{"id":31907,"date":"2023-07-16T20:27:44","date_gmt":"2023-07-16T20:27:44","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=31907"},"modified":"2024-01-16T10:14:30","modified_gmt":"2024-01-16T10:14:30","slug":"absolute-value-definition-function-symbol-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/absolute-value","title":{"rendered":"Absolute Value &#8211; Definition, Function, Symbol, Examples, Facts, FAQs"},"content":{"rendered":"<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-8e9cc659-4ad5-4f7d-92f5-5d60eb26eeb1\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/absolute-value#0-what-is-the-absolute-value-of-a-number>What Is the Absolute Value of a Number?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/absolute-value#3-how-to-find-the-absolute-value-of-a-number>How to Find the Absolute Value of a Number<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/absolute-value#5-absolute-value-properties>Absolute Value Properties<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/absolute-value#14-solved-examples-on-absolute-value>Solved Examples on Absolute Value<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/absolute-value#15-practice-problems-on-absolute-value>Practice Problems on Absolute Value<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/absolute-value#16-frequently-asked-questions-about-absolute-value>Frequently Asked Questions about Absolute Value<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-absolute-value-of-a-number\">What Is the Absolute Value of a Number?<\/h2>\n\n\n\n<p><strong>The absolute value of a number tells us how far a given number is from the origin on a number line.&nbsp;<\/strong><\/p>\n\n\n\n<p>The absolute value only talks about distance, and not direction. We know that distance is a non-negative quantity. Thus, the absolute value of a number can never be negative.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"474\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-of-a-number.png\" alt=\"Absolute value of 7 on a number line\" class=\"wp-image-31912\" title=\"Absolute value of 7 on a number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-of-a-number.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-of-a-number-300x229.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>So, what does absolute value mean? Observe the diagram. Here, we can see that<\/p>\n\n\n\n<p>7 is 7 units to the right of 0.<\/p>\n\n\n\n<p>Thus, the absolute value of 7 is 7.<\/p>\n\n\n\n<p>-7 is 7 units to the left of 0.<\/p>\n\n\n\n<p>Thus, the absolute value of -7 is 7.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-digit-and-1-digit-number-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_3d_1d_pvc_pt.png\" alt=\"Add 3-Digit and 1-Digit Number Using Place Value Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3-Digit and 1-Digit Number Using Place Value Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-digit-and-2-digit-numbers-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_3d_2d_pvc_pt.png\" alt=\"Add 3-Digit and 2-Digit Numbers using Place Value Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3-Digit and 2-Digit Numbers using Place Value Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-digit-number-using-place-value-chart\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_3d_3d_pvc_pt.png\" alt=\"Add 3-Digit Number Using Place Value Chart Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3-Digit Number Using Place Value Chart Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-multiples-of-10-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_column_add_1_pt.png\" alt=\"Add Multiples of 10 using Place Value Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Multiples of 10 using Place Value Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-multiples-of-100-using-place-value-chart\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_multiples_100_pvc_pt.png\" alt=\"Add Multiples of 100 Using Place Value Chart Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Multiples of 100 Using Place Value Chart Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-ones-to-a-2-digit-number-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_column_add_3_pt.png\" alt=\"Add Ones to a 2-digit Number using Place Value Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Ones to a 2-digit Number using Place Value Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-tens-to-a-2-digit-number-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_column_add_2_pt.png\" alt=\"Add Tens to a 2-digit Number using Place Value Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Tens to a 2-digit Number using Place Value Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-using-place-value-chart\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_2d_1d_pvc_pt.png\" alt=\"Add Using Place Value Chart Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Using Place Value Chart Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_2d_2d_pvc_pt.png\" alt=\"Add Using Place Value Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Using Place Value Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/arrange-coins-by-their-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/money_order_coins_value_pnd_pt.png\" alt=\"Arrange Coins by their Value Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Arrange Coins by their Value Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-absolute-value-definition\">Absolute Value: Definition<\/h2>\n\n\n\n<p>Absolute value of a number can be defined as the distance of the number from the origin on a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-line\">number line<\/a>.