{"id":14861,"date":"2022-04-02T11:15:16","date_gmt":"2022-04-02T05:45:16","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=14861"},"modified":"2022-04-07T10:59:59","modified_gmt":"2022-04-07T05:29:59","slug":"big-ideas-math-answers-grade-5-chapter-2","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5-chapter-2\/","title":{"rendered":"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions"},"content":{"rendered":"<p>Make your preparation perfect with the help of the <strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-5\/\">Big Ideas Math Answers Grade 5<\/a> Chapter 2 Numerical Expressions PDF<\/strong>. Every student can become a math expert if they prepare with the Big Ideas Grade 5 Chapter 2 Numerical Expressions Math Answers. The concepts are explained clearly with real-time examples. Therefore, students can easily refer to all the topics and understand them with the help of examples. Check out the problems and also take the practice test to test your knowledge. If you feel lag in any concept, then prepare that topic more and get a grip on all topics.<\/p>\n<h2>Big Ideas 5th Grade Chapter 2 Numerical Expressions Math Book Answer Key<\/h2>\n<p>Follow the step-by-step procedure to learn the complete concept deeply. We have given an explanation for every problem below. Therefore, students also check out the explanation if they feel confused while solving the problems. Quickly, refer to available <em><strong>Big Ideas Numerical Expressions 5th Grade Chapter 2 Math Book Answer Key<\/strong> <\/em>and finish your preparation as early as possible. Click on the links provided below and prepare every individual topic on this page. Also, in this chapter, we were given different topics on Numerical Expressions, Order of operations, Number properties, Evaluating numerical expressions, and practice questions.<\/p>\n<p><strong>Lesson 1 Number Properties<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.1_Number_Properties\">Lesson 2.1 Number Properties<\/a><\/li>\n<li><a href=\"#Number_Properties_Homework_&amp;_Practice 2.1\">Number Properties Homework &amp; Practice 2.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2 Order of Operations<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.2_Order_of_Operations\">Lesson 2.2 Order of Operations<\/a><\/li>\n<li><a href=\"#Order_of_Operations_Homework_&amp;_Practice_2.2\">Order of Operations Homework &amp; Practice 2.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3 Write Numerical Expressions<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_2.3_Write_Numerical_Expressions\">Lesson 2.3 Write Numerical Expressions<\/a><\/li>\n<li><a href=\"#Write_Numerical_Expressions_Homework_&amp;_Practice_2.3\">Write Numerical Expressions Homework &amp; Practice 2.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4 Evaluate Expressions with Grouping Symbols<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson 2.4_Evaluate_Expressions_with_Grouping_Symbols\">Lesson 2.4 Evaluate Expressions with Grouping Symbols<\/a><\/li>\n<li><a href=\"#Evaluate_Expressions_with_Grouping_Symbols_Homework_&amp;_Practice_2.4\">Evaluate Expressions with Grouping Symbols Homework &amp; Practice 2.4<\/a><\/li>\n<\/ul>\n<p><strong style=\"font-size: 16px;\">Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Numerical_Expressions_Performance_Task\">Numerical Expressions Performance Task<\/a><\/li>\n<li><a href=\"#Numerical_Expressions_Activity\">Numerical Expressions Activity<\/a><\/li>\n<li><a href=\"#Numerical_Expressions_Chapter_Practice\">Numerical Expressions Chapter Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Lesson_2.1_Number_Properties\"><\/a> Lesson 2.1 Number Properties<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Use all four numbers on the game card below to write an expression that has a value of 24. You can use any number of the four operations: addition, subtraction, multiplication, and division.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 1\" width=\"289\" height=\"346\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-1.png 289w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-1-251x300.png 251w\" sizes=\"(max-width: 289px) 100vw, 289px\" \/><\/p>\n<p>Answer:<br \/>\nWe will use addition, multiplication, and division to get the value as 24.<\/p>\n<p>Explanation:<br \/>\nIn the game card, we can see that the four numbers are 2, 3, 9, 1. So to get the value as 24 we will add 9 + 3 which is 12 and then we will multiply the value 12 with 2\u00a0 which is 12 \u00d7 2 = 24 and then we will divide the value with 1 which is 24 \u00f7 1= 24. So here the operations used are addition, multiplication, and division to get the value 24.<\/p>\n<p><strong>Reasoning<\/strong><br \/>\nWrite another expression that has a value of 24 using the game card above.<br \/>\nAnswer:<br \/>\nWe will use addition and multiplication to get the value as 24.<\/p>\n<p>Explanation:<br \/>\nIn the game card, we can see that the four numbers are 2, 3, 9, 1. So to get the value as 24 we will add 9 + 3 which is 12 and then we will multiply the value 12 with 2\u00a0 which is 12 \u00d7 2 = 24. So to use another expression we will multiply the value with 1 which is 24 \u00d7 1= 24. So here the operations used are addition and multiplication to get the value 24.<\/p>\n<p><strong>Think and Grow: Use Number Properties<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nHere are several number properties.<br \/>\nCommutative Properties: Changing the order of addends or factors does not change the sum or product.<br \/>\n3 + 5 = 5 + 3<br \/>\n3 \u00d7 5 = 5 \u00d7 3<br \/>\nAssociative Properties: Changing the grouping of addends or factors does not change the sum or product.<br \/>\n(2 + 4) + 1 = 2 + (4 + 1)<br \/>\n(2 \u00d7 4) \u00d7 1 = 2 \u00d7 (4 \u00d7 1)<br \/>\nAddition Property of Zero: The sum of any number and 0 is that number.<br \/>\n8 + 0 = 8<br \/>\nMultiplication Properties of Zero and One:<br \/>\nThe product of any number and 0 is 0. 5 \u00d7 0 = 0<br \/>\nThe product of any number and 1 is that number. 7 \u00d7 1 = 7<br \/>\nDistributive Property: Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 2\" width=\"236\" height=\"80\" \/><br \/>\n<strong>Example<\/strong><br \/>\nComplete the equation. Identify the property shown.<br \/>\n32 + 29 + 8 = 29 + ______ + 8<br \/>\n_______ Property of Addition<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 3\" width=\"646\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-3.png 646w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-3-300x108.png 300w\" sizes=\"(max-width: 646px) 100vw, 646px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 1.<br \/>\nComplete the equation. Identify the property shown.<br \/>\n9 \u00d7 15 = 15 \u00d7 ______<br \/>\nAnswer:<br \/>\nThe equation is 9 \u00d7 15 = 15 \u00d7 9. And the property which is used is the Commutative property.<\/p>\n<p>Explanation:<br \/>\nThe equation is 9 \u00d7 15 = 15 \u00d7 9. And the property which is used is the Commutative property.<br \/>\nCommutative Properties means changing the order of addends or factors does not change the sum or product. So the equation is 9 \u00d7 15 = 15\u00a0 \u00d7 9.<\/p>\n<p>Question 2.<br \/>\nUse the Distributive Property to find 8 \u00d7 49.<br \/>\nAnswer:<br \/>\nThe equation is (8 \u00d7 40) + (8 \u00d7 9) and the property used is Distributive property.<\/p>\n<p>Explanation:<br \/>\nGiven that 8 \u00d7 49, by distributive property the equation will be<br \/>\n= 8 \u00d7 (40 + 9)<br \/>\n= (8 \u00d7 40) + (8 \u00d7 9)<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Complete the equation. Identify the property shown.<\/strong><br \/>\nQuestion 3.<br \/>\n1 \u00d7 _____ = 17<br \/>\nAnswer:<br \/>\nThe equation is 1 \u00d7 17= 17 and the property used is Multiplication Properties of One.<\/p>\n<p>Explanation:<br \/>\nThe equation is 1 \u00d7 17 = 17.<br \/>\nThe property used to complete this equation is Multiplication Properties of One which means the product of any number and 1 is that number. So the equation will be 1 \u00d7 17 = 17.<\/p>\n<p>Question 4.<br \/>\n248 + 0 = ______<br \/>\nAnswer:<br \/>\nThe equation is 248 + 0= 248 and the property used is the Addition Property of Zero.<\/p>\n<p>Explanation:<br \/>\nThe equation is 248 + 0= 248.<br \/>\nThe property used is the Addition Property of Zero which means the sum of any number and 0 is that number. So the equation will be 248 + 0= 248.<\/p>\n<p>Question 5.<br \/>\n23 + 145 + 7 = 23 + 7 + _____<br \/>\nAnswer:<br \/>\nThe equation is 23 + 145 + 7= 23 + 7 + 145. And the property which is used is the Commutative property.<\/p>\n<p>Explanation:<br \/>\nThe equation is 23 + 145 + 7= 23 + 7 + 145. And the property which is used is the Commutative property.<br \/>\nCommutative Properties means changing the order of addends or factors does not change the sum or product. So the equation is 23 + 145 + 7= 23 + 7 + 145.<\/p>\n<p>Question 6.<br \/>\n3 \u00d7 (10 + 2) = (3 \u00d7 10) + (3 \u00d7 ______)<br \/>\nAnswer:<br \/>\nThe equation is 3 \u00d7 (10 + 2)= (3 \u00d7 10) + (3 \u00d7 2) and the property used is the Distributive Property.<\/p>\n<p>Explanation:<br \/>\nThe equation is 3 \u00d7 (10 + 2)= (3 \u00d7 10) + (3 \u00d7 2)<br \/>\nThe Distributive Property is a property in which Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the equation is 3 \u00d7 (10 + 2)= (3 \u00d7 10) + (3 \u00d7 2).<\/p>\n<p><strong>Use the Distributive Property to find the product.<\/strong><br \/>\nQuestion 7.<br \/>\n5 \u00d7 97<br \/>\nAnswer:<br \/>\nThe equation is<br \/>\n5 \u00d7 97 = 5 \u00d7 (90 + 7)<br \/>\n= (5 \u00d7 90) + (5 \u00d7 7) and the property used is Distributive property.<\/p>\n<p>Explanation:<br \/>\nGiven that 5 \u00d7 97, by distributive property the equation will be<br \/>\n= 5 \u00d7 (90 + 7)<br \/>\n= (5 \u00d7 90) + (5 \u00d7 7)<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the equation is<br \/>\n5 \u00d7 97 = 5 \u00d7 (90 + 7)<br \/>\n= (5 \u00d7 90) + (5 \u00d7 7).<\/p>\n<p>Question 8.<br \/>\n83 \u00d7 7<br \/>\nAnswer:<br \/>\nThe equation is<br \/>\n83 \u00d7 7 = 7 \u00d7 (80 + 3)<br \/>\n= (7 \u00d7 80) + (7 \u00d7 3) and the property used is Distributive property.<\/p>\n<p>Explanation:<br \/>\nGiven that 7 \u00d7 83, by distributive property the equation will be<br \/>\n= 7 \u00d7 (80 + 3)<br \/>\n= (7\u00d7 80) + (7 \u00d7 3)<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the equation is<br \/>\n7 \u00d7 83 = 7 \u00d7 (80 + 3)<br \/>\n= (7 \u00d7 80) + (7 \u00d7 3)<\/p>\n<p><strong>Use a property to find the sum or product. Identify the property you used.<\/strong><br \/>\nQuestion 9.<br \/>\n4 + (6 + 27)<br \/>\nAnswer:<br \/>\nThe sum of 4 + (6 + 27) is 37 and the property which is used is the Commutative property.<\/p>\n<p>Explanation:<br \/>\nThe sum of 4 + (6 + 27) is 37 and the property which is used is the Commutative property.<br \/>\nCommutative Properties means changing the order of addends or factors does not change the sum or product. So the sum is 37.<\/p>\n<p>Question 10.<br \/>\n5 \u00d7 49 \u00d7 0<br \/>\nAnswer:<br \/>\nThe product of 5 \u00d7 49 \u00d7 0 is 0 and the property used is Multiplication Properties of Zero.<\/p>\n<p>Explanation:<br \/>\nThe product of 5 \u00d7 49 \u00d7 0 is 0 and the property used is Multiplication Properties of Zero.<br \/>\nMultiplication Properties of Zero is the product of any number and 0 is 0. So 5 \u00d7 49 \u00d7 0 is 0.<\/p>\n<p>Question 11.<br \/>\n11 + 16 + 89<br \/>\nAnswer:<br \/>\nThe sum of 11 + 16 + 89 is 116 and the property which is used is the Commutative property.<\/p>\n<p>Explanation:<br \/>\nThe sum of 11 + 16 + 89 is 116 and the property which is used is the Commutative property.<br \/>\nCommutative Properties means changing the order of addends or factors does not change the sum or product. So the sum is 116.<\/p>\n<p>Question 12.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend uses the Distributive Property to find 4 \u00d7 46. Is your friend correct? Explain.<br \/>\n4 \u00d7 46 = 4 \u00d7 (50 &#8211; 4)<br \/>\n= (4 \u00d7 50) &#8211; (4 \u00d7 4)<br \/>\n= 200 &#8211; 16<br \/>\n= 184<br \/>\nAnswer:<br \/>\nYes, my friend is correct. He uses distributive property correctly.<\/p>\n<p>Explanation:<br \/>\nYes, my friend is correct. By distributive property, the equation will be<br \/>\n4 \u00d7 46 = 4 \u00d7 (50 &#8211; 4)<br \/>\n= (4 \u00d7 50) &#8211; (4 \u00d7 4)<br \/>\n= 200 &#8211; 16<br \/>\n= 184.<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the equation is<\/p>\n<p>Question 13.<br \/>\nCan you use the Associative Property with subtraction? Explain. Use an example to justify your answer.<br \/>\nAnswer:<br \/>\nNo, we cannot use the Associative Property with subtraction.<\/p>\n<p>Explanation:<br \/>\nNo, we cannot use the Associative Property with subtraction. As Associative property means changing the grouping of addends or factors does not change the sum or product. So Associative property can only be used for addition or multiplication. And the subtraction doesn&#8217;t have the associative property because for example if we take 20 and10 and subtract the first two numbers 20 minus 10 then the result will be 10. So changing the way of associating the numbers in subtraction can change the result. So the subtraction doesn&#8217;t have the associative property.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nThere are three types of animals at a shelter. How many animals are there in all?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 4\" width=\"250\" height=\"161\" \/><br \/>\nFind the number of each type of animal at the shelter.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 5\" width=\"582\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-5.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-5-300x60.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><br \/>\nAdd the numbers of dogs, cats, and rabbits.<br \/>\n16 + 22 + 4 = ____ + ____ + ____ Commutative Property of Addition<br \/>\n= _____ + _____ Add.<br \/>\n= _____ Add.<br \/>\nThere are _____ animals in all.<\/p>\n<p>Answer:<br \/>\nThe total number of animals in the shelter is 42 animals.<br \/>\nAdd the numbers of dogs, cats, and rabbits.<br \/>\n16 + 22 + 4 = 4 + 22 + 16 Commutative Property of Addition<br \/>\n= 26 + 16 Add.<br \/>\n= 42 Add.<br \/>\nThere are 42 animals in all.<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-38780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-5-1.png\" alt=\"Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-5\" width=\"582\" height=\"116\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-5-1.