change<\/strong><\/p>\n<p>At the beginning of this chapter, you watched a STEAM video called \u201cShadow Drawings.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-104.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 104\" width=\"274\" height=\"200\" \/><\/p>\n<h3><a id=\"Algebraic_Expressions_and_Properties_Chapter_Review\"><\/a>Algebraic Expressions and Properties Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p><strong>Write the de\ufb01nition and give an example of each vocabulary term.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-105.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 105\" width=\"594\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-105.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-105-300x48.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use an Example and Non-Example Chartto list examples and non-examples of a concept. Here is an Example and Non-Example Chart for the CommutativeProperty of Addition.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-106.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 106\" width=\"423\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-106.png 423w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-106-300x158.png 300w\" sizes=\"(max-width: 423px) 100vw, 423px\" \/><\/p>\n<p>Choose and complete a graphic organizer to help you study the concept.<\/p>\n<ol>\n<li>algebraic expressions<\/li>\n<li>variable<\/li>\n<li>Commutative Property of Multiplication<\/li>\n<li>Associative Property of Addition<\/li>\n<li>Associative Property of Multiplication<\/li>\n<li>Addition Property of Zero<\/li>\n<li>Multiplication Property of Zero<\/li>\n<li>Multiplication Property of One<\/li>\n<li>Distributive Property<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-107.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 107\" width=\"261\" height=\"358\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-107.png 261w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-107-219x300.png 219w\" sizes=\"(max-width: 261px) 100vw, 261px\" \/><\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-108.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 108\" width=\"645\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-108.png 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-108-300x36.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><\/p>\n<p><strong>5.1 Algebraic Expressions (pp. 201 &#8211; 208)<\/strong><\/p>\n<p><strong>Identify the terms, coefficients, and constants in the expression.<\/strong><\/p>\n<p>Question 1.<br \/>\n9x + 2 + 8y<\/p>\n<p>Answer:<br \/>\n2 &#8211; constant<br \/>\n9, 8 &#8211; coefficient<br \/>\nx, y &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 2.<br \/>\n3x<sup>2<\/sup> + x + 7<\/p>\n<p>Answer:<br \/>\n7 &#8211; constant<br \/>\n3, 1 &#8211; coefficient<br \/>\nx &#8211; variable or term<br \/>\n2 is the exponent<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nAn exponent refers to the number of times a number is multiplied by itself.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-109.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 109\" width=\"84\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\n1 &#8211; constant<br \/>\n7, 1\/4 &#8211; coefficient<br \/>\nq &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p><strong>Evaluate the expression when x = 20, y = 4, and z = 7.<\/strong><\/p>\n<p>Question 4.<br \/>\nx \u00f7 5<\/p>\n<p>Answer: 4<\/p>\n<p>Explanation:<br \/>\nGiven expression is x \u00f7 5<br \/>\nWhere x = 20<br \/>\n20 \u00f7 5 = 4<br \/>\nThus x \u00f7 5 = 4<\/p>\n<p>Question 5.<br \/>\n12 &#8211; z<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nGiven expression is 12 &#8211; z<br \/>\nWhere z = 7<br \/>\n12 &#8211; z<br \/>\n= 12 &#8211; 7<br \/>\n= 5<br \/>\nThus 12 &#8211; z = 5<\/p>\n<p>Question 6.<br \/>\n4y<\/p>\n<p>Answer: 16<\/p>\n<p>Explanation:<br \/>\nThe given expression is 4y<br \/>\nWhere<br \/>\ny = 4<br \/>\n4y = 4(4) = 16<\/p>\n<p>Question 7.<br \/>\ny + x<\/p>\n<p>Answer: 24<\/p>\n<p>Explanation:<br \/>\nGiven expression is y + x<br \/>\nWhere<br \/>\ny = 4<br \/>\nx = 20<br \/>\ny + x<br \/>\n= 4 + 20 = 24<br \/>\nThus y + x = 24<\/p>\n<p>Question 8.<br \/>\nx . z<\/p>\n<p>Answer: 80<\/p>\n<p>Explanation:<br \/>\nGiven expression is x . z<br \/>\nWhere<br \/>\nx = 20<br \/>\nz = 7<br \/>\nx . z = 20 \u00d7 7 = 140<br \/>\nThus x . z = 140<\/p>\n<p>Question 9.<br \/>\nx &#8211; y<\/p>\n<p>Answer: 16<\/p>\n<p>Explanation:<br \/>\nGiven expression is x &#8211; y<br \/>\nWhere<br \/>\ny = 4<br \/>\nx = 20<br \/>\n20 &#8211; 4 = 16<br \/>\nThus x &#8211; y = 16<\/p>\n<p>Question 10.<br \/>\n3z + 8<\/p>\n<p>Answer: 29<\/p>\n<p>Explanation:<br \/>\nGiven expression is 3z + 8<br \/>\nWhere<br \/>\nz = 7<br \/>\n3z + 8 = 3(7) + 8<br \/>\n= 21 + 8<br \/>\n= 29<br \/>\nThus 3z + 8 = 29<\/p>\n<p>Question 11.