{"id":2196,"date":"2021-10-05T19:11:35","date_gmt":"2021-10-05T19:11:35","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/?post_type=chapter&#038;p=2196"},"modified":"2022-03-28T18:41:37","modified_gmt":"2022-03-28T18:41:37","slug":"summary-review-10","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/chapter\/summary-review-10\/","title":{"raw":"Summary: Review","rendered":"Summary: Review"},"content":{"raw":"<h2>Key Concepts<\/h2>\r\n<strong>Order of Operations<\/strong>\r\n<ol>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Evaluate expressions within grouping symbols, [latex]( \\ ), [ \\ ] \\ \\mathrm{and} \\ \\{ \\ \\}[\/latex]. Fractions have implied grouping of terms in the numerator and terms in the denominator.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Evaluate exponents and radicals (such as square roots). Expressions under a radical have an implied grouping.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Multiply and divide, left to right.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Add and subtract, left to right.<\/li>\r\n<\/ol>\r\n<strong>Translating Verbal Statements Involving Inequalities to Mathematical Statements<\/strong>\r\n<div align=\"left\">\r\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"1\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 50%; text-align: center;\">Verbal statement\r\n<em>k<\/em> is ...<\/td>\r\n<td style=\"width: 50%; text-align: center;\">Mathematical Statement<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">greater than or equal to <em>k<\/em>\r\nat least <em>k<\/em>\r\nnot less than <em>k<\/em><\/td>\r\n<td style=\"width: 50%; text-align: center;\">[latex]x \\geq k[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">less than or equal to <em>k<\/em>\r\nat most <em>k<\/em>\r\nnot more than <em>k<\/em><\/td>\r\n<td style=\"width: 50%; text-align: center;\">[latex]x \\leq k[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">less than <em>k<\/em>\r\nbelow <em>k<\/em>\r\nfewer than <em>k<\/em><\/td>\r\n<td style=\"width: 50%; text-align: center;\">[latex]x &lt; k[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">greater than <em>k<\/em>\r\nmore than <em>k<\/em>\r\nabove <em>k<\/em><\/td>\r\n<td style=\"width: 50%; text-align: center;\">[latex]x &gt; k[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">equal to <em>k<\/em>\r\nis <em>k<\/em>\r\nexactly <em>k<\/em>\r\nthe same as <em>k<\/em><\/td>\r\n<td style=\"width: 50%; text-align: center;\">[latex]x=k[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td style=\"width: 50%;\">not equal to <em>k<\/em>\r\nnot <em>k<\/em>\r\ndifferent from <em>k<\/em><\/td>\r\n<td style=\"width: 50%; text-align: center;\">[latex]x \\neq k[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h2>Glossary<\/h2>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>Algebraic expression:<\/strong> an expression involving addition, subtraction, multiplication, division, and exponentiation by a rational exponent<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>Complex fraction:<\/strong> a fraction that contains fractions in the numerator and\/or the denominator<\/li>\r\n \t<li><strong>Secondary fraction:<\/strong> a fraction in the numerator or denominator of a complex fraction<\/li>\r\n<\/ul>\r\n<\/div>","rendered":"<h2>Key Concepts<\/h2>\n<p><strong>Order of Operations<\/strong><\/p>\n<ol>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Evaluate expressions within grouping symbols, [latex]( \\ ), [ \\ ] \\ \\mathrm{and} \\ \\{ \\ \\}[\/latex]. Fractions have implied grouping of terms in the numerator and terms in the denominator.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Evaluate exponents and radicals (such as square roots). Expressions under a radical have an implied grouping.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Multiply and divide, left to right.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Add and subtract, left to right.<\/li>\n<\/ol>\n<p><strong>Translating Verbal Statements Involving Inequalities to Mathematical Statements<\/strong><\/p>\n<div style=\"text-align: left;\">\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%; text-align: center;\">Verbal statement<br \/>\n<em>k<\/em> is &#8230;<\/td>\n<td style=\"width: 50%; text-align: center;\">Mathematical Statement<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">greater than or equal to <em>k<\/em><br \/>\nat least <em>k<\/em><br \/>\nnot less than <em>k<\/em><\/td>\n<td style=\"width: 50%; text-align: center;\">[latex]x \\geq k[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">less than or equal to <em>k<\/em><br \/>\nat most <em>k<\/em><br \/>\nnot more than <em>k<\/em><\/td>\n<td style=\"width: 50%; text-align: center;\">[latex]x \\leq k[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">less than <em>k<\/em><br \/>\nbelow <em>k<\/em><br \/>\nfewer than <em>k<\/em><\/td>\n<td style=\"width: 50%; text-align: center;\">[latex]x < k[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">greater than <em>k<\/em><br \/>\nmore than <em>k<\/em><br \/>\nabove <em>k<\/em><\/td>\n<td style=\"width: 50%; text-align: center;\">[latex]x > k[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">equal to <em>k<\/em><br \/>\nis <em>k<\/em><br \/>\nexactly <em>k<\/em><br \/>\nthe same as <em>k<\/em><\/td>\n<td style=\"width: 50%; text-align: center;\">[latex]x=k[\/latex]<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">not equal to <em>k<\/em><br \/>\nnot <em>k<\/em><br \/>\ndifferent from <em>k<\/em><\/td>\n<td style=\"width: 50%; text-align: center;\">[latex]x \\neq k[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Glossary<\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>Algebraic expression:<\/strong> an expression involving addition, subtraction, multiplication, division, and exponentiation by a rational exponent<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\"><strong>Complex fraction:<\/strong> a fraction that contains fractions in the numerator and\/or the denominator<\/li>\n<li><strong>Secondary fraction:<\/strong> a fraction in the numerator or denominator of a complex fraction<\/li>\n<\/ul>\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-2196\">\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><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><\/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":169134,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"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-2196","chapter","type-chapter","status-publish","hentry"],"part":285,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2196","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/users\/169134"}],"version-history":[{"count":10,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2196\/revisions"}],"predecessor-version":[{"id":3892,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2196\/revisions\/3892"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/parts\/285"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapters\/2196\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/media?parent=2196"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/pressbooks\/v2\/chapter-type?post=2196"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/contributor?post=2196"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/introstatscorequisite\/wp-json\/wp\/v2\/license?post=2196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}