{"id":417,"date":"2024-04-18T21:32:03","date_gmt":"2024-04-18T21:32:03","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&#038;p=417"},"modified":"2025-08-20T16:03:18","modified_gmt":"2025-08-20T16:03:18","slug":"algebra-essentials-background-youll-need-2","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/algebra-essentials-background-youll-need-2\/","title":{"raw":"Algebra Essentials: Background You'll Need 2","rendered":"Algebra Essentials: Background You&#8217;ll Need 2"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n \t<li>Add, subtract, multiply and divide fractions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Fractions<\/h2>\r\n<div>\r\n\r\nA fraction is written [latex]\\dfrac{a}{b}[\/latex], where [latex]a[\/latex] and [latex]b[\/latex] are integers and [latex]b \\ne 0[\/latex].\r\n\r\nIn a fraction, [latex]a[\/latex] is called the\u00a0<strong>numerator<\/strong> and [latex]b[\/latex] is called the\u00a0<strong>denominator<\/strong>.\r\n\r\n<\/div>\r\n<section class=\"textbox recall\" aria-label=\"Recall\">A fraction is a way to represent parts of a whole. The denominator [latex]b[\/latex] represents the number of equal parts the whole has been divided into, and the numerator [latex]a[\/latex] represents how many parts are included. The denominator, [latex]b[\/latex], cannot equal zero because division by zero is undefined.<\/section>\r\n<h3>Adding Fractions<\/h3>\r\nThe first step in adding fractions is to check if they have the same bottom number, also known as a '<strong>common denominator<\/strong>.' When the two fractions have a common denominator, adding the two numbers is straightforward - add the numerators, and then place that value in the numerator and the common denominator in the denominator. When the fraction does not have common denominators, we have to transform the fractions so that they do have common denominators. This is technically called finding the <strong>least common multiple<\/strong> (LCM).\r\n\r\nWe can find the least common multiple using the prime factorization method.\r\n\r\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How To: Finding the Least Common Multiple Through Prime Factorization<\/strong>\r\n<ol style=\"list-style-type: decimal;\">\r\n \t<li>Find the prime factors of each denominator. You can use a factor tree or division method to break down each number into its prime factors.<\/li>\r\n \t<li>List down all the unique prime factors that appear in the prime factorization of each number.<\/li>\r\n \t<li>For each unique prime factor, identify the highest power to which it is raised in any of the given numbers.<\/li>\r\n \t<li>Multiply together the highest powers of all the unique prime factors. The result is the least common multiple (LCM) of the given numbers.<\/li>\r\n<\/ol>\r\n<\/section>Now that we know how to find the least common multiple, adding fractions with unlike denominators becomes easier.\r\n\r\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How To: Adding Fractions With Unlike Denominators<\/strong>\r\n<ol>\r\n \t<li>Find a common denominator.<\/li>\r\n \t<li>Rewrite each fraction using the common denominator.<\/li>\r\n \t<li>Now that the fractions have a common denominator, you can add the numerators.<\/li>\r\n \t<li>Simplify by canceling out all common factors in the numerator and denominator.<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox example\">Add [latex]\\Large\\frac{3}{7}+\\Large\\frac{2}{21}[\/latex]. [reveal-answer q=\"520906\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"520906\"]Since the denominators are not alike, find the least common denominator by finding the least common denominators (LCD) of 7 and 21.\r\n<p style=\"padding-left: 40px;\">Multiples of [latex]7: 7, 14, \\textbf{21}[\/latex]<\/p>\r\n<p style=\"padding-left: 40px;\">Multiples of [latex]21:\\textbf{21}[\/latex]<\/p>\r\nRewrite the first fraction to have a denominator of [latex]21[\/latex]. Since [latex]21 = 7*3[\/latex], we want to multiply the first fraction by [latex]\\frac{3}{3}[\/latex]:\r\n<p style=\"text-align: center;\">[latex]\\Large(\\frac{3}{7})(\\frac{3}{3})+\\Large\\frac{2}{21}=\\Large\\frac{9}{21}+\\Large\\frac{2}{21}[\/latex]<\/p>\r\nAdd the fractions by adding the numerators and keeping the denominator the same.