<br \/>\n8y &#8211; x<\/p>\n<p>Answer: 12<\/p>\n<p>Explanation:<br \/>\nGiven expression is 8y &#8211; x<br \/>\nWhere<br \/>\ny = 4<br \/>\nx = 20<br \/>\n8y &#8211; x = 8(4) &#8211; 20<br \/>\n= 32 &#8211; 20<br \/>\n= 12<br \/>\nThus 8y &#8211; x = 12<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-110.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 110\" width=\"31\" height=\"56\" \/><\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\nGiven expression is <img loading=\"lazy\" class=\"alignnone size-full wp-image-24847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-110.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 110\" width=\"31\" height=\"56\" \/><br \/>\nWhere<br \/>\ny = 4<br \/>\nx = 20<br \/>\n(20)\u00b2\/4<br \/>\n= (20 \u00d7 20)\/4<br \/>\n= 5 \u00d7 20<br \/>\n= 100<\/p>\n<p>Question 13.<br \/>\nThe amount earned (in dollars) for recycling pounds of copper is 2p. How much do you earn for recycling 28 pounds of copper?<\/p>\n<p>Answer: 56<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nThe amount earned (in dollars) for recycling pounds of copper is 2p.<br \/>\nSubstitute the value of p in the expression.<br \/>\np = 28<br \/>\n2p = 2(28) = 56<\/p>\n<p>Question 14.<br \/>\nWhile playing a video game, you score p game points and b triple bonus points. An expression for your score is p + 3b. What is your score when you earn 245 game points and 20 triple bonus points?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-111.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 111\" width=\"257\" height=\"303\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-111.png 257w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-111-254x300.png 254w\" sizes=\"(max-width: 257px) 100vw, 257px\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nWhile playing a video game, you score p game points and b triple bonus points. An expression for your score is p + 3b.<br \/>\np = 245<br \/>\nb = 20<br \/>\nSubstitute the value of p and b in the given expression<br \/>\np + 3b = 245 + 3(22)<br \/>\n245 + 66 = 311<\/p>\n<p>Question 15.<br \/>\nTickets for a baseball game cost a dollars for adults and c dollars for children. The expression 2a + 3c represents the cost (in dollars) for a family to go to the game. What is the cost for the family when an adult ticket is $17 and a child ticket is $12?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nTickets for a baseball game cost a dollars for adults and c dollars for children.<br \/>\nThe expression 2a + 3c represents the cost (in dollars) for a family to go to the game.<br \/>\na = 17<br \/>\nc = 12<br \/>\n2a + 3c<br \/>\nSubstitute the value of a and c in the given expression<br \/>\n= 2(17) + 3(12)<br \/>\n= 34 + 36<br \/>\n= 70<\/p>\n<p>Question 16.<br \/>\nAdd one set of parentheses to the expression 2x<sup>2<\/sup> + 4 \u2212 5 so that the value of the expression is 75 when x = 6.<\/p>\n<p>Answer:<br \/>\n2x<sup>2<\/sup> + 4 \u2212 5<br \/>\nx = 6<br \/>\n2(6)<sup>2<\/sup> + 4 \u2212 5<br \/>\n= 2(36) &#8211; 1<br \/>\n= 72 &#8211; 1<br \/>\n= 71<br \/>\nAdd 4 to the expression to get the value 75<br \/>\n2x<sup>2<\/sup> + 4 \u2212 5 + 4<br \/>\nx = 6<br \/>\n2(6)<sup>2<\/sup> + 4 \u2212 5 + 4<br \/>\n= 2(36) &#8211; 1 + 4<br \/>\n= 72 &#8211; 1 + 4<br \/>\n= 71 + 4<br \/>\n= 75<\/p>\n<p><strong>5.2 Writing Expressions<\/strong> (pp. 209\u2013214)<\/p>\n<p>Write the phrase as an expression.<\/p>\n<p>Question 17.<br \/>\n9 fewer than 23<\/p>\n<p>Answer: 9 &#8211; 23<\/p>\n<p>Explanation:<br \/>\nThe phrase &#8220;fewer than&#8221; represents &#8211; symbol<br \/>\nThus the expression would be 9 &#8211; 23<\/p>\n<p>Question 18.<br \/>\n6 more than the quotient of 15 and 3<\/p>\n<p>Answer: 6 + (15 \u00f7 3)<\/p>\n<p>Explanation:<br \/>\nThe phrase more than represents &#8216;+&#8217; and quotient represents &#8216;\u00f7&#8217;<br \/>\nThus the expression would be 6 + (15 \u00f7 3)<\/p>\n<p>Question 19.<br \/>\nthe product of a number d and 32<\/p>\n<p>Answer: 32d<\/p>\n<p>Explanation:<br \/>\nThe phrase product represents &#8216;\u00d7&#8217; symbol.<br \/>\nThus the expression would be 32d<\/p>\n<p>Question 20.<br \/>\na number t decreased by 17<\/p>\n<p>Answer: d &#8211; 17<\/p>\n<p>Explanation:<br \/>\nThe phrase &#8220;decreased&#8221; represents &#8216;-&#8216; symbol.<br \/>\nThus the expression would be d &#8211; 17<\/p>\n<p>Question 21.<br \/>\nYour basketball team scored 4 fewer than twice as many points as the other team.<br \/>\na. Write an expression that represents the number of points your team scored.<\/p>\n<p>Answer:<br \/>\nYour basketball team scored 4 fewer than twice as many points, x, as the other team.<br \/>\nn = 2x &#8211; 4<br \/>\nb. The other team scored 24 points. How many points did your team score?<\/p>\n<p>Answer: 14<\/p>\n<p>Explanation:<br \/>\nThe other team scored 24 points i.e. n=24.