{"id":2173,"date":"2022-04-26T13:20:40","date_gmt":"2022-04-26T13:20:40","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=2173"},"modified":"2024-01-01T07:33:04","modified_gmt":"2024-01-01T07:33:04","slug":"properties-of-multiplication-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication","title":{"rendered":"Properties of Multiplication &#8211; Definition, Examples, Facts, FAQs"},"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-5349659c-9236-45d9-b116-01ade42f9ffd\" 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\/properties-of-multiplication#0-what-are-the-properties-of-multiplication>What Are the Properties of Multiplication?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication#5-identity-property-of-multiplication>Identity Property of Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication#6-zero-property-of-multiplication>Zero Property of Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication#11-solved-examples-on-properties-of-multiplication>Solved Examples on Properties of Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication#12-practice-problems-on-properties-of-multiplication>Practice Problems on Properties of Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication#13-frequently-asked-questions-on-properties-of-multiplication>Frequently Asked Questions on Properties of Multiplication<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\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%\">\n<h2 class=\"wp-block-heading\" id=\"0-what-are-the-properties-of-multiplication\">What Are the Properties of Multiplication?<\/h2>\n\n\n\n<p><strong>The properties of multiplication are certain rules or formulas that help in simplifying the expressions involving multiplication.<\/strong><\/p>\n\n\n\n<p>We know that <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication\">multiplication<\/a> is defined as <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/repeated-addition\">repeated addition<\/a>.&nbsp;<\/p>\n\n\n\n<p>For example, $12 \\times 6$ is 12 added to itself 6 times.<\/p>\n\n\n\n<p>$12 \\times 6= 12 + 12 + 12 + 12 + 12 + 12$<\/p>\n\n\n\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 72$<\/p>\n\n\n\n<p>The five basic properties of multiplication are:&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/commutative-property\">Commutative property<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property\">Associative property<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/distributive-property\">Distributive property<\/a><\/li>\n\n\n\n<li>Identity property<\/li>\n\n\n\n<li><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/zero-property-of-multiplication\">Zero property<\/a><\/li>\n<\/ul>\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\/choose-the-correct-product-for-the-multiplication-expressions\" 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_mult_match_4dby1d_fluently_pt.png\" alt=\"Choose the Correct Product for the Multiplication Expressions 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 Product for the Multiplication Expressions 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-missing-number-in-the-multiplication-solution\" 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_missing_2dby1d_pt.png\" alt=\"Choose the Missing Number in the Multiplication Solution 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 Missing Number in the Multiplication Solution 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-multiplication-expression-representing-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_represent_mult_unit_by_whole_pt.png\" alt=\"Choose the Multiplication Expression Representing 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\">Choose the Multiplication Expression Representing 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 class=\"game-card-container-outer\">\r\n\t<a 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\" 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_mult_match_3dby1d_fluently_pt.png\" alt=\"Choose to Complete each of the Multiplication Expressions 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 to Complete each of the Multiplication Expressions 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-decimal-multiplication-pattern\" 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\/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 class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-fact-of-11\" 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_missing_num_pt.png\" alt=\"Complete the Multiplication Fact of 11 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 Fact of 11 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-facts-of-2\" 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_numMissing2_pt.png\" alt=\"Complete the Multiplication Facts of 2 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 Facts of 2 Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-properties-of-multiplication\">Properties of Multiplication<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-html-table\"><tbody><tr class=\"wj-html-tr\"><td colspan=\"2\"><strong>Properties of Multiplication<\/strong><\/td><\/tr><tr><td>Commutative Property<\/td><td>$a \\times b = b \\times a$<\/td><\/tr><tr><td>Associative Property<\/td><td>$a \\times (b \\times c) = a \\times (b \\times c)$<\/td><\/tr><tr><td>Distributive Property<\/td><td>$a \\times (b + c) = (a \\times b) + (a \\times c)$<br>$a \\times (b\\;-\\;c) = (a \\times b) \\;-\\; (a \\times c)$<\/td><\/tr><tr><td>Identity Property<\/td><td>$a \\times 1 = a$<\/td><\/tr><tr><td>Zero Property<\/td><td>$a \\times 0 = 0$<\/td><\/tr><\/tbody><\/table><\/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\/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-multiplication-in-everyday-life\" 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-multiplication-in-everyday-life.jpeg\" alt=\"Apply Multiplication in Everyday Life 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-the-multiplication-expression\" 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-the-multiplication-expression.jpeg\" alt=\"Break the Multiplication Expression 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\/choose-your-own-multiplication-strategy\" 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\/choose-your-own-multiplication-strategy.jpeg\" alt=\"Choose Your own Multiplication Strategy 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\/commutative-property-of-multiplication\" 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\/commutative-property-of-multiplication.jpeg\" alt=\"Commutative Property of Multiplication Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/compare-the-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\/compare-the-multiplication-expressions.jpeg\" alt=\"Compare the 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\/comparing-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\/comparing-multiplication-expressions.jpeg\" alt=\"Comparing 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\/complete-multiplication-and-division-sentences\" 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\/complete-multiplication-and-division-sentences.jpeg\" alt=\"Complete Multiplication and Division Sentences Worksheet\">\r\n\t    <\/div>\r\n\t\t<div 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container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-commutative-property-of-multiplication\">Commutative Property of Multiplication<\/h2>\n\n\n\n<p><strong>The commutative property of multiplication states that the multiplication of two numbers remains the same even if the order of numbers is changed. Changing the order of multiplication doesn\u2019t change the product.<\/strong><\/p>\n\n\n\n<p><strong>Example 1: <\/strong>Let\u2019s multiply 3 by 5.<\/p>\n\n\n\n<p>$3 \\times 5 = 3 + 3 + 3 + 3 + 3 = 15$<\/p>\n\n\n\n<p>Now on reversing the order of multiplication, we get&nbsp;<\/p>\n\n\n\n<p>$5 \\times 3 = 5 + 5 + 5 = 15$&nbsp;<\/p>\n\n\n\n<p>The answer is the same even after changing the order of the numbers. Thus, the multiplication is commutative.<\/p>\n\n\n\n<p>Look at the same example using a multiplication array.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"421\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/closure-property-of-multiplication-example-with-multiplication-array.png\" alt=\"Closure property of multiplication example with multiplication array\" class=\"wp-image-36906\" title=\"Closure property of multiplication example with multiplication array\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/closure-property-of-multiplication-example-with-multiplication-array.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/closure-property-of-multiplication-example-with-multiplication-array-300x204.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-associative-property-of-multiplication\">Associative Property of Multiplication<\/h2>\n\n\n\n<p><strong>Associative property of multiplication states that if we want to multiply any three numbers together, the answer will always be the same irrespective of the order in which we multiply the numbers.<\/strong><\/p>\n\n\n\n<p>$a \\times (b \\times c)=(a \\times b) \\times c$<\/p>\n\n\n\n<p><strong>Example:<\/strong>&nbsp;<\/p>\n\n\n\n<p>$2 \\times (5 \\times 4)=2 \\times 20 = 40$<\/p>\n\n\n\n<p>$(2 \\times 5) \\times 4=10 \\times 4 = 40$<\/p>\n\n\n\n<p>As in both cases, the answer we get is the same, irrespective of how the numbers are grouped. Hence, multiplication is associative.