{"id":26272,"date":"2023-03-14T02:28:02","date_gmt":"2023-03-14T02:28:02","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26272"},"modified":"2024-03-12T05:17:33","modified_gmt":"2024-03-12T05:17:33","slug":"addition-property-of-equality-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/addition-property-of-equality","title":{"rendered":"Addition Property of Equality: Definition, Formula, Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-e906b90d-a830-4d52-a204-eac31660b93c\" 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\/addition-property-of-equality#0-what-is-the-addition-property-of-equality>What is the Addition Property of Equality?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition-property-of-equality#2-addition-property-of-equality-formula>Addition Property of Equality Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition-property-of-equality#3-verification-of-addition-property-of-equality>Verification of Addition Property of Equality<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition-property-of-equality#6-solved-examples-for-addition-property-of-equality>Solved Examples for Addition Property of Equality<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition-property-of-equality#7-practice-problems-on-addition-property-of-equality>Practice Problems on Addition Property of Equality<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition-property-of-equality#8-frequently-asked-questions-on-addition-property-of-equality>Frequently Asked Questions on Addition Property of Equality<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-addition-property-of-equality\">What is the Addition Property of Equality?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The addition property of equality is an important concept for solving algebraic equations. In algebra, an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, $5 \\times 2 = 10$ is an equation, in which $5 \\times 2$ and 10 are two expressions separated by an \u201cequal $(=)$\u201d sign. Think of an equation like a balanced weighing scale. The left side and the right side should be equal for it to be balanced.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"604\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-visual-representation-of-equation.png\" alt=\"A visual representation of equation\" class=\"wp-image-35660\" title=\"A visual representation of equation\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-visual-representation-of-equation.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/a-visual-representation-of-equation-300x292.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, to keep the scale balanced, if any mathematical operation is applied on one side of an equation, then it must be applied on the other side of an equation as well. This is called the property of equality.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The properties that do not impact the equality in an equation are called the properties of equality<\/strong>. There are many properties of equality but in this article, we will learn about \u201cthe addition property of equality.\u201d<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-addition-property-of-equality-definition-\"><strong>Addition Property of Equality Definition<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>The addition property of equality states that if the same number or value is added to both sides of an equation, then the equality still holds true after addition. Adding the same number on both sides of an equation does not affect the equality.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can again consider the real-life example of the weighing scale. Suppose that initially there are 5 coins on both sides which balances the scale. (Observe the image on the left.)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we add 5 more coins to one of the scales, then to keep the scales balanced, we must add 5 coins to the other scale as well. So, we will have 10 coins each on both sides of the balance. (Observe the image on the right.)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"385\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/addition-property-of-equality-visual-example.png\" alt=\"Addition property of equality: visual example\" class=\"wp-image-35661\" title=\"Addition property of equality: visual example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/addition-property-of-equality-visual-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/addition-property-of-equality-visual-example-300x186.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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-numbers-using-column-addition\" 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_num_2_pt.png\" alt=\"Add Numbers Using Column Addition 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 Numbers Using Column Addition 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-associative-property\" 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_facts_together_we_flee_4_gm.png\" alt=\"Add Using Associative Property 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 Associative Property 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\/addition-by-regrouping\" 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_regrp_2d_1d_vertical_pt.png\" alt=\"Addition By Regrouping 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\">Addition