<br \/>\n24 = 2x &#8211; 4<br \/>\n2x = 24 + 4<br \/>\n2x = 28<br \/>\nx = 28\/2<br \/>\nx = 14<br \/>\nThus the team score 14 points.<\/p>\n<p>Question 22.<br \/>\nThe boiling temperature (in degrees Celsius) of platinum is 199 more than four times the boiling temperature (in degrees Celsius) of zinc.<br \/>\na. Write an expression that represents the boiling temperature (in degrees Celsius) of platinum.<\/p>\n<p>Answer: P = 199 + 4z<br \/>\nb. The boiling temperature of zinc is 907 degrees Celsius. What is the boiling temperature of platinum?<\/p>\n<p>Answer:<br \/>\nThe boiling temperature of zinc is 907 degrees Celsius.<br \/>\nP = 199 + 4z<br \/>\nP = 199 + 4(907)<br \/>\nP = 3827<\/p>\n<p>Question 23.<br \/>\nWrite an algebraic expression with two variables, x and y, that has a value of 50 when x = 3 and y = 5. (pp. 215\u2013220)<\/p>\n<p>Answer: 5x + 7y = 50<\/p>\n<p>Explanation:<br \/>\nLet us assume that the algebraic expression is 5x + 7y = 50<br \/>\nWhere x = 3 and y = 5<br \/>\n5(3) + 7(5) = 50<br \/>\n15 + 35 = 50<br \/>\n50 = 50<br \/>\nOur assumption is correct.<\/p>\n<p><strong>5.3 Properties of Addition and Multiplication<\/strong><\/p>\n<p>Simplify the expression. Explain each step.<\/p>\n<p>Question 24.<br \/>\n10 + (2 + y)<\/p>\n<p>Answer: 12 + y<\/p>\n<p>Explanation:<br \/>\nGiven the expression 10 + (2 + y)<br \/>\nCombine the like terms<br \/>\n10 + 2 + y = 12 + y<\/p>\n<p>Question 25.<br \/>\n(21 + b) + 1<\/p>\n<p>Answer: 22 + b<\/p>\n<p>Explanation:<br \/>\nGiven the expression (21 + b) + 1<br \/>\nCombine the like terms<br \/>\n21+ 1 + b<br \/>\n22 + b<\/p>\n<p>Question 26.<br \/>\n3(7x)<\/p>\n<p>Answer: 21x<\/p>\n<p>Explanation:<br \/>\nGiven the expression 3(7x)<br \/>\n3 \u00d7 7x = 21x<\/p>\n<p>Question 27.<br \/>\n1(3.2w)<\/p>\n<p>Answer: 3.2w<\/p>\n<p>Explanation:<br \/>\nGiven the expression 1(3.2w)<br \/>\n1 \u00d7 3.2w = 3.2w<\/p>\n<p>Question 28.<br \/>\n5.3 + (w + 1.2)<\/p>\n<p>Answer: 6.5 + w<\/p>\n<p>Explanation:<br \/>\nGiven the expression 5.3 + (w + 1.2)<br \/>\nCombine the like terms<br \/>\n5.3 + 1.2 + w<br \/>\n= 6.5 + w<\/p>\n<p>Question 29.<br \/>\n(0 + t) + 9<\/p>\n<p>Answer: t + 9<\/p>\n<p>Explanation:<br \/>\nGiven the expression (0 + t) + 9<br \/>\nCombine the like terms<br \/>\n(0 + t) + 9 = t + 9<\/p>\n<p>Question 30.<br \/>\nThe expression 7 + 3x+ 4 represents the perimeter of the triangle. Simplify the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-112.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 112\" width=\"123\" height=\"162\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThe expression 7 + 3x+ 4 represents the perimeter of the triangle.<br \/>\nCombine the like terms<br \/>\n7 + 3x+ 4 = 11 + 3x<\/p>\n<p>Question 31.<br \/>\nWrite an algebraic expression that can be simpli\ufb01ed using the Associative Property of Addition.<\/p>\n<p>Answer:<br \/>\nAssociative property of addition: Changing the grouping of addends does not change the sum. For example, ( 2 + 3 ) + 4 = 2 + ( 3 + 4 ) (2 + 3) + 4 = 2 + (3 + 4) (2+3)+4=2+(3+4) left parenthesis, 2, plus, 3, right parenthesis, plus, 4, equals, 2, plus, left parenthesis, 3, plus, 4, right parenthesis.<\/p>\n<p><strong>5.4 The Distributive Property<\/strong><\/p>\n<p>Use the Distributive Property to simplify the expression.<\/p>\n<p>Question 32.<br \/>\n2(x + 12)<\/p>\n<p>Answer:<br \/>\nWe can simplify the expression by using the Distributive Property.<br \/>\nThe distributive property explains that multiplying two numbers together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\n2(x + 12) = 2 \u00d7 x + 2 \u00d7 12<br \/>\n= 2x + 24<\/p>\n<p>Question 33.<br \/>\n11(4b &#8211; 3)<\/p>\n<p>Answer:<br \/>\nGiven the expression 11(4b &#8211; 3)<br \/>\nWe can simplify the expression by using the Distributive Property.<br \/>\nThe distributive property explains that multiplying two numbers together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\n11(4b &#8211; 3) = 11 \u00d7 4b &#8211; 11 \u00d7 3<br \/>\n= 44b &#8211; 33<\/p>\n<p>Question 34.<br \/>\n8(s &#8211; 1)<\/p>\n<p>Answer:<br \/>\nGiven the expression 8(s &#8211; 1)<br \/>\nWe can simplify the expression by using the Distributive Property.<br \/>\nThe distributive property explains that multiplying two numbers together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\n8(s &#8211; 1) = 8 \u00d7 s &#8211; 8 \u00d7 1<br \/>\n= 8s &#8211; 8<\/p>\n<p>Question 35.<br \/>\n6(6 + y)<\/p>\n<p>Answer:<br \/>\nGiven the expression 6(6 + y)<br \/>\nWe can simplify the expression by using the Distributive Property.<br \/>\nThe distributive property explains that multiplying two numbers together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\n6(6 + y) = 6 \u00d7 6 + 6 \u00d7 y<br \/>\n36 + 6y<\/p>\n<p><strong>Simplify the expression.<\/strong><\/p>\n<p>Question 36.