{"id":228605,"date":"2024-03-29T05:12:36","date_gmt":"2024-03-29T05:12:36","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=228605"},"modified":"2024-03-29T05:12:36","modified_gmt":"2024-03-29T05:12:36","slug":"what-is-true-about-absolute-value","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/","title":{"rendered":"What is true about absolute value?"},"content":{"rendered":"<p>In mathematics, the absolute value of a number is its distance from zero on the number line. It is denoted by enclosing the number within vertical bars or using the &#8216;|&#8217; symbol. The absolute value function transforms any real number to its non-negative counterpart, considering only magnitude and disregarding its sign. Understanding the true properties of absolute value is crucial in various mathematical operations and problem-solving. Let&#8217;s explore what is true about absolute value.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_62 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\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#What_is_true_about_absolute_value\" title=\"What is true about absolute value?\">What is true about absolute value?<\/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:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#FAQs\" title=\"FAQs:\">FAQs:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#1_What_is_the_absolute_value_of_-5\" title=\"1. What is the absolute value of -5?\">1. What is the absolute value of -5?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#2_Can_the_absolute_value_of_a_number_be_negative\" title=\"2. Can the absolute value of a number be negative?\">2. Can the absolute value of a number be negative?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#3_What_is_the_absolute_value_of_0\" title=\"3. What is the absolute value of 0?\">3. What is the absolute value of 0?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#4_Is_-7_less_than_its_absolute_value\" title=\"4. Is -7 less than its absolute value?\">4. Is -7 less than its absolute value?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#5_Is_the_absolute_value_function_linear\" title=\"5. Is the absolute value function linear?\">5. Is the absolute value function linear?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#6_What_is_the_absolute_value_of_the_product_of_two_positive_numbers\" title=\"6. What is the absolute value of the product of two positive numbers?\">6. What is the absolute value of the product of two positive numbers?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#7_Is_the_absolute_value_function_differentiable\" title=\"7. Is the absolute value function differentiable?\">7. Is the absolute value function differentiable?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#8_What_is_the_absolute_value_of_a_positive_fraction\" title=\"8. What is the absolute value of a positive fraction?\">8. What is the absolute value of a positive fraction?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#9_Does_the_absolute_value_of_a_number_change_when_squared\" title=\"9. Does the absolute value of a number change when squared?\">9. Does the absolute value of a number change when squared?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#10_Can_the_absolute_value_of_a_number_be_imaginary\" title=\"10. Can the absolute value of a number be imaginary?\">10. Can the absolute value of a number be imaginary?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#11_Can_the_absolute_value_of_a_number_be_zero\" title=\"11. Can the absolute value of a number be zero?\">11. Can the absolute value of a number be zero?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#12_How_is_the_absolute_value_used_in_solving_equations\" title=\"12. How is the absolute value used in solving equations?\">12. How is the absolute value used in solving equations?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_true_about_absolute_value\"><\/span><b>What is true about absolute value?<\/b><span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The absolute value of a real number is always non-negative.<\/p>\n<p>The absolute value of a number obeys the triangle inequality, which states that |a + b| \u2264 |a| + |b| for any real numbers a and b.<\/p>\n<p>The absolute value of zero is zero; |0| = 0.<\/p>\n<p>The absolute value of a positive number is the number itself; |a| = a if a > 0.<\/p>\n<p>The absolute value of a negative number is its positive counterpart; |a| = -a if a < 0.\n\n\nThe absolute value function is symmetrical; it remains unchanged when the sign of the number changes; |-a| = |a| for any real number a.\n\n\nThe absolute value of a product is the product of the absolute values of the individual factors; |a * b| = |a| * |b|.\n\n\nThe absolute value of a quotient is the quotient of the absolute values of the numerator and denominator; |a \/ b| = |a| \/ |b| if b \u2260 0.\n\n\nThe absolute value of a sum is less than or equal to the sum of the absolute values of the individual terms; |a + b| \u2264 |a| + |b|.\n\n\nThe absolute value of a difference is greater than or equal to the absolute value of the individual terms; |a &#8211; b| \u2265 |a| &#8211; |b|.\n\n\nThe absolute value of a number is equal to its square root when squared; |a| = \u221a(a^2) for any real number a.\n\n\nThe absolute value of a number can be interpreted as the magnitude or the distance from zero.\n\n\nThe true properties of absolute value make it an invaluable tool in solving equations, inequalities, and various mathematical problems. Its ability to isolate the magnitude of a number, regardless of sign, provides a useful framework for understanding numerical relationships.\n\n\n\n\n<h3><span class=\"ez-toc-section\" id=\"FAQs\"><\/span>FAQs:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<h3><span class=\"ez-toc-section\" id=\"1_What_is_the_absolute_value_of_-5\"><\/span>1. What is the absolute value of -5?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe absolute value of -5 is 5. <\/p>\n<h3><span class=\"ez-toc-section\" id=\"2_Can_the_absolute_value_of_a_number_be_negative\"><\/span>2. Can the absolute value of a number be negative?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the absolute value of a number is always non-negative.