{"id":916,"date":"2022-04-12T10:19:08","date_gmt":"2022-04-12T10:19:08","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=916"},"modified":"2024-01-01T07:46:03","modified_gmt":"2024-01-01T07:46:03","slug":"associative-property-of-addition-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property-of-addition","title":{"rendered":"Associative Property of Addition &#8211; Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><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-025d418d-2ece-4c01-b1c5-fee734b05c69\" 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\/associative-property-of-addition#0-definition>Definition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property-of-addition#1-closely-related-concepts>Closely Related Concepts<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property-of-addition#2-solved-examples-on-associative-property-of-addition>Solved Examples on Associative Property of Addition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property-of-addition#3-practice-problems-on-associative-property-of-addition>Practice Problems on Associative Property of Addition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property-of-addition#5-frequently-asked-questions-on-associative-property-of-addition>Frequently Asked Questions on Associative Property of Addition<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-definition\">Definition:<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>To \u201cassociate\u201d means to connect or join with something.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">According to the associative property of addition the sum of three or more numbers remains the same regardless of how the numbers are grouped.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here\u2019s an example of how the sum does NOT change irrespective of how the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/addend\" title=\"\">addends<\/a> are grouped.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"439\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/addition-of-block-to-understand-associative-property.png\" alt=\"Addition of block to understand associative property\" class=\"wp-image-36909\" title=\"Addition of block to understand associative property\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/addition-of-block-to-understand-associative-property.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/addition-of-block-to-understand-associative-property-300x212.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">As seen in the example above, grouping is defined with parentheses. Whether we group 5 and 3 or 3 and 4 within the parentheses, the final sum is 12. You can verify the final result by checking the colored blocks that stay the same in both the cases.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>General Case:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">For any three numbers a,b and c<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>a + (b + c) = (a + b) + c<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"373\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/associative-property-of-addition.png\" alt=\"Associative property of addition\" class=\"wp-image-36911\" title=\"Associative property of addition\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/associative-property-of-addition.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/associative-property-of-addition-300x180.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">i.e. when you add, you can group the numbers in any combination.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us take another example to understand and prove the formula.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us group 14 + 7 + 5 in two ways.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Step 1: We can group the set of numbers in two different ways as (14 + 7) + 5 or as&nbsp; 14 + (7 + 5).&nbsp;&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Step 2: Add the first set of numbers, that is, (14 + 7) + 5. This can be further solved as 21 + 5 = 26.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Step 3: Add the second set, i.e, 14 + (7 + 5) = 14 + 12 = 26.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Step 4: The sum of both the expressions is 26.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">This shows that the sum remains the same irrespective of how we group the numbers with the help of brackets.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The minimum numbers we require for associative property of addition are 3. However, the associative property of addition holds true for more than three numbers too.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The associative property along with other properties in Mathematics are useful in manipulating equations and their solutions.&nbsp;<\/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-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                }\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=\"1-closely-related-concepts\">Closely Related Concepts:<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The associative property holds for multiplication as well i.e. for any three numbers a, b and c, a $\\times$ (b $\\times$ c) = (a $\\times$ b) $\\times$ c<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Let a = 2, b = 3, c = 4<\/p>\n\n\n\n<p class=\"eplus-wrapper\">a $\\times$ (b $\\times$ c) = 2 $\\times$ (3 $\\times$ 4) = 2 $\\times$ 12 = 24<\/p>\n\n\n\n<p class=\"eplus-wrapper\">(a $\\times$ b) $\\times$ c = (2 $\\times$ 3) $\\times$ 4 = 6 $\\times$ 4 = 24<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, a $\\times$ (b $\\times$ c) = (a $\\times$ b) $\\times$ c&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The associative property does not hold for subtraction. Let us look at an example<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Let a = 2, b = 3, c = 4<\/p>\n\n\n\n<p class=\"eplus-wrapper\">a- (b &#8211; c) = 2 &#8211; (3 &#8211; 4) = 3<\/p>\n\n\n\n<p class=\"eplus-wrapper\">(a &#8211; b) -c = (2 &#8211; 3) &#8211; 4 = -53<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, associative property does not hold for subtraction.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The associative property does not hold for division. Let us look at an example<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">a $\\div$ (b $\\div$ c) = 2 $\\div$ (3 $\\div$ 4) = 2.67<\/p>\n\n\n\n<p class=\"eplus-wrapper\">(a $\\div$ b) $\\div$ c = (2 $\\div$ 3) $\\div$ 4 = 5.97 $\\neq$ 2.67<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, associative property does not hold for division.