<br \/>\n5(n + 3) + 4n<\/p>\n<p>Answer:<br \/>\nGiven the expression 5(n + 3) + 4n<br \/>\nCombine the like terms<br \/>\n5(n + 3) + 4n<br \/>\n= 5 \u00d7 n + 5 \u00d7 3 + 4n<br \/>\n= 5n + 15 + 4n<br \/>\n= 9n + 15<\/p>\n<p>Question 37.<br \/>\nt + 2 + 6t<\/p>\n<p>Answer:<br \/>\nGiven the expression t + 2 + 6t<br \/>\nCombine the like terms<br \/>\nt + 2 + 6t<br \/>\n7t + 2<\/p>\n<p>Question 38.<br \/>\n3z + 14 + 5z &#8211; 9<\/p>\n<p>Answer:<br \/>\nGiven the expression 3z + 14 + 5z &#8211; 9<br \/>\nCombine the like terms<br \/>\n3z + 14 + 5z &#8211; 9<br \/>\n8z &#8211; 5<\/p>\n<p>Question 39.<br \/>\nA family of three goes to a salon. Each person gets a haircut and highlights. The cost of each haircut is $15, and the cost per person for highlights is x dollars. Write and simplify an expression that represents the total cost (in dollars) for the family at the salon.<\/p>\n<p>Answer: 45 + 3(x)<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA family of three goes to a salon. Each person gets a haircut and highlights.<br \/>\nThe cost of each haircut is $15, and the cost per person for highlights is x dollars.<br \/>\nThe expression would be 45 + 3x<br \/>\nEach person gets a haircut = 3 \u00d7 15 = 45<\/p>\n<p>Question 40.<br \/>\nEach day, you take vocal lessons for v minutes and trumpet lessons for 30 minutes. Write and simplify an expression to \ufb01nd how many minutes of lessons you take in 4 days.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-113.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 113\" width=\"281\" height=\"183\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nMinutes of vocal lessons I take each day =<br \/>\nMinutes of trumpet lessons I take each day = 30<br \/>\nTo write and simplify how many minutes of lessons I take in 4 days.<br \/>\nSolution:<br \/>\nTotal number of minutes of lesson I take each day can be calculated by adding the minutes of lessons taken each day and can be given as:<br \/>\n= v + 30<br \/>\nThe expression would be (v + 30)<br \/>\nSo in 4 days I will take = 4(v + 30)<br \/>\n= 4v + 120<br \/>\nThus, total minutes of lessons I take in 4 days = 4v + 120<\/p>\n<p><strong>5.5 Factoring Expressions<\/strong> (pp. 227 &#8211; 232)<\/p>\n<p><strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 41.<br \/>\n42 &#8211; 12<\/p>\n<p>Answer: 6<\/p>\n<p>Explanation:<br \/>\nThe factors of 12 are: 1, 2, 3, 4, 6, 12<br \/>\nThe factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42<br \/>\nThen the greatest common factor is 6.<\/p>\n<p>Question 42.<br \/>\n15 + 35<\/p>\n<p>Answer: 5<\/p>\n<p>Explanation:<br \/>\nThe factors of 15 are: 1, 3, 5, 15<br \/>\nThe factors of 35 are: 1, 5, 7, 35<br \/>\nThen the greatest common factor is 5.<\/p>\n<p>Question 43.<br \/>\n36x &#8211; 28<\/p>\n<p>Answer: 4<\/p>\n<p>Explanation:<br \/>\nThe factors of 28 are: 1, 2, 4, 7, 14, 28<br \/>\nThe factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36<br \/>\nThen the greatest common factor is 4.<\/p>\n<p>Question 44.<br \/>\n24 + 64x<\/p>\n<p>Answer: 8<\/p>\n<p>Explanation:<br \/>\nThe factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThe factors of 64 are: 1, 2, 4, 8, 16, 32, 64<br \/>\nThen the greatest common factor is 8.<\/p>\n<p>Question 45.<br \/>\n60 &#8211; 150x<\/p>\n<p>Answer: 30<\/p>\n<p>Explanation:<br \/>\nThe factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60<br \/>\nThe factors of 150 are: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150<br \/>\nThen the greatest common factor is 30.<\/p>\n<p>Question 46.<br \/>\n16x + 56y<\/p>\n<p>Answer: 8<\/p>\n<p>Explanation:<br \/>\nThe factors of 16 are: 1, 2, 4, 8, 16<br \/>\nThe factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56<br \/>\nThen the greatest common factor is 8.<\/p>\n<p>Question 47.<br \/>\nA soccer team receives a discount on each jersey purchased. The original price of each jersey is x dollars. The team buys 18 jerseys for a total of (18x \u2212 36) dollars. What can you conclude about the discount?<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nA soccer team receives a discount on each jersey purchased.<br \/>\nThe original price of each jersey is x dollars.<br \/>\nThe team buys 18 jerseys for a total of (18x \u2212 36) dollars.<br \/>\nMultiply 18 with the original price after that you decrease 36 dollars.<br \/>\nBy this, we can conclude that $36 is the discount<\/p>\n<p>Question 48.<br \/>\nYou sell apple cider for a fundraiser. For each gallon of cider you sell, the company that makes the cider receives x dollars, and you receive the remaining amount. You sell 15 gallons of cider for (15x + 45) dollars. How much money do you receive for each gallon of cider that you sell?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-113.1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 113.1\" width=\"221\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nYou sell apple cider for a fundraiser. For each gallon of cider you sell, the company that makes the cider receives x dollars, and you receive the remaining amount.