{"id":1441,"date":"2023-06-22T02:28:36","date_gmt":"2023-06-22T02:28:36","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/module-16-background-youll-need-2\/"},"modified":"2024-03-01T20:09:01","modified_gmt":"2024-03-01T20:09:01","slug":"module-16-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/introstatstest\/chapter\/module-16-background-youll-need-2\/","title":{"raw":"Module 15: Background You'll Need 2","rendered":"Module 15: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Simplify complex fractions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12929,&quot;3&quot;:{&quot;1&quot;:0},&quot;10&quot;:2,&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Simplify complex fractions<\/span><\/li>\r\n<\/ul>\r\n<\/section>\r\n<section class=\"textbox keyTakeaway\">\r\n<h3>complex fractions<\/h3>\r\n<p>A <strong>complex fraction<\/strong> is a fraction in which the numerator and\/or the denominator include fractions.<\/p>\r\n<\/section>\r\n<section class=\"textbox problemSolving\">An example of a [pb_glossary id=\"5583\"]complex fraction [\/pb_glossary] is shown below:\r\n\r\n<p style=\"text-align: center;\">[latex]\\dfrac{\\frac{1}{2}}{\\frac{3}{4}}[\/latex]<\/p>\r\n<p>In keeping with the order of operations, you should evaluate the [pb_glossary id=\"5586\"]numerator[\/pb_glossary] and the [pb_glossary id=\"5587\"]denominator[\/pb_glossary] separately before dividing the numerator by the denominator. When using a calculator, use parentheses to indicate that the operations in the numerator and the denominator should be completed first, as shown:<\/p>\r\n<p style=\"text-align: center;\">[latex](1\/2)\/(3\/4) \\approx 0.667[\/latex]<\/p>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3143[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3144[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3145[\/ohm2_question]<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]3146[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li><span data-sheets-value=\"{&quot;1&quot;:2,&quot;2&quot;:&quot;Simplify complex fractions&quot;}\" data-sheets-userformat=\"{&quot;2&quot;:12929,&quot;3&quot;:{&quot;1&quot;:0},&quot;10&quot;:2,&quot;12&quot;:0,&quot;15&quot;:&quot;arial&quot;,&quot;16&quot;:9}\">Simplify complex fractions<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox keyTakeaway\">\n<h3>complex fractions<\/h3>\n<p>A <strong>complex fraction<\/strong> is a fraction in which the numerator and\/or the denominator include fractions.<\/p>\n<\/section>\n<section class=\"textbox problemSolving\">An example of a <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1441_5583\">complex fraction <\/a> is shown below:<\/p>\n<p style=\"text-align: center;\">[latex]\\dfrac{\\frac{1}{2}}{\\frac{3}{4}}[\/latex]<\/p>\n<p>In keeping with the order of operations, you should evaluate the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1441_5586\">numerator<\/a> and the <a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_1441_5587\">denominator<\/a> separately before dividing the numerator by the denominator. When using a calculator, use parentheses to indicate that the operations in the numerator and the denominator should be completed first, as shown:<\/p>\n<p style=\"text-align: center;\">[latex](1\/2)\/(3\/4) \\approx 0.667[\/latex]<\/p>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3143\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3143&theme=lumen&iframe_resize_id=ohm3143&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3144\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3144&theme=lumen&iframe_resize_id=ohm3144&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3145\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3145&theme=lumen&iframe_resize_id=ohm3145&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm3146\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=3146&theme=lumen&iframe_resize_id=ohm3146&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_1441_5583\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1441_5583\"><div tabindex=\"-1\"><p>a fraction in which the numerator and\/or the denominator include fractions<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_1441_5586\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1441_5586\"><div tabindex=\"-1\"><p>top of the fraction <\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_1441_5587\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_1441_5587\"><div tabindex=\"-1\"><p>bottom value of the fraction<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":8,"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":1438,"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\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1441"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/users\/8"}],"version-history":[{"count":8,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1441\/revisions"}],"predecessor-version":[{"id":5851,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1441\/revisions\/5851"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/parts\/1438"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapters\/1441\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/media?parent=1441"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/pressbooks\/v2\/chapter-type?post=1441"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/contributor?post=1441"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/introstatstest\/wp-json\/wp\/v2\/license?post=1441"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}