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-5-1-300x60.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><br \/>\nGiven that each paw is equal to four pets. So the dog has four paws which means 4 \u00d7 4 = 16. The total number of dogs is 16 dogs. And cats have five paws and a half paw so the total number of cats is 5 \u00d7 4= 20 as one paw is equal to four so the half paw is two animals. So the total number of cats is 20 + 2= 22 cats. And rabbit has one paw so the total number of rabbits is 4 rabbits. So to find the total number of animals is we will add all the animals and add the numbers of dogs, cats, and rabbits. So<br \/>\n16 + 22 + 4 = 4 + 22 + 16 Commutative Property of Addition<br \/>\n= 26 + 16 Add.<br \/>\n= 42 Add.<br \/>\nThere are 42 animals in all.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nYou play three different video games in an evening. How many minutes do you play video games in all?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 6\" width=\"250\" height=\"162\" \/><br \/>\nAnswer:<br \/>\nThe total number of minutes the video game is playing is 66 minutes.<\/p>\n<p>Explanation:<br \/>\nGiven that each clock is six minutes. And given that dancing has three clocks and a half clock. So the total number of minutes in playing dancing is 3 \u00d7 6= 18 minutes, as each clock is 6 minutes, so the half clock will be 3 minutes. So the total number of minutes in playing dancing is 18 + 3= 21 minutes. And given that puzzle has two clocks and a half clock, so the total number of minutes in playing puzzle is 1 \u00d7 6= 6 as each clock is 6 minutes, so the half clock will be 3 minutes. So the total number of minutes in playing dancing is 6 + 3= 9 minutes. And given that racing has six clocks. So the total number of minutes in playing racing is 6 \u00d7 6= 36 minutes. So the total number of minutes in playing dancing is 18 + 3= 21 minutes. So the total number of minutes the video game is playing is<br \/>\n21 minutes + 9 minutes + 36 minutes which is 66 minutes.<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTickets for a school play are sold out. The auditorium has 4 sections. Each section has 25 rows with 15 seats in each row. Each ticket costs $2. How much money is raised in ticket sales?<br \/>\nAnswer:<br \/>\nThe total amount raised in the ticket sale is $3,000.<\/p>\n<p>Explanation:<br \/>\nAs there are four sections in the auditorium and each section has 25 rows with 15 seats in each row and each ticket costs $2. So first we need to find the total number of seats. For that, we should multiple numbers of rows and the seats which are 25 \u00d7 15= 375 seats. And there are four sections, so 4 \u00d7 375= 1,500. So there are 1500 total seats. And each ticket costs $2, for 1500 seats it will be 1500 \u00d7 2= 3,000. So the total amount raised in the ticket sale is $3,000.<\/p>\n<h3><a id=\"Number_Properties_Homework_&amp;_Practice 2.1\"><\/a>Number Properties Homework &amp; Practice 2.1<\/h3>\n<p><strong>Complete the equation. Identify the property shown.<\/strong><br \/>\nQuestion 1.<br \/>\n687 \u00d7 ____ = 0<br \/>\nAnswer:<br \/>\nThe equation is 687 \u00d7 0 = 0 and the property used is Multiplication Properties of Zero.<\/p>\n<p>Explanation:<br \/>\nThe equation is 687 \u00d7 0 = 0 and the property used is Multiplication Properties of Zero.<br \/>\nAs Multiplication Properties of Zero is the product of any number and 0 is 0. So 687 \u00d7 0 is 0.<\/p>\n<p>Question 2.<br \/>\n15 + 13 = 13 + _____<br \/>\nAnswer:<br \/>\nThe equation is 15 + 13 = 13 + 15 and the property which is used is the Commutative property.<\/p>\n<p>Explanation:<br \/>\nThe equation is 15 + 13 = 13 + 15 and the property which is used is the Commutative property.<br \/>\nAs the Commutative Properties means changing the order of addends or factors does not change the sum or product. So the equation will be 15 + 13 = 13 + 15.<\/p>\n<p>Question 3.<br \/>\n4 \u00d7 7 \u00d7 25 = 4 \u00d7 _____ \u00d7 7<br \/>\nAnswer:<br \/>\nThe equation is 4 \u00d7 7 \u00d7 25 = 4 \u00d7 25 \u00d7 7 and the property used is Associative Property.<\/p>\n<p>Explanation:<br \/>\nThe equation is 4 \u00d7 7 \u00d7 25 = 4 \u00d7 25 \u00d7 7 and the property used is Associative Property.<br \/>\nAs Associative Property means changing the grouping of addends or factors does not change the sum or product.<br \/>\n4 \u00d7 7 \u00d7 25 = 4 \u00d7 25 \u00d7 7<\/p>\n<p>Question 4.<br \/>\n6 \u00d7 (20 &#8211; 3) = (6 \u00d7 20) &#8211; (6 \u00d7 _____)<br \/>\nAnswer:<br \/>\nThe equation is 6 \u00d7 (20 &#8211; 3) = (6 \u00d7 20) &#8211; (6 \u00d7 3) and the property used is Distributive property.<\/p>\n<p>Explanation:<br \/>\nThe equation is 6 \u00d7 (20 &#8211; 3) = (6 \u00d7 20) &#8211; (6 \u00d7 3) and the property used is Distributive property.<br \/>\nDistributive Property is a property of Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products.<\/p>\n<p><strong>Use the Distributive Property to find the product.<\/strong><br \/>\nQuestion 5.<br \/>\n4 \u00d7 78<br \/>\nAnswer:<br \/>\nThe product is<br \/>\n4 \u00d7 78 = 4 \u00d7 (70 + 8)<br \/>\n= (4 \u00d7 70) + (4 \u00d7 8)<br \/>\n= 280 + 32<br \/>\n= 312<br \/>\nand the property used is the Distributive Property.<\/p>\n<p>Explanation:<br \/>\nThe product is<br \/>\n4 \u00d7 78 = 4 \u00d7 (70 + 8)<br \/>\n= (4 \u00d7 70) + (4 \u00d7 8)<br \/>\n= 280 + 32<br \/>\n= 312<br \/>\nThe Distributive Property is a property in which Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the product of 4 \u00d7 78 is<br \/>\n= 4 \u00d7 (70 + 8)<br \/>\n= (4 \u00d7 70) + (4 \u00d7 8)<br \/>\n= 280 + 32<br \/>\n= 312.<\/p>\n<p>Question 6.<br \/>\n23 \u00d7 8<br \/>\nAnswer:<br \/>\nThe product is<br \/>\n23 \u00d7 8 = 8 \u00d7 (20 + 3)<br \/>\n= (8 \u00d7 20) + (8 \u00d7 3)<br \/>\n= 160 + 24<br \/>\n= 184<br \/>\nand the property used is the Distributive Property.<\/p>\n<p>Explanation:<br \/>\nThe product is<br \/>\n23 \u00d7 8 = 8 \u00d7 (20 + 3)<br \/>\n= (8 \u00d7 20) + (8 \u00d7 3)<br \/>\n= 160 + 24<br \/>\n= 184<br \/>\nThe Distributive Property is a property in which Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the product of 23 \u00d7 8 is<br \/>\n= 8 \u00d7 (20 + 3)<br \/>\n= (8 \u00d7 20) + (8 \u00d7 3)<br \/>\n= 160 + 24<br \/>\n= 184.<\/p>\n<p><strong>Use a property to find the sum or product. Identify the property you used.<\/strong><br \/>\nQuestion 7.<br \/>\n6 \u00d7 43<br \/>\nAnswer:<br \/>\nThe product is<br \/>\n6 \u00d7 43 = 6 \u00d7 (40 + 3)<br \/>\n= (6 \u00d7 40) + (6 \u00d7 3)<br \/>\n= 240 + 18<br \/>\n= 258.<br \/>\nand the property used is the Distributive Property.<\/p>\n<p>Explanation:<br \/>\nThe product is<br \/>\n6 \u00d7 43 = 6 \u00d7 (40 + 3)<br \/>\n= (6 \u00d7 40) + (6 \u00d7 3)<br \/>\n= 240 + 18<br \/>\n= 258.<br \/>\nThe Distributive Property is a property in which Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the product of 6 \u00d7 43 is<br \/>\n= 6 \u00d7 (40 + 3)<br \/>\n= (6 \u00d7 40) + (6 \u00d7 3)<br \/>\n= 240 + 18<br \/>\n= 258.<\/p>\n<p>Question 8.<br \/>\n339 + 0 + 54<br \/>\nAnswer:<br \/>\nThe equation is 23 + 145 + 7= 23 + 7 + 145. And the property which is used is the Commutative property.<\/p>\n<p>Explanation:<br \/>\nThe sum is 339 + 0 + 54 = 393. And the property which is used is the Commutative property.<br \/>\nCommutative Properties means changing the order of addends or factors does not change the sum or product. So the equation is 339 + 0 + 54 = 54 + 339 + 0.<\/p>\n<p>Question 9.<br \/>\n25 \u00d7 8 \u00d7 2<br \/>\nAnswer:<br \/>\nThe equation is 25 \u00d7 8 \u00d7 2 = 400. And the property which is used is the Commutative property.<\/p>\n<p>Explanation:<br \/>\nThe product is 25 \u00d7 8 \u00d7 2 = 400. And the property which is used is the Commutative property.<br \/>\nCommutative Properties means changing the order of addends or factors does not change the sum or product. So the equation is 25 \u00d7 8 \u00d7 2 = 25 \u00d7 8 \u00d7 2.<\/p>\n<p>Question 10.<br \/>\n<strong>Number Sense<\/strong><br \/>\nTo find 29 + (11 + 16), your friend adds 29 and 11. Then he adds 16 to the sum. Which property did he use and why?<br \/>\nAnswer:<br \/>\nThe property which is used is the Commutative property. And the equation can be written as<br \/>\n29 + 11 + 16 = 29 + 11 + 16.<\/p>\n<p>Explanation:<br \/>\nGiven equation is 29 + (11 + 16) and my friend adds 29 and 11 after that he adds 16 to find the sum. And the property which is used is the Commutative property. And Commutative Properties means changing the order of addends or factors does not change the sum or product. So the equation can be written as<br \/>\n29 + 11 + 16 = 29 + 11 + 16.<\/p>\n<p>Question 11.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how using properties can help you mentally find answers to problems.<br \/>\nAnswer:<br \/>\nUsing the properties like Commutative property, Distributive property, Associative Properties, Addition Property of Zero, Multiplication Properties of Zero &amp; One helps us mentally in finding answers to problems by this process and we can solve the problems easily by these properties and everyone can identify this property. With these properties, we can write the equivalent expressions which help us to solve mental problems.<\/p>\n<p>Question 12.<br \/>\n<strong>Number Sense<\/strong><br \/>\nNewton uses two properties to rewrite the expression (4 \u00d7 23) \u00d7 25. Identify the properties he uses. Why would Newton use these properties?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 7\" width=\"201\" height=\"166\" \/><br \/>\nAnswer:<br \/>\nThe property Newton used is the Commutative property.<\/p>\n<p>Explanation:<br \/>\nThe property Newton used is the Commutative property. Newton uses Commutative Property because by Commutative property changing the order of addends or factors does not change the sum or product. So the equation can be written as 4 \u00d7 23 \u00d7 25. = 25 \u00d7 4 \u00d7 23.<\/p>\n<p>Question 13.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nBefore performing an experiment, students are asked to predict which substance will melt an ice cube the fastest. How many students make a prediction? Identify the property you used.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 8\" width=\"267\" height=\"155\" \/><br \/>\nAnswer:<br \/>\nThe total number of students who have participated in the prediction is 76 students and the property used is commutative property.<\/p>\n<p>Explanation:<br \/>\nGiven that each emoji is 8 students, so the salt has two emojis that mean 2 \u00d7 8= 16 students. So the students who have predicted the salt are 16 students. And the sugar has three emojis and a half emoji that means 3 \u00d7 8= 24 students and a half emoji means, as each emoji is 8 students, so half emoji is 4 students and the total number of students is 24 + 4= 28 students. So the students who have predicted the sugar are 28 students. And the water has four emojis that means 4 \u00d7 8= 32 students. So the students who have predicted the water are 32 students.<br \/>\nThe total number of students who have participated in the prediction is<br \/>\n16 students + 28 students + 32 students = 76 students. So the total number of students who have participated in the prediction is 76 students. And the property used is commutative property. And Commutative Properties means changing the order of addends or factors does not change the sum or product. So the equation can be written as<br \/>\n16 + 28 + 32= 32 + 16 +28.<\/p>\n<p>Question 14.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nAn apartment building has 35 floors with 12 apartments on each floor. There are 300 apartments that have 2 bedrooms. The rest of the apartments have 1 bedroom. How many 1-bedroom apartments are in the building? How can you use the Distributive Property to help solve this problem mentally?<br \/>\nAnswer:<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the sum. Check whether your answer is reasonable.<\/strong><br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 9\" width=\"75\" height=\"65\" \/><br \/>\nAnswer:<br \/>\nBy adding 8,968 and 4,683 we will get the sum of 13,651.<\/p>\n<p>Explanation:<br \/>\nBy adding 8,968 and 4,683 we will get the sum of 13,651. To check whether the answer is reasonable we will subtract 4,683 with 13,651 the difference will be 8,968. So the answer is reasonable.<\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 10\" width=\"76\" height=\"68\" \/><br \/>\nAnswer:<br \/>\nBy adding 75,310 and 8,596 we will get the sum of 83,906.<\/p>\n<p>Explanation:<br \/>\nBy adding 75,310 and 8,596 we will get the sum of 83,906. To check whether the answer is reasonable we will subtract8,596 with 83,906 the difference will be 75,310. So the answer is reasonable.<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answer-Key-Grade-5-Chapter-2-Numerical-Expressions-2.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 5 Chapter 2 Numerical Expressions 2.1 11\" width=\"86\" height=\"69\" \/><br \/>\nAnswer:<br \/>\nBy adding 90,583 and 19,877 we will get the sum of 110,460.<\/p>\n<p>Explanation:<br \/>\nBy adding 90,583 and 19,877 we will get the sum of 110,460. To check whether the answer is reasonable we will subtract 19,877 with 110,460 the difference will be 90,583. So the answer is reasonable.<\/p>\n<h3><a id=\"Lesson_2.2_Order_of_Operations\"><\/a>Lesson 2.2 Order of Operations<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Two students were asked to find the value of the expression below and they got different answers. Only one student has the correct answer. The students did not make any mistakes in their calculations. How did they get different answers?<br \/>\n24 + 16 \u00f7 4 &#8211; 2<br \/>\nAnswer:<br \/>\nThe other student did not use the BODMAS rule so the other student calculation is not correct.<\/p>\n<p>Explanation:<br \/>\nTo find the value of the expression 24 + 16 \u00f7 4 &#8211; 2 first we will divide 16 by 4 then the result will be 4. Now we will add result 4 with the number 24 which is 24 + 4= 28. And now we will subtract the number 2 with 28 which is<br \/>\n28 &#8211; 2= 26. This expression was done by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. And this was done by one student. Now the other student has done the same expression in a different way. The expression is 24 + 16 \u00f7 4 &#8211; 2, so the other student solves the expression by first adding 24 and 16 which is 24 + 16= 40, and then we will divide 40 by 4, so the result will be 10. And now we will subtract 2 with 10 and the result will be 10 &#8211; 2= 8. So the other student&#8217;s answer will be 8 which is not correct because the other student did not use the BODMAS rule so the other student&#8217;s calculation is not correct.