{"id":245,"date":"2024-10-18T21:15:18","date_gmt":"2024-10-18T21:15:18","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/probability-background-youll-need-3\/"},"modified":"2024-10-18T21:15:18","modified_gmt":"2024-10-18T21:15:18","slug":"probability-background-youll-need-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/chapter\/probability-background-youll-need-3\/","title":{"raw":"Probability: Background You'll Need 3","rendered":"Probability: Background You&#8217;ll Need 3"},"content":{"raw":"\n<section class=\"textbox learningGoals\">\n<ul>\n\t<li>Add and subtract fractions<\/li>\n<\/ul>\n<\/section>\n<h2>Add Fractions with a Common Denominator<\/h2>\n<p><span data-offset-key=\"4m1mb-16-0\">Adding<\/span><span data-offset-key=\"4m1mb-17-0\"> fractions<\/span><span data-offset-key=\"4m1mb-18-0\"> with<\/span><span data-offset-key=\"4m1mb-19-0\"> the<\/span><span data-offset-key=\"4m1mb-20-0\"> same<\/span><span data-offset-key=\"4m1mb-21-0\"> denomin<\/span><span data-offset-key=\"4m1mb-22-0\">ator<\/span><span data-offset-key=\"4m1mb-23-0\"> is<\/span><span data-offset-key=\"4m1mb-24-0\"> a<\/span><span data-offset-key=\"4m1mb-25-0\"> straightforward<\/span><span data-offset-key=\"4m1mb-26-0\"> process<\/span><span data-offset-key=\"4m1mb-27-0\">.<\/span><span data-offset-key=\"4m1mb-28-0\"> The<\/span><span data-offset-key=\"4m1mb-29-0\"> numer<\/span><span data-offset-key=\"4m1mb-30-0\">ators<\/span><span data-offset-key=\"4m1mb-31-0\"> of<\/span><span data-offset-key=\"4m1mb-32-0\"> the<\/span><span data-offset-key=\"4m1mb-33-0\"> fractions<\/span><span data-offset-key=\"4m1mb-34-0\"> are<\/span><span data-offset-key=\"4m1mb-35-0\"> simply<\/span><span data-offset-key=\"4m1mb-36-0\"> added<\/span><span data-offset-key=\"4m1mb-37-0\"> together<\/span><span data-offset-key=\"4m1mb-38-0\"> to<\/span><span data-offset-key=\"4m1mb-39-0\"> get<\/span><span data-offset-key=\"4m1mb-40-0\"> the<\/span><span data-offset-key=\"4m1mb-41-0\"> numer<\/span><span data-offset-key=\"4m1mb-42-0\">ator<\/span><span data-offset-key=\"4m1mb-43-0\"> of<\/span><span data-offset-key=\"4m1mb-44-0\"> the<\/span><span data-offset-key=\"4m1mb-45-0\"> answer<\/span><span data-offset-key=\"4m1mb-46-0\">.<\/span><span data-offset-key=\"4m1mb-47-0\"> The<\/span><span data-offset-key=\"4m1mb-48-0\"> denomin<\/span><span data-offset-key=\"4m1mb-49-0\">ator<\/span><span data-offset-key=\"4m1mb-50-0\"> will<\/span><span data-offset-key=\"4m1mb-51-0\"> stay<\/span><span data-offset-key=\"4m1mb-52-0\"> the<\/span><span data-offset-key=\"4m1mb-53-0\"> same<\/span><span data-offset-key=\"4m1mb-54-0\">,<\/span><span data-offset-key=\"4m1mb-55-0\"> since<\/span><span data-offset-key=\"4m1mb-56-0\"> the<\/span><span data-offset-key=\"4m1mb-57-0\"> denomin<\/span><span data-offset-key=\"4m1mb-58-0\">ators<\/span><span data-offset-key=\"4m1mb-59-0\"> are<\/span><span data-offset-key=\"4m1mb-60-0\"> the<\/span><span data-offset-key=\"4m1mb-61-0\"> same<\/span><span data-offset-key=\"4m1mb-62-0\"> for<\/span><span data-offset-key=\"4m1mb-63-0\"> all<\/span><span data-offset-key=\"4m1mb-64-0\"> the<\/span><span data-offset-key=\"4m1mb-65-0\"> fractions<\/span><span data-offset-key=\"4m1mb-66-0\"> being<\/span><span data-offset-key=\"4m1mb-67-0\"> added<\/span><span data-offset-key=\"4m1mb-68-0\">.