&nbsp;<\/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\" 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-vertical-addition.jpeg\" alt=\"Add 1 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\/add-1-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\/add-1-within-20-horizontal-addition.jpeg\" alt=\"Add 1 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\/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=\"2-solved-examples-on-associative-property-of-addition\">Solved Examples on Associative Property of Addition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1.<\/strong> <strong>Is (5 + 10) + 4 the same as 5 + (10 + 4)?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Answer: Yes. Let\u2019s solve and check:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">(5 + 10) + 4 = 15 + 4 = 19<\/p>\n\n\n\n<p class=\"eplus-wrapper\">And, 5 + (10 + 4) = 5 + 14 = 19<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If we group these three numbers differently, we get the same answers.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. <\/strong><strong>Fill in the missing numbers:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>21 + (45 + 36) = (21 + 45) + _ = _<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Answer: Using the associative property of addition,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">21 + (45 + 36) = (21 + 45) + 36 = 102<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Solve for x using the associative property formula: <\/strong><strong>(2 + 3) + x = 2 + (3 + 6)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Answer: Given, <strong>&nbsp;<\/strong><strong>(2 + 3) + x = 2 + (3 + 6)<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">According to the associative property of addition, LHS = RHS,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, 5 + x = 2 + 9<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Or 5 + x = 11<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Or x = 6<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-practice-problems-on-associative-property-of-addition\">Practice Problems on Associative Property of Addition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">The Associative Property of Addition<\/h2><p style=\"display:none;\">Attend this Quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Choose the correct option to fill the blank: $20 + (7 + 4) = (20 + \\underline{} ) + 4$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">27<\/div><div class=\"spq_answer_block\" data-value=\"1\">11<\/div><div class=\"spq_answer_block\" data-value=\"2\">7<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/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: 7<br\/>Using the associative property of addition,<br>\r\n$20 + (7 + 4) = (20 + 7) + 4$<\/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\">Which of these equations is correct?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$12 + (18 + 16) = (12 + 18) + 16$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$11 - 2 + 1 = 11 - (2 + 1)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2 + 3 + 1 = 2 + 3 - 1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$78 - 70 + 1 = 78 + 70 - 1$<\/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: $12 + (18 + 16) = (12 + 18) + 16$<br\/>The associative property holds for addition and multiplication only.<br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.<\/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\">Which of the following is an example of the associative property of addition?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(2 + 3) + 5 = (2 + 3) * 5$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(2 + 3) + 5 = 2 x (3 + 5)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(4 - 5) - 6 = 4 - (5 - 6)$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(9 + 10) + 11 = 9 + (10 +  11)$<\/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: $(9 + 10) + 11 = 9 + (10 +  11)$<br\/>The associative property holds for addition and multiplication only. <br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.<\/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\">Which of these equations is correct?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(2 + 3) + 6 = 2 * (3 + 6)$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(2 + 3) + 6 = 2 + (3 + 6)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(7 - 10) - 15 = 7 - (10 - 15)$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(9 \u00f7 3) \u00f7 3 = 9 \u00f7 (3 \u00f7 3)$<\/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: $(2 + 3) + 6 = 2 + (3 + 6)$<br\/>The associative property holds for addition and multiplication only. The property does not apply to subtraction, and hence the other equations are incorrect.<\/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\": \"The Associative Property of Addition\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"The Associative Property of Addition\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Choose the correct option to fill the blank: $$20 + (7 + 4) = (20 + \\\\underline{} ) + 4$$\",\n                    \"text\": \"Choose the correct option to fill the blank: $$20 + (7 + 4) = (20 + \\\\underline{} ) + 4$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Using the associative property of addition,<br>\r\n$$20 + (7 + 4) = (20 + 7) + 4$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"27\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Using the associative property of addition,<br>\r\n$$20 + (7 + 4) = (20 + 7) + 4$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"11\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Using the associative property of addition,<br>\r\n$$20 + (7 + 4) = (20 + 7) + 4$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Using the associative property of addition,<br>\r\n$$20 + (7 + 4) = (20 + 7) + 4$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"7\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Using the associative property of addition,<br>\r\n$$20 + (7 + 4) = (20 + 7) + 4$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Using the associative property of addition,<br>\r\n$$20 + (7 + 4) = (20 + 7) + 4$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of these equations is correct?\",\n                    \"text\": \"Which of these equations is correct?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The associative property holds for addition and multiplication only.<br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$11 - 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70 + 1 = 78 + 70 - 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property holds for addition and multiplication only. <br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$12 + (18 + 16) = (12 + 18) + 16$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The associative property holds for addition and multiplication only. <br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The associative property holds for addition and multiplication only. <br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is an example of the associative property of addition?\",\n                    \"text\": \"Which of the following is an example of the associative property of addition?