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"3_What_is_the_absolute_value_of_0\"><\/span>3. What is the absolute value of 0?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe absolute value of 0 is 0.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"4_Is_-7_less_than_its_absolute_value\"><\/span>4. Is -7 less than its absolute value?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, -7 is greater than its absolute value, which is 7.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"5_Is_the_absolute_value_function_linear\"><\/span>5. Is the absolute value function linear?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the absolute value function is not linear due to its kink at the origin.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"6_What_is_the_absolute_value_of_the_product_of_two_positive_numbers\"><\/span>6. What is the absolute value of the product of two positive numbers?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe absolute value of the product of two positive numbers is the product itself.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"7_Is_the_absolute_value_function_differentiable\"><\/span>7. Is the absolute value function differentiable?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the absolute value function is not differentiable at zero due to the sharp corner in its graph.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"8_What_is_the_absolute_value_of_a_positive_fraction\"><\/span>8. What is the absolute value of a positive fraction?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe absolute value of a positive fraction remains the same as the fraction itself.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"9_Does_the_absolute_value_of_a_number_change_when_squared\"><\/span>9. Does the absolute value of a number change when squared?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the absolute value of a number remains unchanged when squared.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"10_Can_the_absolute_value_of_a_number_be_imaginary\"><\/span>10. Can the absolute value of a number be imaginary?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nNo, the absolute value of a number is always real.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"11_Can_the_absolute_value_of_a_number_be_zero\"><\/span>11. Can the absolute value of a number be zero?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nYes, the absolute value of a number can be zero if the number itself is zero.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"12_How_is_the_absolute_value_used_in_solving_equations\"><\/span>12. How is the absolute value used in solving equations?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\nThe absolute value is used to remove the effect of sign on a variable and solve equations involving different cases.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>In mathematics, the absolute value of a number is its distance from zero on the number line. It is denoted by enclosing the number within vertical bars or using the &#8216;|&#8217; symbol. The absolute value function transforms any real number to its non-negative counterpart, considering only magnitude and disregarding its sign. Understanding the true properties &#8230; <\/p>\n<p class=\"read-more-container\"><a title=\"What is true about absolute value?\" class=\"read-more button\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#more-228605\">Read more<span class=\"screen-reader-text\">What is true about absolute value?<\/span><\/a><\/p>\n","protected":false},"author":57,"featured_media":107420,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[86279],"tags":[],"class_list":["post-228605","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-learn","no-featured-image-padding"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is true about absolute value?<\/title>\n<meta name=\"description\" content=\"In mathematics, the absolute value of a number is its distance from zero on the number line. It is denoted by enclosing the number within vertical bars or\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is true about absolute value?\" \/>\n<meta property=\"og:description\" content=\"In mathematics, the absolute value of a number is its distance from zero on the number line. It is denoted by enclosing the number within vertical bars or\" \/>\n<meta property=\"og:url\" content=\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/\" \/>\n<meta property=\"og:site_name\" content=\"Namso Gen Blog - Free Credit Card Generator [100% Valid]\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/synchronyfinancial\" \/>\n<meta property=\"article:published_time\" content=\"2024-03-29T05:12:36+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/namso-gen.co\/blog\/wp-content\/uploads\/2024\/03\/faq.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"630\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Casey Mayer\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@synchrony\" \/>\n<meta name=\"twitter:site\" content=\"@synchrony\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Casey Mayer\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/\"},\"author\":{\"name\":\"Casey Mayer\",\"@id\":\"https:\/\/namso-gen.co\/blog\/#\/schema\/person\/89e431077ef417dfaa131f435124f18f\"},\"headline\":\"What is true about absolute value?\",\"datePublished\":\"2024-03-29T05:12:36+00:00\",\"dateModified\":\"2024-03-29T05:12:36+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/\"},\"wordCount\":603,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/namso-gen.co\/blog\/#organization\"},\"articleSection\":[\"Learn\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/\",\"url\":\"https:\/\/namso-gen.co\/blog\/what-is-true-about-absolute-value\/\",\"name\":\"What is true about absolute value?\",\"isPartOf\":{\"@id\":\"https:\/\/namso-gen.co\/blog\/#website\"},\"datePublished\":\"2024-03-29T05:12:36+00:00\",\"dateModified\":\"2024-03-29T05:12:36+00:00\",\"description\":\"In mathematics, the absolute value of a number is its distance from zero on the number line. 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