{"id":156334,"date":"2022-03-26T01:38:28","date_gmt":"2022-03-25T20:08:28","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/rationalize-denominator-explanation-steps-calculator-and-faqs\/"},"modified":"2022-12-22T21:38:21","modified_gmt":"2022-12-22T16:08:21","slug":"rationalize-denominator-explanation-steps-calculator-and-faqs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/","title":{"rendered":"Rationalize Denominator &#8211; Explanation, Steps, Calculator and FAQs"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#How_to_Rationalize_the_Denominator\" title=\"How to Rationalize the Denominator?\">How to Rationalize the Denominator?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#What_is_a_Rational_Number\" title=\"What is a Rational Number?\">What is a Rational Number?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#What_is_a_Denominator\" title=\"What is a Denominator?\">What is a Denominator?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#How_to_Use_Rationalize_the_Denominator_Calculator\" title=\"How to Use Rationalize the Denominator Calculator?\">How to Use Rationalize the Denominator Calculator?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#What_is_Rationalization_of_a_Number\" title=\"What is Rationalization of a Number?\">What is Rationalization of a Number?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#Standard_Form\" title=\"Standard Form\">Standard Form<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#What_is_meant_by_rationalization\" title=\"What is meant by rationalization?\">What is meant by rationalization?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#What_is_meant_by_surds\" title=\"What is meant by surds?\">What is meant by surds?<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#Why_Rationalize_the_Denominator\" title=\"Why Rationalize the Denominator?\">Why Rationalize the Denominator?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#How_to_Rationalize_the_Denominator_with_One_Term\" title=\"How to Rationalize the Denominator with One Term?\">How to Rationalize the Denominator with One Term?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#How_to_Rationalize_the_Denominator_with_Two_Terms\" title=\"How to Rationalize the Denominator with Two Terms?\">How to Rationalize the Denominator with Two Terms?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/rationalize-denominator\/#How_to_Rationalize_the_Denominator_Calculator\" title=\"How to Rationalize the Denominator Calculator?\">How to Rationalize the Denominator Calculator?<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Rationalize_the_Denominator\"><\/span>How to Rationalize the Denominator?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In mathematics, rationalization is the process of converting a rational number into a form that is easier to work with. This can be done by multiplying the numerator and denominator by a common factor, or by using the quadratic formula.<\/p>\n<p>For example, the rational number 2\/3 can be rationalized by multiplying both the numerator and denominator by 3, resulting in the value 6\/9. Alternatively, the rational number 2\/3 can be rationalized by using the quadratic formula, which would result in the value 1\/2.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-156333 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/rationalize-denominator-explanation-steps-calculator-and-faqs.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/rationalize-denominator-explanation-steps-calculator-and-faqs.jpg?v=1648238907 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/rationalize-denominator-explanation-steps-calculator-and-faqs-300x212.jpg?v=1648238907 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Rational_Number\"><\/span>What is a Rational Number?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A rational number is a number that can be expressed as a fraction, with a numerator and a denominator. The numerator is the number on top, and the denominator is the number on the bottom. For example, the rational number 1\/2 can be written as the fraction 1\/2, or as the decimal 0.50. Rational numbers can also be expressed as decimals, percentages, and radicals.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Denominator\"><\/span>What is a Denominator?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A denominator is the number below the line in a fraction. It is the number of equal parts the whole is divided into.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Use_Rationalize_the_Denominator_Calculator\"><\/span>How to Use Rationalize the Denominator Calculator?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The procedure to rationalize the denominator calculator is as follows:<\/p>\n<p><strong>Step 1:<\/strong> Enter the numerator and the denominator value in the input field<\/p>\n<p><strong>Step 2:<\/strong> Now click the button \u201cRationalize Denominator\u201d to get the output<\/p>\n<p><strong>Step 3:<\/strong> The result will be displayed in the output field<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_is_Rationalization_of_a_Number\"><\/span>What is Rationalization of a Number?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Rationalization is the process of removing the imaginary numbers from the denominator of an algrabraic expressions. It is the method of moving the radical (i.e., square root or cube root) from the bottom (denominator) of the fraction to the top (numerator). To remove the radicals, multiply both the numerator and denominator by the conjugate of the denominator.