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The associative property holds for addition and multiplication only. <br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(2 + 3) + 5 = (2 + 3) * 5$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property holds for addition and multiplication only. <br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(2 + 3) + 5 = 2 x (3 + 5)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property holds for addition and multiplication only. <br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(4 - 5) - 6 = 4 - (5 - 6)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property holds for addition and multiplication only. <br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(9 + 10) + 11 = 9 + (10 +  11)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The associative property holds for addition and multiplication only.<br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The associative property holds for addition and multiplication only.<br>\r\nThe property does not apply to subtraction, and hence the other equations are incorrect.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of these equations is correct?\",\n                    \"text\": \"Which of these equations is correct?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The associative property holds for addition and multiplication only. The property does not apply to subtraction, and hence the other equations are incorrect.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(2 + 3) + 6 = 2 * (3 + 6)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property holds for addition and multiplication only. The property does not apply to subtraction, and hence the other equations are incorrect.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(7 - 10) - 15 = 7 - (10 - 15)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property holds for addition and multiplication only. The property does not apply to subtraction, and hence the other equations are incorrect.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(9 \u00f7 3) \u00f7 3 = 9 \u00f7 (3 \u00f7 3)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property holds for addition and multiplication only. The property does not apply to subtraction, and hence the other equations are incorrect.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(2 + 3) + 6 = 2 + (3 + 6)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The associative property holds for addition and multiplication only. The property does not apply to subtraction, and hence the other equations are incorrect.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The associative property holds for addition and multiplication only. The property does not apply to subtraction, and hence the other equations are incorrect.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Are you a parent or a teacher? Do you want to make learning math a fun activity for your kids? Join <a href=\"https:\/\/www.splashlearn.com\/\">SplashLearn<\/a>, a creative and complete learning platform, for free!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-frequently-asked-questions-on-associative-property-of-addition\">Frequently Asked Questions on Associative Property of Addition<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-99b5eebb-0b18-4e97-8d80-4735b7102a3a\" 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-0-99b5eebb-0b18-4e97-8d80-4735b7102a3a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-99b5eebb-0b18-4e97-8d80-4735b7102a3a\"><strong>How many numbers are required to apply the associative property of addition?<\/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-0-99b5eebb-0b18-4e97-8d80-4735b7102a3a\">\n\n<p>A minimum of three numbers are required to apply the associative property of addition<strong>.<\/strong><\/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-1-99b5eebb-0b18-4e97-8d80-4735b7102a3a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-99b5eebb-0b18-4e97-8d80-4735b7102a3a\"><strong>Does the associative property apply to subtraction?<\/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-1-99b5eebb-0b18-4e97-8d80-4735b7102a3a\">\n\n<p>No. The associative property applies to <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/addition\" title=\"\">addition<\/a> and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication\" title=\"\">multiplication<\/a> only and not to subtraction or division.&nbsp;<\/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-2-99b5eebb-0b18-4e97-8d80-4735b7102a3a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-99b5eebb-0b18-4e97-8d80-4735b7102a3a\"><strong>What is the benefit of using the associative property of addition?<\/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-2-99b5eebb-0b18-4e97-8d80-4735b7102a3a\">\n\n<p>The associative property of addition helps you add numbers faster. Instead of adding a list of numbers in the order that they\u2019re written, add them in any order convenient to you. In the case of a problem like 4 + 19 + 10 + 16, it would be wise to add 4 and 16 to get 20, then add 20 and 10 to get 30, and finally, add 30 and 19 to get 49.<\/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-3-99b5eebb-0b18-4e97-8d80-4735b7102a3a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-99b5eebb-0b18-4e97-8d80-4735b7102a3a\"><strong>Is\u00a0 there any other property of addition apart from the associative property?<\/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-3-99b5eebb-0b18-4e97-8d80-4735b7102a3a\">\n\n<p>Yes. There are four properties related to addition. The other three properties are commutative property of addition, additive identity of addition, and the distributive property of multiplication over addition.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Definition: To \u201cassociate\u201d means to connect or join with something. According to the associative property of addition the sum of three or more numbers remains the same regardless of how the numbers are grouped. Here\u2019s an example of how the sum does NOT change irrespective of how the addends are grouped. As seen in the &#8230; <a title=\"Associative Property of Addition &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property-of-addition\" aria-label=\"More on Associative Property of Addition &#8211; Definition with 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-916","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\/916","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=916"}],"version-history":[{"count":16,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/916\/revisions"}],"predecessor-version":[{"id":36912,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/916\/revisions\/36912"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=916"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=916"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=916"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}