By Regrouping 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\/addition-sentences-up-to-10\" 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_facts_cmplt_sent_w10_pt.png\" alt=\"Addition Sentences (Up to 10) 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\">Addition Sentences (Up to 10) 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\/addition-symbol\" 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_facts_add_sym_w5_pt.png\" alt=\"Addition Symbol 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\">Addition Symbol 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\/addition-word-problems-on-finding-the-total\" 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_facts_add_to_scenario_pt.png\" alt=\"Addition Word Problems on Finding the Total 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\">Addition Word Problems on Finding the Total 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\/addition-word-problems-on-put-together-scenarios\" 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_facts_put_together_scenario_pt.png\" alt=\"Addition Word Problems on Put-Together Scenarios 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\">Addition Word Problems on Put-Together Scenarios 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\/apply-distributive-property\" 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\/mult_div_facts_mul_dispro_exp1_pt.png\" alt=\"Apply Distributive Property 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\">Apply Distributive Property 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\/break-up-an-addition-sentences\" 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_facts_break_up_add_sentence_1_pt.png\" alt=\"Break up an Addition Sentences 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\">Break up an Addition Sentences 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\/choose-the-correct-addition-sentence-related-to-the-fraction\" 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\/fractions_related_add_sentence_pt.png\" alt=\"Choose the Correct Addition Sentence Related to the Fraction 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\">Choose the Correct Addition Sentence Related to the Fraction 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               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checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-addition-property-of-equality-formula\">Addition Property of Equality Formula<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider an equation $x = y$, where x and y are real numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If a real number \u201c<em>c<\/em>\u201d is added to <em>x<\/em>,<em> <\/em>the left-hand side (L.H.S.) of the equation, then we must add \u201c<em>c<\/em>\u201d to <em>y<\/em>, the right-hand side (R.H.S.) of the equation. So, the formula is given by,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><em>If <\/em>$x = y$ , then $x + c = y + c$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, the <strong>addition property of equality states that the equality holds or the equation is balanced if the same number is added to both sides of the equation.<\/strong><\/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\/1-and-2-more-within-10-horizontal-addition\" 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\/1-and-2-more-within-10-horizontal-addition.jpeg\" alt=\"1 and 2 more within 10: Horizontal Addition 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\/1-and-2-more-within-10-vertical-addition\" 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\/1-and-2-more-within-10-vertical-addition.jpeg\" alt=\"1 and 2 more within 10: Vertical Addition 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\/1-and-2-more-within-20-horizontal-addition\" 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\/1-and-2-more-within-20-horizontal-addition.jpeg\" alt=\"1 and 2 more within 20: Horizontal Addition 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\/1-and-2-more-within-20-vertical-addition\" 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\/1-and-2-more-within-20-vertical-addition.jpeg\" alt=\"1 and 2 more within 20: Vertical Addition 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-1-digit-and-3-digit-numbers-using-addition-tables\" 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-addition-tables.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Addition Tables\">\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-1-digit-and-3-digit-numbers-using-addition-wheel\" 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-addition-wheel.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Addition Wheel\">\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-1-within-10-horizontal-addition\" 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-within-10-horizontal-addition.jpeg\" alt=\"Add 1 within 10: Horizontal Addition 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-1-within-10-vertical-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" 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20: Horizontal Addition 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-1-within-20-vertical-addition\" 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-within-20-vertical-addition.jpeg\" alt=\"Add 1 within 20: Vertical Addition 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><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-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 eplus-wrapper\" id=\"3-verification-of-addition-property-of-equality\">Verification of Addition Property of Equality<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We know the addition property of equality, so we will verify it by taking a few examples.