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Standard_Form\"><\/span>Standard Form<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The standard form to represent the rationalization of a denominator is given as follows:<\/p>\n<p>Consider a fractional number, 1\/(a-\u221ab)<\/p>\n<p>The rationalized form of the number is written as<\/p>\n[1\/(a-\u221ab)] \u00d7 [(a+\u221ab) \/ (a+\u221ab)]\n<p>Rationalized Form= [(a+\u221ab) \/ (a<sup>2<\/sup> -b)]\n<div id=\"Frequently-Asked-Questions-on-Rationalize-The-Denominator\" class=\"faq-section mb30\">\n<div class=\"faq-schema\">\n<div>\n<section>\n<h3><span class=\"ez-toc-section\" id=\"What_is_meant_by_rationalization\"><\/span><span style=\"font-size: 18pt;\">What is meant by rationalization?<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div>\n<div>\n<p>Rationalization in Maths is the process of removing the radical or imaginary number from the denominator of a fraction. This method is also known as rationalizing the denominator. Rationalizing is a mental process that involves making excuses for bad behavior or poor decisions. It can also involve convincing oneself that a wrong decision was the right one.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section>\n<h3><span class=\"ez-toc-section\" id=\"What_is_meant_by_surds\"><\/span><span style=\"font-size: 18pt;\">What is meant by surds?<\/span><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div>\n<div>\n<p>A fraction contains two parts. One is the numerator, and the other is a denominator. The number i.e., square root or cube root that cannot be simplified further is called surd. The surd may be either numerator or denominator.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Why_Rationalize_the_Denominator\"><\/span>Why Rationalize the Denominator?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A rational denominator is simply a fraction where the numerator and denominator are both integers. This makes it much easier to work with fractions, and it also makes it easier to compare fractions. For example, the fraction 5\/8 is much easier to compare to the fraction 7\/12 than the fraction 5\/9. This is because 5\/8 is closer to 1\/2 (which is also a rational number) than 5\/9 is.<\/p>\n<p>There are a few reasons why it might be important to rationalize the denominator. One reason is that it can make calculations with fractions much easier. Another reason is that it can help us to compare fractions more easily. Finally, rationalizing the denominator can also help us to understand fractions better.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Rationalize_the_Denominator_with_One_Term\"><\/span>How to Rationalize the Denominator with One Term?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are a few different ways to rationalize the denominator with one term. One way is to use the distributive property. Another way is to use the multiplication property of equality. Lastly, you can use the addition property of equality.<\/p>\n<p>The distributive property states that for any real numbers a, b, and c, a(b+c) = ab+ac. This property can be used to rationalize the denominator with one term. For example, if you have the fraction \\(\\frac{2}{3}\\), you can rationalize the denominator by multiplying both the numerator and the denominator by 3. This gives you the fraction \\(\\frac{6}{9}\\).<\/p>\n<p>The multiplication property of equality states that for any real numbers a and b, a(b+c) = ab+ac. This property can also be used to rationalize the denominator with one term. For example, if you have the fraction \\(\\frac{1}{2}\\), you can rationalize the denominator by multiplying both the numerator and the denominator by 2. This gives you the fraction \\(\\frac{2}{4}\\).<\/p>\n<p>The addition property of equality states that for any real numbers a and b, a+b = b+a. This property can also be used to rationalize the denominator with one term. For example, if you have the fraction \\(\\frac{1}{3}\\), you can rationalize the denominator by adding both the numerator and the denominator. This gives you the fraction \\(\\frac{2}{3}\\).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Rationalize_the_Denominator_with_Two_Terms\"><\/span>How to Rationalize the Denominator with Two Terms?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A rational number is a number that can be expressed as a fraction where the numerator and the denominator are both integers. A rational number can also be expressed as a decimal where the decimal point is placed between the integer and the fractional parts. In order to rationalize the denominator with one term, the denominator must be a monomial. A monomial is a polynomial with a single term. The most common way to rationalize the denominator with one term is to divide the numerator by the denominator.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Rationalize_the_Denominator_Calculator\"><\/span>How to Rationalize the Denominator Calculator?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A denominator calculator is a mathematical tool used to simplify the process of dividing fractions. The calculator automates the division process by dividing the numerator (top number) of one fraction by the denominator (bottom number) of another fraction. This tool is especially helpful for students who are new to fractions and division.<\/p>\n<p>To use the denominator calculator, enter the numerator and denominator of the two fractions into the designated fields. The calculator will automatically divide the numerator by the denominator and display the result.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How to Rationalize the Denominator? In mathematics, rationalization is the process of converting a rational number into a form that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Rationalize Denominator - Explanation, Steps, Calculator and FAQs","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about rationalize denominator topic of maths in details explained by subject experts on infinitylearn.com. 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