<\/span><span data-offset-key=\"4m1mb-69-0\"> In<\/span><span data-offset-key=\"4m1mb-70-0\"> this<\/span><span data-offset-key=\"4m1mb-71-0\"> section<\/span><span data-offset-key=\"4m1mb-72-0\">,<\/span><span data-offset-key=\"4m1mb-73-0\"> we<\/span><span data-offset-key=\"4m1mb-74-0\"> will<\/span><span data-offset-key=\"4m1mb-75-0\"> discuss<\/span><span data-offset-key=\"4m1mb-76-0\"> how<\/span><span data-offset-key=\"4m1mb-77-0\"> to<\/span><span data-offset-key=\"4m1mb-78-0\"> add<\/span><span data-offset-key=\"4m1mb-79-0\"> fractions<\/span><span data-offset-key=\"4m1mb-80-0\"> with<\/span><span data-offset-key=\"4m1mb-81-0\"> the<\/span><span data-offset-key=\"4m1mb-82-0\"> same<\/span><span data-offset-key=\"4m1mb-83-0\"> denomin<\/span><span data-offset-key=\"4m1mb-84-0\">ator<\/span><span data-offset-key=\"4m1mb-85-0\">,<\/span><span data-offset-key=\"4m1mb-86-0\"> and<\/span><span data-offset-key=\"4m1mb-87-0\"> also<\/span><span data-offset-key=\"4m1mb-88-0\"> look<\/span><span data-offset-key=\"4m1mb-89-0\"> at<\/span><span data-offset-key=\"4m1mb-90-0\"> a<\/span><span data-offset-key=\"4m1mb-91-0\"> few<\/span><span data-offset-key=\"4m1mb-92-0\"> examples<\/span><span data-offset-key=\"4m1mb-93-0\"> to<\/span><span data-offset-key=\"4m1mb-94-0\"> illustrate<\/span><span data-offset-key=\"4m1mb-95-0\"> the<\/span><span data-offset-key=\"4m1mb-96-0\"> process<\/span><span data-offset-key=\"4m1mb-97-0\">.<\/span><\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Fraction Addition<\/h3>\n<p>If [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then<\/p>\n<p>&nbsp;<\/p>\n<center>[latex]\\Large\\frac{a}{c}\\normalsize+\\Large\\frac{b}{c}\\normalsize=\\Large\\frac{a+b}{c}[\/latex]<\/center>\n<p>&nbsp;<\/p>\n<p>To add fractions with a common denominators, add the numerators and place the sum over the common denominator.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<p style=\"text-align: left;\">Find the sum:<\/p>\n<p style=\"text-align: center;\">[latex]\\Large\\frac{3}{5}\\normalsize+\\Large\\frac{1}{5}[\/latex]<\/p>\n<p style=\"text-align: left;\">[reveal-answer q=\"760537\"]Show Answer[\/reveal-answer]<br>\n[hidden-answer a=\"760537\"]<\/p>\n<ol>\n\t<li>[latex]\\Large\\frac{3}{5}\\normalsize+\\Large\\frac{1}{5}[\/latex]<\/li>\n\t<li>Add the numerators and place the sum over the common denominator. [latex]\\Large\\frac{3+1}{5}[\/latex]<\/li>\n\t<li>Simplify.<\/li>\n<\/ol>\n<p style=\"text-align: center;\">The answer is [latex]\\Large\\frac{4}{5}[\/latex]<\/p>\n<p>[\/hidden-answer]<\/p>\n<\/section>\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2787[\/ohm2_question]<\/section>\n<h2>Subtract Fractions with a Common Denominator<\/h2>\n<p><span data-offset-key=\"b1iru-17-0\">Sub<\/span><span data-offset-key=\"b1iru-18-0\">t<\/span><span data-offset-key=\"b1iru-19-0\">ract<\/span><span data-offset-key=\"b1iru-20-0\">ing<\/span><span data-offset-key=\"b1iru-21-0\"> fractions<\/span><span data-offset-key=\"b1iru-22-0\"> with<\/span><span data-offset-key=\"b1iru-23-0\"> the<\/span><span data-offset-key=\"b1iru-24-0\"> same<\/span><span data-offset-key=\"b1iru-25-0\"> denomin<\/span><span data-offset-key=\"b1iru-26-0\">ator<\/span><span data-offset-key=\"b1iru-27-0\"> is<\/span><span data-offset-key=\"b1iru-28-0\"> a<\/span><span data-offset-key=\"b1iru-29-0\"> simple<\/span><span data-offset-key=\"b1iru-30-0\"> process<\/span><span data-offset-key=\"b1iru-31-0\">.