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Arithmetically, we know that $13 + 9 = 22$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, if we add 7 to both sides of the equation, we have<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">L.H.S $= 13 + 9 + 7 = 29$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">R.H.S $= 22 +7 = 29$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">L.H.S $=$ R.H.S<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It implies that when the same number is added to both sides of an equation, the equality still holds or the equation is balanced.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-addition-property-of-equality-for-fractions\">Addition Property of Equality for Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The addition property of equality can also be applied to equations including fractions.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider an equation $\\frac{a}{b} = \\frac{p}{q}$, where $b,\\; q \\neq 0$ and $a,\\; b,\\; p,\\; q$ are real numbers.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If we add the same fraction cd to both sides of the equation, the equation will stay balanced. Thus, we have<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$\\frac{a}{b} = \\frac{p}{q}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\Rightarrow \\frac{a}{b} + \\frac{c}{d} = \\frac{p}{q} + \\frac{c}{d}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The addition property in geometry (where side-lengths, angle measures, etc., are part of an equation) works the same way as it does in algebra.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about the addition property of equality. The addition property of equality states that if we add the same number on both sides of an equation, then the equation remains balanced. Let\u2019s solve a few examples of addition property of equality to understand the concept better!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-solved-examples-for-addition-property-of-equality\">Solved Examples for Addition Property of Equality<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1.<\/strong> <strong>Let <em>k<\/em> be a real number such that <\/strong>$k\\;-\\;5 = 15$<strong>. Use the addition property of equality to find the value of <em>k<\/em>.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> $k\\;-\\;5 = 15$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The addition property of equality states that we should add the same number to both sides of an equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To solve for <em>k<\/em>, we need to isolate the variable (keep only k on the left side and move the other terms on the right side). Add 5 to the left side of the equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$k\\;-\\;5 + 5 = 15 + 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$k = 20$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2.<\/strong> <strong>Martha has 7 marbles in each hand. Her best friend gave her 6 more marbles. Explain how she can balance the number of stickers in each hand.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> Initially, Martha is holding 7 marbles in both hands.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$7 = 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">She gets 6 more marbles. As 6 is an even number, she can divide the 6 marbles in two groups of 3. Now, she can hold 3 more marbles in each hand.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$7 + 3 = 7 + 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$10 = 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. If <em>x<\/em>, <em>y<\/em>, and <em>z<\/em> are real numbers such that <\/strong>$y = z$<strong> and <\/strong>$z = 7 \\;-\\; x$<strong>, then using the addition property of equality show that <\/strong>$x + y = 7$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> It is given that $y = z$ and $z = 7\\;-\\;x$&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$z = 7\\;-\\;x$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Add <em>x<\/em> to both sides, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$z + x = 7\\;-\\;x + x$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$z + x = 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since $y = z$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$y + x = 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Using the addition property of equality, find the value of x in the equation <\/strong>$2x \\;-\\; 3 = 6$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong> The given equation is $2x \\;-\\; 3 = 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Add 3 to both sides, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$2x \\;-\\; 3 + 3 = 6 + 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$2x = 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Divide both sides by 2, we get<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = \\frac{9}{2}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-practice-problems-on-addition-property-of-equality\">Practice Problems on Addition Property of Equality<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Addition Property of Equality: Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/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\">There are two packets of flour of the same weight. If 15 ounces of flour is added to each bag, what will be the equation of the new weights of the packets?