\r\n<p style=\"text-align: center;\">[latex]\\Large\\frac{9}{21}+\\Large\\frac{2}{21}=\\Large\\frac{11}{21}[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex]\\Large\\frac{3}{7}+\\Large\\frac{2}{21}=\\Large\\frac{11}{21}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]12692[\/ohm2_question]<\/section>\r\n<h3>Subtracting Fractions<\/h3>\r\nWhen you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions. When the two fractions have a common denominator, subtracting the two numbers is straightforward - subtract the numerators, and then place that value in the numerator and the common denominator in the denominator.\r\n\r\nJust like when adding fractions, when subtracting fractions that do not have common denominators, we have to transform the fractions so that they do have common denominators. This can be done the same way we did when adding fractions.\r\n\r\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How To: Subtracting Fractions With Unlike Denominators<\/strong>\r\n<ol>\r\n \t<li>Find a common denominator.<\/li>\r\n \t<li>Rewrite each fraction using the common denominator.<\/li>\r\n \t<li>Now that the fractions have a common denominator, you can subtract the numerators.<\/li>\r\n \t<li>Simplify by canceling out all common factors in the numerator and denominator.<\/li>\r\n<\/ol>\r\n<\/section><section class=\"textbox example\" aria-label=\"Example\">Calculate [latex]\\frac{14}{25}-\\frac{9}{70}[\/latex].[reveal-answer q=\"160932\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160932\"]The denominators of the fractions are [latex]25[\/latex] and [latex]70[\/latex]. We need to find the LCM of [latex]25[\/latex] and [latex]70[\/latex].\r\n<p style=\"text-align: center;\">[latex]LCM(25,70)=350[\/latex]<\/p>\r\nNext, we rewrite each fraction with [latex]350[\/latex] as the common denominator.\r\n<p style=\"text-align: center;\">[latex]\\frac{14}{25}=\\frac{14\u00d714}{350}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{9}{70}=\\frac{9\u00d75}{350}[\/latex]<\/p>\r\nNow, we can subtract the two fractions together.\r\n<p style=\"text-align: center;\">[latex]\\frac{14\u00d714}{350}-\\frac{9\u00d75}{350}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{196}{350}-\\frac{45}{350}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{196-45}{350}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{151}{350}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{14}{25}-\\frac{9}{70}=\\frac{151}{350}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]12694[\/ohm2_question]<\/section>\r\n<h3>Multiplying Fractions<\/h3>\r\nJust as you add, subtract, multiply, and divide when working with whole numbers, you also use these operations when working with fractions. Multiplying fractions is less complicated than adding or subtracting fractions, as there is no need to find common denominators. To multiply fractions, multiply the numerators, then multiply the denominators, and write the numerator product divided by the denominator product.\r\n\r\n<section class=\"textbox example\">Calculate [latex]\\frac{12}{25} \\times \\frac{10}{21}[\/latex].[reveal-answer q=\"160936\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160936\"]Multiply the numerators and place that in the numerator, and then multiply the denominators and place that in the denominator.\r\n<p style=\"text-align: center;\">[latex]\\frac{12}{25} \\times \\frac{10}{21}=\\frac{12 \\times 10}{25 \\times 21}=\\frac{120}{525}[\/latex]<\/p>\r\nOnce we have that result, reduce to lowest terms, which gives\r\n\r\n<center>[latex]\\frac{120}{525}=\\frac{15 \\times 8}{15 \\times 35}=\\frac{\\cancel{15}\u00d78}{\\cancel{15}\u00d735}=\\frac{8}{35}[\/latex]<\/center>[\/hidden-answer]\r\n\r\n<\/section><section><section class=\"textbox tryIt\" aria-label=\"Try It\">[ohm2_question hide_question_numbers=1]12695[\/ohm2_question]<\/section>\r\n<h3>Dividing Fractions<\/h3>\r\n<\/section>Before discussing division of fractions, we should look at the <strong>reciprocal <\/strong>of a number. The reciprocal of a number is [latex]1[\/latex] divided by the number. For a fraction, the reciprocal is the fraction formed by switching the numerator and denominator.\u00a0 An important feature for a number and its reciprocal is that their product is [latex]1[\/latex]. Sometimes we call\u00a0the reciprocal\u00a0the \u201cflip\u201d of the other number: flip [latex] \\frac{2}{5}[\/latex] to get the reciprocal [latex]\\frac{5}{2}[\/latex].\r\n\r\nWhen dividing two fractions, find the reciprocal of the divisor (the number that is being divided into the other number). Next, replace the divisor by its reciprocal and change the division into multiplication. Then, perform the multiplication.\r\n\r\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">Any easy way to remember how to divide fractions is the phrase \u201ckeep, change, flip.