<br \/>\nYou sell 15 gallons of cider for (15x + 45) dollars<br \/>\nLet x = 1<br \/>\n15(1) + 45 = 60<br \/>\nx = 2<br \/>\n15(2) + 45 = 30 + 45 = 75<\/p>\n<h3><a id=\"Algebraic_Expressions_and_Properties_Practice_Test\"><\/a>Algebraic Expressions and Properties Practice Test<\/h3>\n<p>Question 1.<br \/>\nIdentify the terms, coefficients, and constants of \\(\\frac{q}{3}\\) + 6 + 9q.<\/p>\n<p>Answer:<br \/>\n6 &#8211; constant<br \/>\n9,\u00a0 \\(\\frac{1}{3}\\) &#8211; coefficient<br \/>\nq &#8211; variable or term<br \/>\nA term without a variable is called a constant.<br \/>\nThe exponent tells us how many times the base is used as a factor<br \/>\nThe numerical factor of a term that contains a variable is called a coefficient.<br \/>\nA variable is a symbol that represents one or more numbers. Each number or variable by itself, or product of numbers and variables in an algebraic expression, is called a term.<\/p>\n<p>Question 2.<br \/>\nEvaluate 4b &#8211; a when a = 12 and b = 7.<\/p>\n<p>Answer: 16<\/p>\n<p>Explanation:<br \/>\nGiven the expression 4b &#8211; a<br \/>\nwhere a = 12 and b = 7<br \/>\n4(7) &#8211; 12<br \/>\n28 &#8211; 12 = 16<br \/>\nThus 4b &#8211; a = 16<\/p>\n<p>Write the phrase as an expression.<\/p>\n<p>Question 3.<br \/>\n25 more than 50<\/p>\n<p>Answer: The phrase for the expression 25 more than 50 is 25 + 50<\/p>\n<p>Question 4.<br \/>\n6 less than the quotient of 32 and a number y.<\/p>\n<p>Answer: The phrase for the expression 6 less than the quotient of 32 and a number y is 6 &#8211; 32 \u00f7 y<\/p>\n<p>Simplify the expression. Explain each step.<\/p>\n<p>Question 5.<br \/>\n3.1 + (8.6 + m)<\/p>\n<p>Answer:<br \/>\nGiven the expression 3.1 + (8.6 + m)<br \/>\nCombine the like terms<br \/>\n3.1 + (8.6 + m)<br \/>\n3.1 + 8.6 + 3<br \/>\n11.7 + m<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-114.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 114\" width=\"95\" height=\"50\" \/><\/p>\n<p>Answer:<br \/>\nGiven the expression (\\(\\frac{2}{3}\\) \u00d7 t) \u00d7 1 \\(\\frac{1}{2}\\)<br \/>\nFirst, convert the mixed fraction to the improper fraction<br \/>\n1 \\(\\frac{1}{2}\\) = \\(\\frac{3}{2}\\)<br \/>\n\\(\\frac{3}{2}\\) \u00d7 \\(\\frac{2}{3}\\) \u00d7 t<br \/>\n= t<br \/>\nThus (\\(\\frac{2}{3}\\) \u00d7 t) \u00d7 1 \\(\\frac{1}{2}\\) = t<\/p>\n<p>Question 7.<br \/>\n4(x + 8)<\/p>\n<p>Answer:<br \/>\nGiven the expression 4(x + 8)<br \/>\n= 4 \u00d7 x + 4 \u00d7 8<br \/>\n= 4x + 32<\/p>\n<p>Question 8.<br \/>\n4t + 7 + 2t &#8211; 2<\/p>\n<p>Answer: 6t + 5<\/p>\n<p>Explanation:<br \/>\nCombine the like terms<br \/>\n4t + 7 + 2t &#8211; 2<br \/>\n6t + 5<br \/>\nThus 4t + 7 + 2t &#8211; 2 = 6t + 5<\/p>\n<p><strong>Factor the expression using the GCF.<\/strong><\/p>\n<p>Question 9.<br \/>\n18 + 24<\/p>\n<p>Answer:<br \/>\nFind the GCF for 18, 24<br \/>\nThe factors of 18 are 1, 2, 3, 6, 9, 18<br \/>\nThe factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24<br \/>\nThe common factors are 1, 2, 3, 6.<br \/>\nThus the GCF of 18 + 24 is 6.<\/p>\n<p>Question 10.<br \/>\n15x + 20<\/p>\n<p>Answer:<br \/>\nSince 15x, 20 contain both numbers and variables, there are two steps to find the GCF.<br \/>\nFind the GCF fo the numerical part 15, 20<br \/>\nThe factors of 20 are 1, 2, 4, 5, 10, 20<br \/>\nThe factors of 15 are 1, 3, 5, 15<br \/>\nThe number do not contain any common variable factors.<br \/>\nThe greatest common factor is 5<\/p>\n<p>Question 11.<br \/>\n32x &#8211; 40y<\/p>\n<p>Answer: 8<\/p>\n<p>Explanation:<br \/>\nSince 32x, 40y contain both numbers and variables, there are two steps to find the GCF.<br \/>\nFind the GCF for the numerical part 32, 40<br \/>\nThe factors of 32 are 1, 2, 4, 8, 16, 32<br \/>\nThe factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40<br \/>\nThe number do not contain any common variable factors.<br \/>\nThen the greatest common factor is 8.<\/p>\n<p>Question 12.<br \/>\nPlaying time is added at the end of a soccer game to make up for stoppages. An expression for the length (in minutes) of a 90-minute soccer game with minutes of stoppage time is 90 + x. How long is a game with 4 minutes of stoppage time?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-114.1.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 114.1\" width=\"411\" height=\"285\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-114.1.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-114.1-300x208.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><\/p>\n<p>Answer: 94<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nPlaying time is added at the end of a soccer game to make up for stoppages.<br \/>\nAn expression for the length (in minutes) of a 90-minute soccer game with minutes of stoppage time is 90 + x.