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$a + 15 = b$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$a + 15 = b + 15$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$a = b + 15$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$a - 15 = b - 15$<\/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: $a + 15 = b + 15$<br\/>Let the weight of the flour packets be a and b respectively. Since both packets have the same weight, so $a = b$.<br>\r\nOn adding 15 ounces to each packet, we get $a + 15 = b + 15$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">If $p\\;-\\;8 = q\\;-\\;8$, then choose the correct option:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$p = q$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$p = q\\;-\\;16$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$p = q + 16$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$p\\;-\\;8 = q\\;-\\;16$<\/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: $p = q$<br\/>According to the addition property of equality, if $a = b$ then $a + c = b + c$.<br>\r\nIn the equation $p\\;-\\;8 = q\\;-\\;8$, add 8 to both sides of the equation.<br>\r\nSo, we get $p\\;-\\;8 + 8 = q\\;-\\;8 + 8$<br>\r\n$ \\Rightarrow p = q$<\/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\">For the equation, $a\\;-\\; \\frac{2}{3} = \\frac{3}{4}$, find the value of a.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{17}{7}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{12}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{7}{17}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{17}{12}$<\/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: $\\frac{17}{12}$<br\/>On adding $\\frac{2}{3}$ to both sides, we get<br>\r\n$a \\;-\\; \\frac{2}{3} + \\frac{2}{3} = \\frac{3}{4} + \\frac{2}{3}$<br>\r\n$a = \\frac{17}{12}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">The addition property of equality is given by the formula:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$x = y \\Rightarrow x + c = y + c$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$x = y \\Rightarrow x\\;-\\;c = y\\;-\\;c$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$x = y \\Rightarrow x = y + c$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$x = y \\Rightarrow x\\;-\\;c = y + c$<\/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: $x = y \\Rightarrow x + c = y + c$<br\/>The addition property equality states that we have to add the same number to both sides.<br>\r\nIf $x = y$, then $x + c = y + c$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Find the value of x for the algebraic equation $x \\;-\\; 22 = \\;-27$. <\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$3$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-3$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-5$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$5$<\/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: $-5$<br\/>On adding 22 to both the sides, we get<br>\r\n$x\\;-\\;22 + 22 = \\;-27 + 22$<br>\r\n$x = \\;-5$<\/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 knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Addition Property of Equality: Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Addition Property of Equality\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"There are two packets of flour of the same weight. 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Since both packets have the same weight, so $$a = b$$.<br>\r\nOn adding 15 ounces to each packet, we get $$a + 15 = b + 15$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a - 15 = b - 15$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let the weight of the flour packets be a and b respectively. Since both packets have the same weight, so $$a = b$$.<br>\r\nOn adding 15 ounces to each packet, we get $$a + 15 = b + 15$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$a + 15 = b + 15$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let the weight of the flour packets be a and b respectively. Since both packets have the same weight, so $$a = b$$.<br>\r\nOn adding 15 ounces to each packet, we get $$a + 15 = b + 15$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let the weight of the flour packets be a and b respectively. Since both packets have the same weight, so $$a = b$$.<br>\r\nOn adding 15 ounces to each packet, we get $$a + 15 = b + 15$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If $$p\\\\;-\\\\;8 = q\\\\;-\\\\;8$$, then choose the correct option:\",\n                    \"text\": \"If $$p\\\\;-\\\\;8 = q\\\\;-\\\\;8$$, then choose the correct option:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the addition property of equality, if $$a = b$$ then $$a + c = b + c$$.<br>\r\nIn the equation $$p\\\\;-\\\\;8 = q\\\\;-\\\\;8$$, add 8 to both sides of the equation.<br>\r\nSo, we get $$p\\\\;-\\\\;8 + 8 = q\\\\;-\\\\;8 + 8$$<br>\r\n$$ \\\\Rightarrow p = q$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$p = q\\\\;-\\\\;16$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the addition property of equality, if $$a = b$$ then $$a + c = b + c$$.