<\/span><span data-offset-key=\"b1iru-32-0\"> When<\/span><span data-offset-key=\"b1iru-33-0\"> the<\/span><span data-offset-key=\"b1iru-34-0\"> denomin<\/span><span data-offset-key=\"b1iru-35-0\">ators<\/span><span data-offset-key=\"b1iru-36-0\"> are<\/span><span data-offset-key=\"b1iru-37-0\"> the<\/span><span data-offset-key=\"b1iru-38-0\"> same<\/span><span data-offset-key=\"b1iru-39-0\">,<\/span><span data-offset-key=\"b1iru-40-0\"> all<\/span><span data-offset-key=\"b1iru-41-0\"> you<\/span><span data-offset-key=\"b1iru-42-0\"> need<\/span><span data-offset-key=\"b1iru-43-0\"> to<\/span><span data-offset-key=\"b1iru-44-0\"> do<\/span><span data-offset-key=\"b1iru-45-0\"> is<\/span><span data-offset-key=\"b1iru-46-0\"> subtract<\/span><span data-offset-key=\"b1iru-47-0\"> the<\/span><span data-offset-key=\"b1iru-48-0\"> numer<\/span><span data-offset-key=\"b1iru-49-0\">ators<\/span><span data-offset-key=\"b1iru-50-0\"> to<\/span><span data-offset-key=\"b1iru-51-0\"> get<\/span><span data-offset-key=\"b1iru-52-0\"> the<\/span><span data-offset-key=\"b1iru-53-0\"> difference<\/span><span data-offset-key=\"b1iru-54-0\">.<\/span><span data-offset-key=\"b1iru-55-0\"> In<\/span><span data-offset-key=\"b1iru-56-0\"> this<\/span><span data-offset-key=\"b1iru-57-0\"> section<\/span><span data-offset-key=\"b1iru-58-0\">,<\/span><span data-offset-key=\"b1iru-59-0\"> we<\/span><span data-offset-key=\"b1iru-60-0\">'ll<\/span><span data-offset-key=\"b1iru-61-0\"> discuss<\/span><span data-offset-key=\"b1iru-62-0\"> the<\/span><span data-offset-key=\"b1iru-63-0\"> steps<\/span><span data-offset-key=\"b1iru-64-0\"> for<\/span><span data-offset-key=\"b1iru-65-0\"> subtract<\/span><span data-offset-key=\"b1iru-66-0\">ing<\/span><span data-offset-key=\"b1iru-67-0\"> fractions<\/span><span data-offset-key=\"b1iru-68-0\"> with<\/span><span data-offset-key=\"b1iru-69-0\"> the<\/span><span data-offset-key=\"b1iru-70-0\"> same<\/span><span data-offset-key=\"b1iru-71-0\"> denomin<\/span><span data-offset-key=\"b1iru-72-0\">ator<\/span><span data-offset-key=\"b1iru-73-0\"> and<\/span><span data-offset-key=\"b1iru-74-0\"> provide<\/span><span data-offset-key=\"b1iru-75-0\"> examples<\/span><span data-offset-key=\"b1iru-76-0\"> to<\/span><span data-offset-key=\"b1iru-77-0\"> illustrate<\/span><span data-offset-key=\"b1iru-78-0\"> the<\/span><span data-offset-key=\"b1iru-79-0\"> process<\/span><span data-offset-key=\"b1iru-80-0\">.<\/span><\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Fraction Subtraction<\/h3>\n<p>If [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]{\\Large\\frac{a}{c}}-{\\Large\\frac{b}{c}}={\\Large\\frac{a-b}{c}}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>To subtract fractions with a common denominators, we subtract the numerators and place the difference over the common denominator.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<p style=\"text-align: left;\">Find the difference:<\/p>\n<p style=\"text-align: center;\">[latex]{\\Large\\frac{23}{24}}-{\\Large\\frac{14}{24}}[\/latex]<\/p>\n<p><br>\n[reveal-answer q=\"969759\"]Show Answer[\/reveal-answer]<br>\n[hidden-answer a=\"969759\"]<\/p>\n<ol>\n\t<li>[latex]{\\Large\\frac{23}{24}}-{\\Large\\frac{14}{24}}[\/latex]<\/li>\n\t<li>Subtract the numerators and place the difference over the common denominator. [latex]{\\Large\\frac{23 - 14}{24}}[\/latex]<\/li>\n\t<li>Simplify the numerator. [latex]{\\Large\\frac{9}{24}}[\/latex]<\/li>\n\t<li>Simplify the fraction by removing common factors.