{"id":2132,"date":"2022-04-26T09:02:58","date_gmt":"2022-04-26T09:02:58","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=2132"},"modified":"2024-02-18T16:34:14","modified_gmt":"2024-02-18T16:34:14","slug":"2132-2","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/associative-property-of-multiplication","title":{"rendered":"Associative Property of Multiplication &#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-978e5393-0327-4e3f-ae4f-f5e00a877db2\" 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\/multiplication\/associative-property-of-multiplication#0-what-is-the-associative-property-of-multiplication>What is the associative property of multiplication?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/associative-property-of-multiplication#1-solved-examples>Solved examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/associative-property-of-multiplication#2-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/associative-property-of-multiplication#3-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<p class=\"eplus-wrapper\">Multiplication is one of the most basic elementary arithmetic operations that a student learns about while growing up. In elementary mathematics, multiplication is a more advanced way of adding a number multiple times. The very foundation of multiplication lies with the concept of repeated addition and hence the operation of multiplication follows the same properties as the addition operator. One of these properties is the associative property of multiplication.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-associative-property-of-multiplication\">What is the Associative Property of Multiplication?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">To \u201cassociate\u201d means to connect or join with something. The associative property of multiplication says that while multiplying three numbers, regardless of the way the numbers are grouped, the end result will always be the same.<br>Let\u2019s try to understand the associative property of multiplication with an example:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s try multiplying the numbers 2, 3, and 5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"293\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/associative-property-of-multiplication-example.png\" alt=\"Associative Property of Multiplication Example\" class=\"wp-image-40139\" title=\"Associative Property of Multiplication Example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/associative-property-of-multiplication-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/associative-property-of-multiplication-example-300x142.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Now, we can multiply these numbers in different ways.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We could first multiply 2 and 3 and then multiply their product with 5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"346\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/verify-associative-property-of-multiplication.png\" alt=\"Verify Associative Property of Multiplication\" class=\"wp-image-40140\" title=\"Verify Associative Property of Multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/verify-associative-property-of-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/verify-associative-property-of-multiplication-300x167.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Or we could multiply 3 and 5 first and then multiply the product of these two numbers with&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">As we can see, the product in both the cases is the same. This property, where the order in which the three numbers are multiplied does not affect the result, is called the associative property of multiplication.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"320\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/associative-property-of-multiplication-definition.png\" alt=\"Associative Property of Multiplication Definition\" class=\"wp-image-40141\" title=\"Associative Property of Multiplication Definition\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/associative-property-of-multiplication-definition.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/associative-property-of-multiplication-definition-300x155.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Since addition is the foundation of multiplication, the associative property is only followed by addition and multiplication. The law of associativity does not apply to the operations of subtraction and division.<\/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-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 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href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-product-for-the-multiplication-questions\" 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_pv_find_product_4dby1d_1_pt.png\" alt=\"Choose the Product for the Multiplication Questions 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 Product for the Multiplication Questions 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-to-complete-each-of-the-multiplication-expressions\" 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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\/dec_mul_div_complete_mul_pattern_pt.png\" alt=\"Complete the Decimal Multiplication Pattern 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\">Complete the Decimal Multiplication Pattern 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\/complete-the-multiplication-between-fractions-and-whole-numbers\" 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_complete_multiplication_pt.png\" alt=\"Complete the Multiplication Between Fractions and Whole Numbers 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\">Complete the Multiplication Between Fractions and Whole Numbers 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\/complete-the-multiplication-expression-using-the-fraction-models\" 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_multiply_models_unit_by_whole_pt.png\" alt=\"Complete the Multiplication Expression Using the Fraction Models 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\">Complete the Multiplication Expression Using the Fraction Models 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            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id=\"1-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: Solve the expression <\/strong>$6 \\times 7 \\times 8$<strong> in two different ways.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Grouping the first two terms in the expression,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(6 \\times 7) \\times 8<strong>&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= (42) \\times 8$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 336$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Grouping the second two terms in the expression,<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;<\/strong>$6 \\times (7 \\times 8)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 6 \\times (56)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 336$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: Does the given equation show the associative property of multiplication?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<\/strong>$2 \\times 3 \\times 4 = 3 \\times 2 \\times&nbsp;4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> For an equation to show the associative property of multiplication, a minimum of three numbers must be multiplied. The given equation is the multiplication of 3, 2, and 4. The order of the numbers reversed gives the same answer, that is, 24. Thus, it shows an associative property.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3: Use associative property of multiplication to find a and b in the equation,<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(3 \\times a) \\times 9 = 3 \\times (4 \\times b)$<br><strong>Solution:<\/strong> If the equation follows the associative property of multiplication, though grouped differently, the three terms on either side of the equation should be the same. 3 is present on either side. It follows that $a = 4$ and $9 = 6$.