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-distributive-property-of-multiplication\">Distributive Property of Multiplication<\/h2>\n\n\n\n<p><strong>The distributive property of multiplication states that multiplication can be distributed over <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/addition\"><strong>addition<\/strong><\/a><strong> as well as <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/subtraction\/subtract\"><strong>subtraction<\/strong><\/a><strong>. <\/strong>This property helps us solve the expressions with brackets. It also speeds up the calculation by reducing the steps.&nbsp;<\/p>\n\n\n\n<p>Distributive property of multiplication over addition:<\/p>\n\n\n\n<p>$a (b + c) = ab + ac$<\/p>\n\n\n\n<p>Distributive property of multiplication over subtraction:&nbsp;<\/p>\n\n\n\n<p>$a(b\\;-\\;c) = ab\\;-\\;ac$<\/p>\n\n\n\n<p><strong>Example 1:&nbsp; <\/strong>$2 \\times (3 + 1)$<\/p>\n\n\n\n<p>$2 \\times (3 + 1) = 2 \\times 4 = 8$&nbsp;<\/p>\n\n\n\n<p>$2 \\times (3 + 1) =(2 \\times 3) + (2 \\times 1) = 6 + 2 = 8$<\/p>\n\n\n\n<p>In both cases, we get the same answer. Hence, the multiplication is distributive over addition.<\/p>\n\n\n\n<p><strong>Example 2:&nbsp; <\/strong>$5 \\times (4\\;-\\;2)$<\/p>\n\n\n\n<p>$5 \\times (4\\;-\\;2) = 5 \\times 2 = 10$&nbsp;<\/p>\n\n\n\n<p>$5 \\times (4\\;-\\;2) = (5 \\times 4)\\;-\\;(5 \\times 2) = 20\\;-\\;10 = 10$<\/p>\n\n\n\n<p>The multiplication is distributive over subtraction.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-identity-property-of-multiplication\">Identity Property of Multiplication<\/h2>\n\n\n\n<p><strong>The identity property of multiplication states that if you multiply any number by 1, the answer will be the number itself.<\/strong> <strong>It is represented as <\/strong>$a \\times 1 = a$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Examples:<\/strong><\/p>\n\n\n\n<p>$3 \\times 1 = 3$<\/p>\n\n\n\n<p>$7 \\times 1 = 7$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-zero-property-of-multiplication\">Zero Property of Multiplication<\/h2>\n\n\n\n<p><strong>According to the zero property of multiplication, when a number is multiplied with 0, the product is always 0.<\/strong>&nbsp;<\/p>\n\n\n\n<p>It is represented as, $a \\times 0 = 0$.<\/p>\n\n\n\n<p><strong>Examples:<\/strong>&nbsp;&nbsp;<\/p>\n\n\n\n<p>$42 \\times 0 = 0$<\/p>\n\n\n\n<p>$0 \\times 23 = 0$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-other-important-properties-of-multiplication\">Other Important Properties of Multiplication<\/h2>\n\n\n\n<p>Let\u2019s discuss a few other important properties of multiplication.<\/p>\n\n\n\n<p><strong>Closure Property of Multiplication<\/strong><\/p>\n\n\n\n<p><strong>The closure property of multiplication states that when a set of numbers is closed under multiplication, then the product of any two numbers from the set belongs to the set itself.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Example 1:<\/strong> The multiplication of two integers is also an integer. If a and b are integers, then $c = a \\times b$ will also be an integer. So, integers are closed under multiplication. For example,&nbsp;$(\\;-\\;2) \\times 8 = (\\;-\\;16)$.<\/p>\n\n\n\n<p><strong>Example 2: <\/strong>The product of any two rational numbers is also a rational number.<\/p>\n\n\n\n<p><strong>Multiplication Property of Equality<\/strong><\/p>\n\n\n\n<p><strong>If we multiply both sides of an equation with the same number, the equality holds.&nbsp;<\/strong><\/p>\n\n\n\n<p>If $a = b$, then $a \\times c = b \\times c$<\/p>\n\n\n\n<p>Consider an equation $\\frac{1}{2}x = 50$<\/p>\n\n\n\n<p>Multiply both sides by 2, we get<\/p>\n\n\n\n<p>$\\frac{1}{2}x \\times 2 = 50 \\times 2$<\/p>\n\n\n\n<p>$x = 100$<\/p>\n\n\n\n<p><strong>Inverse Property of Multiplication<\/strong><\/p>\n\n\n\n<p><strong>The multiplicative inverse property states that if we multiply a number with its reciprocal (multiplicative inverse), the product is always equal to 1.<\/strong><\/p>\n\n\n\n<p>The reciprocal is defined as the multiplicative inverse of a number and the reciprocal of a number is given by 1 divided by that number.<\/p>\n\n\n\n<p>It represented by $a \\times 1a = 1$.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-rules-of-multiplying-signed-numbers\">Rules of Multiplying Signed Numbers<\/h2>\n\n\n\n<figure class=\"wp-block-table wj-custom-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Operation<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Sign<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">$(+) \\times (+)$<br>Positive $\\times$ Positive<\/td><td class=\"has-text-align-center\" data-align=\"center\">&nbsp;$(+)$ Positive<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$(\\;-\\;) \\times (\\;-\\;)$<br>Negative $\\times$ Negative<\/td><td class=\"has-text-align-center\" data-align=\"center\">$(+)$ Positive<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$(+) \\times (\\;-\\;)$<br>Positive \u00d7 Negative<\/td><td class=\"has-text-align-center\" data-align=\"center\">&nbsp; $(-)$ Negative<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">$(\\;-\\;) \\times (+)$<br>Negative $\\times$ Positive<\/td><td class=\"has-text-align-center\" data-align=\"center\">&nbsp; $(-)$ Negative<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-facts-about-properties-of-multiplication\">Facts about Properties of Multiplication<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/multiplicative-inverse\">Multiplicative inverse<\/a> of 0 is undefined.