<\/li>\n<\/ol>\n<p style=\"text-align: center;\">The answer is [latex]{\\Large\\frac{3}{8}}[\/latex]<\/p>\n<p>[\/hidden-answer]<\/p>\n<\/section>\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2788[\/ohm2_question]<\/section>\n<h2>Add or Subtract Fractions with Different Denominators<\/h2>\n<p>To add or subtract fractions with different denominators, we first must write them as equivalent fractions having the same denominator. We\u2019ll use the techniques from the previous section to find the LCM of the denominators of the fractions. Recall that we call this the LCD (the least common denominator).&nbsp;We only use the denominators of the fractions, not the numerators, when finding the LCD.<\/p>\n<p>Then we can use the Equivalent Fractions Property to algebraically change a fraction to an equivalent one. Remember, two fractions are equivalent if they have the same value. The steps for finding the LCD and the Equivalent Fractions Property are repeated below for reference.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Least Common Denominator<\/h3>\n<p>The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.<\/p>\n<p><br>\nEquivalent Fractions Property: If [latex]a,b,c[\/latex] are whole numbers where [latex]b\\ne 0,c\\ne 0,\\text{then}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]\\Large\\frac{a}{b}=\\Large\\frac{a\\cdot c}{b\\cdot c}\\normalsize\\text{ and }\\Large\\frac{a\\cdot c}{b\\cdot c}=\\Large\\frac{a}{b}[\/latex]<\/p>\n<\/div>\n<\/section>\n<p>Once we have converted two fractions to equivalent forms with common denominators, we can add or subtract them by adding or subtracting the numerators.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How to: Add or Subtract Fractions with Different Denominators<\/strong><\/p>\n<ol>\n\t<li><strong>Find the Least Common Denominator (LCD)<\/strong>: Identify the smallest number that both denominators can divide into evenly. This is the least common denominator.<\/li>\n\t<li><strong>Convert Each Fraction to an Equivalent Form with the LCD as the Denominator<\/strong>: For each fraction, determine what number you must multiply the denominator by to reach the LCD. Multiply both the numerator and denominator of the fraction by this number to create an equivalent fraction with the LCD.<\/li>\n\t<li><strong>Add or Subtract the Fractions<\/strong>: Now that both fractions have the same denominator, you can add or subtract the numerators directly. Keep the common denominator the same.<\/li>\n\t<li><strong>Write the Result in Simplified Form<\/strong>: If the numerator is larger than the denominator, you may need to convert it to a mixed number. Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2790[\/ohm2_question]<\/section>\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]2791[\/ohm2_question]<\/section>\n","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Add and subtract fractions<\/li>\n<\/ul>\n<\/section>\n<h2>Add Fractions with a Common Denominator<\/h2>\n<p><span data-offset-key=\"4m1mb-16-0\">Adding<\/span><span data-offset-key=\"4m1mb-17-0\"> fractions<\/span><span data-offset-key=\"4m1mb-18-0\"> with<\/span><span data-offset-key=\"4m1mb-19-0\"> the<\/span><span data-offset-key=\"4m1mb-20-0\"> same<\/span><span data-offset-key=\"4m1mb-21-0\"> denomin<\/span><span data-offset-key=\"4m1mb-22-0\">ator<\/span><span data-offset-key=\"4m1mb-23-0\"> is<\/span><span data-offset-key=\"4m1mb-24-0\"> a<\/span><span data-offset-key=\"4m1mb-25-0\"> straightforward<\/span><span data-offset-key=\"4m1mb-26-0\"> process<\/span><span data-offset-key=\"4m1mb-27-0\">.