{"id":969,"date":"2024-05-01T18:26:39","date_gmt":"2024-05-01T18:26:39","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=969"},"modified":"2024-11-20T15:07:48","modified_gmt":"2024-11-20T15:07:48","slug":"module-3-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/module-3-background-youll-need-2\/","title":{"raw":"Linear Equations and Inequalities: Background You'll Need 2","rendered":"Linear Equations and Inequalities: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Use the order of operations - PEMDAS<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Order of Operations<\/h2>\r\nYou may or may not recall the order of operations for applying several mathematical operations to one expression. Just as it is a social convention for us to drive on the right-hand side of the road, the order of operations is a set of conventions used to provide order when you are required to use several mathematical operations for one expression.\r\n\r\n<section class=\"textbox questionHelp\"><strong>How to: Perform the Order of Operations<\/strong>\r\n<ol>\r\n \t<li>Perform all operations within grouping symbols first. Grouping symbols include parentheses ( ), brackets [ ], braces { }, and fraction bars.<\/li>\r\n \t<li>Evaluate exponents or square roots.<\/li>\r\n \t<li>Multiply or divide, from left to right.<\/li>\r\n \t<li>Add or subtract, from left to right.<\/li>\r\n<\/ol>\r\nThis order of operations is true for all real numbers.\r\n\r\n<\/section><section class=\"textbox proTip\">Some people use a saying to help them remember the order of operations. This saying is called PEMDAS or <strong>P<\/strong>lease <strong>E<\/strong>xcuse <strong>M<\/strong>y <strong>D<\/strong>ear <strong>A<\/strong>unt <strong>S<\/strong>ally. The first letter of each word begins with the same letter of an arithmetic operation.\r\n<ul>\r\n \t<li><strong>P<\/strong>lease [latex] \\displaystyle \\Rightarrow [\/latex] <strong>P<\/strong>arentheses (and other grouping symbols)<\/li>\r\n \t<li><strong>E<\/strong>xcuse [latex] \\displaystyle \\Rightarrow [\/latex] <strong>E<\/strong>xponents<\/li>\r\n \t<li><strong>M<\/strong>y <strong>D<\/strong>ear [latex] \\displaystyle \\Rightarrow [\/latex] <strong>M<\/strong>ultiplication and <strong>D<\/strong>ivision (from left to right)<\/li>\r\n \t<li><strong>A<\/strong>unt <strong>S<\/strong>ally [latex] \\displaystyle \\Rightarrow [\/latex] <strong>A<\/strong>ddition and <strong>S<\/strong>ubtraction (from left to right)<\/li>\r\n<\/ul>\r\nEven though multiplication comes before division in the saying, division could be performed first. Which is performed first, between multiplication and division, is determined by which comes first when reading from left to right. The same is true of addition and subtraction. Don't let the saying confuse you about this!\r\n\r\n<\/section><section class=\"textbox example\">Simplify the following:<center>[latex]7\u20135+3\\cdot8[\/latex]<\/center>[reveal-answer q=\"796973\"]Show Answer[\/reveal-answer] [hidden-answer a=\"796973\"]According to the order of operations, multiplication comes before addition and subtraction.Multiply [latex]3\\cdot8[\/latex]\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}7\u20135+3\\cdot8\\\\7\u20135+24\\end{array}[\/latex]<\/p>\r\nNow, add and subtract from left to right. [latex]7\u20135[\/latex] comes first.\r\n<p style=\"text-align: center;\">[latex]2+24[\/latex]<\/p>\r\nFinally, add.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}2+24=26\\\\7\u20135+3\\cdot8=26\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]290016[\/ohm_question]<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]290015[\/ohm_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-root=\"1\">Use the order of operations &#8211; PEMDAS<\/span><\/li>\n<\/ul>\n<\/section>\n<h2>Order of Operations<\/h2>\n<p>You may or may not recall the order of operations for applying several mathematical operations to one expression. Just as it is a social convention for us to drive on the right-hand side of the road, the order of operations is a set of conventions used to provide order when you are required to use several mathematical operations for one expression.<\/p>\n<section class=\"textbox questionHelp\"><strong>How to: Perform the Order of Operations<\/strong><\/p>\n<ol>\n<li>Perform all operations within grouping symbols first. Grouping symbols include parentheses ( ), brackets [ ], braces { }, and fraction bars.<\/li>\n<li>Evaluate exponents or square roots.<\/li>\n<li>Multiply or divide, from left to right.<\/li>\n<li>Add or subtract, from left to right.<\/li>\n<\/ol>\n<p>This order of operations is true for all real numbers.<\/p>\n<\/section>\n<section class=\"textbox proTip\">Some people use a saying to help them remember the order of operations. This saying is called PEMDAS or <strong>P<\/strong>lease <strong>E<\/strong>xcuse <strong>M<\/strong>y <strong>D<\/strong>ear <strong>A<\/strong>unt <strong>S<\/strong>ally. The first letter of each word begins with the same letter of an arithmetic operation.<\/p>\n<ul>\n<li><strong>P<\/strong>lease [latex]\\displaystyle \\Rightarrow[\/latex] <strong>P<\/strong>arentheses (and other grouping symbols)<\/li>\n<li><strong>E<\/strong>xcuse [latex]\\displaystyle \\Rightarrow[\/latex] <strong>E<\/strong>xponents<\/li>\n<li><strong>M<\/strong>y <strong>D<\/strong>ear [latex]\\displaystyle \\Rightarrow[\/latex] <strong>M<\/strong>ultiplication and <strong>D<\/strong>ivision (from left to right)<\/li>\n<li><strong>A<\/strong>unt <strong>S<\/strong>ally [latex]\\displaystyle \\Rightarrow[\/latex] <strong>A<\/strong>ddition and <strong>S<\/strong>ubtraction (from left to right)<\/li>\n<\/ul>\n<p>Even though multiplication comes before division in the saying, division could be performed first. Which is performed first, between multiplication and division, is determined by which comes first when reading from left to right. The same is true of addition and subtraction. Don&#8217;t let the saying confuse you about this!<\/p>\n<\/section>\n<section class=\"textbox example\">Simplify the following:<\/p>\n<div style=\"text-align: center;\">[latex]7\u20135+3\\cdot8[\/latex]<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q796973\">Show Answer<\/button> <\/p>\n<div id=\"q796973\" class=\"hidden-answer\" style=\"display: none\">According to the order of operations, multiplication comes before addition and subtraction.Multiply [latex]3\\cdot8[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}7\u20135+3\\cdot8\\\\7\u20135+24\\end{array}[\/latex]<\/p>\n<p>Now, add and subtract from left to right. [latex]7\u20135[\/latex] comes first.<\/p>\n<p style=\"text-align: center;\">[latex]2+24[\/latex]<\/p>\n<p>Finally, add.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}2+24=26\\\\7\u20135+3\\cdot8=26\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm290016\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=290016&theme=lumen&iframe_resize_id=ohm290016&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm290015\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=290015&theme=lumen&iframe_resize_id=ohm290015&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":12,"menu_order":3,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":75,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/969"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/users\/12"}],"version-history":[{"count":10,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/969\/revisions"}],"predecessor-version":[{"id":4677,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/969\/revisions\/4677"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/75"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/969\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=969"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=969"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=969"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}