<\/li>\n\n\n\n<li>1 is called the identity element of multiplication as any number multiplied by it gives the number itself.<\/li>\n\n\n\n<li>Any number multiplied by 0 gives 0.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the properties of multiplication: associative property, commutative property of multiplication, distributive property of multiplication, identity property of multiplication, zero property of multiplication. Let\u2019s solve a few examples and practice problems now to understand the concept better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-solved-examples-on-properties-of-multiplication\">Solved Examples on Properties of Multiplication<\/h2>\n\n\n\n<p><strong>1. Identify the properties of multiplication used in each equation.<\/strong><\/p>\n\n\n\n<p>(i) &nbsp; $7 \\times 5 = 5 \\times 7 = 12$<\/p>\n\n\n\n<p>(ii)&nbsp; $4 \\times (3 \\times 8) = (4 \\times 3) \\times 8$<\/p>\n\n\n\n<p>(iii) $1 \\times 46 = 46$<\/p>\n\n\n\n<p>(iv) $34 \\times \\frac{1}{34} = 1$<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p>(i) &nbsp; $7 \\times 5 = 5 \\times 7 = 12$<\/p>\n\n\n\n<p>Commutative property of multiplication<\/p>\n\n\n\n<p>(ii)&nbsp; $4 \\times (3 \\times 8) = (4 \\times 3) \\times 8$<\/p>\n\n\n\n<p>Associative property of multiplication<\/p>\n\n\n\n<p>(iii) $1 \\times 46 = 46$<\/p>\n\n\n\n<p>Identity property of multiplication<\/p>\n\n\n\n<p>(iv) $34 \\times \\frac{1}{34} = 1$<\/p>\n\n\n\n<p>Inverse property of multiplication.<\/p>\n\n\n\n<p><strong>2.<\/strong><strong> <\/strong><strong>Find the missing numbers.&nbsp;<\/strong><\/p>\n\n\n\n<p>$12 \\times (4 + 3)= \\underline{} + \\underline{}$<\/p>\n\n\n\n<p><strong>Solution:<\/strong><strong>&nbsp;<\/strong><\/p>\n\n\n\n<p>The distributive property of multiplication over addition is given by<\/p>\n\n\n\n<p>&nbsp;$a(b + c) = ab + ac$<\/p>\n\n\n\n<p>Thus, we can write<\/p>\n\n\n\n<p>$(4 + 3) \\times 12 = (4 \\times 12) +(3 \\times 12)$<\/p>\n\n\n\n<p>$(4 + 3) \\times 12 = 48 + 36$<\/p>\n\n\n\n<p><strong>3. Fill in the blanks: <\/strong>$17 \\times (90 \\times 11) = (17 \\times \\underline{}) \\times 11$<\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>By the associative property of multiplication, we have<\/p>\n\n\n\n<p>$a \\times (b \\times c) = (a \\times b) \\times c$<\/p>\n\n\n\n<p>Thus,&nbsp;<\/p>\n\n\n\n<p>$17 \\times (90 \\times 11) = (17 \\times 90) \\times 11$<\/p>\n\n\n\n<p><strong>4. Find the product of <\/strong>$75 \\times \\;-\\;31 \\times \\frac{1}{75}$<strong> using suitable properties.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>$75 \\times (\\;-\\;31) \\times \\frac{1}{75} = (75 \\times \\frac{1}{75}) \\times (\\;-\\;31)$ ..Commutative and associative property&nbsp;<\/p>\n\n\n\n<p>$= 1 \\times(\\;-\\;31)$ ..Inverse property<\/p>\n\n\n\n<p><strong>&nbsp;<\/strong>$=\\;-\\;31$&nbsp; ..Identity property<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-practice-problems-on-properties-of-multiplication\">Practice Problems on Properties of Multiplication<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Properties of Multiplication - Definition, Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following expressions uses the inverse property of multiplication?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$0 \\times 5 = 0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$4 \\times 3 = 3 \\times 4 = 12$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$1 \\times 46 = 46$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$4 \\times \\frac{1}{4} = 1$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $4 \\times \\frac{1}{4} = 1$<br\/>The inverse property of multiplication states that the product of a number with its reciprocal is 1. It can be represented as $a \\times \\frac{1}{a} = 1$<br>\r\nPutting $a = 4$, we get $4 \\times \\frac{1}{4} = 1$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Identify the associative property of multiplication.