\u201d This means to <strong>KEEP<\/strong> the first number, <strong>CHANGE<\/strong> the division sign to multiplication, and then <strong>FLIP<\/strong> (use the reciprocal) of the second number.<\/section><section class=\"textbox example\">Divide [latex] \\frac{2}{3}\\div \\frac{1}{6}[\/latex].[reveal-answer q=\"160931\"]Show Solution[\/reveal-answer] [hidden-answer a=\"160931\"]<strong>KEEP<\/strong> [latex] \\frac{2}{3}[\/latex] <strong>CHANGE<\/strong>\u00a0 [latex] \\div [\/latex] to \u00a0[latex] \\times [\/latex] <strong>FLIP\u00a0<\/strong> [latex]\\frac{1}{6}[\/latex]\r\n<p style=\"text-align: center;\">[latex] \\frac{2}{3} \\times \\frac{6}{1}[\/latex]<\/p>\r\nMultiply numerators and multiply denominators.\r\n<p style=\"text-align: center;\">[latex]\\frac{2 \\times 6}{3 \\times 1}=\\frac{12}{3}[\/latex]<\/p>\r\nSimplify.\r\n<p style=\"text-align: center;\">[latex] \\frac{12}{3}=4[\/latex]<\/p>\r\n\r\n<h4>Answer<\/h4>\r\n[latex] \\frac{2}{3}\\div \\frac{1}{6}=4[\/latex][\/hidden-answer]\r\n\r\n<\/section><section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]12696[\/ohm2_question]<\/section>\r\n<div class=\"textbox shaded\">\r\n\r\n<img class=\"wp-image-2132 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/22011815\/traffic-sign-160659-300x265.png\" alt=\"Caution\" width=\"62\" height=\"55\" \/>Caution! Division by zero is undefined and so is the reciprocal of any fraction that has a zero in the numerator. For any real number [latex]a[\/latex], [latex]\\frac{a}{0}[\/latex] is undefined. Additionally, the reciprocal of [latex]\\frac{0}{a}[\/latex] will always be undefined.\r\n\r\n<\/div>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Add, subtract, multiply and divide fractions<\/li>\n<\/ul>\n<\/section>\n<h2>Fractions<\/h2>\n<div>\n<p>A fraction is written [latex]\\dfrac{a}{b}[\/latex], where [latex]a[\/latex] and [latex]b[\/latex] are integers and [latex]b \\ne 0[\/latex].<\/p>\n<p>In a fraction, [latex]a[\/latex] is called the\u00a0<strong>numerator<\/strong> and [latex]b[\/latex] is called the\u00a0<strong>denominator<\/strong>.<\/p>\n<\/div>\n<section class=\"textbox recall\" aria-label=\"Recall\">A fraction is a way to represent parts of a whole. The denominator [latex]b[\/latex] represents the number of equal parts the whole has been divided into, and the numerator [latex]a[\/latex] represents how many parts are included. The denominator, [latex]b[\/latex], cannot equal zero because division by zero is undefined.<\/section>\n<h3>Adding Fractions<\/h3>\n<p>The first step in adding fractions is to check if they have the same bottom number, also known as a &#8216;<strong>common denominator<\/strong>.&#8217; When the two fractions have a common denominator, adding the two numbers is straightforward &#8211; add the numerators, and then place that value in the numerator and the common denominator in the denominator. When the fraction does not have common denominators, we have to transform the fractions so that they do have common denominators. This is technically called finding the <strong>least common multiple<\/strong> (LCM).<\/p>\n<p>We can find the least common multiple using the prime factorization method.<\/p>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How To: Finding the Least Common Multiple Through Prime Factorization<\/strong><\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>Find the prime factors of each denominator. You can use a factor tree or division method to break down each number into its prime factors.<\/li>\n<li>List down all the unique prime factors that appear in the prime factorization of each number.<\/li>\n<li>For each unique prime factor, identify the highest power to which it is raised in any of the given numbers.<\/li>\n<li>Multiply together the highest powers of all the unique prime factors. The result is the least common multiple (LCM) of the given numbers.<\/li>\n<\/ol>\n<\/section>\n<p>Now that we know how to find the least common multiple, adding fractions with unlike denominators becomes easier.<\/p>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How To: Adding Fractions With Unlike Denominators<\/strong><\/p>\n<ol>\n<li>Find a common denominator.<\/li>\n<li>Rewrite each fraction using the common denominator.<\/li>\n<li>Now that the fractions have a common denominator, you can add the numerators.<\/li>\n<li>Simplify by canceling out all common factors in the numerator and denominator.