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-the-numbers-using-commutative-property-of-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-the-numbers-using-commutative-property-of-addition.jpeg\" alt=\"Add the Numbers Using Commutative Property of Addition\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expression-for-array\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expression-for-array.jpeg\" alt=\"Addition and Multiplication Expression for Array Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expressions.jpeg\" alt=\"Addition and Multiplication Expressions 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\/apply-commutative-property-of-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\/apply-commutative-property-of-addition.jpeg\" alt=\"Apply Commutative Property of 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\/apply-commutative-property\" 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\/apply-commutative-property.jpeg\" alt=\"Apply Commutative Property 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 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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\/break-it-down-using-distributive-property\" 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\/break-it-down-using-distributive-property.jpeg\" alt=\"Break it Down using Distributive Property 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\/break-multiply-add-using-distributive-property\" 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});\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Associative Property of Multiplication - 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\">Which of the following does not show the associative property of multiplication?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$(a \\times b) \\times c = a \\times (b \\times c)$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$(p \\times q) \\times r = a \\times (b \\times c)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$(c \\times e) \\times d = c \\times (e \\times d)$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(m \\times n) \\times o = m \\times (n \\times o)$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $(p \\times q) \\times r = a \\times (b \\times c)$<br\/>The terms on the left are not the same as the ones on the right of the equation. The associative property is only valid for grouping the terms.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Given that $(10 \\times m) \\times 2 = 10 \\times (5 \\times 2)$, what is the value of m to make the equation true?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">20<\/div><div class=\"spq_answer_block\" data-value=\"1\">10<\/div><div class=\"spq_answer_block\" data-value=\"2\">5<\/div><div class=\"spq_answer_block\" data-value=\"3\">100<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 5<br\/>To make the equation true, it should follow the associative property of multiplication. The three terms on the left are 10, m, and 2, and on the right are 10, 5, and 2. Hence, clearly, $m = 5$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If the following equation follows the associative property of multiplication, find p and q. $(8 \\times p) \\times 6 = 8 \\times (11 \\times q)<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$p = 11, q = 6$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$p = 6, q = 11$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$p = 8, q = 11$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$p = 11, q = 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: $p = 11, q = 6$<br\/>If the equation follows the associative property of multiplication, though grouped differently, the three terms on either side of the equation should be the same. 8 is present on either side. It naturally follows that $p = 11$ and $q = 6$, to ensure 8, 11, and 6 are present on either side as well.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following does not show the associative property?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Addition<\/div><div class=\"spq_answer_block\" data-value=\"1\">Multiplication<\/div><div class=\"spq_answer_block\" data-value=\"2\">Subtraction<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/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: Subtraction<br\/>The associative property applies to addition and multiplication but not to subtraction and division. The grouping of three or more terms multiplied or added does not affect the result.<\/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\": \"Associative Property of Multiplication - Definition With Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Associative Property of Multiplication\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following does not show the associative property of multiplication?\",\n                    \"text\": \"Which of the following does not show the associative property of multiplication?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The terms on the left are not the same as the ones on the right of the equation. 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The associative property is only valid for grouping the terms.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(c \\\\times e) \\\\times d = c \\\\times (e \\\\times d)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The terms on the left are not the same as the ones on the right of the equation. The associative property is only valid for grouping the terms.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$(m \\\\times n) \\\\times o = m \\\\times (n \\\\times o)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The terms on the left are not the same as the ones on the right of the equation. The associative property is only valid for grouping the terms.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(p \\\\times q) \\\\times r = a \\\\times (b \\\\times c)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The terms on the left are not the same as the ones on the right of the equation. The associative property is only valid for grouping the terms.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The terms on the left are not the same as the ones on the right of the equation. The associative property is only valid for grouping the terms.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Given that $$(10 \\\\times m) \\\\times 2 = 10 \\\\times (5 \\\\times 2)$$, what is the value of m to make the equation true?\",\n                    \"text\": \"Given that $$(10 \\\\times m) \\\\times 2 = 10 \\\\times (5 \\\\times 2)$$, what is the value of m to make the equation true?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"To make the equation true, it should follow the associative property of multiplication. The three terms on the left are 10, m, and 2, and on the right are 10, 5, and 2. Hence, clearly, $$m = 5$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"20\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To make the equation true, it should follow the associative property of multiplication. The three terms on the left are 10, m, and 2, and on the right are 10, 5, and 2. Hence, clearly, $$m = 5$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To make the equation true, it should follow the associative property of multiplication. The three terms on the left are 10, m, and 2, and on the right are 10, 5, and 2. Hence, clearly, $$m = 5$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"100\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To make the equation true, it should follow the associative property of multiplication. The three terms on the left are 10, m, and 2, and on the right are 10, 5, and 2. Hence, clearly, $$m = 5$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"To make the equation true, it should follow the associative property of multiplication. The three terms on the left are 10, m, and 2, and on the right are 10, 5, and 2. Hence, clearly, $$m = 5$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"To make the equation true, it should follow the associative property of multiplication. The three terms on the left are 10, m, and 2, and on the right are 10, 5, and 2. Hence, clearly, $$m = 5$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If the following equation follows the associative property of multiplication, find p and q. $$(8 \\\\times p) \\\\times 6 = 8 \\\\times (11 \\\\times q)\",\n                    \"text\": \"If the following equation follows the associative property of multiplication, find p and q. $$(8 \\\\times p) \\\\times 6 = 8 \\\\times (11 \\\\times q)\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If the equation follows the associative property of multiplication, though grouped differently, the three terms on either side of the equation should be the same. 8 is present on either side. It naturally follows that $$p = 11$$ and $$q = 6$$, to ensure 8, 11, and 6 are present on either side as well.