{"id":2707,"date":"2025-08-13T18:29:35","date_gmt":"2025-08-13T18:29:35","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/precalculus\/?post_type=chapter&#038;p=2707"},"modified":"2025-10-13T17:34:28","modified_gmt":"2025-10-13T17:34:28","slug":"trigonometric-functions-background-youll-need-1","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/precalculus\/chapter\/trigonometric-functions-background-youll-need-1\/","title":{"raw":"Trigonometric Functions: Background You'll Need 1","rendered":"Trigonometric Functions: Background You&#8217;ll Need 1"},"content":{"raw":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\r\n<ul>\r\n \t<li><span data-sheets-root=\"1\">Add and subtract fractions with whole numbers<\/span><\/li>\r\n<\/ul>\r\n<\/section><section class=\"textbox questionHelp\" aria-label=\"Question Help\"><b>How To: Add or Subtract Fractions with Whole Numbers<\/b>Consider an expression in the form: [latex]a+\\frac{b}{c}[\/latex]\r\n<ol>\r\n \t<li>Write the whole number as a fraction with a denominator of [latex]1[\/latex]: [latex]\\frac{a}{1}[\/latex]<\/li>\r\n \t<li>Make a common denominator: Multiply the whole number (now a fraction) by the fraction [latex]\\frac{c}{c}=1[\/latex] to create a common denominator.<\/li>\r\n \t<li>Add the numerators: Combine the fractions by adding their numerators and keeping the common denominator.<\/li>\r\n \t<li>Simplify the result.<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">\r\n<ol>\r\n \t<li data-start=\"479\" data-end=\"514\">Add [latex]3 + \\frac{1}{4}[\/latex].<\/li>\r\n \t<li data-start=\"479\" data-end=\"514\">Subtract [latex]5 - \\frac{2}{3}[\/latex].<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"343068\"]Show Solutions[\/reveal-answer]\r\n[hidden-answer a=\"343068\"]\r\n<ol>\r\n \t<li>[latex]3 + \\frac{1}{4}[\/latex]\r\n\r\n[latex]\\begin{align} &amp;= \\frac{3}{1} + \\frac{1}{4} &amp;&amp; \\text{Write } 3 \\text{ as } \\frac{3}{1} \\\\ &amp;= \\frac{12}{4} + \\frac{1}{4} &amp;&amp; \\text{Make a common denominator of } 4\u00a0 \\\\ &amp;= \\frac{13}{4} &amp;&amp; \\text{Add the numerators}\u00a0 \\end{align} [\/latex]<\/li>\r\n \t<li>[latex]5 - \\frac{2}{3}[\/latex]\r\n\r\n[latex]\\begin{align}\r\n&amp;= \\frac{5}{1} - \\frac{2}{3} &amp;&amp; \\text{Write } 5 \\text{ as } \\frac{5}{1} \\\\\r\n&amp;= \\frac{15}{3} - \\frac{2}{3} &amp;&amp; \\text{Make a common denominator of } 3 \\\\\r\n&amp;= \\frac{13}{3} &amp;&amp; \\text{Subtract the numerators}\r\n\\end{align}\r\n[\/latex]\r\n[\/hidden-answer]<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm_question hide_question_numbers=1]313567[\/ohm_question]<\/section><section class=\"textbox proTip\" aria-label=\"Pro Tip\">Always change the whole number to a fraction before combining.<\/section>","rendered":"<section class=\"textbox learningGoals\" aria-label=\"Learning Goals\">\n<ul>\n<li><span data-sheets-root=\"1\">Add and subtract fractions with whole numbers<\/span><\/li>\n<\/ul>\n<\/section>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><b>How To: Add or Subtract Fractions with Whole Numbers<\/b>Consider an expression in the form: [latex]a+\\frac{b}{c}[\/latex]<\/p>\n<ol>\n<li>Write the whole number as a fraction with a denominator of [latex]1[\/latex]: [latex]\\frac{a}{1}[\/latex]<\/li>\n<li>Make a common denominator: Multiply the whole number (now a fraction) by the fraction [latex]\\frac{c}{c}=1[\/latex] to create a common denominator.<\/li>\n<li>Add the numerators: Combine the fractions by adding their numerators and keeping the common denominator.<\/li>\n<li>Simplify the result.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">\n<ol>\n<li data-start=\"479\" data-end=\"514\">Add [latex]3 + \\frac{1}{4}[\/latex].<\/li>\n<li data-start=\"479\" data-end=\"514\">Subtract [latex]5 - \\frac{2}{3}[\/latex].<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q343068\">Show Solutions<\/button><\/p>\n<div id=\"q343068\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]3 + \\frac{1}{4}[\/latex]\n<p>[latex]\\begin{align} &= \\frac{3}{1} + \\frac{1}{4} && \\text{Write } 3 \\text{ as } \\frac{3}{1} \\\\ &= \\frac{12}{4} + \\frac{1}{4} && \\text{Make a common denominator of } 4\u00a0 \\\\ &= \\frac{13}{4} && \\text{Add the numerators}\u00a0 \\end{align}[\/latex]<\/li>\n<li>[latex]5 - \\frac{2}{3}[\/latex]\n<p>[latex]\\begin{align}  &= \\frac{5}{1} - \\frac{2}{3} && \\text{Write } 5 \\text{ as } \\frac{5}{1} \\\\  &= \\frac{15}{3} - \\frac{2}{3} && \\text{Make a common denominator of } 3 \\\\  &= \\frac{13}{3} && \\text{Subtract the numerators}  \\end{align}[\/latex]\n<\/p><\/div>\n<\/div>\n<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm313567\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=313567&theme=lumen&iframe_resize_id=ohm313567&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">Always change the whole number to a fraction before combining.<\/section>\n","protected":false},"author":67,"menu_order":2,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":178,"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\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2707"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/users\/67"}],"version-history":[{"count":13,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2707\/revisions"}],"predecessor-version":[{"id":4618,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2707\/revisions\/4618"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/parts\/178"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapters\/2707\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/media?parent=2707"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/pressbooks\/v2\/chapter-type?post=2707"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/contributor?post=2707"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/precalculus\/wp-json\/wp\/v2\/license?post=2707"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}