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">If $a = b$, then $a \\times c = b \\times c$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$a (b + c) = ab + ac$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$a \\times b = b \\times a$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$(a \\times b) \\times c = a \\times (b \\times c)$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $(a \\times b) \\times c = a \\times (b \\times c)$<br\/>The associative property of multiplication can be represented by<br>\r\n$(a \\times b) \\times c = a \\times (b \\times c)$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Fill in the blanks : $45 \\times (79 \\times 3) = (45 \\times 79) \\times \\_$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">45<\/div><div class=\"spq_answer_block\" data-value=\"1\">75<\/div><div class=\"spq_answer_block\" data-value=\"2\">125<\/div><div class=\"spq_answer_block\" data-value=\"3\">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: 3<br\/>By the associative property of multiplication, we have<br>\r\n$(a \\times b) \\times c = a \\times (b \\times c)$<br>\r\nThus, $45 \\times (79 \\times 3) = (45 \\times 79) \\times 3$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">$(\\;-9\\;) \\times \\frac{1}{9}=$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">$-1$<\/div><div class=\"spq_answer_block\" data-value=\"2\">0<\/div><div class=\"spq_answer_block\" data-value=\"3\">81<\/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: $-1$<br\/>The product of a number and its reciprocal is 1.<br>\r\nThus, $9 \\times\\frac{1}{9} = 1$<br>\r\nAlso, multiplication of a positive number and a negative number results in a negative number. Thus, $(\\;-\\;9) \\times \\frac{1}{9} = \\;-1$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Identify the property of multiplication used in the expression: $999 \\times 0 = 0$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Inverse property<\/div><div class=\"spq_answer_block\" data-value=\"1\">Associative property<\/div><div class=\"spq_answer_block\" data-value=\"2\">Zero property<\/div><div class=\"spq_answer_block\" data-value=\"3\">Identity property<\/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: Zero property<br\/>According to the zero property of multiplication, when a number is multiplied with 0, the product is always 0.<br>\r\nIt is represented as $a \\times 0 = 0$.<\/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\": \"Properties of Multiplication - Definition, Examples, Facts, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Properties of Multiplication\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following expressions uses the inverse property of multiplication?\",\n                    \"text\": \"Which of the following expressions uses the inverse property of multiplication?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The inverse property of multiplication states that the product of a number with its reciprocal is 1. It can be represented as $$a \\\\times \\\\frac{1}{a} = 1$$<br>\r\nPutting $$a = 4$$, we get $$4 \\\\times \\\\frac{1}{4} = 1$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$0 \\\\times 5 = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The inverse property of multiplication states that the product of a number with its reciprocal is 1. It can be represented as $$a \\\\times \\\\frac{1}{a} = 1$$<br>\r\nPutting $$a = 4$$, we get $$4 \\\\times \\\\frac{1}{4} = 1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$4 \\\\times 3 = 3 \\\\times 4 = 12$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The inverse property of multiplication states that the product of a number with its reciprocal is 1. It can be represented as $$a \\\\times \\\\frac{1}{a} = 1$$<br>\r\nPutting $$a = 4$$, we get $$4 \\\\times \\\\frac{1}{4} = 1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$1 \\\\times 46 = 46$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The inverse property of multiplication states that the product of a number with its reciprocal is 1. It can be represented as $$a \\\\times \\\\frac{1}{a} = 1$$<br>\r\nPutting $$a = 4$$, we get $$4 \\\\times \\\\frac{1}{4} = 1$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$4 \\\\times \\\\frac{1}{4} = 1$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The inverse property of multiplication states that the product of a number with its reciprocal is 1. It can be represented as $$a \\\\times \\\\frac{1}{a} = 1$$<br>\r\nPutting $$a = 4$$, we get $$4 \\\\times \\\\frac{1}{4} = 1$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The inverse property of multiplication states that the product of a number with its reciprocal is 1. It can be represented as $$a \\\\times \\\\frac{1}{a} = 1$$<br>\r\nPutting $$a = 4$$, we get $$4 \\\\times \\\\frac{1}{4} = 1$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the associative property of multiplication.\",\n                    \"text\": \"Identify the associative property of multiplication.