<\/span><span data-offset-key=\"4m1mb-28-0\"> The<\/span><span data-offset-key=\"4m1mb-29-0\"> numer<\/span><span data-offset-key=\"4m1mb-30-0\">ators<\/span><span data-offset-key=\"4m1mb-31-0\"> of<\/span><span data-offset-key=\"4m1mb-32-0\"> the<\/span><span data-offset-key=\"4m1mb-33-0\"> fractions<\/span><span data-offset-key=\"4m1mb-34-0\"> are<\/span><span data-offset-key=\"4m1mb-35-0\"> simply<\/span><span data-offset-key=\"4m1mb-36-0\"> added<\/span><span data-offset-key=\"4m1mb-37-0\"> together<\/span><span data-offset-key=\"4m1mb-38-0\"> to<\/span><span data-offset-key=\"4m1mb-39-0\"> get<\/span><span data-offset-key=\"4m1mb-40-0\"> the<\/span><span data-offset-key=\"4m1mb-41-0\"> numer<\/span><span data-offset-key=\"4m1mb-42-0\">ator<\/span><span data-offset-key=\"4m1mb-43-0\"> of<\/span><span data-offset-key=\"4m1mb-44-0\"> the<\/span><span data-offset-key=\"4m1mb-45-0\"> answer<\/span><span data-offset-key=\"4m1mb-46-0\">.<\/span><span data-offset-key=\"4m1mb-47-0\"> The<\/span><span data-offset-key=\"4m1mb-48-0\"> denomin<\/span><span data-offset-key=\"4m1mb-49-0\">ator<\/span><span data-offset-key=\"4m1mb-50-0\"> will<\/span><span data-offset-key=\"4m1mb-51-0\"> stay<\/span><span data-offset-key=\"4m1mb-52-0\"> the<\/span><span data-offset-key=\"4m1mb-53-0\"> same<\/span><span data-offset-key=\"4m1mb-54-0\">,<\/span><span data-offset-key=\"4m1mb-55-0\"> since<\/span><span data-offset-key=\"4m1mb-56-0\"> the<\/span><span data-offset-key=\"4m1mb-57-0\"> denomin<\/span><span data-offset-key=\"4m1mb-58-0\">ators<\/span><span data-offset-key=\"4m1mb-59-0\"> are<\/span><span data-offset-key=\"4m1mb-60-0\"> the<\/span><span data-offset-key=\"4m1mb-61-0\"> same<\/span><span data-offset-key=\"4m1mb-62-0\"> for<\/span><span data-offset-key=\"4m1mb-63-0\"> all<\/span><span data-offset-key=\"4m1mb-64-0\"> the<\/span><span data-offset-key=\"4m1mb-65-0\"> fractions<\/span><span data-offset-key=\"4m1mb-66-0\"> being<\/span><span data-offset-key=\"4m1mb-67-0\"> added<\/span><span data-offset-key=\"4m1mb-68-0\">.<\/span><span data-offset-key=\"4m1mb-69-0\"> In<\/span><span data-offset-key=\"4m1mb-70-0\"> this<\/span><span data-offset-key=\"4m1mb-71-0\"> section<\/span><span data-offset-key=\"4m1mb-72-0\">,<\/span><span data-offset-key=\"4m1mb-73-0\"> we<\/span><span data-offset-key=\"4m1mb-74-0\"> will<\/span><span data-offset-key=\"4m1mb-75-0\"> discuss<\/span><span data-offset-key=\"4m1mb-76-0\"> how<\/span><span data-offset-key=\"4m1mb-77-0\"> to<\/span><span data-offset-key=\"4m1mb-78-0\"> add<\/span><span data-offset-key=\"4m1mb-79-0\"> fractions<\/span><span data-offset-key=\"4m1mb-80-0\"> with<\/span><span data-offset-key=\"4m1mb-81-0\"> the<\/span><span data-offset-key=\"4m1mb-82-0\"> same<\/span><span data-offset-key=\"4m1mb-83-0\"> denomin<\/span><span data-offset-key=\"4m1mb-84-0\">ator<\/span><span data-offset-key=\"4m1mb-85-0\">,<\/span><span data-offset-key=\"4m1mb-86-0\"> and<\/span><span data-offset-key=\"4m1mb-87-0\"> also<\/span><span data-offset-key=\"4m1mb-88-0\"> look<\/span><span data-offset-key=\"4m1mb-89-0\"> at<\/span><span data-offset-key=\"4m1mb-90-0\"> a<\/span><span data-offset-key=\"4m1mb-91-0\"> few<\/span><span data-offset-key=\"4m1mb-92-0\"> examples<\/span><span data-offset-key=\"4m1mb-93-0\"> to<\/span><span data-offset-key=\"4m1mb-94-0\"> illustrate<\/span><span data-offset-key=\"4m1mb-95-0\"> the<\/span><span data-offset-key=\"4m1mb-96-0\"> process<\/span><span data-offset-key=\"4m1mb-97-0\">.