<br \/>\nx = 4<br \/>\nSubstitute the value of x in the expression<br \/>\n90 + 4 = 94<\/p>\n<p>Question 13.<br \/>\nThe expression 15 . x . 6 represents the volume of a rectangular prism with a length of 15, a width of x, and a height of 6. Simplify the expression.<\/p>\n<p>Answer:<br \/>\nGiven,<br \/>\nThe expression 15 . x . 6 represents the volume of a rectangular prism with a length of 15, a width of x, and a height of 6.<br \/>\nThe formula for the volume of a rectangular prism is lwh<br \/>\nV = 15 \u00d7 x \u00d7 6<br \/>\nV = 90x<\/p>\n<p>Question 14.<br \/>\nThe Coiling Dragon Cliff Skywalk in China is 128 feet longer than the length x (in feet) of the Tianmen Skywalk in China. The world\u2019s longest glass-bottom bridge, located in China\u2019s Zhangjiajie National Park, is about 4.3 times longer than the Coiling Dragon Cliff Skywalk. Write and simplify an expression that represents the length (in feet) of the world\u2019s longest glass-bottom bridge.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-115.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 115\" width=\"259\" height=\"182\" \/><\/p>\n<p>Answer:<br \/>\nThe Coiling Dragon Cliff Skywalk in China is 128 feet longer than the length x (in feet) of the Tianmen Skywalk in China.<br \/>\n128 + x<br \/>\nThe world\u2019s longest glass-bottom bridge, located in China\u2019s Zhangjiajie National Park, is about 4.3 times longer than the Coiling Dragon Cliff Skywalk.<br \/>\n(128 + x) \u00d7 4.3<br \/>\n128 \u00d7 4.3 + 4.3 \u00d7 x<br \/>\n550.4 + 4.3x<br \/>\nThus the expression is 4.3x + 550.4ft<\/p>\n<p>Question 15.<br \/>\nA youth group is making and selling sandwiches to raise money. The cost to make each sandwich is dollars. The group sells 150 sandwiches for a total of (150h + 450) dollars. How much pro\ufb01t does the group earn for each sandwich sold?<\/p>\n<p>Answer:<br \/>\nWe are given that<br \/>\nCost to make each sandwich= h dollar<br \/>\nThe total selling price of 150 sandwiches=(150h+450 )dollars<br \/>\nWe have to find the profit earn by the group on each sandwich sold.<br \/>\nTotal cost for making 150 sandwiches= 150 \u00d7 h<br \/>\nTotal cost for making 150 sandwiches=150 h<br \/>\nNow,<br \/>\nProfit made by the group on 150 sandwiches<br \/>\n=150h+450-150h<br \/>\n=450 dollars<br \/>\nProfit earn by group for each sandwich sold= 450\/150<br \/>\nProfit earn by group for each sandwich sold=$ 3<\/p>\n<p>Question 16.<br \/>\nYou make party favors for an event. You tie 9 inches of ribbon around each party favor. Write an expression for the number of inches of ribbon needed for n party favors. The ribbon costs $3 for each yard. Write an expression for the total cost (in dollars) of the ribbon.<\/p>\n<p>Answer:<br \/>\nNeed 9n inches of ribbon Cost is $0.75n<br \/>\nSince you need 9 inches per party favor and you have n party favors, the amount of ribbon you need is 9 times n inches.<br \/>\nSo R = 9n inches<br \/>\nSince the ribbon costs $3 per yard and our current equation is inches, we need to do a bit of conversion.<br \/>\nThere are 36 inches per yard and 9 inches per ribbon, so each yard of ribbon can make 36\/9 = 4 ribbons for the party favors.<br \/>\nSo the cost per party favor will be one-fourth of the cost per yard of ribbon per party favor.<br \/>\nSo $3.00 \/ 4 = $0.75, making the cost equation: C = $0.75n<\/p>\n<h3><a id=\"Algebraic_Expressions_and_Properties_Cumulative_Practice\"><\/a>Algebraic Expressions and Properties Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nThe student council is organizing a school fair. Council members are making signs to show the prices for admission and for each game a person can play.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-116.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 116\" width=\"218\" height=\"130\" \/><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-24857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-117.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 117\" width=\"334\" height=\"405\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-117.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-117-247x300.png 247w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Let x represent the number of games. Which expression can you use to determine the total amount (in dollars) a person pays for admission and playing x games?<br \/>\nA. 2.25<br \/>\nB. 2.25x<br \/>\nC. 2 + 0.25x<br \/>\nD. 2x + 0.25<\/p>\n<p>Answer: 2 + 0.25x<\/p>\n<p>Explanation:<br \/>\nGiven the data,<br \/>\nThe student council is organizing a school fair. Council members are making signs to show the prices for admission and for each game a person can play.<br \/>\nAdmission fee is $2<br \/>\nPrice per game is $0.25<br \/>\nLet x represent the number of games.