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The associative property of multiplication can be represented by<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"If $$a = b$$, then $$a \\\\times c = b \\\\times c$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property of multiplication can be represented by<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a (b + c) = ab + ac$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property of multiplication can be represented by<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$a \\\\times b = b \\\\times a$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property of multiplication can be represented by<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The associative property of multiplication can be represented by<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The associative property of multiplication can be represented by<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Fill in the blanks : $$45 \\\\times (79 \\\\times 3) = (45 \\\\times 79) \\\\times \\\\_$$\",\n                    \"text\": \"Fill in the blanks : $$45 \\\\times (79 \\\\times 3) = (45 \\\\times 79) \\\\times \\\\_$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"By the associative property of multiplication, we have<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$<br>\r\nThus, $$45 \\\\times (79 \\\\times 3) = (45 \\\\times 79) \\\\times 3$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"45\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the associative property of multiplication, we have<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$<br>\r\nThus, $$45 \\\\times (79 \\\\times 3) = (45 \\\\times 79) \\\\times 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"75\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the associative property of multiplication, we have<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$<br>\r\nThus, $$45 \\\\times (79 \\\\times 3) = (45 \\\\times 79) \\\\times 3$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"125\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"By the associative property of multiplication, we have<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$<br>\r\nThus, $$45 \\\\times (79 \\\\times 3) = (45 \\\\times 79) \\\\times 3$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"3\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"By the associative property of multiplication, we have<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$<br>\r\nThus, $$45 \\\\times (79 \\\\times 3) = (45 \\\\times 79) \\\\times 3$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"By the associative property of multiplication, we have<br>\r\n$$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$<br>\r\nThus, $$45 \\\\times (79 \\\\times 3) = (45 \\\\times 79) \\\\times 3$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$(\\\\;-9\\\\;) \\\\times \\\\frac{1}{9}=$$\",\n                    \"text\": \"$$(\\\\;-9\\\\;) \\\\times \\\\frac{1}{9}=$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The product of a number and its reciprocal is 1.<br>\r\nThus, $$9 \\\\times\\\\frac{1}{9} = 1$$<br>\r\nAlso, multiplication of a positive number and a negative number results in a negative number. Thus, $$(\\\\;-\\\\;9) \\\\times \\\\frac{1}{9} = \\\\;-1$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The product of a number and its reciprocal is 1.<br>\r\nThus, $$9 \\\\times\\\\frac{1}{9} = 1$$<br>\r\nAlso, multiplication of a positive number and a negative number results in a negative number. Thus, $$(\\\\;-\\\\;9) \\\\times \\\\frac{1}{9} = \\\\;-1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The product of a number and its reciprocal is 1.<br>\r\nThus, $$9 \\\\times\\\\frac{1}{9} = 1$$<br>\r\nAlso, multiplication of a positive number and a negative number results in a negative number. Thus, $$(\\\\;-\\\\;9) \\\\times \\\\frac{1}{9} = \\\\;-1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"81\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The product of a number and its reciprocal is 1.<br>\r\nThus, $$9 \\\\times\\\\frac{1}{9} = 1$$<br>\r\nAlso, multiplication of a positive number and a negative number results in a negative number. Thus, $$(\\\\;-\\\\;9) \\\\times \\\\frac{1}{9} = \\\\;-1$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$-1$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The product of a number and its reciprocal is 1.<br>\r\nThus, $$9 \\\\times\\\\frac{1}{9} = 1$$<br>\r\nAlso, multiplication of a positive number and a negative number results in a negative number. Thus, $$(\\\\;-\\\\;9) \\\\times \\\\frac{1}{9} = \\\\;-1$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The product of a number and its reciprocal is 1.<br>\r\nThus, $$9 \\\\times\\\\frac{1}{9} = 1$$<br>\r\nAlso, multiplication of a positive number and a negative number results in a negative number. Thus, $$(\\\\;-\\\\;9) \\\\times \\\\frac{1}{9} = \\\\;-1$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify the property of multiplication used in the expression: $$999 \\\\times 0 = 0$$\",\n                    \"text\": \"Identify the property of multiplication used in the expression: $$999 \\\\times 0 = 0$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the zero property of multiplication, when a number is multiplied with 0, the product is always 0.