<\/span><\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Fraction Addition<\/h3>\n<p>If [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then<\/p>\n<p>&nbsp;<\/p>\n<div style=\"text-align: center;\">[latex]\\Large\\frac{a}{c}\\normalsize+\\Large\\frac{b}{c}\\normalsize=\\Large\\frac{a+b}{c}[\/latex]<\/div>\n<p>&nbsp;<\/p>\n<p>To add fractions with a common denominators, add the numerators and place the sum over the common denominator.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<p style=\"text-align: left;\">Find the sum:<\/p>\n<p style=\"text-align: center;\">[latex]\\Large\\frac{3}{5}\\normalsize+\\Large\\frac{1}{5}[\/latex]<\/p>\n<p style=\"text-align: left;\">\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q760537\">Show Answer<\/button><\/p>\n<div id=\"q760537\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]\\Large\\frac{3}{5}\\normalsize+\\Large\\frac{1}{5}[\/latex]<\/li>\n<li>Add the numerators and place the sum over the common denominator. [latex]\\Large\\frac{3+1}{5}[\/latex]<\/li>\n<li>Simplify.<\/li>\n<\/ol>\n<p style=\"text-align: center;\">The answer is [latex]\\Large\\frac{4}{5}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2787\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2787&theme=lumen&iframe_resize_id=ohm2787&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h2>Subtract Fractions with a Common Denominator<\/h2>\n<p><span data-offset-key=\"b1iru-17-0\">Sub<\/span><span data-offset-key=\"b1iru-18-0\">t<\/span><span data-offset-key=\"b1iru-19-0\">ract<\/span><span data-offset-key=\"b1iru-20-0\">ing<\/span><span data-offset-key=\"b1iru-21-0\"> fractions<\/span><span data-offset-key=\"b1iru-22-0\"> with<\/span><span data-offset-key=\"b1iru-23-0\"> the<\/span><span data-offset-key=\"b1iru-24-0\"> same<\/span><span data-offset-key=\"b1iru-25-0\"> denomin<\/span><span data-offset-key=\"b1iru-26-0\">ator<\/span><span data-offset-key=\"b1iru-27-0\"> is<\/span><span data-offset-key=\"b1iru-28-0\"> a<\/span><span data-offset-key=\"b1iru-29-0\"> simple<\/span><span data-offset-key=\"b1iru-30-0\"> process<\/span><span data-offset-key=\"b1iru-31-0\">.<\/span><span data-offset-key=\"b1iru-32-0\"> When<\/span><span data-offset-key=\"b1iru-33-0\"> the<\/span><span data-offset-key=\"b1iru-34-0\"> denomin<\/span><span data-offset-key=\"b1iru-35-0\">ators<\/span><span data-offset-key=\"b1iru-36-0\"> are<\/span><span data-offset-key=\"b1iru-37-0\"> the<\/span><span data-offset-key=\"b1iru-38-0\"> same<\/span><span data-offset-key=\"b1iru-39-0\">,<\/span><span data-offset-key=\"b1iru-40-0\"> all<\/span><span data-offset-key=\"b1iru-41-0\"> you<\/span><span data-offset-key=\"b1iru-42-0\"> need<\/span><span data-offset-key=\"b1iru-43-0\"> to<\/span><span data-offset-key=\"b1iru-44-0\"> do<\/span><span data-offset-key=\"b1iru-45-0\"> is<\/span><span data-offset-key=\"b1iru-46-0\"> subtract<\/span><span data-offset-key=\"b1iru-47-0\"> the<\/span><span data-offset-key=\"b1iru-48-0\"> numer<\/span><span data-offset-key=\"b1iru-49-0\">ators<\/span><span data-offset-key=\"b1iru-50-0\"> to<\/span><span data-offset-key=\"b1iru-51-0\"> get<\/span><span data-offset-key=\"b1iru-52-0\"> the<\/span><span data-offset-key=\"b1iru-53-0\"> difference<\/span><span data-offset-key=\"b1iru-54-0\">.