{"id":7606,"date":"2017-04-28T20:05:10","date_gmt":"2017-04-28T20:05:10","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=7606"},"modified":"2019-05-27T05:31:27","modified_gmt":"2019-05-27T05:31:27","slug":"solve-equations-using-the-division-and-multiplication-properties-of-equality","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/monroecc-prealgebra\/chapter\/solve-equations-using-the-division-and-multiplication-properties-of-equality\/","title":{"raw":"Introduction to Solving Equations Using the Division and Multiplication Properties of Equality","rendered":"Introduction to Solving Equations Using the Division and Multiplication Properties of Equality"},"content":{"raw":"<h2>What you'll learn to do: Solve single and multi-step equations using the division and multiplication properties of equality<\/h2>\r\n[caption id=\"attachment_11982\" align=\"aligncenter\" width=\"1024\"]<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/13213219\/23332463371_b035085201_o.jpg\"><img class=\"wp-image-11982 size-large\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/13213219\/23332463371_b035085201_o-1024x683.jpg\" alt=\"A platter of various sliced meats, cheeses, and bread on a table with a candle in the middle of it, and a wine glass and silverware nearby.\" width=\"1024\" height=\"683\" \/><\/a> A dinner with friends often ends with a math problem.[\/caption]\r\n\r\nWhile out for dinner with your friends, you decide to share a few appetizers. At the end of the meal, you want to split the bill evenly among the four of you. How much should each person pay? In this chapter, you'll learn how to solve equations using the Division and Multiplication Properties of Equality so you and your friends can accurately divide the bill.\r\n<div>\r\n\r\nBefore you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Readiness quiz<\/h3>\r\n1)\r\n\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141840&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\n2)\r\n<iframe id=\"mom20\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141842&amp;theme=oea&amp;iframe_resize_id=mom20\" width=\"100%\" height=\"350\"><\/iframe>\r\nIf you missed these problems, review the following video.\r\nhttps:\/\/youtu.be\/IM991IqCi44\r\n\r\n3)\r\n<iframe id=\"mom200\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141843&amp;theme=oea&amp;iframe_resize_id=mom200\" width=\"100%\" height=\"250\"><\/iframe>\r\nIf you missed this problem, review the following video.\r\nhttps:\/\/youtu.be\/-HvuxIwA1Gk\r\n\r\n4)\r\n\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142137&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\nIf you missed this problem, review this video:\r\nhttps:\/\/youtu.be\/9AtYeBKP7RI\r\n\r\n5)\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=611&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\nIf you missed this problem, review this video:\r\nhttps:\/\/youtu.be\/b0xYYV9XL9c\r\n\r\n6)\r\n\r\n<iframe id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142137&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe>\r\n\r\nIf you missed this problem, review this video:\r\nhttps:\/\/youtu.be\/JFAwf01nPG8\r\n\r\n<\/div>","rendered":"<h2>What you&#8217;ll learn to do: Solve single and multi-step equations using the division and multiplication properties of equality<\/h2>\n<div id=\"attachment_11982\" style=\"width: 1034px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/13213219\/23332463371_b035085201_o.jpg\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-11982\" class=\"wp-image-11982 size-large\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/13213219\/23332463371_b035085201_o-1024x683.jpg\" alt=\"A platter of various sliced meats, cheeses, and bread on a table with a candle in the middle of it, and a wine glass and silverware nearby.\" width=\"1024\" height=\"683\" \/><\/a><\/p>\n<p id=\"caption-attachment-11982\" class=\"wp-caption-text\">A dinner with friends often ends with a math problem.<\/p>\n<\/div>\n<p>While out for dinner with your friends, you decide to share a few appetizers. At the end of the meal, you want to split the bill evenly among the four of you. How much should each person pay? In this chapter, you&#8217;ll learn how to solve equations using the Division and Multiplication Properties of Equality so you and your friends can accurately divide the bill.<\/p>\n<div>\n<p>Before you get started in this module, try a few practice problems and review\u00a0prior\u00a0concepts.<\/p>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Readiness quiz<\/h3>\n<p>1)<\/p>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141840&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><br \/>\n2)<br \/>\n<iframe loading=\"lazy\" id=\"mom20\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141842&amp;theme=oea&amp;iframe_resize_id=mom20\" width=\"100%\" height=\"350\"><\/iframe><br \/>\nIf you missed these problems, review the following video.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Determine the Reciprocal of Integers, Fractions, and Mixed Numbers\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/IM991IqCi44?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>3)<br \/>\n<iframe loading=\"lazy\" id=\"mom200\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=141843&amp;theme=oea&amp;iframe_resize_id=mom200\" width=\"100%\" height=\"250\"><\/iframe><br \/>\nIf you missed this problem, review the following video.<br \/>\n<iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex: Substitute and Evaluate Basic Expressions x+2, 2x, x^2, 2^x\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/-HvuxIwA1Gk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>4)<\/p>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142137&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><br \/>\nIf you missed this problem, review this video:<br \/>\n<iframe loading=\"lazy\" id=\"oembed-3\" title=\"Multiply Various Forms of Fractions Using Formal Rules\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/9AtYeBKP7RI?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>5)<br \/>\n<iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=611&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><br \/>\nIf you missed this problem, review this video:<br \/>\n<iframe loading=\"lazy\" id=\"oembed-4\" title=\"Determine a Least Common Denominator and Equivalent Fractions\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/b0xYYV9XL9c?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>6)<\/p>\n<p><iframe loading=\"lazy\" id=\"mom2\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=142137&amp;theme=oea&amp;iframe_resize_id=mom2\" width=\"100%\" height=\"250\"><\/iframe><\/p>\n<p>If you missed this problem, review this video:<br \/>\n<iframe loading=\"lazy\" id=\"oembed-5\" title=\"Multiply Decimals by 10, 100, and 1000\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/JFAwf01nPG8?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\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-7606\">\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>Question ID: 141840, 141842, 141843, 142137. <strong>Provided 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, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Substitute and Evaluate Basic Expressions x+2, 2x, x^2, 2^x . <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/-HvuxIwA1Gk\">https:\/\/youtu.be\/-HvuxIwA1Gk<\/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 Reciprocal of Integers, Fractions, and Mixed Numbers. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/IM991IqCi44\">https:\/\/youtu.be\/IM991IqCi44<\/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>Bread, meat, cheese, wine. <strong>Authored by<\/strong>: winecountrymedia at www.napavalley.com. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/www.flickr.com\/photos\/winecountrymedia\/23332463371\/\">https:\/\/www.flickr.com\/photos\/winecountrymedia\/23332463371\/<\/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: 611. <strong>Authored by<\/strong>: Bryan Johns. <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":7,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Ex: Substitute and Evaluate Basic Expressions x+2, 2x, x^2, 2^x \",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/-HvuxIwA1Gk\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Determine the Reciprocal 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