<\/p>\n<p><strong>Structure<\/strong><br \/>\nWhy is it important to have rules when finding values of expressions that contain more than one operation?<br \/>\nAnswer:<br \/>\nIt is important to have the rules when finding the values of expressions that contain more than one operation because the rules tell that the right order in which we will solve different parts of a math problem. And the order of operations is very important because it guarantees that we can all read and solve the problem in the same way.<\/p>\n<p><strong>Think and Grow: Use Order of Operations<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nA numerical expression is an expression that contains numbers and operations. When you evaluate a numerical expression, you find the value of the expression.<br \/>\nWhen evaluating a numerical expression, use a set of rules called the order of operations. These rules tell you the order in which to perform the operations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-1.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 1\" width=\"197\" height=\"253\" \/><br \/>\nOrder of Operations<br \/>\n1. Perform operations in parentheses<br \/>\n2. Multiply and divide from left to right<br \/>\n3. Add and subtract from left to right<\/p>\n<p><strong>Example<\/strong><br \/>\nEvaluate 19 &#8211; 18 \u00f7 6.<br \/>\nUsing the order of operations, divide first. Then subtract.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-2.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 2\" width=\"396\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-2.png 396w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-2-300x52.png 300w\" sizes=\"(max-width: 396px) 100vw, 396px\" \/><br \/>\nSo, 19 &#8211; 18 \u00f7 6 = _______.<\/p>\n<p><strong>Example<\/strong><br \/>\nEvaluate 30 \u00f7 (3 + 7) \u00d7 2.<br \/>\nUsing the order of operations, perform the addition in the parentheses first. Then multiply and divide from left to right.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-3.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 3\" width=\"558\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-3.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-3-300x59.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><br \/>\nSo, 30 \u00f7 (3 + 7) \u00d7 2 = ______.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n24 + 4 \u00f7 2<br \/>\nAnswer:<br \/>\nThe value of the expression 24 + 4 \u00f7 2 is 26.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right.\u00a0 And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the division part of the expression which is 4 \u00f7 2 = 2 and the result will be 2. Now we solve the addition part, we will add the result with 24 which is 24 + 2 = 26. So the value of the expression is 26.<\/p>\n<p>Question 2.<br \/>\n12 + (10 &#8211; 3) \u00d7 8<br \/>\nAnswer:<br \/>\nThe value of the expression 12 + (10 &#8211; 3) \u00d7 8 is 68.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the parentheses part which is (10 &#8211; 3)= 7 and the result will be 7. Now we will solve the multiplication part which is 7 \u00d7 8= 56 and the result will be 56. And now we will solve the addition part which is 12 + 56= 68. So the value of the expression is 68.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 3.<br \/>\n25 + (10 \u00f7 5)<br \/>\nAnswer:<br \/>\nThe value of the expression is 27.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the parentheses part which is (10 \u00f7 5)= 2 and the result will be 2. Now we will add the result with 25 which is 25 + 2= 27. So the value of the expression is 27.<\/p>\n<p>Question 4.<br \/>\n10 + 10 + 7<br \/>\nAnswer:<br \/>\nThe sum of the expression 10 + 10 +7 is 27.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. As there are no other expressions rather than addition we will perform addition to the given expression 10 + 10 + 7 and the sum of the expression<br \/>\n10 + 10 +7 is 27.<\/p>\n<p>Question 5.<br \/>\n48 \u00f7 (8 &#8211; 2)<br \/>\nAnswer:<br \/>\nThe value of the expression 48 \u00f7 (8 &#8211; 2) is 8.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. So first we will solve the parentheses which is (8 &#8211; 2)= 6. Now we will perform division operation for 48 by 6 and the result will be 8. So the value of the expression 48 \u00f7 (8 &#8211; 2) is 8.<\/p>\n<p>Question 6.<br \/>\n(45 + 25) \u00f7 10<br \/>\nAnswer:<br \/>\nThe value of the expression (45 + 25) \u00f7 10 is 7.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. So first will solve the parentheses part which is (45 + 25)= 70 and now we will perform division 70 \u00f7 10 and the result will be 7. So the value of the expression (45 + 25) \u00f7 10 is 7.<\/p>\n<p>Question 7.<br \/>\n63 &#8211; 54 \u00f7 9<br \/>\nAnswer:<br \/>\nThe value of the expression 63 &#8211; 54 \u00f7 9 is 57.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition and Subtraction. Now first we will solve the division part which is 54 \u00f7 9= 6 and the result is 6. Now we will subtract the result with 63 which is 63 &#8211; 6= 57. So the value of the expression 63 &#8211; 54 \u00f7 9 is 57.<\/p>\n<p>Question 8.<br \/>\n\\(\\left(\\frac{1}{2}+\\frac{1}{2}\\right) \\times 5\\)<br \/>\nAnswer:<br \/>\nThe value of the expression \\(\\left(\\frac{1}{2}+\\frac{1}{2}\\right) \\times 5\\) is 5.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the parentheses part which is \\(\\left(\\frac{1}{2}+\\frac{1}{2}\\right) so the value will be 1. And now we will perform the multiplication part which is 1 \u00d7 5= 5. So the value of the expression [latex]\\left(\\frac{1}{2}+\\frac{1}{2}\\right) \\times 5\\) is 5.<\/p>\n<p>Question 9.<br \/>\n15 + (16 &#8211; 6) \u00d7 1<br \/>\nAnswer:<br \/>\nThe value of the expression 15 + (16 &#8211; 6) \u00d7 1 is 25.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will perform the parentheses part which is (16 &#8211; 6)= 10 and the result will be 6. Now we will perform the multiplication part which is 10 \u00d7 1= 10 and the result will be 10. And now we will perform the addition which is 15 + 10 then the result will be 25. So the value of the expression 15 + (16 &#8211; 6) \u00d7 1 is 25.<\/p>\n<p>Question 10.<br \/>\n(18 + 23 + 22) \u00f7 9<br \/>\nAnswer:<br \/>\nThe value of the expression (18 + 23 + 22) \u00f7 9 is 7.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will perform the parentheses part which is (18 + 23 + 22)= 63 and the result will be 63. Now we will perform division which is<br \/>\n63 \u00f7 9= 7. So the value of the expression (18 + 23 + 22) \u00f7 9 is 7.<\/p>\n<p>Question 11.<br \/>\n80 &#8211; 6 \u00d7 5 \u00d7 2<br \/>\nAnswer:<br \/>\nThe value of the expression 80 &#8211; 6 \u00d7 5 \u00d7 2 will be 20.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the multiplication part which is 6 \u00d7 5 \u00d7 2= 60 and the result will be 60. Now we will solve the subtraction part which is 80 &#8211; 60= 20. So the value of the expression 80 &#8211; 6 \u00d7 5 \u00d7 2 will be 20.<\/p>\n<p><strong>Insert parentheses to make the statement true.<\/strong><br \/>\nQuestion 12.<br \/>\n6 + 2 \u00d7 7 = 56<br \/>\nAnswer:<br \/>\nThe expression after inserting parentheses is (6 +2) \u00d7 7.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 6 + 2 \u00d7 7. So we will insert the parentheses for 6 + 2, then the expression will be<br \/>\n(6 +2) \u00d7 7. So we will solve the expression using the BODMAS rule, now first we will perform the parentheses part which is (6 +2)= 8. And now we will perform the multiplication part which is 8 \u00d7 7= 56. So the statement is true by inserting the parentheses for 6 + 2.<\/p>\n<p>Question 13.<br \/>\n18 &#8211; 6 \u00f7 2 + 5 = 11<br \/>\nAnswer:<br \/>\nThe expression after inserting parentheses is (18 &#8211; 6) \u00f7 2 + 5.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 18 &#8211; 6 \u00f7 2 + 5. So we will insert the parentheses for 18 &#8211; 6, then the expression will be<br \/>\n(18 &#8211; 6) \u00f7 2 + 5. So we will solve the expression using the BODMAS rule, now first we will perform the parentheses part which is (18 &#8211; 6)= 12. And now we will perform division which is 12 \u00f7 2= 6. Now we will perform the addition part which is 6 + 5= 11. So the statement is true by inserting the parentheses for 18 &#8211; 6.<\/p>\n<p>Question 14.<br \/>\n10 + 2 \u00d7 4 &#8211; 1 = 16<br \/>\nAnswer:<br \/>\nThe statement is true by inserting parentheses for 4 \u2013 1 and the expression is 10 + 2 \u00d7(4 \u2013 1).<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 10 + 2 \u00d7 4 &#8211; 1. So we will insert the parentheses for 4 &#8211; 1, then the expression will be<br \/>\n10 + 2 \u00d7(4 \u2013 1). So we will solve the expression using the BODMAS rule, now first we will perform the parentheses part which is (4 \u2013 1)= 3. And now we will perform the multiplication part which is 2 \u00d7 3= 6. And now we will add the result 6 with 10 which is 10 + 6= 16. So the statement is true by inserting parentheses for 4 \u2013 1.<\/p>\n<p>Question 15.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nIs Newton correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-4.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 4\" width=\"168\" height=\"146\" \/><br \/>\nAnswer:<br \/>\nNo, Newton is not correct.<\/p>\n<p>Explanation:<br \/>\nNo, Newton is not correct. Because Newton did not use the BODMAS rule to solve the expression. By using the BODMAS rule first Newton should solve the division part and then he should solve the addition part.<\/p>\n<p>Question 16.<br \/>\n<strong>Writing<\/strong><br \/>\nDescribe how you can evaluate 9 \u00d7 (40 + 5) two different ways.<br \/>\nAnswer:<br \/>\nThe expression 9 \u00d7 (40 + 5) can be solved by the BODMAS way and the other way to solve the expression is by Distributive property.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 9 \u00d7 (40 + 5), so to solve the expression we will use the BODMAS rule. So by the BODMAS rule first we will solve the parentheses part which is (40 + 5)= 45 and then we will solve the multiplication part which s 9 \u00d7 45= 405. This process is one way to solve the given expression. Another way to solve the expression is by Distributive property and the equation can be solved as<br \/>\n9 \u00d7 (40 + 5) = (9 \u00d7 40) + (9 + 5)<br \/>\n= 360 + 451<br \/>\n= 405.<br \/>\nand this property is called as Distributive property which means Distributive Property is a property of Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA robotics team orders 14 shirts. The order has a $9 shipping fee. Use the expression 14 \u00d7 12 + 9 to find how much the team spends on the order.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-5.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 5\" width=\"254\" height=\"221\" \/><br \/>\nEvaluate 14 \u00d7 12 + 9 using the order of operations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-6.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 6\" width=\"380\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-6.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-6-300x59.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><br \/>\nThe team spends _____ on the order.<\/p>\n<p>Answer:<br \/>\nThe team spends $177 on the order.<\/p>\n<p>Explanation:<br \/>\nAs robotic team orders, 14 shirts and the order has a $9 shipping fee and the given expression is 14 \u00d7 12 + 9. We can solve this expression by the BODMAS rule in which BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the multiplication part which is stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the multiplication part which is 14 \u00d7 12= 168 and then we will solve the addition part which is 168 + 9= 177. So the team spends $177 on the order.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-40468\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-6-1.png\" alt=\"Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-6\" width=\"188\" height=\"66\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 17.<br \/>\nA parking garage has 7 floors with 109 spaces on each floor. There are 486 spaces being used. Use the expression 7 \u00d7 109 &#8211; 486 to find how many spaces are not being used.<br \/>\nAnswer:<br \/>\nThe number of spaces that are not being used is 1,367.<\/p>\n<p>Explanation:<br \/>\nAs a parking garage has 7 floors with 109 spaces on each floor and there are 486 spaces being used, so given expression is 7 \u00d7 109 &#8211; 486. So the given expression first we will solve the multiplication part by the BODMAS rule in which BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So now first we will solve the multiplication part which is 7 \u00d7 109= 1,853 and then we will solve the subtraction part which is<br \/>\n1853 &#8211; 486= 1,367. So the number of spaces that are not being used is 1,367.<\/p>\n<p>Question 18.<br \/>\nAt a fair, you ride the swinging ship 3 times and the bumper cars 5 times. Use the expression (3 \u00d7 2) + (5 \u00d7 4) to find how many tickets you use in all.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-7.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 7\" width=\"290\" height=\"167\" \/><br \/>\nAnswer:<br \/>\nThe number of tickets I have used is 26 tickets.<\/p>\n<p>Explanation:<br \/>\nAs a fair has a swinging ship and a bumper car and I rode the swinging ship 3 times and the bumper cars 5 times, so the given expression is (3 \u00d7 2) + (5 \u00d7 4). By the BODMAS rule first, we will solve the parentheses part and in which BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So now first we will solve the parentheses part which is (3 \u00d7 2) + (5 \u00d7 4)= 6 + 20 and then we will solve the addition part which is 6 + 20= 26. So the number of tickets I have used is 26 tickets.<\/p>\n<p>Question 19.<br \/>\nYou download 128 songs and divide them into4 equal-sized playlists. You delete 1 playlist. Then you download 56 more songs. Use the expression 128 &#8211; (128 \u00f7 4) + 56 to find how many songs you have now.<br \/>\nAnswer:<br \/>\nThe number of songs we had is 40 songs.<\/p>\n<p>Explanation:<br \/>\nAs I have downloaded 128 songs and divide them into 4 equal-sized playlists and then deleted 1 playlist. Then I have downloaded 56 more songs, so the given expression is 128 &#8211; (128 \u00f7 4) + 56. By the BODMAS rule first we will solve the parentheses part and in which BODMAS stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So now first we will solve the parentheses part which is (128 \u00f7 4)= 32 and now we will solve the addition part which is 32 + 56= 88, and now we will solve the subtraction part which is 128 &#8211; 88= 40. So the number of songs we have is 40 songs.