<\/span><span data-offset-key=\"b1iru-55-0\"> In<\/span><span data-offset-key=\"b1iru-56-0\"> this<\/span><span data-offset-key=\"b1iru-57-0\"> section<\/span><span data-offset-key=\"b1iru-58-0\">,<\/span><span data-offset-key=\"b1iru-59-0\"> we<\/span><span data-offset-key=\"b1iru-60-0\">&#8216;ll<\/span><span data-offset-key=\"b1iru-61-0\"> discuss<\/span><span data-offset-key=\"b1iru-62-0\"> the<\/span><span data-offset-key=\"b1iru-63-0\"> steps<\/span><span data-offset-key=\"b1iru-64-0\"> for<\/span><span data-offset-key=\"b1iru-65-0\"> subtract<\/span><span data-offset-key=\"b1iru-66-0\">ing<\/span><span data-offset-key=\"b1iru-67-0\"> fractions<\/span><span data-offset-key=\"b1iru-68-0\"> with<\/span><span data-offset-key=\"b1iru-69-0\"> the<\/span><span data-offset-key=\"b1iru-70-0\"> same<\/span><span data-offset-key=\"b1iru-71-0\"> denomin<\/span><span data-offset-key=\"b1iru-72-0\">ator<\/span><span data-offset-key=\"b1iru-73-0\"> and<\/span><span data-offset-key=\"b1iru-74-0\"> provide<\/span><span data-offset-key=\"b1iru-75-0\"> examples<\/span><span data-offset-key=\"b1iru-76-0\"> to<\/span><span data-offset-key=\"b1iru-77-0\"> illustrate<\/span><span data-offset-key=\"b1iru-78-0\"> the<\/span><span data-offset-key=\"b1iru-79-0\"> process<\/span><span data-offset-key=\"b1iru-80-0\">.<\/span><\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Fraction Subtraction<\/h3>\n<p>If [latex]a,b,\\text{ and }c[\/latex] are numbers where [latex]c\\ne 0[\/latex], then<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]{\\Large\\frac{a}{c}}-{\\Large\\frac{b}{c}}={\\Large\\frac{a-b}{c}}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p>To subtract fractions with a common denominators, we subtract the numerators and place the difference over the common denominator.<\/p>\n<\/div>\n<\/section>\n<section class=\"textbox example\">\n<p style=\"text-align: left;\">Find the difference:<\/p>\n<p style=\"text-align: center;\">[latex]{\\Large\\frac{23}{24}}-{\\Large\\frac{14}{24}}[\/latex]<\/p>\n<div class=\"wp-nocaption \"><\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><button class=\"show-answer show-answer-button collapsed\" data-target=\"q969759\">Show Answer<\/button><\/p>\n<div id=\"q969759\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]{\\Large\\frac{23}{24}}-{\\Large\\frac{14}{24}}[\/latex]<\/li>\n<li>Subtract the numerators and place the difference over the common denominator. [latex]{\\Large\\frac{23 - 14}{24}}[\/latex]<\/li>\n<li>Simplify the numerator. [latex]{\\Large\\frac{9}{24}}[\/latex]<\/li>\n<li>Simplify the fraction by removing common factors.<\/li>\n<\/ol>\n<p style=\"text-align: center;\">The answer is [latex]{\\Large\\frac{3}{8}}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2788\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2788&theme=lumen&iframe_resize_id=ohm2788&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<h2>Add or Subtract Fractions with Different Denominators<\/h2>\n<p>To add or subtract fractions with different denominators, we first must write them as equivalent fractions having the same denominator. We\u2019ll use the techniques from the previous section to find the LCM of the denominators of the fractions. Recall that we call this the LCD (the least common denominator).