{"id":3932,"date":"2020-02-11T04:26:22","date_gmt":"2020-02-11T04:26:22","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/mathforlibscoreq\/?post_type=chapter&#038;p=3932"},"modified":"2021-02-05T23:57:09","modified_gmt":"2021-02-05T23:57:09","slug":"simplifying-expressions-with-decimals-and-fractions","status":"web-only","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/chapter\/simplifying-expressions-with-decimals-and-fractions\/","title":{"raw":"Simplifying Expressions With Decimals and Fractions","rendered":"Simplifying Expressions With Decimals and Fractions"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Use the order of operations to simplify expressions that contain decimals<\/li>\r\n<\/ul>\r\n<\/div>\r\nThe order of operations introduced in an earlier lesson also applies to decimals. Do you remember what the phrase \"Please excuse my dear Aunt Sally\" stands for?\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify the expressions:\r\n1.\u00a0\u00a0 [latex]7\\left(18.3 - 21.7\\right)[\/latex]\r\n2.\u00a0\u00a0 [latex]{\\Large\\frac{2}{3}}\\left(8.3 - 3.8\\right)[\/latex]\r\n\r\nSolution\r\n<table id=\"eip-id1168467118743\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]7\\left(18.3 - 21.7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify inside parentheses.<\/td>\r\n<td>[latex]7\\left(-3.4\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]-23.8[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469628501\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\Large\\frac{2}{3}}\\left(8.3 - 3.8\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify inside parentheses.<\/td>\r\n<td>[latex]{\\Large\\frac{2}{3}}\\left(4.5\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Write [latex]4.5[\/latex] as a fraction.<\/td>\r\n<td>[latex]{\\Large\\frac{2}{3}}\\left({\\Large\\frac{4.5}{1}}\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]{\\Large\\frac{9}{3}}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]3[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146295[\/ohm_question]\r\n\r\n[ohm_question]146297[\/ohm_question]\r\n\r\n<\/div>\r\nFor more examples similar to the ones above, watch the following video\r\n\r\nhttps:\/\/youtu.be\/xO1cjj_TqaY\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nSimplify each expression:\r\n1.\u00a0\u00a0 [latex]6\\div 0.6+\\left(0.2\\right)4-{\\left(0.1\\right)}^{2}[\/latex]\r\n2.\u00a0\u00a0 [latex]{\\left({\\Large\\frac{1}{10}}\\right)}^{2}+\\left(3.5\\right)\\left(0.9\\right)[\/latex]\r\n[reveal-answer q=\"547008\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"547008\"]\r\n\r\nSolution\r\n<table id=\"eip-id1168468572938\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>1.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]6\\div 0.6+\\left(0.2\\right)4-{\\left(0.1\\right)}^{2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify exponents.<\/td>\r\n<td>[latex]6\\div 0.6+\\left(0.2\\right)4 - 0.01[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Divide.<\/td>\r\n<td>[latex]10+\\left(0.2\\right)4 - 0.01[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]10+0.8 - 0.01[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]10.8 - 0.01[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Subtract.<\/td>\r\n<td>[latex]10.79[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<table id=\"eip-id1168469464796\" class=\"unnumbered unstyled\" summary=\".\">\r\n<tbody>\r\n<tr>\r\n<td>2.<\/td>\r\n<td><\/td>\r\n<\/tr>\r\n<tr>\r\n<td><\/td>\r\n<td>[latex]{\\left({\\Large\\frac{1}{10}}\\right)}^{2}+\\left(3.5\\right)\\left(0.9\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify exponents.<\/td>\r\n<td>[latex]{\\Large\\frac{1}{100}}+\\left(3.5\\right)\\left(0.9\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Multiply.<\/td>\r\n<td>[latex]{\\Large\\frac{1}{100}}+3.15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Convert [latex]\\frac{1}{100}[\/latex] to a decimal.<\/td>\r\n<td>[latex]0.01+3.15[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add.<\/td>\r\n<td>[latex]3.16[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146309[\/ohm_question]\r\n\r\n[ohm_question]146310[\/ohm_question]\r\n\r\n<\/div>\r\nThe following two videos contain more examples of how to use the order of operations to simplify expressions with decimals.\r\n\r\nhttps:\/\/youtu.be\/c-iknWD7piU\r\n\r\nhttps:\/\/youtu.be\/CMQrctqdz6g","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Use the order of operations to simplify expressions that contain decimals<\/li>\n<\/ul>\n<\/div>\n<p>The order of operations introduced in an earlier lesson also applies to decimals. Do you remember what the phrase &#8220;Please excuse my dear Aunt Sally&#8221; stands for?<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify the expressions:<br \/>\n1.\u00a0\u00a0 [latex]7\\left(18.3 - 21.7\\right)[\/latex]<br \/>\n2.\u00a0\u00a0 [latex]{\\Large\\frac{2}{3}}\\left(8.3 - 3.8\\right)[\/latex]<\/p>\n<p>Solution<\/p>\n<table id=\"eip-id1168467118743\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]7\\left(18.3 - 21.7\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify inside parentheses.<\/td>\n<td>[latex]7\\left(-3.4\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]-23.8[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469628501\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\Large\\frac{2}{3}}\\left(8.3 - 3.8\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify inside parentheses.<\/td>\n<td>[latex]{\\Large\\frac{2}{3}}\\left(4.5\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Write [latex]4.5[\/latex] as a fraction.