<br \/>\nThe expression would be the sum of admission and product of price and number of games<br \/>\nThat is 2 + 0.25x<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 2.<br \/>\nWhich ratio relationship is represented in the graph?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-118.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 118\" width=\"203\" height=\"193\" \/><br \/>\nF. 2 cups of \ufb02our for every cup of sugar \\(\\frac{1}{2}\\) up of sugar<br \/>\nG. 6 cups of \ufb02our for every 3 cups of sugar<br \/>\nH. 1 cup of \ufb02our for every 4 cups of sugar<br \/>\nI. \\(\\frac{1}{2}\\) cup of \ufb02our for every 1 cup of sugar<\/p>\n<p>Answer: 2 cups of \ufb02our for every cup of sugar \\(\\frac{1}{2}\\) up of sugar<\/p>\n<p>Explanation:<br \/>\nThe graph represents that 2 cups of flour for every cup of sugar.<br \/>\nThus the correct answer is option F.<\/p>\n<p>Question 3.<br \/>\nAt a used bookstore, you can purchase two types of books.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-119.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 119\" width=\"82\" height=\"75\" \/><br \/>\nYou can use the expression 3h + 2p to \ufb01nd the total cost (in dollars) for h hardcover books and p paperback books. What is the total cost (in dollars) for 6 hardcover books and 4 paperback books?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-120.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 120\" width=\"294\" height=\"240\" \/><\/p>\n<p>Answer:<br \/>\nGiven expression 3h + 2p<br \/>\nh represents hardcover books<br \/>\np represents paperback books<br \/>\nThe cost of hardcover books is $3<br \/>\nThe cost of paperback books is $2<br \/>\n3h + 2p = 3(3) + 2(2)<br \/>\n= 9 + 4<br \/>\n= 13<br \/>\nWe have to find the total cost (in dollars) for 6 hardcover books and 4 paperback books.<br \/>\nThe equation will be 6h + 4p<br \/>\n= 6(3) + 4(5)<br \/>\n= 18 + 20<br \/>\n= 38<br \/>\nThe total cost (in dollars) for 6 hardcover books and 4 paperback books is $38.<\/p>\n<p>Question 4.<br \/>\nYour friend divided two decimal numbers. Her work is shown in the box below. What should your friend change in order to divide the two decimal numbers correctly?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-121.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 121\" width=\"381\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-121.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-121-300x188.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><\/p>\n<p>Answer: C<\/p>\n<p>Explanation:<br \/>\n0.07 \u00f7 14.56 can be written as<br \/>\n7 \u00f7 0.1456<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 5.<br \/>\nWhat is the value of 4.391 + 5.954?<br \/>\nF. 9.12145<br \/>\nG. 9.245<br \/>\nH. 9.345<br \/>\nI. 10.345<\/p>\n<p>Answer: 10.345<\/p>\n<p>Explanation:<br \/>\nAdd two decimal numbers 4.391 and 5.954<br \/>\n4.391<br \/>\n<span style=\"text-decoration: underline;\">+5.954<\/span><br \/>\n10.345<br \/>\nThus the correct answer is option I.<\/p>\n<p>Question 6.<br \/>\nThe circle graph shows the eye color of students in a sixth-grade class. Nine students in the class have brown eyes. How many students are in the class?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-122.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 122\" width=\"220\" height=\"237\" \/><br \/>\nA. 4 students<br \/>\nB. 18 students<br \/>\nC. 20 students<br \/>\nD. 405 students<\/p>\n<p>Answer: 20 students<\/p>\n<p>Explanation:<br \/>\nBy seeing the above figure we can find the number of students in the class.<br \/>\nThe circle graph shows the eye color of students in a sixth-grade class. Nine students in the class have brown eyes.<br \/>\n45\/9 = 5<br \/>\nEach student is equal to 5%<br \/>\n35\/5 = 7 students<br \/>\n20\/5 = 4 students<br \/>\n9 + 7 + 4 = 20 students<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 7.<br \/>\nProperties of Addition and Multiplication are used to simplify an expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-123.png\" alt=\"Big Ideas Math Solutions Grade 6 Chapter 5 Algebraic Expressions and Properties 123\" width=\"484\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-123.png 484w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-123-300x99.png 300w\" sizes=\"(max-width: 484px) 100vw, 484px\" \/><br \/>\nWhat number belongs in place of the x?<\/p>\n<p>Answer:<br \/>\n36 \u00d7 23 + 33 \u00d7 64 = 36 \u00d7 23 + 64 \u00d7 33<br \/>\n= 36 \u00d7 23 + 64 \u00d7 (23 + 10)<br \/>\n= 36 \u00d7 23 + 64 \u00d7 23 + 64 \u00d7 10<br \/>\n= 23(36 + 64) + 64 \u00d7 10<br \/>\n= 100 \u00d7 23 + 64 \u00d7 10<br \/>\nx = 100<br \/>\nThus the number that belong to x is 100.<\/p>\n<p>Question 8.<br \/>\nWhat is the prime factorization of 1350?<br \/>\nF. 10 . 135<br \/>\nG. 2 . 3 . 5<br \/>\nH. 6 . 225<br \/>\nI. 2 . 3<sup>3<\/sup> . 