<\/p>\n<p>Question 20.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA politician buys 3 boxes of campaign buttons. There are 60 buttons in each box. He divides the buttons into4 equal groups. How many buttons are in each group?<br \/>\nAnswer:<br \/>\nThere will be 45 buttons in each group.<\/p>\n<p>Explanation:<br \/>\nAs a politician buys 3 boxes of campaign buttons and there are 60 buttons in each box. So the total number of buttons is 3 \u00d7 60= 180 buttons and then he divides the buttons into four equal groups. So the number of buttons in each group is 180 \u00f7 4= 45. So there will be 45 buttons in each group.<\/p>\n<h3><a id=\"Order_of_Operations_Homework_&amp;_Practice_2.2\"><\/a>Order of Operations Homework &amp; Practice 2.2<\/h3>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n(8 &#8211; 2) \u00d7 4<br \/>\nAnswer:<br \/>\nThe value of the expression (8 &#8211; 2) \u00d7 4 will be 24.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the parentheses part which is (8 &#8211; 2)= 6 and the result will be 6. Now we will solve the multiplication part which is 6 \u00d7 4= 24. So the value of the expression (8 &#8211; 2) \u00d7 4 will be 24.<\/p>\n<p>Question 2.<br \/>\n7 + (6 \u00f7 3)<br \/>\nAnswer:<br \/>\nThe value of the expression 7 + (6 \u00f7 3) will be 10.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the parentheses part which is (6 \u00f7 3)= 3 and the result will be 3. Now we will solve the addition part which is 7 + 3= 10. So the value of the expression 7 + (6 \u00f7 3) will be 10.<\/p>\n<p>Question 3.<br \/>\n5 \u00d7 (6 + 2)<br \/>\nAnswer:<br \/>\nThe value of the expression 5 \u00d7 (6 + 2) will be 40.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the parentheses part which is (6 + 2)= 8 and the result will be 8. Now we will solve the multiplication part which is 5 \u00d7 8= 40. So the value of the expression 5 \u00d7 (6 + 2) will be 40.<\/p>\n<p>Question 4.<br \/>\n21 + 42 \u00f7 7<br \/>\nAnswer:<br \/>\nThe value of the expression 21 + 42 \u00f7 7 will be 27.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the Division part which is 42 \u00f7 7= 6 and the result will be 6. Now we will solve the addition part which is 21 + 6= 27. So the value of the expression 21 + 42 \u00f7 7 will be 27.<\/p>\n<p>Question 5.<br \/>\n\\(\\left(\\frac{1}{4}+\\frac{2}{4}+\\frac{3}{4}\\right)\\) \u00d7 2<br \/>\nAnswer:<br \/>\nThe value of the expression \\(\\left(\\frac{1}{4}+\\frac{2}{4}+\\frac{3}{4}\\right)\\) \u00d7 2 will be 3.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve parentheses part which is \\(\\left(\\frac{1}{4}+\\frac{2}{4}+\\frac{3}{4}\\right)\\)= 6\/4 and the result will be 3\/2. Now we will solve the multiplication part which is 3\/2 \u00d7 2= 3. So the value of the expression<br \/>\n\\(\\left(\\frac{1}{4}+\\frac{2}{4}+\\frac{3}{4}\\right)\\) \u00d7 2 will be 3.<\/p>\n<p>Question 6.<br \/>\n86 &#8211; 9 \u00d7 6<br \/>\nAnswer:<br \/>\nThe value of the expression 86 &#8211; 9 \u00d7 6 will be 32.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the multiplication part which is 9 \u00d7 6= 54 and the result will be 54. Now we will solve the subtraction part which is 86 &#8211; 54= 32. So the value of the expression 86 &#8211; 9 \u00d7 6 will be 32.<\/p>\n<p>Question 7.<br \/>\n56 &#8211; 22 \u00f7 2<br \/>\nAnswer:<br \/>\nThe value of the expression 56 &#8211; 22 \u00f7 2 will be 45.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the division part which is 22 \u00f7 2= 11 and the result will be 11. Now we will solve the subtraction part which is 56 &#8211; 11= 45. So the value of the expression 56 &#8211; 22 \u00f7 2 will be 45.<\/p>\n<p>Question 8.<br \/>\n27 + 11 \u00d7 4<br \/>\nAnswer:<br \/>\nThe value of the expression 27 + 11 \u00d7 4 will be 71.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the multiplication part which is 11 \u00d7 4= 44 and the result will be 44. Now we will solve the addition part which is 27 + 44= 71. So the value of the expression 27 + 11 \u00d7 4 will be 71.<\/p>\n<p>Question 9.<br \/>\n21 &#8211; (12 + 6) \u00f7 9<br \/>\nAnswer:<br \/>\nThe value of the expression 21 &#8211; (12 + 6) \u00f7 9 will be 19.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the parentheses part which is (12 + 6)= 18 and the result will be 18. Now we will solve the division part which is 18 \u00f7 9= 2 and now we will solve the subtraction part which is 21 &#8211; 2= 19. So the value of the expression 21 &#8211; (12 + 6) \u00f7 9 will be 19.<\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 10.<br \/>\n9 \u00d7 (5 + 15) &#8211; 42<br \/>\nAnswer:<br \/>\nThe value of the expression 9 \u00d7 (5 + 15) &#8211; 42 will be 138.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the parentheses part which is (5 + 15)= 20 and the result will be 20. Now we will solve the multiplication part which is 9 \u00d7 20= 180 and now we will solve the subtraction part which is 180 &#8211; 42= 138. So the value of the expression 9 \u00d7 (5 + 15) &#8211; 42 will be 138.<\/p>\n<p>Question 11.<br \/>\n14 + 56 \u00f7 7 &#8211; 6<br \/>\nAnswer:<br \/>\nThe value of the expression 14 + 56 \u00f7 7 &#8211; 6 will be 16.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the division part which is 56 \u00f7 7= 8 and the result will be 8. Now we will solve the addition part which is 14 + 8= 22 and now we will solve the subtraction part which is 22- 6= 16. So the value of the expression 14 + 56 \u00f7 7 &#8211; 6 will be 16.<\/p>\n<p>Question 12.<br \/>\n(106 + 350 + 244) \u00f7 10<br \/>\nAnswer:<br \/>\nThe value of the expression (106 + 350 + 244) \u00f7 10 will be 70.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will solve the parentheses part which is (106 + 350 + 244) and the result will be 700. Now we will solve the division part which is 700 \u00f7 10= 70. So the value of the expression (106 + 350 + 244) \u00f7 10 will be 70.<\/p>\n<p><strong>Insert parentheses to make the statement true.<\/strong><br \/>\nQuestion 13.<br \/>\n36 &#8211; 9 \u00f7 9 = 3<br \/>\nAnswer:<br \/>\nThe statement is true by inserting parentheses for 36 \u2013 9.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 36 &#8211; 9 \u00f7 9 = 3. So we will insert the parentheses for 36 &#8211; 9, then the expression will be<br \/>\n(36 &#8211; 9) \u00f7 9. So we will solve the expression using the BODMAS rule, now first we will perform the parentheses part which is (36 \u2013 9)= 27. And now we will perform the division part which is 27 \u00f7 9= 3. So the statement is true by inserting parentheses for 36 \u2013 9.<\/p>\n<p>Question 14.<br \/>\n12 + 8 \u00f7 4 + 1 = 6<br \/>\nAnswer:<br \/>\nThe statement is true by inserting parentheses for 12 + 8.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 12 + 8 \u00f7 4 + 1 = 6. So we will insert the parentheses for 12 + 8, then the expression will be<br \/>\n(12 + 8) \u00f7 4 + 1. So we will solve the expression using the BODMAS rule, now first we will perform the parentheses part which is (12 + 8)= 20. And now we will perform the division part which is 20 \u00f7 4= 5, now we will solve the addition part which is 5 + 1=6. So the statement is true by inserting parentheses for 12 + 8.<\/p>\n<p>Question 15.<br \/>\n10 + 4 \u00d7 12 &#8211; 6 = 34<br \/>\nAnswer:<br \/>\nThe statement is true by inserting parentheses for 12 &#8211; 6.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 10 + 4 \u00d7 12 &#8211; 6 = 34. So we will insert the parentheses for 12 + 8, then the expression will be 10 + 4 \u00d7 (12 &#8211; 6). So we will solve the expression using the BODMAS rule, now first we will perform the parentheses part which is (12 &#8211; 6)= 6. And now we will perform the multiplication part which is 4 \u00d7 6= 24, now we will solve the addition part which is 10 + 24=34. So the statement is true by inserting parentheses for 12 &#8211; 6.<\/p>\n<p>Question 16.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend says that because of the order of operations, the expressions are equivalent. Is your friend correct? Explain.<br \/>\n10 &#8211; (5 \u00d7 2) + 7\u00a0 \u00a0 10 &#8211; 5 \u00d7 2 + 7<br \/>\nAnswer:<br \/>\nYes, my friend is correct.<\/p>\n<p>Explanation:<br \/>\nYes, my friend is correct. The expressions are equivalent because of the order of operations. By the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So if we solve the expression without parentheses we will get the same result. So my friend is correct.<\/p>\n<p>Question 17.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich expressions have a value of 9?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-8.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 8\" width=\"292\" height=\"112\" \/><br \/>\nAnswer:<br \/>\nOn solving all the expressions the expression 5 + 40 \u00f7 5 &#8211; 4, 5 \u00d7 (10 &#8211; 4) &#8211; 21 has got the value of 9.<\/p>\n<p>Explanation:<br \/>\nTo check which expression has a value of 9, we will follow the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So the first expression is<br \/>\n2 + 1 \u00d7 3= 2 + 3, here first we will solve the multiplication part by the order of operations and then we will solve the addition part.<br \/>\non solving we will get the result as 5.<br \/>\nSo the first expression didn&#8217;t get the value as 9.<br \/>\nThe second expression is<br \/>\n3 \u00d7 4 &#8211; 1= 12 &#8211; 1, here first we will solve the multiplication part by the order of operations and then we will solve the addition part.<br \/>\non solving we will get the result as 11.<br \/>\nSo the second expression didn&#8217;t get the value as 9.<br \/>\nThe third expression is<br \/>\n5 + 40 \u00f7 5 &#8211; 4 = 5 + 8 &#8211; 4<br \/>\n= 13 &#8211; 4, here first we will solve the division part by the order of operations then we will solve the addition part, and then the subtraction part.<br \/>\nOn solving we will get the result as 9.<br \/>\nSo the expression has the value 9.<br \/>\nThe fourth expression is<br \/>\n40 &#8211; 30 \u00f7 10 + 8 = 40 &#8211; 3 +8<br \/>\n= 40 &#8211; 11, here first we will solve the division part by the order of operations then we will solve the addition part, and then the subtraction part.<br \/>\nOn solving we will get the result as 29.<br \/>\nSo the expression didn&#8217;t get the value as 9.<br \/>\nThe fifth expression is<br \/>\n18 \u00f7 (8+0+18) = 18 \u00f7 (26), here first we will solve the parentheses part by the order of operations then we will solve the division part. By seeing the solution we can say that the expression didn&#8217;t get the value 9.<br \/>\nThe sixth expression is<br \/>\n5 \u00d7 (10 &#8211; 4) &#8211; 21 = 5 \u00d7 (6) &#8211; 21<br \/>\n= 30 &#8211; 21, here first we will solve the parentheses part by order of operations then we will solve the multiplication part, and then we will solve the subtraction part.<br \/>\nOn solving we will get the result as 9.<br \/>\nSo the expression has the value 9.<br \/>\nOn solving all the expressions the expression 5 + 40 \u00f7 5 &#8211; 4, 5 \u00d7 (10 &#8211; 4) &#8211; 21 has got the value of 9.<\/p>\n<p>Question 18.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nFifth graders at a school write a paper about a historical person for a contest. There are 5 classes of 25 students and 1 class of 28 students participating in the contest. Use the expression 5 \u00d7 25 + 28 to find how many students participate in the contest.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-9.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 9\" width=\"234\" height=\"196\" \/><br \/>\nAnswer:<br \/>\nThe number of students who participated in the contest is 153.<\/p>\n<p>Explanation:<br \/>\nAs there are 5 classes of 25 students and 1 class of 28 students participating in the contest and the given expression is 5 \u00d7 25 + 28. So, here first we will solve the multiplication part by the order of operations then we will solve the addition part. So<br \/>\n5 \u00d7 25 + 28= 125 + 28<br \/>\nOn solving the expression we will get the result as 153. So the number of students who participated in the contest is 153.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Divide. Then check your answer.<\/strong><br \/>\nQuestion 19.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-10.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 10\" width=\"57\" height=\"53\" \/><br \/>\nAnswer:<br \/>\nOn dividing 832 \u00f7 8 we will get the result as 104.<\/p>\n<p>Explanation:<br \/>\nOn dividing 832 \u00f7 8 we will get the result as 104. To check the answer we will multiply the result 104 and 8 which is 104 \u00d7 8= 832.<\/p>\n<p>Question 20.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-11.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 11\" width=\"126\" height=\"59\" \/><br \/>\nAnswer:<br \/>\nOn dividing 215 \u00f7 7 we will get the result as 30.71.<\/p>\n<p>Explanation:<br \/>\nOn dividing 215 \u00f7 7 we will get the result as 30.71. To check the answer we will multiply the result 30.71 and 7 which is 30.71 \u00d7 7= 214.97.<\/p>\n<p>Question 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-5th-Grade-Chapter-2-Numerical-Expressions-2.2-12.png\" alt=\"Big Ideas Math Answers 5th Grade Chapter 2 Numerical Expressions 2.2 12\" width=\"144\" height=\"57\" \/><br \/>\nAnswer:<br \/>\nOn dividing 5,078 \u00f7 5 we will get the result as 1015.6.<\/p>\n<p>Explanation:<br \/>\nOn dividing 5,078 \u00f7 5 we will get the result as 1015.6. To check the answer we will multiply the result 1015.6 and 5 which is 1015.6 \u00d7 7= 5,078.<\/p>\n<h3><a id=\"Lesson_2.3_Write_Numerical_Expressions\"><\/a>Lesson 2.3 Write Numerical Expressions<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Write a real-life problem that can be represented by one of the expressions below. Switch papers with your partner. Which expression represents your partner\u2019s problem? Explain.<br \/>\n7 \u00d7 (8 + 5)<br \/>\n(7 \u00d7 8) + 5<br \/>\nAnswer:<br \/>\nThe expression represented by the partner is (7 \u00d7 8) + 5.<\/p>\n<p>Explanation:<br \/>\nGiven that the expressions are 7 \u00d7 (8 + 5) and (7 \u00d7 8) + 5. So the solution for my problem is<br \/>\n7 \u00d7 (8 + 5)= 7 \u00d7 (12), here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. On solving we will get the result as 84. While checking my friend&#8217;s paper he solved the expression (7 \u00d7 8) + 5= 56 +5, here first we will solve the parentheses part by the order of operations then we will solve the addition part. On solving we will get the result as 61. AS the parentheses are different in the expression so the answer differs.