<br>\r\nIn the equation $$p\\\\;-\\\\;8 = q\\\\;-\\\\;8$$, add 8 to both sides of the equation.<br>\r\nSo, we get $$p\\\\;-\\\\;8 + 8 = q\\\\;-\\\\;8 + 8$$<br>\r\n$$ \\\\Rightarrow p = q$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$p = q + 16$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the addition property of equality, if $$a = b$$ then $$a + c = b + c$$.<br>\r\nIn the equation $$p\\\\;-\\\\;8 = q\\\\;-\\\\;8$$, add 8 to both sides of the equation.<br>\r\nSo, we get $$p\\\\;-\\\\;8 + 8 = q\\\\;-\\\\;8 + 8$$<br>\r\n$$ \\\\Rightarrow p = q$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$p\\\\;-\\\\;8 = q\\\\;-\\\\;16$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the addition property of equality, if $$a = b$$ then $$a + c = b + c$$.<br>\r\nIn the equation $$p\\\\;-\\\\;8 = q\\\\;-\\\\;8$$, add 8 to both sides of the equation.<br>\r\nSo, we get $$p\\\\;-\\\\;8 + 8 = q\\\\;-\\\\;8 + 8$$<br>\r\n$$ \\\\Rightarrow p = q$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$p = q$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the addition property of equality, if $$a = b$$ then $$a + c = b + c$$.<br>\r\nIn the equation $$p\\\\;-\\\\;8 = q\\\\;-\\\\;8$$, add 8 to both sides of the equation.<br>\r\nSo, we get $$p\\\\;-\\\\;8 + 8 = q\\\\;-\\\\;8 + 8$$<br>\r\n$$ \\\\Rightarrow p = q$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the addition property of equality, if $$a = b$$ then $$a + c = b + c$$.<br>\r\nIn the equation $$p\\\\;-\\\\;8 = q\\\\;-\\\\;8$$, add 8 to both sides of the equation.<br>\r\nSo, we get $$p\\\\;-\\\\;8 + 8 = q\\\\;-\\\\;8 + 8$$<br>\r\n$$ \\\\Rightarrow p = q$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"For the equation, $$a\\\\;-\\\\; \\\\frac{2}{3} = \\\\frac{3}{4}$$, find the value of a.\",\n                    \"text\": \"For the equation, $$a\\\\;-\\\\; \\\\frac{2}{3} = \\\\frac{3}{4}$$, find the value of a.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"On adding $$\\\\frac{2}{3}$$ to both sides, we get<br>\r\n$$a \\\\;-\\\\; \\\\frac{2}{3} + \\\\frac{2}{3} = \\\\frac{3}{4} + \\\\frac{2}{3}$$<br>\r\n$$a = \\\\frac{17}{12}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{17}{7}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On adding $$\\\\frac{2}{3}$$ to both sides, we get<br>\r\n$$a \\\\;-\\\\; \\\\frac{2}{3} + \\\\frac{2}{3} = \\\\frac{3}{4} + \\\\frac{2}{3}$$<br>\r\n$$a = \\\\frac{17}{12}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{12}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On adding $$\\\\frac{2}{3}$$ to both sides, we get<br>\r\n$$a \\\\;-\\\\; \\\\frac{2}{3} + \\\\frac{2}{3} = \\\\frac{3}{4} + \\\\frac{2}{3}$$<br>\r\n$$a = \\\\frac{17}{12}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{7}{17}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On adding $$\\\\frac{2}{3}$$ to both sides, we get<br>\r\n$$a \\\\;-\\\\; \\\\frac{2}{3} + \\\\frac{2}{3} = \\\\frac{3}{4} + \\\\frac{2}{3}$$<br>\r\n$$a = \\\\frac{17}{12}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{17}{12}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"On adding $$\\\\frac{2}{3}$$ to both sides, we get<br>\r\n$$a \\\\;-\\\\; \\\\frac{2}{3} + \\\\frac{2}{3} = \\\\frac{3}{4} + \\\\frac{2}{3}$$<br>\r\n$$a = \\\\frac{17}{12}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"On adding $$\\\\frac{2}{3}$$ to both sides, we get<br>\r\n$$a \\\\;-\\\\; \\\\frac{2}{3} + \\\\frac{2}{3} = \\\\frac{3}{4} + \\\\frac{2}{3}$$<br>\r\n$$a = \\\\frac{17}{12}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The addition property of equality is given by the formula:\",\n                    \"text\": \"The addition property of equality is given by the formula:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The addition property equality states that we have to add the same number to both sides.<br>\r\nIf $$x = y$$, then $$x + c = y + c$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x = y \\\\Rightarrow x\\\\;-\\\\;c = y\\\\;-\\\\;c$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The addition property equality states that we have to add the same number to both sides.<br>\r\nIf $$x = y$$, then $$x + c = y + c$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x = y \\\\Rightarrow x = y + c$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The addition property equality states that we have to add the same number to both sides.<br>\r\nIf $$x = y$$, then $$x + c = y + c$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$x = y \\\\Rightarrow x\\\\;-\\\\;c = y + c$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The addition property equality states that we have to add the same number to both sides.<br>\r\nIf $$x = y$$, then $$x + c = y + c$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$x = y \\\\Rightarrow x + c = y + c$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The addition property equality states that we have to add the same number to both sides.<br>\r\nIf $$x = y$$, then $$x + c = y + c$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The addition property equality states that we have to add the same number to both sides.