{"id":524,"date":"2022-03-11T12:50:49","date_gmt":"2022-03-11T12:50:49","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test\/?page_id=524"},"modified":"2023-04-04T15:32:26","modified_gmt":"2023-04-04T15:32:26","slug":"associative-property-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property","title":{"rendered":"Associative Property &#8211; Definition, Examples, FAQs, Practice Problems"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 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-bd4c96c4-5e6d-45dd-bfb3-d4c12ece0cd5\" 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#0-what-is-associative-property-in-math>What Is Associative Property in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property#1-associative-property-of-addition>Associative Property of Addition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property#2-associative-property-of-multiplication>Associative Property of Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property#3-difference-between-associative-property-and-commutative-property>Difference between Associative Property and Commutative Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property#10-practice-problems-on-associative-property>Practice Problems On Associative Property<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property#11-frequently-asked-questions-on-associative-property>Frequently Asked Questions On Associative Property<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-associative-property-in-math\">What Is Associative Property in Math?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Associative property is defined as, when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For instance,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">2 \u00d7 (7 \u00d7 6) = (2 \u00d7 7) \u00d7 6<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">2 + (7 + 6) = (2 + 7) + 6<\/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-associative-property-of-addition\">Associative Property of Addition<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Associative property for addition implies that regardless of how numbers are grouped, the final sum of the numbers will remain the same. This can be expressed as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>(<\/strong><strong><em>x<\/em><\/strong><strong> + <\/strong><strong><em>y<\/em><\/strong><strong>) + <\/strong><strong><em>z<\/em><\/strong><strong> = <\/strong><strong><em>x<\/em><\/strong><strong> + (<\/strong><strong><em>y<\/em><\/strong><strong> + <\/strong><strong><em>z<\/em><\/strong><strong>)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"359\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/pasted-image-0-8.png\" alt=\"Associative property of addition visual\" class=\"wp-image-7328\" title=\"Associative property of addition visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/pasted-image-0-8.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/pasted-image-0-8-300x174.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\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 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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-associative-property-of-multiplication\">Associative Property of Multiplication<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Associative property for multiplication implies that regardless of how numbers are grouped, the final product of the numbers will remain the same. This can be expressed as:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong><em>p <\/em><\/strong><strong>\u00d7<\/strong><strong><em> (q <\/em><\/strong><strong>\u00d7<\/strong><strong><em> r) = (p <\/em><\/strong><strong>\u00d7<\/strong><strong><em> q) <\/em><\/strong><strong>\u00d7<\/strong><strong><em> r<\/em><\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"678\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/pasted-image-0-1-2.png\" alt=\"Associative property of multiplication visual\" class=\"wp-image-7327\" title=\"Associative property of multiplication visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/pasted-image-0-1-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/08\/pasted-image-0-1-2-274x300.png 274w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-difference-between-associative-property-and-commutative-property\"><br>Difference between Associative Property and Commutative Property<\/h2>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-commutative-property-\"><strong>Commutative Property<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Commutative Property implies that when multiplication or addition is performed on two numbers, the result remains the same, irrespective of their arrangement.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, when you know about both the properties, you must have figured out that the only difference lies in the number of numbers involved in the operation.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Two numbers are involved in commutative property and more than two numbers are involved in associative property.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-is-associative-property-applicable-to-division-and-subtraction-\">Is Associative Property Applicable to Division and Subtraction?&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">You must be wondering why these properties don\u2019t apply to division and subtraction. Let\u2019s take an example to answer this \u201cWhy?\u201d.&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading eplus-wrapper\" id=\"6-in-the-case-of-subtraction-\"><strong>In the case of subtraction:<\/strong><\/h4>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">12 \u2013 (6 \u2013 2) = 12 \u2013 4 = 8<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(12 \u2013 6) \u2013 2 = 6 \u2013 2 = 4<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This implies, 12 \u2013 (6 \u2013 2) \u2260 (12 \u2013 6) \u2013 2. So, the associative property is not applicable for subtraction.