5<sup>2<\/sup><\/p>\n<p>Answer:<br \/>\nThe prime factorisation of 1350 is<br \/>\n1350 = 2 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 5 \u00d7 5<br \/>\n1350 = 2 . 3<sup>3<\/sup> . 5<sup>2<\/sup><br \/>\nThus the correct answer is option I.<\/p>\n<p>Question 9.<br \/>\nA horse gallops at a speed of 44 feet per second. What is the speed of the horse in miles per hour?<br \/>\nA. \\(\\frac{1}{2}\\) mile per hour<br \/>\nB. 30 miles per hour<br \/>\nC. 64\\(\\frac{8}{15}\\) miles per hour<br \/>\nD. 158,400 miles per hour<\/p>\n<p>Answer: 30 miles per hour<\/p>\n<p>Explanation:<br \/>\nGiven,<br \/>\nA horse gallops at a speed of 44 feet per second.<br \/>\nConvert from feet per second to miles per hour.<br \/>\n1 foot per second = 0.68 miles per hour<br \/>\n44 feet per second = 30 miles per hour<br \/>\nThus the correct answer is option B.<\/p>\n<p>Question 10.<br \/>\nWhich equation correctly demonstrates the Distributive Property?<br \/>\nF. a(b + c) = ab + ac<br \/>\nG. a(b + c) = ab + ac<br \/>\nH. a + (b + c) = (a + b) + (a + c)<br \/>\nI. a + (b + c) = (a + b) . (a + c)<\/p>\n<p>Answer: F<\/p>\n<p>Explanation:<br \/>\nThe distributive property explains that multiplying two numbers (factors) together will result in the same thing as breaking up one factor into two addends, multiplying both addends by the other factor, and adding together both products.<br \/>\na(b + c) = ab + ac<br \/>\nThus the correct answer is option F.<\/p>\n<p>Question 11.<br \/>\nWhich number is equivalent to 2\\(\\frac{4}{5}\\) . 1\\(\\frac{2}{7}\\) ?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-124.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 124\" width=\"344\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-124.png 344w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-124-300x82.png 300w\" sizes=\"(max-width: 344px) 100vw, 344px\" \/><\/p>\n<p>Answer: C<\/p>\n<p>Explanation:<br \/>\nConvert the mixed fraction to the improper fraction.<br \/>\n2\\(\\frac{4}{5}\\) = \\(\\frac{14}{5}\\)<br \/>\n1\\(\\frac{2}{7}\\) = \\(\\frac{9}{7}\\)<br \/>\nNow multiply both the fractions<br \/>\n\\(\\frac{14}{5}\\) \u00d7 \\(\\frac{9}{7}\\) = \\(\\frac{126}{35}\\)<br \/>\nNow convert from improper fraction to the mixed fractions.<br \/>\n\\(\\frac{126}{35}\\) = 3 \\(\\frac{3}{5}\\)<br \/>\nThus the correct answer is option C.<\/p>\n<p>Question 12.<br \/>\nWhich pair of numbers does not have a least common multiple of 24?<br \/>\nF. 2, 12<br \/>\nG. 3, 8<br \/>\nH. 6, 8<br \/>\nI. 12, 24<\/p>\n<p>Answer: 6, 8<br \/>\nThe least common multiple of 24 is 24.<br \/>\n2, 12 is 24<br \/>\n3, 8 is 24<br \/>\n6, 8 is 48<br \/>\nThus the correct answer is option H.<\/p>\n<p>Question 13.<br \/>\nUse the Properties of Multiplication to simplify the expression in an efficient way. Show your work and explain how you used the Properties of Multiplication.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-125.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 125\" width=\"78\" height=\"69\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-24826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-6-Chapter-5-Algebraic-Expressions-and-Properties-126.png\" alt=\"Big Ideas Math Answer Key Grade 6 Chapter 5 Algebraic Expressions and Properties 126\" width=\"140\" height=\"68\" \/><\/p>\n<p>Answer:<br \/>\nWe can use the associative property of multiplication to simplify the expression.<br \/>\nThe associative property is a math rule that says that the way in which factors are grouped in a multiplication problem does not change the product.<br \/>\n(25 \u00d7 18) \u00d7 4 = 25 \u00d7 (18 \u00d7 4)<br \/>\n450 \u00d7 4 = 1800<\/p>\n<p>Question 14.<br \/>\nWhich number is not a perfect square?<br \/>\nA. 64<br \/>\nB. 81<br \/>\nC. 96<br \/>\nD. 100<\/p>\n<p>Answer: 96<\/p>\n<p>Explanation:<br \/>\nA. 64 = 8 \u00d7 8<br \/>\nIt is a perfect square.<br \/>\nB. 81 = 9 \u00d7 9<br \/>\nIt is a perfect square.<br \/>\nC. 96 = 12 \u00d7 8<br \/>\n96 is not a perfect square.<br \/>\nD. 100 = 10 \u00d7 10<br \/>\nIt is a perfect square.<br \/>\nThus the correct answer is option C.<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties is here along with the solutions. Check all the problems and solutions in the above sections along with the examples. For all the queries, you can question us in the below comment box. Share the above article and pdf links with your friends and peers to overcome all the issues in maths. To clear all your doubts and questions, check all the links given in the above sections.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Follow a free step-by-step guide to Big Ideas Math Answers Grade 6 Chapter 5 Algebraic Expressions and Properties available here. There are various topics involved in Big Ideas Math Answers like Properties of Addition and Multiplication, Writing Expressions, Algebraic Expressions, and so on. 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