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-place-value.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Place Value\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-3-digit-and-1-digit-numbers-using-place-value\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-3-digit-and-1-digit-numbers-using-place-value.jpeg\" alt=\"Add 3-Digit and 1-Digit Numbers Using Place Value Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-using-place-value-cards-with-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-using-place-value-cards-with-regrouping.jpeg\" alt=\"Add Using Place Value Cards With Regrouping Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-using-place-value-cards-without-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-using-place-value-cards-without-regrouping.jpeg\" alt=\"Add Using Place Value Cards Without Regrouping Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-using-place-value-cards\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-using-place-value-cards.jpeg\" alt=\"Addition Using Place Value Cards Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-using-place-value-chart\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-using-place-value-chart.jpeg\" alt=\"Addition Using Place Value Chart Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-and-find-greater-place-value-blocks-within-20\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-and-find-greater-place-value-blocks-within-20.jpeg\" alt=\"Compare and Find Greater Place Value Blocks within 20\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-numbers-using-place-value-blocks-within-20\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-numbers-using-place-value-blocks-within-20.jpeg\" alt=\"Compare Numbers Using Place Value Blocks within 20\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-place-value-blocks-using-more-or-less-within-20\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/compare-place-value-blocks-using-more-or-less-within-20.jpeg\" alt=\"Compare Place Value Blocks Using More or Less within 20\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-place-value-blocks-with-10\" data-vars-ga-category=\"splashlearn_vocab\" 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maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-absolute-value-symbol\">Absolute Value: Symbol<\/h2>\n\n\n\n<p>Absolute value of a number is represented by writing the number between two vertical bars. Note that the vertical bars are not to be confused with parentheses or <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/brackets\">brackets<\/a>.&nbsp;<\/p>\n\n\n\n<p>The absolute value of x is represented by |x|, and we read it as \u201c<strong>absolute value of <\/strong><strong>x<\/strong>.\u201d It is also read as \u201c<strong>modulus of <\/strong><strong>x<\/strong>.\u201d Sometimes, the absolute value of a number n is also written using the notion \u201cabs(n).\u201d<\/p>\n\n\n\n<p>In the previous example, we can write<\/p>\n\n\n\n<p>&nbsp;$|7| = | \\;\u2013\\; 7| = 7$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-find-the-absolute-value-of-a-number\">How to Find the Absolute Value of a Number<\/h2>\n\n\n\n<p>The absolute value of a positive number is the number itself. The absolute value of a negative number is written as the numeric value ignoring the negative sign. The absolute value of 0 is 0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-absolute-value-of-0\">Absolute Value of 0<\/h2>\n\n\n\n<p>The distance of the point zero from zero is 0 itself. Thus, the absolute value of 0 is 0.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-absolute-value-properties\">Absolute Value Properties<\/h2>\n\n\n\n<p><strong>Non negativity:<\/strong> Absolute value of a number is always non-negative.<\/p>\n\n\n\n<p>$&nbsp;| n | \\ge 0$<\/p>\n\n\n\n<p><strong>Symmetry:<\/strong> The absolute value of a number equals the absolute value of its additive inverse.&nbsp;<\/p>\n\n\n\n<p>$| \\;-\\; x | = | x |$<\/p>\n\n\n\n<p><strong>Positive definiteness:<\/strong> Absolute value of a number is 0 only if the number is 0.