&nbsp;We only use the denominators of the fractions, not the numerators, when finding the LCD.<\/p>\n<p>Then we can use the Equivalent Fractions Property to algebraically change a fraction to an equivalent one. Remember, two fractions are equivalent if they have the same value. The steps for finding the LCD and the Equivalent Fractions Property are repeated below for reference.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>Least Common Denominator<\/h3>\n<p>The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.<\/p>\n<p>\nEquivalent Fractions Property: If [latex]a,b,c[\/latex] are whole numbers where [latex]b\\ne 0,c\\ne 0,\\text{then}[\/latex]<\/p>\n<p>&nbsp;<\/p>\n<p style=\"text-align: center;\">[latex]\\Large\\frac{a}{b}=\\Large\\frac{a\\cdot c}{b\\cdot c}\\normalsize\\text{ and }\\Large\\frac{a\\cdot c}{b\\cdot c}=\\Large\\frac{a}{b}[\/latex]<\/p>\n<\/div>\n<\/section>\n<p>Once we have converted two fractions to equivalent forms with common denominators, we can add or subtract them by adding or subtracting the numerators.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How to: Add or Subtract Fractions with Different Denominators<\/strong><\/p>\n<ol>\n<li><strong>Find the Least Common Denominator (LCD)<\/strong>: Identify the smallest number that both denominators can divide into evenly. This is the least common denominator.<\/li>\n<li><strong>Convert Each Fraction to an Equivalent Form with the LCD as the Denominator<\/strong>: For each fraction, determine what number you must multiply the denominator by to reach the LCD. Multiply both the numerator and denominator of the fraction by this number to create an equivalent fraction with the LCD.<\/li>\n<li><strong>Add or Subtract the Fractions<\/strong>: Now that both fractions have the same denominator, you can add or subtract the numerators directly. Keep the common denominator the same.<\/li>\n<li><strong>Write the Result in Simplified Form<\/strong>: If the numerator is larger than the denominator, you may need to convert it to a mixed number. Reduce the fraction to its simplest form by dividing both the numerator and denominator by their greatest common divisor (GCD).<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2790\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2790&theme=lumen&iframe_resize_id=ohm2790&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm2791\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=2791&theme=lumen&iframe_resize_id=ohm2791&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":6,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":241,"module-header":"","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\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/245"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":0,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/245\/revisions"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/parts\/241"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapters\/245\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/media?parent=245"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/pressbooks\/v2\/chapter-type?post=245"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/contributor?post=245"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/collegealgebrademo\/wp-json\/wp\/v2\/license?post=245"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}