<\/p>\n<p><strong>Make Sense of Problems<\/strong><br \/>\nHow can parentheses change the meaning of an expression? Explain.<br \/>\nAnswer:<br \/>\nThese parentheses in the expression represent that the expression or the equation should be solved first before any other calculation has done. The path between the parentheses represents as one number.<\/p>\n<p><strong>Think and Grow: Write an Interpret Expressions<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nWrite the words as an expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-1.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions 2.3 1\" width=\"139\" height=\"259\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-2.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions 2.3 2\" width=\"295\" height=\"86\" \/><br \/>\n10 \u00f7 _______<br \/>\nThe numerical expression is ______.<\/p>\n<p>Answer:<br \/>\nThe numerical expression is 10 \u00f7 (9 &#8211; 4).<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is 10 \u00f7 (9 &#8211; 4). So, here first we will solve the parentheses part by the order of operations then we will solve the division part. So<br \/>\n10 \u00f7 (9 &#8211; 4) = 10 \u00f7 5<br \/>\non solving we will get the result as 5.<\/p>\n<p><strong>Example<\/strong><br \/>\nWrite the words as an expression. Then interpret the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-3.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions 2.3 3\" width=\"263\" height=\"92\" \/><br \/>\nThe numerical expression is _____.<br \/>\nThe value of the expression is _______ times the sum 54 + 97.<\/p>\n<p>Answer:<br \/>\nThe numerical expression is (54 + 97) \u00d7 2.<br \/>\nThe value of the expression is 2 times the sum of 54 + 97.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (54 + 97) \u00d7 2. So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n(54 + 97) \u00d7 2 = 151 \u00d7 2<br \/>\non solving we will get the result as 302.<br \/>\nThe numerical expression is (54 + 97) \u00d7 2.<br \/>\nThe value of the expression is 2 times the sum of 54 + 97.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Write the words as an expression<\/strong><br \/>\nQuestion 1.<br \/>\nMultiply 8 and 5, then divide by 4.<br \/>\nAnswer:<br \/>\nThe numerical expression using parenthesis is (8 \u00d7 5) \u00f7 4.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (8 \u00d7 5) \u00f7 4. So, here first we will solve the parentheses part by the order of operations then we will solve the division part. So<br \/>\n(8 \u00d7 5) \u00f7 4= 40 \u00f7 4<br \/>\non solving we will get the result as 10.<\/p>\n<p>Question 2.<br \/>\nMultiply the sum of 14 and 18 by 4.<br \/>\nAnswer:<br \/>\nThe numerical expression using parenthesis is (14 + 18) \u00d7 4.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (14 + 18) \u00d7 4. So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n(14 + 18) \u00d7 4= 32 \u00d7 4<br \/>\non solving we will get the result as 128.<\/p>\n<p><strong>Write the words as an expression. Then interpret the expression.<\/strong><br \/>\nQuestion 3.<br \/>\nMultiply 3 by the sum of 12 and 3.<br \/>\nAnswer:<br \/>\nThe numerical expression using parenthesis is 3 \u00d7 (12 + 3).<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is 3 \u00d7 (12 + 3). So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n3 \u00d7 (12 + 3)= 3 \u00d7 15<br \/>\non solving we will get the result as 45.<\/p>\n<p>Question 4.<br \/>\nSubtract 30 from 50, then divide by 10.<br \/>\nAnswer:<br \/>\nThe numerical expression using parenthesis is (50 &#8211; 30) \u00f7 10.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (50 &#8211; 30) \u00f7 10. So, here first we will solve the parentheses part by the order of operations then we will solve the division part. So<br \/>\n(50 &#8211; 30) \u00f7 10= 20 \u00f7 10<br \/>\non solving we will get the result as 2.<\/p>\n<p>Apply and Grow: Practice<\/p>\n<p><strong>Write the words as an expression. Then interpret the expression.<\/strong><br \/>\nQuestion 5.<br \/>\nAdd 238 and 12, then multiply by 3.<br \/>\nAnswer:<br \/>\nThe numerical expression using parenthesis is (238 + 12) \u00d7 3.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (238 + 12) \u00d7 3. So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n(238 + 12) \u00d7 3= 250 \u00d7 3<br \/>\non solving we will get the result as 750.<\/p>\n<p>Question 6.<br \/>\nSubtract 15 from 60, then divide by 9.<br \/>\nAnswer:<br \/>\nThe numerical expression using parenthesis is (60 &#8211; 15) \u00f7 9.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (60 &#8211; 15) \u00f7 9. So, here first we will solve the parentheses part by the order of operations then we will solve the division part. So<br \/>\n(60 &#8211; 15) \u00f7 9= 45 \u00f7 9<br \/>\non solving we will get the result as 5.<\/p>\n<p><strong>Write the words as an expression. Then evaluate the expression.<\/strong><br \/>\nQuestion 7.<br \/>\nMultiply 5 by the difference of 25 and 20.<br \/>\nAnswer:<br \/>\nThe numerical expression is 5 \u00d7 (25 &#8211; 20) and on evaluating we will get the value as 25.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is 5 \u00d7 (25 &#8211; 20). So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n5 \u00d7 (25 &#8211; 20)= 5 \u00d7 5<br \/>\non solving we will get the result as 25.<\/p>\n<p>Question 8.<br \/>\nAdd the product of 60 and 4 to the product of 5 and 4.<br \/>\nAnswer:<br \/>\nThe numerical expression is (60 \u00d7 4) + (5 \u00d7 4) and on evaluating we will get the value as 260.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (60 \u00d7 4) + (5 \u00d7 4). So, here first we will solve the parentheses part by the order of operations then we will solve the addition part. So<br \/>\n(60 \u00d7 4) + (5 \u00d7 4)= 240 + 20<br \/>\non solving we will get the result as 260.<\/p>\n<p><strong>Write the expression in words.<\/strong><br \/>\nQuestion 9.<br \/>\n13 + (4 \u00d7 6)<br \/>\nAnswer:<br \/>\nAdd 13 to the product of 4 and 6.<\/p>\n<p>Explanation:<br \/>\nTo expand the given expression 13 + (4 \u00d7 6) in words we will be written as<br \/>\nAdd 13 to the product of 4 and 6.<\/p>\n<p>Question 10.<br \/>\n(4 + 8) \u00f7 2<br \/>\nAnswer:<br \/>\nAdd 4 and 8 and then divide by 2.<\/p>\n<p>Explanation:<br \/>\nTo expand the given expression 13 + (4 \u00d7 6) in words we will be written as<br \/>\nadd 4 and 8 and then divide by 2.<\/p>\n<p>Question 11.<br \/>\nNewton has $20. He spends $4 on lunch and $13 at the store. Write an expression to represent the situation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-4.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions 2.3 4\" width=\"135\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nThe expression can be represented as<br \/>\n$20 &#8211; ($13 + $4)= $20 &#8211; ($17)<\/p>\n<p>Explanation:<br \/>\nAs Newton has $20 and he spends $4 on lunch and $13 at the store. So the expression can be represented as<br \/>\n$20 &#8211; ($13 + $4)= $20 &#8211; ($17)<br \/>\nhere first we will solve the parentheses part by the order of operations then we will solve the subtraction part. On solving we will get $3.<\/p>\n<p>Question 12.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how you know which operation to use when writing words as an expression.<br \/>\nAnswer:<br \/>\nThe operation to use when writing words as expressions are<br \/>\nThe sum is used as addition and the difference is used as subtraction and the product is used as the product and the quotient is used as the division.<\/p>\n<p>Question 13.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWrite the words as an expression. Then use a property of addition to write an equivalent expression.<br \/>\nAdd 9 to the sum of 21 and 6.<br \/>\nAnswer:<br \/>\nThe numerical expression of the given expression is 9 + (21 + 6) and the property used to solve the expression is Distributive property.<\/p>\n<p>Explanation:<br \/>\nGiven that the expression in words is Add 9 to the sum of 21 and 6. The numerical expression of the given expression is 9 + (21 + 6). The property we can use to solve the expression is distributive property. By Distributive Property is a property in which Multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So by the distributive property, the expression will be solved as<br \/>\n9 + (21 + 6)= 9 + 27, here first we will solve the parentheses part by the order of operations then we will solve the addition part. On solving we will get the result as 36.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nOn your turn of a word game, you draw the card shown and create the word MATH. Your word score is the sum of the points of the letters you use. How many points do you earn on your turn?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-5.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.3 5\" width=\"271\" height=\"241\" \/><br \/>\nWrite an expression.<br \/>\nThink: Add _____, _____, _____, and _____, then multiply by _____. (____ + ____ + _____ + _____) \u00d7 _____<br \/>\nInterpret the expression.<br \/>\nYou earn ____ times as many points as the value of your word score.<\/p>\n<p>Answer:<br \/>\nAdd 3 + 1 + 1 + 4, then multiply by 3. (3 + 1 + 1 + 4) \u00d7 3<br \/>\nYou earn 3 times as many points as the value of your word score.<\/p>\n<p>Explanation:<br \/>\nGiven that the word M has a score of 3 and the word A has a score of 1 and the word T has a score of 1 and the word H has a score of 4. As word score is the sum of the points of the letters you use so we will add the total score which is 3 + 1 + 1 + 4= 9 and now we will multiply by 3 to triple the score. So the expression will be<br \/>\n(3 + 1 + 1 + 4) \u00d7 3= (9) \u00d7 3, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. On solving we will get the result as 27.<\/p>\n<p>Evaluate the expression.<br \/>\n(3 + 1 + 1 + 4) \u00d7 3 = ______ \u00d7 _____<br \/>\n= ____<br \/>\nSo, you earn _____ points on your turn.<\/p>\n<p>Answer:<br \/>\nThe points that I have earned in my turn is 27.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is (3 + 1 + 1 + 4) \u00d7 3= (9) \u00d7 3, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. On solving we will get the result as 27. So the points that I have earned in my turn are 27.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 14.<br \/>\nYou make 2 batches of fruit salad. How many cups of fruit do you use in all?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-6.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions 2.3 6\" width=\"226\" height=\"144\" \/><br \/>\nAnswer:<br \/>\nThe number of cups of fruit does we use in all is 14 cups.<\/p>\n<p>Explanation:<br \/>\nAs there are two cups of strawberries, 1 1\/2 cups blueberries, 2 1\/2 cups grapes,1 cup pineapple and there are two batches of fruit salad. So the expression will be 2 \u00d7 ( 2 + 1 1\/2 + 2 1\/2 + 1).<br \/>\n2 \u00d7 ( 2 + 1 1\/2 + 2 1\/2 + 1)= 2 \u00d7 ((4 + 3 + 5 + 2)\/2)<br \/>\n= 2 \u00d7 (14\/2) here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. On solving we will get the result as 14. So the number of cups of fruit do we use in all is 14 cups.<\/p>\n<p>Question 15.<br \/>\nA customer places an online order for a video game that costs $49 and 3 books that each cost $12. Shipping costs $6. What is the total cost of the order?<br \/>\nAnswer:<br \/>\nThe numerical expression will be 49 + (3 \u00d7 12) + 6 on solving the result will be 91.<\/p>\n<p>Explanation:<br \/>\nAs the customer places an online order for a video game that costs $49 and 3 books and each book costs $12 and the shipping cost is $6. So the numerical expression will be 49 + (3 \u00d7 12) + 6.<br \/>\n49 + (3 \u00d7 12) + 6= 49 + 36 +6, here first we will solve the parentheses part by the order of operations then we will solve the addition part. On solving we will get the result as 91.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nEight students use2 sets of 52 cards to play a game. The cards are divided equally among the players. How many cards does each player get?<br \/>\nAnswer:<br \/>\nThe numerical expression is (2 \u00d7 52) \u00f7 8 on solving the result will be 13.<\/p>\n<p>Explanation:<br \/>\nAs there are eight students and uses two sets of 52 cards to play a game, so the cards are equally divided among the players. So the numerical expression will be (2 \u00d7 52) \u00f7 8.<br \/>\n(2 \u00d7 52) \u00f7 8= 104 \u00f7 8, here first we will solve the parentheses part by the order of operations then we will solve the division part. On solving we will get the result as 13.<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nHow much more does it cost to rent 2 adult bikes for 4 hours than a tandem bike for 4 hours? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-7.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions 2.3 7\" width=\"127\" height=\"212\" \/><br \/>\nAnswer:<br \/>\nIt costs four times more than the tandem bike.<\/p>\n<p>Explanation:<br \/>\nTo rent a two adult bike for four hours then a tandem bike for four hours.<br \/>\nSo the numerical expression will be (2 \u00d7 4) &#8211; 4.<br \/>\n(2 \u00d7 4) &#8211; 4= 8 &#8211; 4, here first we will solve the parentheses part by the order of operations then we will solve the subtraction part. On solving we will get the result as 4.<\/p>\n<h3><a id=\"Write_Numerical_Expressions_Homework_&amp;_Practice_2.3\"><\/a>Write Numerical Expressions Homework &amp; Practice 2.3<\/h3>\n<p><strong>Write the words as an expression.<\/strong><br \/>\nQuestion 1.<br \/>\nAdd 10 to the quotient of 72 and 8.<br \/>\nAnswer:<br \/>\nThe numerical expression is\u00a0 (72 \u00f7 8) + 10 and on evaluating we will get the value as 19.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (72 \u00f7 8) + 10. So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n(72 \u00f7 8) + 10= 9 + 10<br \/>\non solving we will get the result as 19.<\/p>\n<p>Question 2.<br \/>\nSubtract 55 from the sum of 124 and 56.<br \/>\nAnswer:<br \/>\nThe numerical expression is\u00a0 (124 + 56) &#8211; 10 and on evaluating we will get the value as 170.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (124 + 56) &#8211; 10. So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n(124 + 56) &#8211; 10= 180 &#8211; 10<br \/>\non solving we will get the result as 170.<\/p>\n<p>Write the words as an expression. Then interpret the expression.<br \/>\nQuestion 3.