&nbsp;<\/p>\n\n\n\n<h4 class=\"wp-block-heading eplus-wrapper\" id=\"7-in-the-case-of-division-\"><strong>In the case of division:<\/strong><\/h4>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(24 \u00f7 4) \u00f7 2 = 6 \u00f7 2 = 3<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">24 \u00f7 (4 \u00f7 2) = 24 \u00f7 2 = 12<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This implies, (24 \u00f7 4) \u00f7 2 \u2260 24 \u00f7 (4 \u00f7 2). So, the associative property is not applicable for the division.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-fun-fact\">Fun Fact!<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The associative property gets its name from the word \u201cassociate\u201d, and it refers to the grouping of numbers.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-solved-examples-on-associative-property\">Solved Examples On Associative Property<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1: <\/strong>If (30 \u00d7 20) \u00d7 15 = 9000, then use associative property to find (15 \u00d7 30) \u00d7 20.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong>According to the associative property of multiplication, (30 \u00d7 20) \u00d7 15 = (15 \u00d7 30) \u00d7 20.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Given that (30 \u00d7 20) \u00d7 15 = 9000,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(15 \u00d7 30) \u00d7 20 = 9000.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2: <\/strong>Check whether the associative property of addition is implied in the following equations.<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">20 + (60 + 5) = (20 + 60) + 5<\/li>\n\n\n\n<li class=\" eplus-wrapper\">30 + (40 + 20) = (30 + 10) + 50<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">According to the associative property of addition, 20 + (60 + 5) = (20 + 60) + 5. Let&#8217;s check further.&nbsp;<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>LHS<\/strong>: 20 + (60 + 5)&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong>20 +(65)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;85<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>RHS<\/strong>: (20 + 60) + 5<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(80) + 5<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;85<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">LHS = RHS. Thus, the associative property of addition is implied in this equation.&nbsp;<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">According to the associative property of addition, 30 + (40 + 20) = (30 + 10) + 50. Let\u2019s check further,&nbsp;<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>LHS: <\/strong>30 + (40 + 20)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong>30 + (60)<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;90<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>RHS: <\/strong>(30 + 10) + 50<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong>(40) + 50<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;90<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">LHS \u2260 RHS. Thus, the associative property of addition is not implied in this equation.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 3: <\/strong>According to the associative property, fill in the missing number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(5 + 10) + 4&nbsp;=&nbsp;(5 + 4) + __ = 14<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution: <\/strong>According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped.&nbsp;Hence, (5 + 10) + 4&nbsp;=&nbsp;(5 + 4) + 10 = 14<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-practice-problems-on-associative-property\">Practice Problems On Associative Property<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">What is Associative Property? 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\">Complete the following equation:  2 \u00d7 ( _ \u00d7 6) = (2 \u00d7 5) \u00d7 _<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2, 4<\/div><div class=\"spq_answer_block\" data-value=\"1\">5, 6<\/div><div class=\"spq_answer_block\" data-value=\"2\">4, 6<\/div><div class=\"spq_answer_block\" data-value=\"3\">7, 8<\/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, 6<br\/>According to the associative property, when more than two numbers are multiplied the result remains the same, irrespective of how they are grouped.<br>\r\nHence, $2 \u00d7 (5 \u00d7 6) = (2 \u00d7 5) \u00d7 6$<\/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\">Fill in the blanks: 20 + 9 + _ = 9 + 5 + _<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5, 20<\/div><div class=\"spq_answer_block\" data-value=\"1\">2, 3<\/div><div class=\"spq_answer_block\" data-value=\"2\">4, 5<\/div><div class=\"spq_answer_block\" data-value=\"3\">7, 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: 5, 20<br\/>According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped.<br>\r\nHence, $20 + 9 + 5 = 9 + 5 + 20$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of these equations is correct?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(2 + 3) + 6 = 2 \u00d7 (3 + 6)$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(5 + 6) + 4 = 5 + (6 + 4)$<\/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: $(5 + 6) + 4 = 5 + (6 + 4)$<br\/>The associative property holds for addition and multiplication only. The property does not apply to subtraction or division, 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\": \"What is Associative Property? 