{"id":839837,"date":"2024-08-09T13:57:40","date_gmt":"2024-08-09T08:27:40","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=839837"},"modified":"2024-08-09T13:57:40","modified_gmt":"2024-08-09T08:27:40","slug":"exam-prep-additive-inverse","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/","title":{"rendered":"Additive Inverse: Definition, Properties, Formulas, and Solved Examples"},"content":{"rendered":"\n<p>The additive inverse is a fundamental concept in mathematics, particularly in <a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-algebraic-identities\/\"><strong>algebra<\/strong><\/a> and number theory. It refers to a number that, when added to a given number, results in zero. This concept is important for solving equations and understanding the structure of various mathematical systems. In this blog, we will understand the definition of the additive inverse, explore its essential properties, and important formulas, and work through solved examples to solve its practical applications.<\/p>\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-definition-of-additive-inverse\">Definition of Additive Inverse<\/h2>\n\n\n\n<p>The additive inverse of a number is a value that, when added to the original number, results in zero. This concept is essential in various branches of mathematics, particularly in algebra, where it plays a key role in solving equations and understanding numerical structures.<\/p>\n\n\n\n<p>For any given number aaa, its additive inverse is \u2212a. Mathematically, this can be expressed as:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>a+(\u2212a) = 0<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Existence<\/strong>: Every real number has an additive inverse. For any number a, there exists a number \u2212a such that:&nbsp;<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>a+(\u2212a) = 0<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>Uniqueness<\/strong>: The additive inverse of a number is unique. For any number a, there is only one number \u2212a that satisfies the equation:&nbsp;<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>a+(\u2212a) = 0<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>Additive Inverse of Zero<\/strong>: The additive inverse of zero is zero itself:&nbsp;<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>0+0 = 0<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><strong>Double Inverse<\/strong>: The additive inverse of the additive inverse of a number is the number itself:&nbsp;<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>\u2212(\u2212a) = a<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"5\">\n<li><strong>Inverse of a Sum<\/strong>: The additive inverse of the sum of two numbers is equal to the sum of their additive inverses:&nbsp;<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>\u2212(a+b) = \u2212a + (\u2212b)<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"6\">\n<li><strong>Distributive Property<\/strong>: The additive inverse distributes over addition:&nbsp;<\/li>\n<\/ol>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><strong>\u2212(a+b) = \u2212a \u2212b<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center has-electric-grass-gradient-background has-background has-medium-font-size\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-division-of-algebraic-expressions\/\"><strong>Division of Algebraic Expressions<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-properties-of-additive-inverse\">Properties of Additive Inverse<\/h2>\n\n\n\n<p>The additive inverse of a number is an important concept in mathematics, particularly in algebra. Here, we explore the properties of additive inverses along with examples to illustrate each property.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Existence of Additive Inverse<\/strong>:\n<ul class=\"wp-block-list\">\n<li>For every real number aaa, there exists an additive inverse \u2212a such that a+(\u2212a) = 0.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For a=5, the additive inverse is \u22125, since 5+(\u22125)=0.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Uniqueness<\/strong>:\n<ul class=\"wp-block-list\">\n<li>The additive inverse of a number is unique. For any number aaa, there is only one number \u2212a that satisfies a+(\u2212a) = 0.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For a=\u22127, the additive inverse is 7, and there is no other number that will satisfy \u22127+x = 0 except x=7.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Additive Inverse of Zero<\/strong>:\n<ul class=\"wp-block-list\">\n<li>The additive inverse of zero is zero itself: 0+0 = 0.<\/li>\n\n\n\n<li><strong>Example<\/strong>: 0 has an additive inverse of 0, since 0+0 = 0.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Double Inverse<\/strong>:\n<ul class=\"wp-block-list\">\n<li>The additive inverse of the additive inverse of a number is the number itself: \u2212(\u2212a) = a.<\/li>\n\n\n\n<li><strong>Example<\/strong>: If a = 3, the additive inverse is \u22123. The additive inverse of \u22123 is 3, so \u2212(\u22123) = 3.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Inverse of a Sum<\/strong>:\n<ul class=\"wp-block-list\">\n<li>The additive inverse of the sum of two numbers is equal to the sum of their additive inverses: \u2212(a+b) = \u2212a+(\u2212b).<\/li>\n\n\n\n<li><strong>Example<\/strong>: For a=4 and b=\u22126, the additive inverse of 4+(\u22126)=\u22122 is 2. This is the same as \u22124+6 = 2.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Distributive Property<\/strong>:\n<ul class=\"wp-block-list\">\n<li>The additive inverse distributes over addition: \u2212(a+b) = \u2212a\u2212b.<\/li>\n\n\n\n<li><strong>Example<\/strong>: For a=2 and b=5, \u2212(2+5)=\u22127. Distributing the additive inverse gives \u22122\u22125 = \u22127.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Additive Inverse in Subtraction<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Subtraction can be interpreted using additive inverses: a\u2212b = a+(\u2212b).<\/li>\n\n\n\n<li><strong>Example<\/strong>: For a=8 and b=3, 8\u22123=8+(\u22123) = 5.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-additive-inverse-solved-examples\">Additive Inverse Solved Examples<\/h2>\n\n\n\n<p>Here are five solved examples to illustrate the concept of the additive inverse:<\/p>\n\n\n\n<p><strong>Example 1: Finding the Additive Inverse of a Positive Number<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> What is the additive inverse of 7?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>The additive inverse of 7 is \u22127 because: 7+(\u22127) = 0<\/p>\n\n\n\n<p><strong>Example 2: Finding the Additive Inverse of a Negative Number<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> What is the additive inverse of \u221212?