<\/p>\n\n\n\n<p>$| n | = 0$ if and only if $n = 0$<\/p>\n\n\n\n<p>On the same lines, we can say that $| x \\;\u2013\\; y | = 0 \u2194 x = y$<\/p>\n\n\n\n<p><strong>Multiplicativity:<\/strong> The absolute value of the product of two numbers is the product of the absolute values of the individual numbers.<\/p>\n\n\n\n<p>$|x\\times y| = | \\times | \\times | y |$<\/p>\n\n\n\n<p><strong>Preservation of division (equivalent to multiplicativity):<\/strong>&nbsp;<\/p>\n\n\n\n<p>$|\\frac{x}{y}| = |\\frac{x}{y}| \u2026y \\neq 0$<\/p>\n\n\n\n<p><strong>Sub-additivity: <\/strong>The absolute value of the sum of two numbers is less than or equal to the addition of the absolute values of the individual numbers.<\/p>\n\n\n\n<p>$|x + y| \\le | x | + | y |$<\/p>\n\n\n\n<p><strong>Equivalent to sub-additivity: <\/strong>$| x \\;\u2013\\; y | \\ge | | x | \\;\u2013\\; | y | |$<\/p>\n\n\n\n<p><strong>Triangle inequality (equivalent to subadditivity):<\/strong> $| x \\;\u2013\\; y | \\le | x \\;\u2013\\; z | + | z \\;\u2013\\; x |$<\/p>\n\n\n\n<p><strong>Idempotence:<\/strong> The absolute value of an absolute value of a number is simply the absolute value.<\/p>\n\n\n\n<p>$| | x | | = | x |$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-absolute-value-inequalities\">Absolute Value Inequalities<\/h2>\n\n\n\n<p>Let\u2019s discuss two important absolute value inequalities.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>$| x | \\le a&nbsp; \u21d4 \\;\u2212\\; a \\le x \\le a$<\/li>\n<\/ol>\n\n\n\n<p>This is often referred to as AND inequality.<\/p>\n\n\n\n<p><strong>Example: <\/strong>$|x \\;\u2212\\; 5| \\le 7 \u21d4 \\;\u2212\\;7 \\le x \\;\u2212\\; 5 \\le 7$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp; &nbsp; $\u21d4 \\;\u2212\\; 2 \\le x \\le 12$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"307\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-inequality.png\" alt=\"Absolute value inequality |x| \u2264 a\" class=\"wp-image-31913\" title=\"Absolute value inequality |x| \u2264 a\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-inequality.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-inequality-300x149.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>$| x | \\ge a \u21d4 x \\le \\;\u2212\\; a\\; or\\; x \\ge a$<\/li>\n<\/ol>\n\n\n\n<p>This is often referred to as OR inequality.<\/p>\n\n\n\n<p><strong>Example: <\/strong>$| x | \\ge 3 \u21d4 x \\le \\;\u2212\\;3$ <strong>or<\/strong> $x \\ge 3$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"378\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-inequality1.png\" alt=\"Absolute value inequality |x| \u2265 a\" class=\"wp-image-31914\" title=\"Absolute value inequality |x| \u2265 a\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-inequality1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-inequality1-300x183.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-absolute-value-of-real-numbers\">Absolute Value of Real Numbers<\/h2>\n\n\n\n<p>The absolute value of a positive real number is the number itself. The absolute value of a negative real number is the number without a negative sign. The absolute value of 0 is 0.<\/p>\n\n\n\n<p>Thus, for a real number x, the absolute value is given by:&nbsp;<\/p>\n\n\n\n<p>$| x | = x$ if $x \\ge 0$<\/p>\n\n\n\n<p>$| x | = \\;\u2013\\; x$ if $x \\lt 0$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-absolute-value-on-a-number-line\">Absolute Value on a Number Line<\/h2>\n\n\n\n<p>As mentioned earlier, the absolute value of a number tells us the distance of a number from zero on a number line.&nbsp;<\/p>\n\n\n\n<p>It is easy to understand the absolute value of integers (or any number) using the number line.<\/p>\n\n\n\n<p><strong>Example:<\/strong> The absolute value of 8 is 8.<\/p>\n\n\n\n<p>$| 8 | = 8$.<\/p>\n\n\n\n<p>Note that the absolute value of $\\;\u2013\\; 8$ is also 8.&nbsp;<\/p>\n\n\n\n<p>$| \\;\u2013\\; 8 | = 8$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"236\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-on-numberline.png\" alt=\"Absolute value of 8 and \u2013 8 on a number line\" class=\"wp-image-31915\" title=\"Absolute value of 8 and \u2013 8 on a number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-on-numberline.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-on-numberline-300x114.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-absolute-value-of-a-number-examples\">Absolute Value of a Number Examples<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$| 1 | = 1$<\/li>\n\n\n\n<li>$| \\;-\\;1| = 1$<\/li>\n\n\n\n<li>$| 3.5 | = 3.5$<\/li>\n\n\n\n<li>$| 0 | = 0$<\/li>\n\n\n\n<li>$| 7.9 | = 7.9$<\/li>\n\n\n\n<li>$| 5 \\;\u2013\\; 3 | = | 2 | = 2$<\/li>\n\n\n\n<li>$|&nbsp;\\;\u2013\\; 1 + 6 | = | 5 | = 5$<\/li>\n\n\n\n<li>$| \\;\u2013\\; 6 \\times 2| = | \\;\u2013\\; 12 | = 12$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-absolute-value-function\">Absolute Value Function<\/h2>\n\n\n\n<p>The absolute value function can be given by f(x) = |x| such that:&nbsp;&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$| x | = + x$&nbsp; for $x \\gt 0$<\/li>\n\n\n\n<li>$| x | = \\;\u2013\\; x$&nbsp; for&nbsp; $x \\lt 0$<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"642\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-function-graph.png\" alt=\"Graph of absolute value function\" class=\"wp-image-31916\" title=\"Graph of absolute value function\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-function-graph.