<br \/>\nAdd 14 and 13, then divide by 3.<br \/>\nAnswer:<br \/>\nThe numerical expression is\u00a0 (14 + 13) \u00f7 3 and on evaluating we will get the value as 9.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (14 + 13) \u00f7 3. So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n(14 + 13) \u00f7 3= 27 \u00f7 3<br \/>\non solving we will get the result as 9.<\/p>\n<p>Question 4.<br \/>\nSubtract 29 from 39, then multiply by \\(\\frac{1}{2}\\).<br \/>\nAnswer:<br \/>\nThe numerical expression is\u00a0 (39 &#8211; 29) \u00d7 1\/2 and on evaluating we will get the value as 5.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (39 &#8211; 29) \u00d7 1\/2. So, here first we will solve the parentheses part by the order of operations then we will solve the multiplication part. So<br \/>\n(39 &#8211; 29) \u00d7 1\/2= 10 \u00d7 1\/2<br \/>\non solving we will get the result as 5.<\/p>\n<p>Write the words as an expression. Then evaluate the expression.<br \/>\nQuestion 5.<br \/>\nSubtract the product of 5 and 8 from the product of 10 and 9.<br \/>\nAnswer:<br \/>\nThe numerical expression is (10 \u00d7 9) &#8211; (5 \u00d7 8) and on evaluating we will get the value as 50.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (10 \u00d7 9) &#8211; (5 \u00d7 8). So, here first we will solve the parentheses part by the order of operations then we will solve the subtraction part. So<br \/>\n(10 \u00d7 9) &#8211; (5 \u00d7 8)= 90 &#8211; 40<br \/>\non solving we will get the result as 50.<\/p>\n<p>Question 6.<br \/>\nAdd 15 to the quotient of 60 and 3.<br \/>\nAnswer:<br \/>\nThe numerical expression is 15 + (60 \u00f7 3) and on evaluating we will get the value as 35.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is 15 + (60 \u00f7 3). So, here first we will solve the parentheses part by the order of operations then we will solve the addition part. So<br \/>\n15 + (60 \u00f7 3)= 15 + (20)<br \/>\non solving we will get the result as 35.<\/p>\n<p><strong>Write the expression in words.<\/strong><br \/>\nQuestion 7.<br \/>\n35 &#8211; (14 + 17)<br \/>\nAnswer:<br \/>\nThe expression in words is Subtract the sum of 14 and 17 with 35.<\/p>\n<p>Explanation:<br \/>\nTo expand the given expression 35 &#8211; (14 + 17) in words we will be written as<br \/>\nSubtract the sum of 14 and 17 with 35.<\/p>\n<p>Question 8.<br \/>\n(30 &#8211; 20) \u00d7 10<br \/>\nAnswer:<br \/>\nThe expression in words is Subtract 30 and 20 and then multiply by 10.<\/p>\n<p>Explanation:<br \/>\nTo expand the given expression (30 &#8211; 20) \u00d7 10 in words we will be written as<br \/>\nSubtract 30 and 20 and then multiply by 10.<\/p>\n<p>Question 9.<br \/>\nDescartes has $9. He works 5 hours and earns $8 each hour. Write an expression to represent the situation.<br \/>\nAnswer:<br \/>\nThe expression will be (5 \u00d7 8)+ 9 and on solving the expression we will get the result as 49.<\/p>\n<p>Explanation:<br \/>\nAs Descartes has $9 and he works 5 hours and earns $8 each hour, so the expression will be (5 \u00d7 8)+ 9.<br \/>\n(5 \u00d7 8)+ 9= 40 + 9, here first we will solve the parentheses part by the order of operations then we will solve the addition part. On solving the expression we will get the result as 49.<\/p>\n<p>Question 10.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nWrite a real-life problem that can be represented by the phrase \u201c5 more than the sum of 15 and 7.\u201d<br \/>\nAnswer:<br \/>\nThe numerical expression is (15 + 7) +5.<\/p>\n<p>Explanation:<br \/>\nTo represent the phrase 5 more than the sum of 15 and 7 in a numerical expression is (15 + 7) +5. As given that the 5 more than the sum of 15 and 7so we will add the number 5 to the sum of 15 and 7.<\/p>\n<p>Question 11.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nWrite two different expressions that each represent the combined area of the rectangles. Then evaluate the expressions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-8.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions 2.3 8\" width=\"426\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-8.png 426w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-8-300x78.png 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><br \/>\nAnswer:<\/p>\n<p>Explanation:<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA music teacher replaces the strings on 3 violins, 2 violas, 4 cellos, and 1 bass. There are 4 strings on each of the instruments. How many strings does the teacher replace?<br \/>\nAnswer:<br \/>\nThe total number of strings replaced by the teacher is 37.<\/p>\n<p>Explanation:<br \/>\nAs music teacher replaces the strings on 3 violins, 2 violas, 4 cellos, and 1 bass and there are 4 strings on each of the instruments. So the teacher replaces 3 \u00d7 4= 12 violins and 2 \u00d7 4= 8 violas and 4 \u00d7 4= 16 cellos and 1 \u00d7 4= 1 bass. So the total number of strings replaced by the teacher is 12 + 8 + 16 + 1= 37.<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA customer buys 2 shirts that cost $10 each and a pair of jeans that costs $14. What is the customer\u2019s total after using the coupon?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Answers-Grade-5-Chapter-2-Numerical-Expressions-2.3-9.png\" alt=\"Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions 2.3 9\" width=\"206\" height=\"136\" \/><br \/>\nAnswer:<br \/>\nThe customer\u2019s total after using the coupon is $24.<\/p>\n<p>Explanation:<br \/>\nAs the customer buys 2 shirts that cost $10 each which is 2 \u00d7 10= 20 and a pair of jeans that costs $14 which is<br \/>\n2 \u00d7 14= 28. So the total purchase is 20 + 28= 48 and the coupon is 1\/2 off on the entire purchase. This means<br \/>\n48 \u00d7 1\/2= 24. So the customer\u2019s total after using the coupon is $24.<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Subtract.<\/strong><br \/>\nQuestion 14.<br \/>\n9\\(\\frac{3}{4}\\) &#8211; 5\\(\\frac{1}{4}\\) = _____<br \/>\nAnswer:<br \/>\nOn subtracting 9\\(\\frac{3}{4}\\) &#8211; 5\\(\\frac{1}{4}\\) we will get the result as<br \/>\n4\\(\\frac{2}{4}\\).<\/p>\n<p>Explanation:<br \/>\nTo subtract 9\\(\\frac{3}{4}\\) &#8211; 5\\(\\frac{1}{4}\\) first we need to convert mixed fraction into improper fraction. So the improper fraction will be \\(\\frac{39}{4}\\) &#8211; \\(\\frac{21}{4}\\). As the denominator is equal which is 4 so on subtracting \\(\\frac{39}{4}\\) &#8211; \\(\\frac{21}{4}\\) we will get the result as \\(\\frac{18}{4}\\). So the mixed fraction of the result is 4\\(\\frac{2}{4}\\).<\/p>\n<p>Question 15.<br \/>\n6\\(\\frac{1}{3}\\) &#8211; 3\\(\\frac{1}{3}\\) = ______<br \/>\nAnswer:<br \/>\nOn subtracting 6\\(\\frac{1}{3}\\) &#8211; 3\\(\\frac{1}{3}\\) we will get the result as<br \/>\n\\(\\frac{3}\\).<\/p>\n<p>Explanation:<br \/>\nTo subtract 6\\(\\frac{1}{3}\\) &#8211; 3\\(\\frac{1}{3}\\) first we need to convert mixed fraction into improper fraction. So the improper fraction will be \\(\\frac{19}{3}\\) &#8211; \\(\\frac{10}{3}\\). As the denominator is equal which is 3 so on subtracting \\(\\frac{19}{3}\\) &#8211; \\(\\frac{10}{3}\\) we will get the result as \\(\\frac{9}{3}\\) which is \\(\\frac{3}\\).<\/p>\n<p>Question 16.<br \/>\n4\\(\\frac{7}{12}\\) &#8211; 1\\(\\frac{11}{12}\\) = ______<br \/>\nAnswer:<br \/>\nOn subtracting 4\\(\\frac{7}{12}\\) &#8211; 1\\(\\frac{11}{12}\\) we will get the result as<br \/>\n\\(\\frac{8}{3}\\).<\/p>\n<p>Explanation:<br \/>\nTo subtract 4\\(\\frac{7}{12}\\) &#8211; 1\\(\\frac{11}{12}\\) first we need to convert mixed fraction into improper fraction. So the improper fraction will be \\(\\frac{55}{12}\\) &#8211; \\(\\frac{23}{12}\\). As the denominator is equal which is 12 so on subtracting \\(\\frac{55}{12}\\) &#8211; \\(\\frac{23}{12}\\) we will get the result as \\(\\frac{32}{12}\\) which is \\(\\frac{8}{3}\\).<\/p>\n<h3><a id=\"Lesson 2.4_Evaluate_Expressions_with_Grouping_Symbols\"><\/a>Lesson 2.4 Evaluate Expressions with Grouping Symbols<\/h3>\n<p><strong>Explore and Grow<\/strong><\/p>\n<p>Write the words as an expression. How is the expression different from the expressions you wrote in previous lessons?<\/p>\n<p>Multiply the sum of 4 and 5 by the difference of 8 and 7.<br \/>\nAnswer:<br \/>\nThe numerical expression is ( 4 + 5 ) \u00d7 (8 &#8211; 7 ) and on evaluating we will get the result as 9.<\/p>\n<p>Explanation:<br \/>\nGiven, Multiply the sum of 4 and 5 by the difference of 8 and 7.<br \/>\nthe sum of 4 and 5 is ( 4 + 5 )<br \/>\nthe difference between 8 and 7 is ( 8 &#8211; 7 )<br \/>\nAnd the Multiplication of these two is\u00a0 ( 4 + 5 ) \u00d7 (8 &#8211; 7 ) = 9 \u00d7 1 = 9 .<br \/>\nHere we used simple mathematic rules for the expression other than using any properties and methods. And here we have only one pair of grouping symbols.<\/p>\n<p><strong>Precision<\/strong><br \/>\nHow can you evaluate an expression that has more than one pair of parentheses?<br \/>\nAnswer: The expressions having more than one parenthesis can be evaluated by performing grouping symbols and in the next step, multiply and divide from left to right, Add and subtract from left to write if there are any,<br \/>\nparentheses( ), brackets [ ], braces { } are very helpful in grouping the symbols and to evaluate the numerical expression by performing inside operations parentheses, inside brackets, or inside braces.<\/p>\n<p><strong>Think and Grow: Evaluate with Grouping Symbols<\/strong><\/p>\n<p><strong>Key Idea<\/strong><br \/>\nParentheses ( ), brackets [ ], and braces { } are called grouping symbols. You can write and evaluate numerical expressions that have more than one pair of grouping symbols.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-1.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.4 1\" width=\"172\" height=\"240\" \/><br \/>\nOrder of Operations (with Grouping Symbols)<br \/>\n1. Perform operations in grouping symbols.<br \/>\n2. Multiply and divide from left to right.<br \/>\n3. Add and subtract from left to right.<br \/>\n<strong>Example<\/strong><br \/>\nEvaluate (25 &#8211; 5) \u00f7 (3 + 1).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-2.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.4 2\" width=\"598\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-2.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-2-300x33.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><br \/>\nSo, (25 &#8211; 5) \u00f7 (3 + 1) = ______ .<\/p>\n<p><strong>Example<\/strong><br \/>\nEvaluate [60 &#8211; (3 + 7)] \u00d7 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-3.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.4 3\" width=\"631\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-3.png 631w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-3-300x125.png 300w\" sizes=\"(max-width: 631px) 100vw, 631px\" \/><\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n(18 &#8211; 12) \u00d7 (8 \u00f7 4)<br \/>\nAnswer:<br \/>\nOn evaluating we will get the result as 12<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is (18 &#8211; 12) \u00d7 (8 \u00f7 4)<br \/>\nFirstly perform the operations within the parentheses,<br \/>\nThen we have,(8 \u00f7 4) = 2,<br \/>\n(18 &#8211; 12) = 6, and now we will perform the multiplication part.<br \/>\nTo evaluate the expression, multiply the resulting output from the inside parentheses operations, then 6 \u00d7 2 = 12<br \/>\nSo , (18 &#8211; 12) \u00d7 (8 \u00f7 4) = 12<\/p>\n<p>Question 2.<br \/>\n35 &#8211; [6 \u00d7 (1 + 4)]<br \/>\nAnswer:<br \/>\nOn evaluating we will get the result as 5.<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is 35 &#8211; [6 \u00d7 (1 + 4)]<br \/>\nFirstly perform the operations within the parentheses,<br \/>\nwe have , (1 + 4) = 5 ,<br \/>\nNow performing operation inside brackets we get, [6 \u00d7 5] = 30,<br \/>\nand now we will\u00a0 perform the subtraction part<br \/>\nNext, apply the resulted output in the expression then we have, 35 &#8211; 30 = 5.<br \/>\nSo,\u00a0 35 &#8211; [6 \u00d7 (1 + 4)] = 5.<\/p>\n<p><strong>Apply and Grow: Practice<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 3.<br \/>\n(60 &#8211; 12) \u00f7 (3 + 5)<br \/>\nAnswer:<br \/>\nOn evaluating we will get the result as 6<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is\u00a0 (60 &#8211; 12) \u00f7 (3 + 5)<br \/>\nFirstly perform the operations within the parentheses,<br \/>\nwe have , (60 &#8211; 12) = 48 ,<br \/>\n(3 + 5) = 8, now we will perform the subtraction part<br \/>\nNext, Divide the resulted outputs, we get 48 \u00f7 8 = 6.<br \/>\nSo , (60 &#8211; 12) \u00f7 (3 + 5) = 6<\/p>\n<p>Question 4.<br \/>\n95 &#8211; (26 + 14) \u00d7 (4 \u00f7 2)<br \/>\nAnswer:<br \/>\nOn evaluating we will get the result as 15<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is 95 &#8211; (26 + 14) \u00d7 (4 \u00f7 2)<br \/>\nFirstly perform the operations within the parentheses,<br \/>\nwe have (26 + 14) = 40 ,<br \/>\n(4 \u00f7 2) = 2, now we will perform the multiplication part and then we will perform the subtraction part.<br \/>\nNow we have the given expression as 95 &#8211; ( 40 \u00d7 2 ), And calculating the inside parentheses we get ( 40 \u00d7 2 )= 80<br \/>\nThen 95 &#8211; 80 = 15<br \/>\nSo , 95 &#8211; (26 + 14) \u00d7 (4 \u00f7 2) = 15 .<\/p>\n<p>Question 5.<br \/>\n(8 + 2) \u00d7 (13 + 7 + 5)<br \/>\nAnswer:<br \/>\nOn evaluating we will get the result as 250<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is (8 + 2) \u00d7 (13 + 7 + 5)<br \/>\nFirstly perform the operations within the parentheses,<br \/>\nwe have (8 + 2)\u00a0 = 10,<br \/>\n(13 + 7 + 5) = 20, and now we will perform the multiplication part.<br \/>\nTo evaluate the given expression apply the resulted output as 10 \u00d7 25= 250<br \/>\nSo, (8 + 2) \u00d7 (13 + 7 + 5) = 250.<\/p>\n<p>Question 6.<br \/>\n2 \u00d7 [(96 &#8211; 72) \u00f7 8]<br \/>\nAnswer:<br \/>\nOn evaluating the numerical expression the result is 72.<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is 2 \u00d7 [(96 &#8211; 72) \u00f7 8]<br \/>\nFirstly perform the operations within the parentheses,<br \/>\nwe have (96 &#8211; 72)\u00a0 = 24,<br \/>\n[24 \u00f7 8]= 3, and now we will perform the multiplication part.<br \/>\nTo evaluate the given expression apply the resulted output as 24 \u00d7 3= 72<br \/>\nSo, 2 \u00d7 [(96 &#8211; 72) \u00f7 8]= 72.<\/p>\n<p>Question 7.<br \/>\n[(4 &#8211; 9) &#8211; (30 \u00f7 6)] \u00d7 4<br \/>\nAnswer:<br \/>\nOn evaluating the expression we will get the result as 40.<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is [(4 &#8211; 9) &#8211; (30 \u00f7 6)] \u00d7 4<br \/>\nFirstly perform the operations within the parentheses,<br \/>\nwe have (4 &#8211; 9)\u00a0 = (-5),<br \/>\n(30 \u00f7 6) =5 which is [-5 -5]= 10 and now we will perform the multiplication part.