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>The additive inverse of \u221212 is 12 because: \u221212+12 = 0<\/p>\n\n\n\n<p><strong>Example 3: Using the Additive Inverse in an Equation<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> Solve the equation x+9 = 0.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>To solve for x, we need to find the additive inverse of 9, which is \u22129: x=\u22129 Check: \u22129+9 = 0<\/p>\n\n\n\n<p><strong>Example 4: Additive Inverse of a Fraction<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> What is the additive inverse of 5\/8?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>The additive inverse of 5\/8\u200b is \u22125\/8\u200b because: 5\/8+(\u22125\/8) = 0<\/p>\n\n\n\n<p><strong>Example 5: Applying the Additive Inverse to Solve a Real-World Problem<\/strong><\/p>\n\n\n\n<p><strong>Problem:<\/strong> If the temperature is 15\u2218C and it drops by 15\u2218C, what is the final temperature?<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong><br><\/strong>The temperature drop is the additive inverse of 15\u2218C, which is \u221215\u2218C. Therefore, the final temperature is: 15\u2218C+(\u221215\u2218C) = 0<\/p>\n\n\n\n<p class=\"has-text-align-center has-electric-grass-gradient-background has-background\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-reciprocal\/\"><strong>Reciprocal: Definition, Meaning, Properties, and Solved Examples<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-faqs\">FAQs<\/h2>\n\n\n\n<div class=\"schema-faq wp-block-yoast-faq-block\"><div class=\"schema-faq-section\" id=\"faq-question-1723185846367\"><strong class=\"schema-faq-question\">What is the additive inverse of \u2212 7?<\/strong> <p class=\"schema-faq-answer\">The additive inverse of -7 is 7. When added together, -7 and 7 equal 0.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1723185857676\"><strong class=\"schema-faq-question\">What is the additive inverse of 12?<\/strong> <p class=\"schema-faq-answer\">The additive inverse of 12 is -12. When added together, they equal zero.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1723185872616\"><strong class=\"schema-faq-question\">What is the additive inverse of 11 \/- 15?<\/strong> <p class=\"schema-faq-answer\">The additive inverse of 11\/-15 is 15\/11. When added together, they equal zero.<\/p> <\/div> <\/div>\n\n\n\n<p>This was all about \u201c<strong>Additive Inverse<\/strong>\u201d. For more such informative blogs, check out our<a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/study-material\/\"> Study Material Section<\/a>, or you can learn more about us by visiting our<a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/\">&nbsp; Indian exams<\/a> page.<\/p>\n","protected":false},"excerpt":{"rendered":"The additive inverse is a fundamental concept in mathematics, particularly in algebra and number theory. It refers to&hellip;\n","protected":false},"author":115,"featured_media":839848,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[369,476,396],"tags":[],"class_list":{"0":"post-839837","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-indian-exams","8":"category-maths","9":"category-study-material"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Additive Inverse: Definition, Properties, Formulas, and Solved Examples - Leverage Edu Discover<\/title>\n<meta name=\"description\" content=\"Read this article on Additive Inverse.Learn more about how to solve questions related to it easily in no time.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Additive Inverse: Definition, Properties, Formulas, and Solved Examples\" \/>\n<meta property=\"og:description\" content=\"Read this article on Additive Inverse.Learn more about how to solve questions related to it easily in no time.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/\" \/>\n<meta property=\"og:site_name\" content=\"Leverage Edu Discover\" \/>\n<meta property=\"article:published_time\" content=\"2024-08-09T08:27:40+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogassets.leverageedu.com\/media\/uploads\/sites\/9\/2024\/08\/15080911\/Additive-Inverse-1.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"640\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Mohit Rajak\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mohit Rajak\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Additive Inverse: Definition, Properties, Formulas, and Solved Examples - 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I find peace and purpose in crafting verses that dance between the lines of poetry. With my pen as my wand, I weave intricate tales and heartfelt musings, breathing life into the blank canvas of each page. Blogging is my window to the world way of sharing thoughts, emotions, and a perspective uniquely my own. Every word I write is a brushstroke in the ever-evolving painting of my literary journey.","sameAs":["https:\/\/www.instagram.com\/xx_a.m.strings_xiv\/","https:\/\/www.linkedin.com\/in\/mohit-rajak-a9a5a2162\/"],"url":"https:\/\/leverageedu.com\/discover\/author\/mohit\/"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/#faq-question-1723185846367","position":1,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/#faq-question-1723185846367","name":"What is the additive inverse of \u2212 7?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"The additive inverse of -7 is 7. When added together, -7 and 7 equal 0.","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/#faq-question-1723185857676","position":2,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/#faq-question-1723185857676","name":"What is the additive inverse of 12?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"The additive inverse of 12 is -12. When added together, they equal zero.","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/#faq-question-1723185872616","position":3,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-additive-inverse\/#faq-question-1723185872616","name":"What is the additive inverse of 11 \/- 15?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"The additive inverse of 11\/-15 is 15\/11. When added together, they equal zero.","inLanguage":"en-US"},"inLanguage":"en-US"}]}},"acf":[],"_links":{"self":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/839837","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/users\/115"}],"replies":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/comments?post=839837"}],"version-history":[{"count":0,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/839837\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media\/839848"}],"wp:attachment":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media?parent=839837"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/categories?post=839837"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/tags?post=839837"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}