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/absolute-value-function-graph-290x300.png 290w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-applications-of-absolute-value\">Applications of Absolute Value<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To find the distance between two points.<\/li>\n<\/ul>\n\n\n\n<p>The absolute value of the difference of two real numbers (absolute difference) is the distance between them.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"361\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-distance-using-absolute-value.png\" alt=\"Absolute value of difference\" class=\"wp-image-31917\" title=\"Absolute value of difference\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-distance-using-absolute-value.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/07\/finding-distance-using-absolute-value-300x175.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To identify and remove outliers in data analysis.<\/li>\n\n\n\n<li>To set tolerance in quality analysis.<\/li>\n\n\n\n<li>To determine the degree of variation in the data compared from a certain point.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-facts-about-absolute-value\">Facts about Absolute Value<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The absolute value of x, denoted by | x |, is also known as \u201c<strong>modulus<\/strong>\u201d of x.<\/li>\n\n\n\n<li>$|&nbsp;x | \\lt$ a implies that&nbsp; $\\;-\\;a \\lt x \\lt a$<\/li>\n\n\n\n<li>$|&nbsp;x | \\gt$ a implies that $x\\lt (\\;-\\;a)$ or $x \\gt a$<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the absolute value of a number, its symbol, properties, absolute value function, and we also learned its applications. Let\u2019s move ahead and solve a few examples and MCQs based on the concept of absolute value for practice.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-solved-examples-on-absolute-value\">Solved Examples on Absolute Value<\/h2>\n\n\n\n<p><strong>1. What is the absolute value of&nbsp; <\/strong>$\\;\u2013\\;18$<strong>?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>The absolute value of a negative number is written as the numeric value, ignoring the negative sign.&nbsp;<\/p>\n\n\n\n<p>The absolute value of $\\;-\\;18 = |\\;-\\;18| = 18$<\/p>\n\n\n\n<p><strong>2. Find the value of <\/strong>$-|\\frac{\\;-\\;15}{22}|$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>First, focus on the absolute value part.<\/p>\n\n\n\n<p>The absolute value of<strong> <\/strong>$\\;-\\;\\frac{15}{22} = |\\frac{-15}{22}| = |\\frac{15}{22}|$<\/p>\n\n\n\n<p>There\u2019s a minus sign outside the absolute value. It will get tagged along with the answer.<\/p>\n\n\n\n<p>$-|\\frac{-15}{22}| = \\frac{-15}{22}$<\/p>\n\n\n\n<p><strong>3. Find: <\/strong>$|-9| + |10|$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Here,<strong>&nbsp;<\/strong><\/p>\n\n\n\n<p>|\\;-\\; 9 = 9|<\/p>\n\n\n\n<p>$|10| = 10$<\/p>\n\n\n\n<p>Thus, $|\\;-\\;9| + |10| = 9 + 10 = 19$<\/p>\n\n\n\n<p><strong>4. <\/strong><strong>Find the absolute value.<\/strong><\/p>\n\n\n\n<p>$|5|, |\\;-\\;11|, |0|, |\\;-\\;7|, |\\;-\\;10|$<\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>$|5| = 5$<\/p>\n\n\n\n<p>$|\\;-\\;11| = 11$<\/p>\n\n\n\n<p>$|0| = 0$<\/p>\n\n\n\n<p>$|\\;-\\;7| = 7$<\/p>\n\n\n\n<p>$|\\;-\\;10| = 10$<\/p>\n\n\n\n<p><strong>5. Simplify: <\/strong>$|x \\;\u2212\\; 1| \\le 2$<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$|x \\;\u2212\\; 1| \\le 2$<\/p>\n\n\n\n<p>$\\;\u2212\\;2 \\le x \\;\u2212\\; 1 \\le 2$<\/p>\n\n\n\n<p>$(\\;\u2212\\;2 + 1) \\le&nbsp; x &nbsp;\\le (2 + 1)$<\/p>\n\n\n\n<p>$\\;\u2212\\; 1 \\le&nbsp; x &nbsp;\\le 3$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"15-practice-problems-on-absolute-value\">Practice Problems on Absolute Value<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Absolute Value - Definition, Function, Symbol, Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowldege.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The absolute value of $\\;\u2013\\; 25$ is ___.