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\">Add [latex]\\Large\\frac{3}{7}+\\Large\\frac{2}{21}[\/latex]. <\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q520906\">Show Solution<\/button><\/p>\n<div id=\"q520906\" class=\"hidden-answer\" style=\"display: none\">Since the denominators are not alike, find the least common denominator by finding the least common denominators (LCD) of 7 and 21.<\/p>\n<p style=\"padding-left: 40px;\">Multiples of [latex]7: 7, 14, \\textbf{21}[\/latex]<\/p>\n<p style=\"padding-left: 40px;\">Multiples of [latex]21:\\textbf{21}[\/latex]<\/p>\n<p>Rewrite the first fraction to have a denominator of [latex]21[\/latex]. Since [latex]21 = 7*3[\/latex], we want to multiply the first fraction by [latex]\\frac{3}{3}[\/latex]:<\/p>\n<p style=\"text-align: center;\">[latex]\\Large(\\frac{3}{7})(\\frac{3}{3})+\\Large\\frac{2}{21}=\\Large\\frac{9}{21}+\\Large\\frac{2}{21}[\/latex]<\/p>\n<p>Add the fractions by adding the numerators and keeping the denominator the same.<\/p>\n<p style=\"text-align: center;\">[latex]\\Large\\frac{9}{21}+\\Large\\frac{2}{21}=\\Large\\frac{11}{21}[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]\\Large\\frac{3}{7}+\\Large\\frac{2}{21}=\\Large\\frac{11}{21}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm12692\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=12692&theme=lumen&iframe_resize_id=ohm12692&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h3>Subtracting Fractions<\/h3>\n<p>When you subtract fractions, you must think about whether they have a common denominator, just like with adding fractions. When the two fractions have a common denominator, subtracting the two numbers is straightforward &#8211; subtract the numerators, and then place that value in the numerator and the common denominator in the denominator.<\/p>\n<p>Just like when adding fractions, when subtracting fractions that do not have common denominators, we have to transform the fractions so that they do have common denominators. This can be done the same way we did when adding fractions.<\/p>\n<section class=\"textbox questionHelp\" aria-label=\"Question Help\"><strong>How To: Subtracting Fractions With Unlike Denominators<\/strong><\/p>\n<ol>\n<li>Find a common denominator.<\/li>\n<li>Rewrite each fraction using the common denominator.<\/li>\n<li>Now that the fractions have a common denominator, you can subtract the numerators.<\/li>\n<li>Simplify by canceling out all common factors in the numerator and denominator.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox example\" aria-label=\"Example\">Calculate [latex]\\frac{14}{25}-\\frac{9}{70}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160932\">Show Solution<\/button> <\/p>\n<div id=\"q160932\" class=\"hidden-answer\" style=\"display: none\">The denominators of the fractions are [latex]25[\/latex] and [latex]70[\/latex]. We need to find the LCM of [latex]25[\/latex] and [latex]70[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]LCM(25,70)=350[\/latex]<\/p>\n<p>Next, we rewrite each fraction with [latex]350[\/latex] as the common denominator.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{14}{25}=\\frac{14\u00d714}{350}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{9}{70}=\\frac{9\u00d75}{350}[\/latex]<\/p>\n<p>Now, we can subtract the two fractions together.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{14\u00d714}{350}-\\frac{9\u00d75}{350}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{196}{350}-\\frac{45}{350}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{196-45}{350}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{151}{350}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{14}{25}-\\frac{9}{70}=\\frac{151}{350}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm12694\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=12694&theme=lumen&iframe_resize_id=ohm12694&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h3>Multiplying Fractions<\/h3>\n<p>Just as you add, subtract, multiply, and divide when working with whole numbers, you also use these operations when working with fractions. Multiplying fractions is less complicated than adding or subtracting fractions, as there is no need to find common denominators. To multiply fractions, multiply the numerators, then multiply the denominators, and write the numerator product divided by the denominator product.