<br \/>\nTo evaluate the given expression apply the resulted output as 10 \u00d7 4= 40<br \/>\nSo, [(4 &#8211; 9) &#8211; (30 \u00f7 6)] \u00d7 4 = 40.<\/p>\n<p>Question 8.<br \/>\n36 + {[(7 + 5) \u00f7 6 \u00d7 9] + 24}<br \/>\nAnswer:<\/p>\n<p><strong>Write the words as an expression. Then evaluate the expression.<\/strong><br \/>\nQuestion 9.<br \/>\nDivide the sum of 35 and 28 by the sum of 3 and 4.<br \/>\nAnswer:<br \/>\nThe numerical expression is (35 + 28) \u00f7 (3 + 4) and on evaluating we will get the value as 9.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is (35 + 28) \u00f7 (3 + 4). So, here first we will solve the parentheses part by the order of operations then we will solve the division part. So<br \/>\n(35 + 28) \u00f7 (3 + 4)= 63 \u00f7 7<br \/>\non solving we will get the result as 9.<\/p>\n<p>Question 10.<br \/>\nAdd 11 to the product of 4 and 6, then divide by 5.<br \/>\nAnswer:<br \/>\nThe numerical expression is [(4 \u00d7 6) + 11] \u00f7 5 and on evaluating we will get the value as 9.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression using parenthesis is [(4 \u00d7 6) + 11] \u00f7 5. So, here first we will solve the parentheses part by the order of operations then we will solve the addition part after that we will solve the division part. So<br \/>\n(35 + 28) \u00f7 (3 + 4)= 63 \u00f7 7<br \/>\non solving we will get the result as 9.<\/p>\n<p>Question 11.<br \/>\n<strong>Reasoning<\/strong><br \/>\nWill the value of {3 + [(38 &#8211; 10) &#8211; 1]} \u00f7 3 change when the braces are removed? Explain.<br \/>\nAnswer: Yes, the value will be changed if we remove the braces.<\/p>\n<p>Explanation:<br \/>\nYes, the value will be changed if we remove the braces because if the expression with braces means first we will solve the part of the braces and then we will solve by the order of operations. So by that, the value of the expression will be changed when the braces are removed.<\/p>\n<p>Question 12.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nUse each symbol once to make the number sentence true.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-4.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.4 4\" width=\"305\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-4.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-4-300x94.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><br \/>\nAnswer:<br \/>\nThe numerical expression will be (8 + 2) \u00d7 (20 \u00f7 4) &#8211; 11.<\/p>\n<p>Explanation:<br \/>\nThe numerical expression will be (8 + 2) \u00d7 (20 \u00f7 4) &#8211; 11. Let&#8217;s solve the expression to check the answer.<br \/>\n(8 + 2) \u00d7 (20 \u00f7 4) &#8211; 11= (10) \u00d7 (5) &#8211; 11<br \/>\n= 50 &#8211; 11, here first we will solve the parentheses part by the order of operations then we will solve the addition part after that we will solve the subtraction part. On solving we will get the result as 39.<\/p>\n<p><strong>Think and Grow: Modeling Real Life<\/strong><\/p>\n<p><strong>Example<\/strong><br \/>\nA woman walks 2 miles from her house to the lake, walks 3 laps on the sidewalk around the lake, then walks2 miles back to her house. She does this each day for 3 days. How many miles does the woman walk in all?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-5.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.4 5\" width=\"217\" height=\"237\" \/><br \/>\nThink: How many laps does she walk around the lake? How far does she walk to and from her house?<br \/>\nWrite an expression.<br \/>\n[____ + (_____ \u00d7 _____) + _____] \u00d7 _____<br \/>\nEvaluate the expression.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-6.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.4 6\" width=\"595\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-6.png 595w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-6-300x94.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><br \/>\nSo, the woman walks ______ miles in all.<\/p>\n<p><strong>Show and Grow<\/strong><\/p>\n<p>Question 13.<br \/>\nYou collect 12 coins and 4 gems, complete 2 missions, and fail to complete 1 mission. How many points do you earn?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-7.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.4 7\" width=\"290\" height=\"189\" \/><br \/>\nAnswer:<br \/>\nThe total number of points earned is 175.<\/p>\n<p>Explanation:<br \/>\nThe number of coins collected is 12, so the number of points earned for one coin is 5 so for 12 coins it will be<br \/>\n12 \u00d7 5= 60 points and the number of gems collected is 4, so the number of points earned for each gem is 10 so for 4 gems it will be 4 \u00d7 10= 40 points. The completed missions is 2, so the number of points earned for completing one mission is 50 so for 2 missions it will be 2 \u00d7 50= 100 points and the missions failed is 1, so the number of points lost for failing one mission is -25 so for 1 failed mission it will be 1\u00d7 -25= -25 points. So the total number of points earned is (60 + 40 + 100) &#8211; 25= 200 -25, here first we will solve the parentheses part by the order of operations then we will solve the addition part after that we will solve the subtraction part. On solving we will get the result as 175. So the total number of points earned is 175.<\/p>\n<p>Question 14.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA book has 200 pages. You read 10 pages twice each day for 1 week. What fraction of the book, in tenths, do you have left to read?<br \/>\nAnswer:<br \/>\nTh fraction in tenths is 3\/10.<\/p>\n<p>Explanation:<br \/>\nAs the book has 200 pages and 10 pages were read twice a day for a week as a week means seven days and twice a day means 2 \u00d7 7= 14. So the number of pages were read is 14 \u00d7 10= 140 pages. And the number of pages left is 200 &#8211; 140= 60. So to represent this in a fraction it will be 60\/200 which is 3\/10.<\/p>\n<h3><a id=\"Lesson 2.4_Evaluate_Expressions_with_Grouping_Symbols\"><\/a>Evaluate Expressions with Grouping Symbols Homework &amp; Practice 2.4<\/h3>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n15 \u00f7 (5 \u00d7 1) &#8211; (2 \u00d7 1)<br \/>\nAnswer:<br \/>\nOn evaluating the given expression result will be 5.<\/p>\n<p>Explanation:<br \/>\nGiven the numerical expression is 15 \u00f7 (5 \u00d7 1) &#8211; (2 \u00d7 1). By the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will perform the parentheses part which is (5 \u00d7 1) &#8211; (2 \u00d7 1)= 5 &#8211; 2= 3 and the result will be 3. Now we will perform division which is<br \/>\n15 \u00f7 3= 5. So the value of the expression 15 \u00f7 (5 \u00d7 1) &#8211; (2 \u00d7 1) is 5.<\/p>\n<p>Question 2.<br \/>\n(7 + 9) \u00f7 (2 + 4 + 2)<br \/>\nAnswer:<br \/>\nOn evaluating the given expression we will get the result as 2.<\/p>\n<p>Explanation:<br \/>\nGiven the numerical expression is (7 + 9) \u00f7 (2 + 4 + 2). By the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will perform the parentheses part which is (7 + 9) \u00f7 (2 + 4 + 2)= 16 \u00f7 8 and the result will be 16 \u00f7 8. Now we will perform division which is<br \/>\n16 \u00f7 8= 2. So the value of the expression (7 + 9) \u00f7 (2 + 4 + 2) is 2.<\/p>\n<p>Question 3.<br \/>\n(1 + 5) \u00d7 (2 + 3)<br \/>\nAnswer:<br \/>\nOn evaluating the given expression result will be 25.<\/p>\n<p>Explanation:<br \/>\nGiven the numerical expression is (1 + 5) \u00d7 (2 + 3). By the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will perform the parentheses part which is (1 + 5) \u00d7 (2 + 3)= 5 \u00d7 5 and the result will be 5 \u00d7 5. Now we will perform the multiplication part which is 5 \u00d7 5= 25. So the value of the expression<br \/>\n(1 + 5) \u00d7 (2 + 3) is 25.<\/p>\n<p>Question 4.<br \/>\n[(16 &#8211; 14) + (9 \u00d7 4)] \u00f7 2<br \/>\nAnswer:<br \/>\nOn evaluating the given expression result will be 9.<\/p>\n<p>Explanation:<br \/>\nGiven the numerical expression is [(16 &#8211; 14) + (9 \u00d7 4)] \u00f7 2. By the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will perform the parentheses part which is (16 &#8211; 14) + (9 \u00d7 4)= 2 + 36 and the result will be 38. Now we will perform the division part which is 38 \u00f7 2= 19. So the value of the expression<br \/>\n[(16 &#8211; 14) + (9 \u00d7 4)] \u00f7 2 is 19.<\/p>\n<p>Question 5.<br \/>\n70 \u00f7 [(463 &#8211; 443) \u00f7 2]<br \/>\nAnswer:<br \/>\nOn evaluating the given expression result will be 7.<\/p>\n<p>Explanation:<br \/>\nGiven the numerical expression is 70 \u00f7 [(463 &#8211; 443) \u00f7 2]. By the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will perform the parentheses part which is (463 &#8211; 443)= 20 and the result will be 20. Now we will perform the division part which is 20 \u00f7 2= 10. And there is another division part which is 70 \u00f7 10= 70. So the value of the expression 70 \u00f7 [(463 &#8211; 443) \u00f7 2] is 7.<\/p>\n<p>Question 6.<br \/>\n9 \u00d7 {[14 \u00f7 2 + (4 &#8211; 1)] &#8211; 8}<br \/>\nAnswer:<br \/>\nOn evaluating the given expression result will be 18.<\/p>\n<p>Explanation:<br \/>\nGiven the numerical expression is 9 \u00d7 {[14 \u00f7 2 + (4 &#8211; 1)] &#8211; 8}. By the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. Now first we will perform the parentheses part which is (4 &#8211; 1)= 3 and the result will be 3. Now we will perform the other parentheses part which is [14 \u00f7 2 + (3)] = 7 + 3 and the result will be 10. Now we will perform the other parentheses part which is {10 &#8211; 8}= 2. Now we will perform the multiplication part which is 9 \u00d7 2= 18. So the value of the expression 9 \u00d7 {[14 \u00f7 2 + (4 &#8211; 1)] &#8211; 8} is 18.<\/p>\n<p><strong>Write the words as an expression. Then evaluate the expression.<\/strong><br \/>\nQuestion 7.<br \/>\nMultiply the sum of 4 and 5 by the difference of 14 and 8.<br \/>\nAnswer:<br \/>\nThe numerical expression is (4 + 5) \u00d7 (14 &#8211; 8) on evaluating the numerical expression we will get the result as 54.<\/p>\n<p>Explanation:<br \/>\nGiven that Multiply the sum of 4 and 5 by the difference of 14 and 8, so to represent this in an expression it will be (4 + 5) \u00d7 (14 &#8211; 8). Now we will solve the numerical expression which is (4 + 5) \u00d7 (14 &#8211; 8) = 9 \u00d7 6<br \/>\nNow first we have solved the parentheses part which is (4 + 5) \u00d7 (14 &#8211; 8) and the result will be 9 \u00d7 6. And then we will perform the multiplication part which is 9 \u00d7 6= 54. So on evaluating the numerical expression we will get the result as 54.<\/p>\n<p>Question 8.<br \/>\nAdd 23, 26, and 17, then divide by 7.<br \/>\nAnswer:<br \/>\nThe numerical expression is (23 +26 +17) \u00f7 7 on evaluating the numerical expression we will get the result as 9.4.<\/p>\n<p>Explanation:<br \/>\nGiven that Add 23, 26, and 17, then divide by 7, so to represent this in an expression it will be (23 +26 +17) \u00f7 7. Now we will solve the numerical expression which is (23 +26 +17) \u00f7 7= 66 \u00f7 7<br \/>\nNow first we have solved the parentheses part which is (23 +26 +17) and the result will be 66. And then we will perform the division part which is 66 \u00f7 7= 9.4. So on evaluating the numerical expression we will get the result as 9.4.<\/p>\n<p>Question 9.<br \/>\n<strong>Writing<\/strong><br \/>\nExplain how to evaluate the expression.<br \/>\n8 \u00d7 [(36 &#8211; 33) \u00d7 2]<br \/>\nAnswer:<br \/>\nOn evaluating the numerical expression we will get the result as 48.<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is 8 \u00d7 [(36 &#8211; 33) \u00d7 2]= 8 \u00d7 [3 \u00d7 2]<br \/>\nNow first we have solved the parentheses part which is (36 &#8211; 33) and the result will be 3 and then we will perform the other parentheses part which is [3 \u00d7 2]= 6. And then we will perform the multiplication part which is<br \/>\n8 \u00d7 6= 48. So on evaluating the numerical expression we will get the result as 48.<\/p>\n<p>Question 10.<br \/>\n<strong>Open-Ended<\/strong><br \/>\nWrite and evaluate two equivalent numerical expressions that show the Distributive Property.<br \/>\nAnswer:<br \/>\nThe two numerical equations are 5 \u00d7 (90 + 7) and 83 \u00d7 7.<\/p>\n<p>Explanation:<br \/>\nLet the equation be 5 \u00d7 97, by distributive property the equation will be<br \/>\n= 5 \u00d7 (90 + 7)<br \/>\n= (5 \u00d7 90) + (5 \u00d7 7)<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the equation is<br \/>\n5 \u00d7 97 = 5 \u00d7 (90 + 7)<br \/>\n= (5 \u00d7 90) + (5 \u00d7 7).<\/p>\n<p>Let the equation is 83 \u00d7 7,\u00a0by distributive property the equation will be<br \/>\n= 7 \u00d7 (80 + 3)<br \/>\n= (7\u00d7 80) + (7 \u00d7 3)<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. So the equation is<br \/>\n7 \u00d7 83 = 7 \u00d7 (80 + 3)<br \/>\n= (7 \u00d7 80) + (7 \u00d7 3)<\/p>\n<p>Question 11.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nYour friend has 3 California postcards, 2 Hawaii postcards, and 4 New York postcards. He gives 1 postcard away, then divides the rest equally among 4 pages of a scrapbook. How many postcards are on each page?<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nA nutritionist recommends that fifth graders should eat about 305 grams of fruit each day.You eat the apple shown. How many more grams of fruit should you eat today?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.4-8.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2.4 8\" width=\"240\" height=\"174\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Find the product. Check whether your answer is reasonable.<\/strong><br \/>\nQuestion 13.<br \/>\n639 \u00d7 5 = _____<br \/>\nAnswer:<br \/>\nThe product of 639 \u00d7 5= 3195.<\/p>\n<p>Explanation:<br \/>\nThe product of 639 \u00d7 5 is 3,195. So to check the answer is reasonable we will divide the result by 5 which is<br \/>\n3195 \u00f7 5= 639. So the answer is reasonable.<\/p>\n<p>Question 14.<br \/>\n7 \u00d7 1,926 = _____<br \/>\nAnswer:<br \/>\nThe product of 7 \u00d7 1,926 is\u00a0 13,482.<\/p>\n<p>Explanation:<br \/>\nThe product of 7 \u00d7 1,926 is 13,482. So to check the answer is reasonable we will divide the result by 7 which is<br \/>\n13,482 \u00f7 7= 1,926. So the answer is reasonable.<\/p>\n<p>Question 15.<br \/>\n507 \u00d7 3 = ______<br \/>\nAnswer:<br \/>\nThe product of 507 \u00d7 3 is 1,521.<\/p>\n<p>Explanation:<br \/>\nThe product of 507 \u00d7 3 is 1,521. So to check the answer is reasonable we will divide the result by 3 which is<br \/>\n1,521 \u00f7 3= 507. So the answer is reasonable.