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\;\u2013\\; 25$<\/div><div class=\"spq_answer_block\" data-value=\"1\">25<\/div><div class=\"spq_answer_block\" data-value=\"2\">0<\/div><div class=\"spq_answer_block\" data-value=\"3\">50<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 25<br\/>$|\\;\u2013\\; 25| = 25$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">$|11| \\times | \\;-\\; 12| =$ ___<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\;\u2013\\; 132$<\/div><div class=\"spq_answer_block\" data-value=\"1\">0<\/div><div class=\"spq_answer_block\" data-value=\"2\">132<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\;\u2013\\; 264$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 132<br\/>$|11| = 11$<br>\r\n$|\\;-\\;12| = 12$<br>\r\n$|11| \\times | \\;-\\;12| = 11 \\times 12 = 132$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Find the value of $|\\frac{-3}{5}| \\times |\\frac{5}{6}|$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\;\u2013 \\;\\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">0<\/div><div class=\"spq_answer_block\" data-value=\"2\">1<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{2}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{1}{2}$<br\/>$|\\frac{-3}{5}| \\times |\\frac{5}{6}| = \\frac{3}{5} \\times \\frac{5}{6} = \\frac{1}{2}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">$|x \\;-\\; y| = 0$ if and only if<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$x = \\;-\\; y$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$x = y$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$x \\neq y$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$xy = 0$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $x = y$<br\/>$|x\\;-\\;y| = 0$ if and only if $x = y$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">$| 0 | =$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">0<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\;-\\;1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">Not defined<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 0<br\/>Absolute value of 0 is 0.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">6<\/span><h3 class=\"sqp_question_text\">The absolute value of 8 is the distance between ____ on a number line.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">8 and -8<\/div><div class=\"spq_answer_block\" data-value=\"1\">8 and 1<\/div><div class=\"spq_answer_block\" data-value=\"2\">8 and 0<\/div><div class=\"spq_answer_block\" data-value=\"3\">-8 and 1<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 8 and 0<br\/>The absolute value of 8 is the distance between 8 and 0 on a number line.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowldege.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": 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                         \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;\u2013\\\\; 132$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$|11| = 11$$<br>\r\n$$|\\\\;-\\\\;12| = 12$$<br>\r\n$$|11| \\\\times | \\\\;-\\\\;12| = 11 \\\\times 12 = 132$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$|11| = 11$$<br>\r\n$$|\\\\;-\\\\;12| = 12$$<br>\r\n$$|11| \\\\times | \\\\;-\\\\;12| = 11 \\\\times 12 = 132$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\;\u2013\\\\; 264$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$|11| = 11$$<br>\r\n$$|\\\\;-\\\\;12| = 12$$<br>\r\n$$|11| \\\\times | \\\\;-\\\\;12| = 11 \\\\times 12 = 132$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"132\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          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}, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x \\\\neq y$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$|x\\\\;-\\\\;y| = 0$$ if and only if $$x = y$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$xy = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$|x\\\\;-\\\\;y| = 0$$ if and only if $$x = y$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$x = y$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$|x\\\\;-\\\\;y| = 0$$ if and only if $$x = y$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$|x\\\\;-\\\\;y| = 0$$ if and only if $$x = y$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$| 0 | =$$\",\n               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\"text\": \"$$\\\\;-\\\\;1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Absolute value of 0 is 0.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Not defined\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Absolute value of 0 is 0.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Absolute value of 0 is 0.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Absolute value of 0 is 0.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The absolute value of 8 is the distance between ____ on a number line.\",\n                    \"text\": \"The absolute value of 8 is the distance between ____ on a number line.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The absolute value of 8 is the distance between 8 and 0 on a number line.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8 and -8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The absolute value of 8 is the distance between 8 and 0 on a number line.