{"id":156390,"date":"2022-03-26T01:42:13","date_gmt":"2022-03-25T20:12:13","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/multiplicative-inverse\/"},"modified":"2024-09-20T14:46:17","modified_gmt":"2024-09-20T09:16:17","slug":"multiplicative-inverse","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/","title":{"rendered":"Multiplicative Inverse &#8211; Infinity Learn"},"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\/multiplicative-inverse\/#What_is_the_Multiplicative_Inverse\" title=\"What is the Multiplicative Inverse?\">What is the Multiplicative Inverse?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/#Multiplicative_Inverse_of_Integers\" title=\"Multiplicative Inverse of Integers\">Multiplicative Inverse of Integers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/#Multiplicative_Inverse_of_a_Mixed_Fraction\" title=\"Multiplicative Inverse of a Mixed Fraction\">Multiplicative Inverse of a Mixed Fraction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/#Multiplicative_Inverse_of_0\" title=\"Multiplicative Inverse of 0\">Multiplicative Inverse of 0<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/#Multiplicative_Inverse_Property\" title=\"Multiplicative Inverse Property\">Multiplicative Inverse Property<\/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\/multiplicative-inverse\/#How_to_Find_the_Multiplicative_Inverse\" title=\"How to Find the Multiplicative Inverse?\">How to Find the Multiplicative Inverse?<\/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\/multiplicative-inverse\/#Additive_Inverse_and_Multiplicative_Inverse\" title=\"Additive Inverse and Multiplicative Inverse\">Additive Inverse and Multiplicative Inverse<\/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\/multiplicative-inverse\/#Multiplicative_Inverse_Solved_Examples\" title=\"Multiplicative Inverse: Solved Examples\">Multiplicative Inverse: Solved Examples<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/#Multiplicative_Inverse_Practice_Questions\" title=\"Multiplicative Inverse: Practice Questions\">Multiplicative Inverse: Practice Questions<\/a><\/li><\/ul><\/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\/multiplicative-inverse\/#Multiplicative_Inverse_FAQs\" title=\"Multiplicative Inverse FAQs\">Multiplicative Inverse FAQs<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/#What_is_the_multiplicative_inverse_of_a_number\" title=\"What is the multiplicative inverse of a number?\">What is the multiplicative inverse of a number?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/#How_do_you_find_the_multiplicative_inverse_of_a_fraction\" title=\"How do you find the multiplicative inverse of a fraction?\">How do you find the multiplicative inverse of a fraction?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/multiplicative-inverse\/#Can_the_multiplicative_inverse_of_0_be_defined\" title=\"Can the multiplicative inverse of 0 be defined?\">Can the multiplicative inverse of 0 be defined?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>The multiplicative inverse of a number is its reciprocal. In simple terms, the multiplicative inverse of a number is the number you multiply it by to get a product of 1. For example, the multiplicative inverse of 5 is 1\/5 because 5 \u00d7 1\/5 = 1.<\/p>\n<p>The term &#8220;inverse&#8221; refers to something that counters the effect of the original. When applied to multiplication, it means multiplying a number by its multiplicative inverse will always result in 1.<\/p>\n<p>In this article, we will study about multiplicative inverse of a number, its examples, properties and more.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_the_Multiplicative_Inverse\"><\/span>What is the Multiplicative Inverse?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The multiplicative inverse of a number is the value you multiply the original number by to get a product of 1. It is often called the reciprocal of the number. If you have a number &#8220;a&#8221;, its multiplicative inverse is written as 1\/a or a\u207b\u00b9.<\/p>\n<p>Two numbers are considered multiplicative inverses of each other if their product is 1. For example, for the number 3, its multiplicative inverse is 1\/3 because 3 \u00d7 1\/3 = 1. Similarly, the multiplicative inverse of 110 is 1\/110 because 110 \u00d7 1\/110 = 1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Multiplicative_Inverse_of_Integers\"><\/span>Multiplicative Inverse of Integers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The concept of the multiplicative inverse applies similarly to integers, both positive and negative.<\/p>\n<ul>\n<li><strong>Natural Numbers:<\/strong> These are positive integers starting from 1. For a natural number &#8220;a&#8221;, its multiplicative inverse is 1\/a. For instance, the multiplicative inverse of 5 is 1\/5 because 5 \u00d7 1\/5 = 1.<\/li>\n<li><strong>Fractions:<\/strong> The reciprocal of a fraction like 2\/3 is 3\/2. Multiplying 2\/3 by its reciprocal 3\/2 results in 1.