<\/td>\n<td>[latex]{\\Large\\frac{2}{3}}\\left({\\Large\\frac{4.5}{1}}\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]{\\Large\\frac{9}{3}}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]3[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146295\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146295&theme=oea&iframe_resize_id=ohm146295&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146297\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146297&theme=oea&iframe_resize_id=ohm146297&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>For more examples similar to the ones above, watch the following video<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex 1:  Simplify an Expression Involving Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/xO1cjj_TqaY?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Simplify each expression:<br \/>\n1.\u00a0\u00a0 [latex]6\\div 0.6+\\left(0.2\\right)4-{\\left(0.1\\right)}^{2}[\/latex]<br \/>\n2.\u00a0\u00a0 [latex]{\\left({\\Large\\frac{1}{10}}\\right)}^{2}+\\left(3.5\\right)\\left(0.9\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q547008\">Show Solution<\/span><\/p>\n<div id=\"q547008\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<\/p>\n<table id=\"eip-id1168468572938\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>1.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]6\\div 0.6+\\left(0.2\\right)4-{\\left(0.1\\right)}^{2}[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td>[latex]6\\div 0.6+\\left(0.2\\right)4 - 0.01[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Divide.<\/td>\n<td>[latex]10+\\left(0.2\\right)4 - 0.01[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]10+0.8 - 0.01[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]10.8 - 0.01[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Subtract.<\/td>\n<td>[latex]10.79[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469464796\" class=\"unnumbered unstyled\" summary=\".\">\n<tbody>\n<tr>\n<td>2.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>[latex]{\\left({\\Large\\frac{1}{10}}\\right)}^{2}+\\left(3.5\\right)\\left(0.9\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify exponents.<\/td>\n<td>[latex]{\\Large\\frac{1}{100}}+\\left(3.5\\right)\\left(0.9\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Multiply.<\/td>\n<td>[latex]{\\Large\\frac{1}{100}}+3.15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Convert [latex]\\frac{1}{100}[\/latex] to a decimal.<\/td>\n<td>[latex]0.01+3.15[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add.<\/td>\n<td>[latex]3.16[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146309\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146309&theme=oea&iframe_resize_id=ohm146309&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146310\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146310&theme=oea&iframe_resize_id=ohm146310&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>The following two videos contain more examples of how to use the order of operations to simplify expressions with decimals.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-2\" title=\"Ex 2:  Simplify an Expression Involving Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/c-iknWD7piU?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-3\" title=\"Ex 3:  Simplify an Expression Involving Signed Decimals\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/CMQrctqdz6g?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/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-3932\">\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 146310, 146309, 146295, 146297. <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><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex 1: Simplify an Expression Involving Decimals. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/xO1cjj_TqaY\">https:\/\/youtu.be\/xO1cjj_TqaY<\/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 2: Simplify an Expression Involving Decimals. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/c-iknWD7piU\">https:\/\/youtu.be\/c-iknWD7piU<\/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 3: Simplify an Expression Involving Signed Decimals. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/CMQrctqdz6g\">https:\/\/youtu.be\/CMQrctqdz6g<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/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":25777,"menu_order":13,"template":"","meta":{"_candela_citation":"[{\"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\":\"cc\",\"description\":\"Ex 1: Simplify an Expression Involving Decimals\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/xO1cjj_TqaY\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 2: Simplify an Expression Involving Decimals\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/c-iknWD7piU\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex 3: Simplify an Expression Involving Signed Decimals\",\"author\":\"James Sousa (Mathispower4u.com)\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/CMQrctqdz6g\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Question ID 146310, 146309, 146295, 146297\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3932","chapter","type-chapter","status-web-only","hentry"],"part":377,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3932","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":1,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3932\/revisions"}],"predecessor-version":[{"id":3933,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3932\/revisions\/3933"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/parts\/377"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapters\/3932\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/media?parent=3932"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=3932"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/contributor?post=3932"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/slcc-mathforliberalartscorequisite\/wp-json\/wp\/v2\/license?post=3932"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}