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"8 and 1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The absolute value of 8 is the distance between 8 and 0 on a number line.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"-8 and 1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The absolute value of 8 is the distance between 8 and 0 on a number line.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8 and 0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The absolute value of 8 is the distance between 8 and 0 on a number line.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The absolute value of 8 is the distance between 8 and 0 on a number line.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"16-frequently-asked-questions-about-absolute-value\">Frequently Asked Questions about Absolute Value<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>What is the value of <\/strong>$\\;-\\;| \\;-\\; x|$<strong>?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>$|\\;-\\;x| = x$<\/p>\n\n\n\n<p>So, $-\\; |\\;-\\;x| = \\;-\\; x$<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>How to simplify the absolute value inequality <\/strong>$| x | \\le a$<strong>?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>$| x | \\le$ a can be written as a compound inequality $\\;\u2212\\; a \\le x \\le a$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>How to simplify the absolute value inequality <\/strong>$| x | \\ge a$<strong>?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>$| x | \\ge a$ can be simplified as $x \\le \\;\u2212\\; a$ or $x \\ge a$.<\/p>\n\n\n\n<p>Example:&nbsp;$| x | \\ge 1$ means $x \\le \\;\u2212\\;1$ or $x \\ge 1$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>Can two different numbers have the same absolute value?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>Yes, two different numbers can have the same absolute value. The two numbers $\\;\u2013\\;10$, and 10 have the same absolute value of 10.&nbsp;<br>$| \\;\u2013\\; 10 | = | 10 | = 10$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>What is the absolute value of 0?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>The absolute value of 0 is always 0 as the distance of 0 from 0 is 0.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>What are absolute numbers?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>Absolute numbers or absolute values simply refer to numeric values, ignoring the sign of the given numbers.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-6-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>Why is the absolute value always positive?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-6-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>Absolute value is a distance, and distance can never be negative. Thus, the absolute value is always positive. To be more accurate, the absolute value is a non-negative number. Absolute value of 0 is 0. 0 is neither positive nor negative. It is considered a non-negative as well as a non-positive integer.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-7-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>What do absolute value bars mean?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-7-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>We use a bar on either side of a number to mean absolute value. The absolute value bars or the vertical bars | | represent \u201cmodulus symbol.\u201d It gives us the distance of the number from 0.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-8-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\"><strong>What are the other names for absolute values?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-8-0b9ee7e6-51e6-4fa9-bc10-a39a18de1596\">\n\n<p>Absolute value is also commonly referred to as numerical value or magnitude.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Absolute Value of a Number? The absolute value of a number tells us how far a given number is from the origin on a number line.&nbsp; The absolute value only talks about distance, and not direction. We know that distance is a non-negative quantity. Thus, the absolute value of a number can &#8230; <a title=\"Absolute Value &#8211; Definition, Function, Symbol, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/absolute-value\" aria-label=\"More on Absolute Value &#8211; Definition, Function, Symbol, Examples, Facts, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-31907","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31907","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=31907"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31907\/revisions"}],"predecessor-version":[{"id":37396,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/31907\/revisions\/37396"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=31907"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=31907"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=31907"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}