{"id":7378,"date":"2017-05-02T16:14:46","date_gmt":"2017-05-02T16:14:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=7378"},"modified":"2019-05-27T05:24:44","modified_gmt":"2019-05-27T05:24:44","slug":"commutative-and-associative-properties","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/commutative-and-associative-properties\/","title":{"raw":"Introduction to Using the Commutative and Associative Properties","rendered":"Introduction to Using the Commutative and Associative Properties"},"content":{"raw":"<h2>What you'll learn to do: Use the commutative and associative properties to simplify and evaluate expressions<\/h2>\r\n[caption id=\"attachment_11348\" align=\"aligncenter\" width=\"1024\"]<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/05\/07222408\/30560307010_ce4a3d43c3_o.jpg\"><img class=\"wp-image-11348 size-large\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/05\/07222408\/30560307010_ce4a3d43c3_o-1024x768.jpg\" alt=\"A group of children wearing matching t-shirts at a camp\" width=\"1024\" height=\"768\" \/><\/a> When adding up the number of kids in a family, does order matter?[\/caption]\r\n\r\nJanelle is helping to plan a family reunion, and she wants to order shirts for all the kids who will attend. She starts thinking about the best way to tally up the number of kids in each family. Should she start with the oldest child's family? Should she add them up alphabetically? Will her method change the total number of shirts she needs to order, or will she arrive at the same number no matter how she does it? In this section, you'll learn about the commutative\u00a0and associative properties, which can help Janelle figure out her answer.\r\n\r\nBefore you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.\r\n<div class=\"textbox examples\">\r\n<h3>readiness quiz<\/h3>\r\n1)\r\n\r\n[ohm_question]144900[\/ohm_question]\r\n\r\nIf you missed this problem, review the following video.\r\n\r\nhttps:\/\/youtu.be\/KMUCQ_Pwt7o\r\n\r\n2)\r\n\r\n[ohm_question]146024[\/ohm_question]\r\n\r\nIf you missed this problem, review this video.\r\n\r\nhttps:\/\/youtu.be\/Rxz7OUzNyV0\r\n\r\n3)\r\n\r\n[ohm_question]144926[\/ohm_question]\r\n\r\nIf you missed this problem, review the video below.\r\n\r\nhttps:\/\/youtu.be\/suk9KMzOKkU\r\n\r\n<\/div>\r\nIn the next few sections, we will take a look at the properties of real numbers. Many of these properties will describe things you already know, but it will help to give names to the properties and define them formally. This way we\u2019ll be able to refer to them and use them as we solve equations in the next chapter.","rendered":"<h2>What you&#8217;ll learn to do: Use the commutative and associative properties to simplify and evaluate expressions<\/h2>\n<div id=\"attachment_11348\" style=\"width: 1034px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/05\/07222408\/30560307010_ce4a3d43c3_o.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-11348\" class=\"wp-image-11348 size-large\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/05\/07222408\/30560307010_ce4a3d43c3_o-1024x768.jpg\" alt=\"A group of children wearing matching t-shirts at a camp\" width=\"1024\" height=\"768\" \/><\/a><\/p>\n<p id=\"caption-attachment-11348\" class=\"wp-caption-text\">When adding up the number of kids in a family, does order matter?<\/p>\n<\/div>\n<p>Janelle is helping to plan a family reunion, and she wants to order shirts for all the kids who will attend. She starts thinking about the best way to tally up the number of kids in each family. Should she start with the oldest child&#8217;s family? Should she add them up alphabetically? Will her method change the total number of shirts she needs to order, or will she arrive at the same number no matter how she does it? In this section, you&#8217;ll learn about the commutative\u00a0and associative properties, which can help Janelle figure out her answer.<\/p>\n<p>Before you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.<\/p>\n<div class=\"textbox examples\">\n<h3>readiness quiz<\/h3>\n<p>1)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm144900\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144900&theme=oea&iframe_resize_id=ohm144900&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review the following video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Simplify Expressions by Combining Like Terms (No Negatives)\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/KMUCQ_Pwt7o?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>2)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146024\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146024&theme=oea&iframe_resize_id=ohm146024&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review this video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 2: Multiply Fractions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/Rxz7OUzNyV0?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>3)<\/p>\n<p><iframe loading=\"lazy\" id=\"ohm144926\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=144926&theme=oea&iframe_resize_id=ohm144926&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p>If you missed this problem, review the video below.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex:  Determine the Opposites of Integers\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/suk9KMzOKkU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>In the next few sections, we will take a look at the properties of real numbers. Many of these properties will describe things you already know, but it will help to give names to the properties and define them formally. This way we\u2019ll be able to refer to them and use them as we solve equations in the next chapter.<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-7378\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Simplify Expressions by Combining Like Terms (No Negatives). <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/KMUCQ_Pwt7o\">https:\/\/youtu.be\/KMUCQ_Pwt7o<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/about\/pdm\">Public Domain: No Known Copyright<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Children wearing matching t-shirts. <strong>Authored by<\/strong>: Virginia State Parks. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.flickr.com\/photos\/vastateparksstaff\/30560307010\/\">https:\/\/www.flickr.com\/photos\/vastateparksstaff\/30560307010\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Ex: Determine the Opposites of Integers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/suk9KMzOKkU\">https:\/\/youtu.be\/suk9KMzOKkU<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Question ID: 144900, 144926, 146024. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: IMathAS Community License CC-BY + GPL<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":21,"menu_order":6,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Children wearing matching t-shirts\",\"author\":\"Virginia State Parks\",\"organization\":\"\",\"url\":\"https:\/\/www.flickr.com\/photos\/vastateparksstaff\/30560307010\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Simplify Expressions by Combining Like Terms (No Negatives)\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/KMUCQ_Pwt7o\",\"project\":\"\",\"license\":\"pd\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Determine the Opposites of Integers\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/suk9KMzOKkU\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Question ID: 144900, 144926, 146024\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"IMathAS Community License CC-BY + GPL\"}]","CANDELA_OUTCOMES_GUID":"2c8bc7de-2167-4792-a7b5-2470d8367924","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-7378","chapter","type-chapter","status-publish","hentry"],"part":7349,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/7378","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/users\/21"}],"version-history":[{"count":22,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/7378\/revisions"}],"predecessor-version":[{"id":15906,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/7378\/revisions\/15906"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/parts\/7349"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapters\/7378\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/media?parent=7378"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=7378"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/contributor?post=7378"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/wp-json\/wp\/v2\/license?post=7378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}