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                   \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the associative property, when more than two numbers are multiplied the result remains the same, irrespective of how they are grouped.<br>\r\nHence, $$2 \u00d7 (5 \u00d7 6) = (2 \u00d7 5) \u00d7 6$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"7, 8\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the associative property, when more than two numbers are multiplied the result remains the same, irrespective of how they are grouped.<br>\r\nHence, $$2 \u00d7 (5 \u00d7 6) = (2 \u00d7 5) \u00d7 6$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5, 6\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the associative property, when more than two numbers are multiplied the result remains the same, irrespective of how they are grouped.<br>\r\nHence, $$2 \u00d7 (5 \u00d7 6) = (2 \u00d7 5) \u00d7 6$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the associative property, when more than two numbers are multiplied the result remains the same, irrespective of how they are grouped.<br>\r\nHence, $$2 \u00d7 (5 \u00d7 6) = (2 \u00d7 5) \u00d7 6$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Fill in the blanks: 20 + 9 + _ = 9 + 5 + _\",\n                    \"text\": \"Fill in the blanks: 20 + 9 + _ = 9 + 5 + _\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped.<br>\r\nHence, $$20 + 9 + 5 = 9 + 5 + 20$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2, 3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped.<br>\r\nHence, $$20 + 9 + 5 = 9 + 5 + 20$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4, 5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped.<br>\r\nHence, $$20 + 9 + 5 = 9 + 5 + 20$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"7, 4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped.<br>\r\nHence, $$20 + 9 + 5 = 9 + 5 + 20$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5, 20\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped.<br>\r\nHence, $$20 + 9 + 5 = 9 + 5 + 20$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the associative property, when more than two numbers are added, the result remains the same irrespective of how they are grouped.<br>\r\nHence, $$20 + 9 + 5 = 9 + 5 + 20$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": 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The property does not apply to subtraction or division, 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\": \"$$(2 + 3) + 6 = 2 \u00d7 (3 + 6)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property holds for addition and multiplication only. The property does not apply to subtraction or division, 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 or division, 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 or division, and hence the other equations are incorrect.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(5 + 6) + 4 = 5 + (6 + 4)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The associative property holds for addition and multiplication only. The property does not apply to subtraction or division, 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 or division, 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=\"11-frequently-asked-questions-on-associative-property\">Frequently Asked Questions On Associative Property<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\" 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-0-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\">Associative property of addition and multiplication can be used for how many numbers?<\/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-0-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\">\n\n<p class=\"wp-block-paragraph\">The associative property of addition and multiplication holds true for 3 or more numbers.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\">Does the associative property apply to fractional numbers?<\/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-1-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\">\n\n<p class=\"wp-block-paragraph\">Yes, the associative property of addition and multiplication holds true for fractional numbers.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\">Does the associative property apply to an equation that has 0 in it?<\/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-2-592fd0ca-cfb1-46e9-971e-c61cd3d79c47\">\n\n<p class=\"wp-block-paragraph\">Yes, the associative property holds true for an equation that has 0 in it.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Is Associative Property in Math? Associative property is defined as, when more than two numbers are added or multiplied, the result remains the same, irrespective of how they are grouped. For instance,&nbsp; 2 \u00d7 (7 \u00d7 6) = (2 \u00d7 7) \u00d7 6 2 + (7 + 6) = (2 + 7) + 6 &#8230; <a title=\"Associative Property &#8211; Definition, Examples, FAQs, Practice Problems\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property\" aria-label=\"More on Associative Property &#8211; Definition, Examples, FAQs, Practice Problems\">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-524","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\/524","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=524"}],"version-history":[{"count":38,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/524\/revisions"}],"predecessor-version":[{"id":27330,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/524\/revisions\/27330"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=524"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=524"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=524"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}