<br>\r\nIt is represented as $$a \\\\times 0 = 0$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Inverse property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the zero property of multiplication, when a number is multiplied with 0, the product is always 0.<br>\r\nIt is represented as $$a \\\\times 0 = 0$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Associative property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the zero property of multiplication, when a number is multiplied with 0, the product is always 0.<br>\r\nIt is represented as $$a \\\\times 0 = 0$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Identity property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the zero property of multiplication, when a number is multiplied with 0, the product is always 0.<br>\r\nIt is represented as $$a \\\\times 0 = 0$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Zero property\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the zero property of multiplication, when a number is multiplied with 0, the product is always 0.<br>\r\nIt is represented as $$a \\\\times 0 = 0$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the zero property of multiplication, when a number is multiplied with 0, the product is always 0.<br>\r\nIt is represented as $$a \\\\times 0 = 0$$.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-frequently-asked-questions-on-properties-of-multiplication\">Frequently Asked Questions on Properties of Multiplication<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-8b489836-e4fc-4353-99e7-5ef670fc753e\" 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-0-8b489836-e4fc-4353-99e7-5ef670fc753e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b489836-e4fc-4353-99e7-5ef670fc753e\"><strong>What is multiplicative identity?<\/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-0-8b489836-e4fc-4353-99e7-5ef670fc753e\">\n\n<p>The multiplicative identity is a number, which when multiplied to any number \u201ca,\u201d gives a product as \u201ca.\u201d Multiplicative identity is a real number is 1, because $a \\times 1 = a$. This is another name for the identity property of multiplication.<\/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-1-8b489836-e4fc-4353-99e7-5ef670fc753e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b489836-e4fc-4353-99e7-5ef670fc753e\"><strong>What is a multiplicand and a multiplier?<\/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-1-8b489836-e4fc-4353-99e7-5ef670fc753e\">\n\n<p><strong>Multiplicand <\/strong>$\\times$<strong> Multiplier <\/strong>$=$<strong> Product<\/strong><\/p>\n\n\n\n<p>Multiplicand: The first number being multiplied.&nbsp;<\/p>\n\n\n\n<p><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplier\">Multiplier<\/a>: The second number (factor).&nbsp;<\/p>\n\n\n\n<p>Product: The final result or answer.<\/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-2-8b489836-e4fc-4353-99e7-5ef670fc753e\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b489836-e4fc-4353-99e7-5ef670fc753e\"><strong>Can we apply properties of multiplication on integers and fractions as well?<\/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-2-8b489836-e4fc-4353-99e7-5ef670fc753e\">\n\n<p>Yes, we can apply properties of multiplication on all the real numbers (such as <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/integers\">integers<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/whole-numbers\">whole numbers<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers\">rational numbers<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number\/irrational-numbers\">irrational numbers<\/a>, etc.)<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Are the Properties of Multiplication? The properties of multiplication are certain rules or formulas that help in simplifying the expressions involving multiplication. We know that multiplication is defined as repeated addition.&nbsp; For example, $12 \\times 6$ is 12 added to itself 6 times. $12 \\times 6= 12 + 12 + 12 + 12 + &#8230; <a title=\"Properties of Multiplication &#8211; Definition, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication\" aria-label=\"More on Properties of Multiplication &#8211; Definition, Examples, Facts, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-2173","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\/2173","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=2173"}],"version-history":[{"count":25,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2173\/revisions"}],"predecessor-version":[{"id":36907,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2173\/revisions\/36907"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=2173"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=2173"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=2173"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}