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$p = 6, q = 11$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the equation follows the associative property of multiplication, though grouped differently, the three terms on either side of the equation should be the same. 8 is present on either side. It naturally follows that $$p = 11$$ and $$q = 6$$, to ensure 8, 11, and 6 are present on either side as well.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$p = 8, q = 11$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the equation follows the associative property of multiplication, though grouped differently, the three terms on either side of the equation should be the same. 8 is present on either side. It naturally follows that $$p = 11$$ and $$q = 6$$, to ensure 8, 11, and 6 are present on either side as well.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$p = 11, q = 8$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If the equation follows the associative property of multiplication, though grouped differently, the three terms on either side of the equation should be the same. 8 is present on either side. It naturally follows that $$p = 11$$ and $$q = 6$$, to ensure 8, 11, and 6 are present on either side as well.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$p = 11, q = 6$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If the equation follows the associative property of multiplication, though grouped differently, the three terms on either side of the equation should be the same. 8 is present on either side. It naturally follows that $$p = 11$$ and $$q = 6$$, to ensure 8, 11, and 6 are present on either side as well.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If the equation follows the associative property of multiplication, though grouped differently, the three terms on either side of the equation should be the same. 8 is present on either side. It naturally follows that $$p = 11$$ and $$q = 6$$, to ensure 8, 11, and 6 are present on either side as well.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following does not show the associative property?\",\n                    \"text\": \"Which of the following does not show the associative property?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The associative property applies to addition and multiplication but not to subtraction and division. The grouping of three or more terms multiplied or added does not affect the result.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Addition\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property applies to addition and multiplication but not to subtraction and division. The grouping of three or more terms multiplied or added does not affect the result.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Multiplication\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property applies to addition and multiplication but not to subtraction and division. The grouping of three or more terms multiplied or added does not affect the result.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property applies to addition and multiplication but not to subtraction and division. The grouping of three or more terms multiplied or added does not affect the result.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Subtraction\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The associative property applies to addition and multiplication but not to subtraction and division. The grouping of three or more terms multiplied or added does not affect the result.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The associative property applies to addition and multiplication but not to subtraction and division. The grouping of three or more terms multiplied or added does not affect the result.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\" 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-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\"><strong>What is the benefit of using the associative property of multiplication?<\/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-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\">\n\n<p class=\"eplus-wrapper\">The associative property of multiplication helps you multiply numbers faster. Instead of multiplying a list of numbers in the order in which they\u2019re written, group them differently to multiply in an order convenient to you. In the expression $5 \\times 5 \\times (8)$, it would be wise to multiply 5 and 8 to get 40, then multiply 5 to get 200.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(5 \\times 5) \\times (8)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= (5 \\times 8) \\times (5)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 40 \\times 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 200$<\/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-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\"><strong>Apart from associative property, which other properties does multiplication follow?<\/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-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\">\n\n<p class=\"eplus-wrapper\">The arithmetic operation of multiplication follows two other properties, which include commutative property and distributive property.<\/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-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\"><strong>What is the difference between the commutative and associative property of multiplication?<\/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-b03ef6e0-5d32-4a76-9831-7d6f2499f85f\">\n\n<p class=\"eplus-wrapper\">The commutative property is concerned with the order of numbers, whereas the associative property is concerned with the grouping of numbers. In both cases, the result is not affected.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Commutative: $4 \\times 5 = 5 \\times 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Associative: $2 \\times (4 \\times 5) = 5 \\times (4 \\times 2)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The commutative property can be applied to two terms. As more than two numbers are required for grouping, three or more terms must be present to apply the associative property.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiplication is one of the most basic elementary arithmetic operations that a student learns about while growing up. In elementary mathematics, multiplication is a more advanced way of adding a number multiple times. The very foundation of multiplication lies with the concept of repeated addition and hence the operation of multiplication follows the same properties &#8230; <a title=\"Associative Property of Multiplication &#8211; Definition With Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/associative-property-of-multiplication\" aria-label=\"More on Associative Property of Multiplication &#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-2132","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\/2132","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=2132"}],"version-history":[{"count":32,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2132\/revisions"}],"predecessor-version":[{"id":40142,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2132\/revisions\/40142"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=2132"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=2132"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=2132"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}