<br>\r\nIf $$x = y$$, then $$x + c = y + c$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the value of x for the algebraic equation $$x \\\\;-\\\\; 22 = \\\\;-27$$. \",\n                    \"text\": \"Find the value of x for the algebraic equation $$x \\\\;-\\\\; 22 = \\\\;-27$$. \",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"On adding 22 to both the sides, we get<br>\r\n$$x\\\\;-\\\\;22 + 22 = \\\\;-27 + 22$$<br>\r\n$$x = \\\\;-5$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On adding 22 to both the sides, we get<br>\r\n$$x\\\\;-\\\\;22 + 22 = \\\\;-27 + 22$$<br>\r\n$$x = \\\\;-5$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-3$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On adding 22 to both the sides, we get<br>\r\n$$x\\\\;-\\\\;22 + 22 = \\\\;-27 + 22$$<br>\r\n$$x = \\\\;-5$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"On adding 22 to both the sides, we get<br>\r\n$$x\\\\;-\\\\;22 + 22 = \\\\;-27 + 22$$<br>\r\n$$x = \\\\;-5$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-5$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"On adding 22 to both the sides, we get<br>\r\n$$x\\\\;-\\\\;22 + 22 = \\\\;-27 + 22$$<br>\r\n$$x = \\\\;-5$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"On adding 22 to both the sides, we get<br>\r\n$$x\\\\;-\\\\;22 + 22 = \\\\;-27 + 22$$<br>\r\n$$x = \\\\;-5$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-frequently-asked-questions-on-addition-property-of-equality\">Frequently Asked Questions on Addition Property of Equality<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-a4586a9d-8915-4c2f-b44f-09643e677666\" 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-a4586a9d-8915-4c2f-b44f-09643e677666\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4586a9d-8915-4c2f-b44f-09643e677666\"><strong>Can the number that we add to both sides be 0 in the addition property of equality?<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, the number that we add to both sides can be 0. Note that adding 0 to any number results in the number itself.<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4586a9d-8915-4c2f-b44f-09643e677666\"><strong>What is the difference between the addition property of equality and the subtraction property of equality?<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The addition property of equality is the property that states that if a value is added to two equal quantities, then the sums are also equal, i.e., if $x = y$, then $x + c = y + c$.The subtraction property of equality is the property that states that if a value is subtracted from two equal quantities, then the differences are also equal i.e. if $x = y$, then $x\\;-\\;c = y\\;-\\;c$.<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4586a9d-8915-4c2f-b44f-09643e677666\"><strong>What is the addition property of inequality?<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The addition property of inequality states that if the same number is added to both sides of any given inequality, then the inequality remains the same.<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4586a9d-8915-4c2f-b44f-09643e677666\"><strong>Can the number that we add to both sides be negative in the addition property of equality?<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, the number which we add to both sides can be negative.<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4586a9d-8915-4c2f-b44f-09643e677666\"><strong>What are the applications of the addition property of equality?<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can simplify, balance, and solve equations using the addition property of equality. It also helps in simplifying complex algebraic expressions.<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-a4586a9d-8915-4c2f-b44f-09643e677666\"><strong>How to solve the addition property of equality with fractions?<\/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-a4586a9d-8915-4c2f-b44f-09643e677666\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can also apply the addition property of equality to fractions. Adding the same fractions on both sides of an equation maintains the equality.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example: $x \\;-\\; \\frac{1}{2} = \\frac{3}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $x \\;-\\; \\frac{1}{2} + \\frac{1}{2} = 1 + \\frac{1}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$x = \\frac{3}{2}$<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What is the Addition Property of Equality? The addition property of equality is an important concept for solving algebraic equations. In algebra, an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, $5 \\times 2 = 10$ is an equation, in which $5 \\times 2$ and 10 are two &#8230; <a title=\"Addition Property of Equality: Definition, Formula, Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition-property-of-equality\" aria-label=\"More on Addition Property of Equality: Definition, Formula, Examples\">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-26272","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\/26272","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=26272"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26272\/revisions"}],"predecessor-version":[{"id":40882,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26272\/revisions\/40882"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26272"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26272"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26272"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}