<\/li>\n<li><strong>Negative Numbers:<\/strong> The multiplicative inverse of a negative number works the same way. For example, the multiplicative inverse of -4 is 1\/-4 because -4 \u00d7 1\/-4 = 1.<\/li>\n<li><strong>Unit Fractions:<\/strong> A unit fraction is a fraction with a numerator of 1. To find the multiplicative inverse of a unit fraction 1\/x, simply take x as the result. For example,\n<ul>\n<li>The multiplicative inverse of 1\/7 is 7 because 1\/7 \u00d7 7 = 1.<\/li>\n<li>The multiplicative inverse of 1\/50 is 50, since 1\/50 x 50 = 1.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-school-prep?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/one-stop-solution-for-school-exam.jpg\" alt=\"one-stop-solutions school exam\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/one-stop-solution-for-school-exam.jpg\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/one-stop-solutions-for-school-prep?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>One Stop Solutions for School Exam Preparation<\/strong><\/button><\/a><\/p>\n<div style=\"text-align: center;\">Boost your school preparation with our comprehensive guide for CBSE, ICSE, and State Board exams. Get all the resources you need in one place and excel in your academic journey. Discover the ultimate one-stop solution at Infinity Learn today!<\/div>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"Multiplicative_Inverse_of_a_Mixed_Fraction\"><\/span>Multiplicative Inverse of a Mixed Fraction<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>To find the multiplicative inverse of a mixed fraction, follow these steps:<\/p>\n<ol>\n<li><strong>Convert the Mixed Fraction to an Improper Fraction:<\/strong> First, transform the mixed fraction into an improper fraction. For example, for 3 1\/2, convert it to 7\/2.<\/li>\n<li><strong>Find the Reciprocal:<\/strong> Determine the reciprocal of the improper fraction. For 7\/2, the reciprocal is 2\/7. So, Multiplicative Inverse of 3x 1\/2, the reciprocal is 2\/7 therefore, 7\/2 x 2\/7 = 1<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Multiplicative_Inverse_of_0\"><\/span>Multiplicative Inverse of 0<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The multiplicative inverse of a number is defined as the value that, when multiplied by the original number, gives out a product of 1. However, for the number 0, this concept does not apply.this is because multiplying 0 by any number always results in 0, not 1. Hence, there is no number that you can multiply by 0 to get a product of 1.<\/p>\n<p>The concept of the multiplicative inverse involves division. The multiplicative inverse of 0 would be represented as 1\/0. However, division by zero is undefined in mathematics because it does not result in a finite or meaningful number.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Multiplicative_Inverse_Property\"><\/span>Multiplicative Inverse Property<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The multiplicative inverse property is a fundamental concept in mathematics. It states that the product of a number and its reciprocal or multiplicative inverse is always equal to 1.<\/p>\n<ul>\n<li>If you have a number &#8220;n&#8221;, its multiplicative inverse is 1\/n.<\/li>\n<li>According to the property, when you multiply &#8220;n&#8221; by its multiplicative inverse 1\/n, the result will be 1. In other words, n x 1\/n = 1.<\/li>\n<\/ul>\n<p>For example: The multiplicative inverse of 4 is 1\/4. Multiplying them together, we get 4 \u00d7 1\/4 = 1.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"How_to_Find_the_Multiplicative_Inverse\"><\/span>How to Find the Multiplicative Inverse?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Finding the multiplicative inverse or reciprocal of a number is simple. Follow these steps:<\/p>\n<ol>\n<li>If the number is not already in fraction form, convert it to a fraction. For example, if the number is 5, express it as 5\/1.<\/li>\n<li>Swap the numerator and the denominator of the fraction. If the fraction is a\/b, its multiplicative inverse is b\/a.<\/li>\n<li>Simplify the fraction if necessary.<\/li>\n<\/ol>\n<h3><span class=\"ez-toc-section\" id=\"Additive_Inverse_and_Multiplicative_Inverse\"><\/span>Additive Inverse and Multiplicative Inverse<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>There are two properties of numbers: the additive inverse and the multiplicative inverse. These properties are related to addition and multiplication, respectively.<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td style=\"text-align: center;\"><strong>Additive Inverse<\/strong><\/td>\n<td style=\"text-align: center;\"><strong>Multiplicative Inverse<\/strong><\/td>\n<\/tr>\n<tr>\n<td>To find the additive inverse of a number, change the sign of the number.<\/td>\n<td>To find the multiplicative inverse, take the reciprocal of the number.<\/td>\n<\/tr>\n<tr>\n<td>The additive inverse is added to the original number to get 0.