<\/p>\n<h3><a id=\"Numerical_Expressions_Performance_Task\"><\/a>Numerical Expressions Performance Task<\/h3>\n<p>Atoms are the basic building blocks of matter. When two or more atoms bond together, they form a molecule or a compound.<br \/>\n\u2022 The chemical formula for a water molecule is H<sub>2<\/sub>O because it has 2 atoms of hydrogen (H) and 1 atom of oxygen (O).<br \/>\n\u2022 The chemical formula for the compound sodium chloride, also known as table salt, is NaCl because it has 1 atom of sodium (Na) and 1 atom of chlorine (Cl) in a repeating pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-1.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 1\" width=\"203\" height=\"275\" \/><br \/>\nQuestion 1.<br \/>\nHow many atoms are in 52 molecules of water?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nYou and your friend want to make models for a science fair.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-2.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 2\" width=\"194\" height=\"173\" \/><br \/>\na. Your friend wants to make a model of sodium chloride. The model has the same number of green and orange atoms. There are 4 \u00d7 4 \u00d7 4 atoms in all. How many orange atoms do you need?<br \/>\nb. You make a model of a salt-water mixture. You use 14 atoms of sodium, 14 atoms of chlorine, and 10 molecules of H<sub>2<\/sub>O. Write an expression that represents the number of atoms in your salt-water model. Use the Distributive Property to rewrite your expression. Find the number of atoms in your model.<br \/>\nc. You and your friend buy 3 boxes of foam balls to represent atoms. There are 45 foam balls in each box. How many foam balls are left after you and your friend make the models above?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Numerical_Expressions_Activity\"><\/a>Numerical Expressions Activity<\/h3>\n<p><strong>Expression Boss<\/strong><br \/>\n<strong>Directions:<\/strong><br \/>\n1. Each player rolls three dice to complete the numerical expression. Players can arrange the numbers however they choose.<br \/>\n2. Each player evaluates the numerical expression.<br \/>\n3. Players compare their values. The player with the greater value earns one point.<br \/>\n4. If the values are equal, each player earns one point.<br \/>\n5. The player with the most points at the end of the game wins!<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-3.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions 3\" width=\"688\" height=\"743\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-3.png 688w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-3-278x300.png 278w\" sizes=\"(max-width: 688px) 100vw, 688px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Numerical_Expressions_Chapter_Practice\"><\/a>Numerical Expressions Chapter Practice<\/h3>\n<p><strong>2.1 Number Properties<\/strong><\/p>\n<p><strong>Complete the equation. Identify the property shown.<\/strong><br \/>\nQuestion 1.<br \/>\n56 \u00d7 _____ = 0<br \/>\nAnswer:<br \/>\nThe product of 56 \u00d7 0 is 0 and the property used is Multiplication Properties of Zero.<\/p>\n<p>Explanation:<br \/>\nThe product of 56 \u00d7 0 is 0 and the property used is Multiplication Properties of Zero.<br \/>\nAs Multiplication Properties of Zero is the product of any number and 0 is 0. So 56 \u00d7 0 is 0.<\/p>\n<p>Question 2.<br \/>\n8 + (242 + 32) = (8 + 242) + _____<br \/>\nAnswer:<br \/>\nThe sum of 8 + (242 + 32) = (8 + 242) + 32 and the property which is used is the Commutative property. And the sum of the given expression is 282.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 8 + (242 + 32) = (8 + 242) + 32 and the property which is used is the Commutative property. Commutative Properties means changing the order of addends or factors does not change the sum or product. And the sum of the given expression is 282.<\/p>\n<p><strong>Use the Distributive Property to find the product.<\/strong><br \/>\nQuestion 3.<br \/>\n8 \u00d7 64<br \/>\nAnswer:<br \/>\nThe equation is 8 \u00d7 64= 8 \u00d7 (60 + 4)<br \/>\n= (8 \u00d7 60) + (8 \u00d7 4) and the property used is Distributive property.<br \/>\nAnd the product of the given expression is 512.<\/p>\n<p>Explanation:<br \/>\nGiven that 8 \u00d7 64, by distributive property the equation will be<br \/>\n= 8 \u00d7 (60 + 4)<br \/>\n= (8 \u00d7 60) + (8 \u00d7 4)<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. And the product of the given expression is 512.<\/p>\n<p>Question 4.<br \/>\n57 \u00d7 9<br \/>\nAnswer:<br \/>\nThe equation is 57 \u00d7 9= 9 \u00d7 (50 + 7)<br \/>\n= (9 \u00d7 50) + (9 \u00d7 7) and the property used is Distributive property.<br \/>\nAnd the product of the given expression is 513.<\/p>\n<p>Explanation:<br \/>\nGiven that 57 \u00d7 9, by distributive property the equation will be<br \/>\n= 9 \u00d7 (50 + 7)<br \/>\n= (9 \u00d7 50) + (9 \u00d7 7)<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. And the product of the given expression is 513.<\/p>\n<p><strong>Use a property to find the sum or product. Identify the property you used.<\/strong><br \/>\nQuestion 5.<br \/>\n3 \u00d7 92<br \/>\nAnswer:<br \/>\nThe equation is 3 \u00d7 92= 3 \u00d7 (90 + 2)<br \/>\n= (3 \u00d7 90) + (3 \u00d7 2) and the property used is Distributive property.<br \/>\nAnd the product of the given expression is 276.<\/p>\n<p>Explanation:<br \/>\nGiven that 3 \u00d7 92, by distributive property the equation will be<br \/>\n= 3 \u00d7 (90 + 2)<br \/>\n= (3 \u00d7 90) + (3 \u00d7 2)<br \/>\nSo, Distributive Property is a property that multiplying a sum (or difference) by a number is the same as multiplying each number in the sum (or difference) by the number and adding (or subtracting) the products. And the product of the given expression is 276.<\/p>\n<p>Question 6.<br \/>\n41 \u00d7 6 \u00d7 0<br \/>\nAnswer:<br \/>\nThe product of 41 \u00d7 6 \u00d7 0 is 0 and the property used is Multiplication Properties of Zero.<\/p>\n<p>Explanation:<br \/>\nThe product of 41 \u00d7 6 \u00d7 0 is 0 and the property used is Multiplication Properties of Zero.<br \/>\nAs Multiplication Properties of Zero is the product of any number and 0 is 0. So 41 \u00d7 6 \u00d7 0 is 0.<\/p>\n<p>Question 7.<br \/>\n13 + 24 + 57<br \/>\nAnswer:<br \/>\nThe sum of 13 + 24 + 57 = 24 + 57 + 13 and the property which is used is the Commutative property. And the sum of the given expression is 94.<\/p>\n<p>Explanation:<br \/>\nGiven the expression is 13 + 24 + 57 = 24 + 57 + 13 and the property which is used is the Commutative property. Commutative Properties means changing the order of addends or factors does not change the sum or product. And the sum of the given expression is 94.<\/p>\n<p>Question 8.<br \/>\n<strong>Modeling Real Life<\/strong><br \/>\nThe graph shows the number Favorite Apple of votes each apple received. How many people were surveyed? Identify the property you used.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-chp-8.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions chp 8\" width=\"258\" height=\"157\" \/><br \/>\nAnswer:<br \/>\nThe total number of people surveyed is 46. And the property which can be used is the Commutative property<\/p>\n<p>Explanation:<br \/>\nAs given that each apple image is equal to four votes, so to know how many people are surveyed let&#8217;s first find the count of the apples and then the count of the votes. So Fuji has four apple images and a half apple image, so the total number of votes for Fuji is 4\u00d74= 16 and a half apple image means two votes. So the total number of votes is 16 + 2= 18 votes. So the total number of votes for Fuji is 18 votes. And Granny Smith has three apple images, so the total number of votes for Granny Smith is 3\u00d74= 12. And Honeycrisp has four apple images, so the total number of votes for Granny Smith is 4\u00d74= 16. So the total number of people surveyed is 18 + 12 + 16= 46.<br \/>\nAnd the property which can be used is the Commutative property, as the Commutative Properties means changing the order of addends or factors does not change the sum or product. So the expression can be written as 18 + 12 + 16= 16 + 18 +12.<\/p>\n<p><strong>2.2 Order of Operations<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 9.<br \/>\n18 \u00d7 (9 &#8211; 3) \u00f7 2<br \/>\nAnswer:<br \/>\nThe value of the expression 18 \u00d7 (9 &#8211; 3) \u00f7 2 is 54.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the parentheses part which is (9 &#8211; 3)= 6 and the result will be 6. Now we will solve the division part which is 6 \u00f7 2= 3 and the result will be 3. And now we will solve the multiplication part which is 18 \u00d7 3= 54. So the value of the expression is 54.<\/p>\n<p>Question 10.<br \/>\n50 &#8211; 18 \u00f7 3 \u00d7 7<br \/>\nAnswer:<br \/>\nThe value of the expression 50 &#8211; 18 \u00f7 3 \u00d7 7 is 8.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the division part which is 18 \u00f7 3= 6 and the result will be 6. Now we will solve the multiplication part which is 6 \u00d7 7= 42 and the result will be 42. And now we will solve the subtraction part which is 50 &#8211; 42= 8. So the value of the expression is 8.<\/p>\n<p>Question 11.<br \/>\n(36 + 14) \u00d7 4 \u00f7 5<br \/>\nAnswer:<br \/>\nThe value of the expression (36 + 14) \u00d7 4 \u00f7 5 is 40.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the parentheses part which is (36 + 14)\u00d74= 50 \u00d7 4\u00a0 and the result will be 200. Now we will solve the division part which is<br \/>\n200 \u00f7 5 = 40 and the result will be 40. So the value of the expression is 40.<\/p>\n<p>Question 12.<br \/>\n<strong>Number Sense<\/strong><br \/>\nWhich expressions have a value of 6?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-14906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-chp-12.png\" alt=\"Big Ideas Math Solutions Grade 5 Chapter 2 Numerical Expressions chp 12\" width=\"557\" height=\"75\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-chp-12.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/Big-Ideas-Math-Solutions-Grade-5-Chapter-2-Numerical-Expressions-chp-12-300x40.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>2.3 Write Numerical Expressions<\/strong><\/p>\n<p><strong>Write the words as an expression. Then interpret the expression.<\/strong><br \/>\nQuestion 13.<br \/>\nMultiply 8 by the difference of 54 and 49.<br \/>\nAnswer:<br \/>\nThe numerical expression is (54 &#8211; 49) \u00d7 8 on evaluating the numerical expression we will get the result as 40.<\/p>\n<p>Explanation:<br \/>\nGiven that Multiply 8 by the difference of 54 and 49, so to represent this in an expression it will be (54 &#8211; 49) \u00d7 8. Now we will solve the numerical expression which is (54 &#8211; 49) \u00d7 8 = 5 \u00d7 8<br \/>\nNow first we have solved the parentheses part which is (54 &#8211; 49) and the result will be 5. And then we will perform the multiplication part which is 5 \u00d7 8= 40. So on evaluating the numerical expression we will get the result as 40.<\/p>\n<p>Question 14.<br \/>\nSubtract 58 from 94, then divide by4.<br \/>\nAnswer:<br \/>\nThe numerical expression is (94 &#8211; 58) \u00f7 4 on evaluating the numerical expression we will get the result as 9.<\/p>\n<p>Explanation:<br \/>\nGiven that Subtract 58 from 94, then divide by4, so to represent this in an expression it will be (94 &#8211; 58) \u00f7 4. Now we will solve the numerical expression which is (94 &#8211; 58) \u00f7 4= 36 \u00f7 4<br \/>\nNow first we have solved the parentheses part which is (94 &#8211; 58) and the result will be 36. And then we will perform the division part which is 36 \u00f7 4= 9. So on evaluating the numerical expression we will get the result as 9.<\/p>\n<p>Question 15.<br \/>\nYour friend buys a bag of 24 party favors and a bag of 16 party favors. She shares them equally among 5 friends. Write an expression to represent the problem.<br \/>\nAnswer:<\/p>\n<p><strong>Write the expression in words.<\/strong><br \/>\nQuestion 16.<br \/>\n45 + (7 \u00d7 8)<br \/>\nAnswer:<br \/>\nAdd 45 to the product of 7 and 8<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is 45 + (7 \u00d7 8), so in words, it will be represented as add 45 to the product of 7 and 8<\/p>\n<p>Question 17.<br \/>\n(18 \u00f7 2) &#8211; 5<br \/>\nAnswer:<br \/>\nDivide 18 by 2 and then subtract 5.<\/p>\n<p>Explanation:<br \/>\nGiven that the numerical expression is (18 \u00f7 2) &#8211; 5 so in words, it will be represented as divide 18 by 2 and then subtract 5.<\/p>\n<p><strong>2.4 Evaluate Expressions with Grouping Symbols<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 18.<br \/>\n(28 &#8211; 14) \u00d7 (42 \u00f7 6)<br \/>\nAnswer:<br \/>\nThe value of the expression (28 &#8211; 14) \u00d7 (42 \u00f7 6) is 98.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the parentheses part which is (28 &#8211; 14) \u00d7 (42 \u00f7 6)= 14 \u00d7 7. Now we will solve the multiplication part which is 14 \u00d7 7= 98 and the result will be 98. So the value of the expression is 98.<\/p>\n<p>Question 19.<br \/>\n6 \u00d7 [(21 &#8211; 9) \u00f7 3]<br \/>\nAnswer:<br \/>\nThe value of the expression 6 \u00d7 [(21 &#8211; 9) \u00f7 3] is 24.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the parentheses part which is(21 &#8211; 9)= 12. Now we will solve the other parentheses part which is [12 \u00f7 3]= 4 and the result will be 4. Now we will solve the multiplication part which is 6 \u00d7 4= 24. So the value of the expression is 24.<\/p>\n<p>Question 20.<br \/>\n[(2 \u00d7 2) + (10 \u00f7 5)] \u00d7 4<br \/>\nAnswer:<br \/>\nThe value of the expression [(2 \u00d7 2) + (10 \u00f7 5)] \u00d7 4 is 32.<\/p>\n<p>Explanation:<br \/>\nBy the order of operations, we will perform the addition in the parentheses first and then multiply and divide from left to right. And then we will add and subtract from left to right. So this is performed by the BODMAS rule which stands for Bracket, Of, Division, Multiplication, Addition, and Subtraction. So first we will solve the parentheses part which is (2 \u00d7 2) + (10 \u00f7 5)= 4 + 2 and the result will be 8. Now we will solve the multiplication part which is<br \/>\n8 \u00d7 4= 32. So the value of the expression is 32.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Make your preparation perfect with the help of the Big Ideas Math Answers Grade 5 Chapter 2 Numerical Expressions PDF. Every student can become a math expert if they prepare with the Big Ideas Grade 5 Chapter 2 Numerical Expressions Math Answers. The concepts are explained clearly with real-time examples. 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