<\/p>\n<section class=\"textbox example\">Calculate [latex]\\frac{12}{25} \\times \\frac{10}{21}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160936\">Show Solution<\/button> <\/p>\n<div id=\"q160936\" class=\"hidden-answer\" style=\"display: none\">Multiply the numerators and place that in the numerator, and then multiply the denominators and place that in the denominator.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{12}{25} \\times \\frac{10}{21}=\\frac{12 \\times 10}{25 \\times 21}=\\frac{120}{525}[\/latex]<\/p>\n<p>Once we have that result, reduce to lowest terms, which gives<\/p>\n<div style=\"text-align: center;\">[latex]\\frac{120}{525}=\\frac{15 \\times 8}{15 \\times 35}=\\frac{\\cancel{15}\u00d78}{\\cancel{15}\u00d735}=\\frac{8}{35}[\/latex]<\/div>\n<\/div>\n<\/div>\n<\/section>\n<section>\n<section class=\"textbox tryIt\" aria-label=\"Try It\"><iframe loading=\"lazy\" id=\"ohm12695\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=12695&theme=lumen&iframe_resize_id=ohm12695&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h3>Dividing Fractions<\/h3>\n<\/section>\n<p>Before discussing division of fractions, we should look at the <strong>reciprocal <\/strong>of a number. The reciprocal of a number is [latex]1[\/latex] divided by the number. For a fraction, the reciprocal is the fraction formed by switching the numerator and denominator.\u00a0 An important feature for a number and its reciprocal is that their product is [latex]1[\/latex]. Sometimes we call\u00a0the reciprocal\u00a0the \u201cflip\u201d of the other number: flip [latex]\\frac{2}{5}[\/latex] to get the reciprocal [latex]\\frac{5}{2}[\/latex].<\/p>\n<p>When dividing two fractions, find the reciprocal of the divisor (the number that is being divided into the other number). Next, replace the divisor by its reciprocal and change the division into multiplication. Then, perform the multiplication.<\/p>\n<section class=\"textbox proTip\" aria-label=\"Pro Tip\">Any easy way to remember how to divide fractions is the phrase \u201ckeep, change, flip.\u201d This means to <strong>KEEP<\/strong> the first number, <strong>CHANGE<\/strong> the division sign to multiplication, and then <strong>FLIP<\/strong> (use the reciprocal) of the second number.<\/section>\n<section class=\"textbox example\">Divide [latex]\\frac{2}{3}\\div \\frac{1}{6}[\/latex].<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q160931\">Show Solution<\/button> <\/p>\n<div id=\"q160931\" class=\"hidden-answer\" style=\"display: none\"><strong>KEEP<\/strong> [latex]\\frac{2}{3}[\/latex] <strong>CHANGE<\/strong>\u00a0 [latex]\\div[\/latex] to \u00a0[latex]\\times[\/latex] <strong>FLIP\u00a0<\/strong> [latex]\\frac{1}{6}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2}{3} \\times \\frac{6}{1}[\/latex]<\/p>\n<p>Multiply numerators and multiply denominators.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2 \\times 6}{3 \\times 1}=\\frac{12}{3}[\/latex]<\/p>\n<p>Simplify.<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{12}{3}=4[\/latex]<\/p>\n<h4>Answer<\/h4>\n<p>[latex]\\frac{2}{3}\\div \\frac{1}{6}=4[\/latex]<\/p><\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm12696\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=12696&theme=lumen&iframe_resize_id=ohm12696&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<div class=\"textbox shaded\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2132 alignleft\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/03\/22011815\/traffic-sign-160659-300x265.png\" alt=\"Caution\" width=\"62\" height=\"55\" \/>Caution! Division by zero is undefined and so is the reciprocal of any fraction that has a zero in the numerator. For any real number [latex]a[\/latex], [latex]\\frac{a}{0}[\/latex] is undefined. Additionally, the reciprocal of [latex]\\frac{0}{a}[\/latex] will always be undefined.<\/p>\n<\/div>\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":32,"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\/417"}],"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":46,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/417\/revisions"}],"predecessor-version":[{"id":7953,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/417\/revisions\/7953"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/parts\/32"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/417\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/media?parent=417"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=417"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/contributor?post=417"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/wp-json\/wp\/v2\/license?post=417"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}