<\/td>\n<td>The multiplicative inverse is multiplied by the original number to get 1.<\/td>\n<\/tr>\n<tr>\n<td>For any number &#8220;n&#8221;, the equation for additive inverse is: n + (-n) = 0.<\/td>\n<td>For any number &#8220;n&#8221;, the equation for multiplicative inverse is: n \u00d7 1\/n = 1.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"Multiplicative_Inverse_Solved_Examples\"><\/span>Multiplicative Inverse: Solved Examples<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>Ques: Find the multiplicative inverse of 9.<\/strong><\/p>\n<p><strong>Answer:<\/strong> The multiplicative inverse of 9 is 1\/9.<\/p>\n<p><strong>Ques: Find the multiplicative inverse of 6 1\/3.<\/strong><\/p>\n<p><strong>Answer:<\/strong> The improper fraction of 6 1\/3 is 19\/3. Therefore, the multiplicative inverse of 6 1\/3 is 3\/19.<\/p>\n<p><strong>Ques: Find the multiplicative inverse of 187.<\/strong><\/p>\n<p><strong>Answer:<\/strong> The multiplicative inverse of 187 is 1\/187.<\/p>\n<div class=\"card\" style=\"text-align: center;\"><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-mock-tests?utm_source=surge&amp;utm_medium=interlinking\"><br \/>\n<img loading=\"lazy\" class=\" lazyloaded\" style=\"width: 100%; border-radius: 10px;\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/cvc.png\" alt=\"online mock test\" width=\"1201\" height=\"636\" data-src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2024\/09\/cvc.png\" \/><\/a><a class=\"btn btn-primary\" href=\"https:\/\/infinitylearn.com\/online-mock-tests?utm_source=surge&amp;utm_medium=interlinking\"><button><strong>Online Mock Test<\/strong><\/button><\/a><\/p>\n<div style=\"text-align: center;\">Boost Your Preparation With Our Free Online Mock Tests For IIT-JEE, NEET And CBSE Exams<\/div>\n<\/div>\n<h3><span class=\"ez-toc-section\" id=\"Multiplicative_Inverse_Practice_Questions\"><\/span>Multiplicative Inverse: Practice Questions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>Find the multiplicative inverse of 7\/9.<\/li>\n<li>What is the multiplicative inverse of 12?<\/li>\n<li>Determine the multiplicative inverse of 4&#215;1\/2.<\/li>\n<li>Find the multiplicative inverse of the complex number 2 \u2212 3i.<\/li>\n<li>Find the modular multiplicative inverse of 7 x 5\/11.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Multiplicative_Inverse_FAQs\"><\/span>Multiplicative Inverse FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_multiplicative_inverse_of_a_number\"><\/span>What is the multiplicative inverse of a number?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe multiplicative inverse of a number x is another number that, when multiplied by x, yields a product of 1. It is also known as the reciprocal of x. For example, the multiplicative inverse of 4 is <sup>1<\/sup>\u2044<sub>4<\/sub>, because 4 \u00d7 <sup>1<\/sup>\u2044<sub>4<\/sub> = 1.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_find_the_multiplicative_inverse_of_a_fraction\"><\/span>How do you find the multiplicative inverse of a fraction?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTo find the multiplicative inverse of a fraction <sup>a<\/sup>\u2044<sub>b<\/sub>, simply flip the numerator and the denominator. The multiplicative inverse of <sup>a<\/sup>\u2044<sub>b<\/sub> is <sup>b<\/sup>\u2044<sub>a<\/sub>\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Can_the_multiplicative_inverse_of_0_be_defined\"><\/span>Can the multiplicative inverse of 0 be defined?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tNo, the multiplicative inverse of 0 is not defined. Since multiplying 0 by any number always results in 0.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the multiplicative inverse of a number?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The multiplicative inverse of a number x is another number that, when multiplied by x, yields a product of 1. It is also known as the reciprocal of x. For example, the multiplicative inverse of 4 is 1\u20444, because 4 \u00d7 1\u20444 = 1.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you find the multiplicative inverse of a fraction?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"To find the multiplicative inverse of a fraction a\u2044b, simply flip the numerator and the denominator. The multiplicative inverse of a\u2044b is b\u2044a\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Can the multiplicative inverse of 0 be defined?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"No, the multiplicative inverse of 0 is not defined. Since multiplying 0 by any number always results in 0.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>The multiplicative inverse of a number is its reciprocal. In simple terms, the multiplicative inverse of a number is the [&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":"Multiplicative Inverse - Infinity Learn","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"A multiplicative inverse for a number a is a number b such that ab = 1. 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