{"id":2104,"date":"2022-04-26T08:37:16","date_gmt":"2022-04-26T08:37:16","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=2104"},"modified":"2024-02-19T07:35:08","modified_gmt":"2024-02-19T07:35:08","slug":"commutative-property-of-ultiplication-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/commutative-property-of-multiplication","title":{"rendered":"Commutative 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-ed9dc34f-5a51-4a6f-80f0-770674ee40d1\" 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\/commutative-property-of-multiplication#0-what-is-the-commutative-property-of-multiplication-in-math->What Is the Commutative Property of Multiplication in Math?&nbsp;<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/commutative-property-of-multiplication#1-what-is-multiplication>What Is Multiplication?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/commutative-property-of-multiplication#2-commutative-property-of-multiplication->Commutative Property of Multiplication&nbsp;<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/commutative-property-of-multiplication#5-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/commutative-property-of-multiplication#6-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/commutative-property-of-multiplication#7-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-the-commutative-property-of-multiplication-in-math-\">What Is the Commutative Property of Multiplication in Math?&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Commutative comes from the word \u201ccommute\u201d, which can be defined as moving around or traveling. According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s understand this with an example.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example of Commutative Property of Multiplication<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Place 3 bricks in a row.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"314\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/one-row-of-3-bricks.png\" alt=\"One row of 3 bricks\" class=\"wp-image-40249\" title=\"One row of 3 bricks\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/one-row-of-3-bricks.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/one-row-of-3-bricks-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Now place another row of bricks above this row.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"314\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/two-rows-of-3-bricks-each-.png\" alt=\"Two rows of 3 bricks each \" class=\"wp-image-40250\" title=\"Two rows of 3 bricks each \" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/two-rows-of-3-bricks-each-.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/two-rows-of-3-bricks-each--300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Repeat this process 4 times.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"314\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/four-rows-of-3-bricks-each.png\" alt=\"Four rows of 3 bricks each\" class=\"wp-image-40252\" title=\"Four rows of 3 bricks each\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/four-rows-of-3-bricks-each.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/four-rows-of-3-bricks-each-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;Now count the number of bricks used.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"314\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-number-of-bricks-using-multiplication.png\" alt=\"Finding the total number of bricks using multiplication\" class=\"wp-image-40253\" title=\"Finding the total number of bricks using multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-number-of-bricks-using-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-number-of-bricks-using-multiplication-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Total bricks $=$ Number of rows $\\times$ Number of bricks in each row&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=&nbsp; 4 \\times 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 12$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, create a row by placing 4 bricks.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"298\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/one-row-of-4-bricks.png\" alt=\"One row of 4 bricks\" class=\"wp-image-40254\" title=\"One row of 4 bricks\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/one-row-of-4-bricks.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/one-row-of-4-bricks-300x144.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Place two more rows above this row.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"298\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-number-of-bricks-in-four-rows-using-multiplication.png\" alt=\"Finding the total number of bricks in four rows using multiplication\" class=\"wp-image-40255\" title=\"Finding the total number of bricks in four rows using multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-number-of-bricks-in-four-rows-using-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-number-of-bricks-in-four-rows-using-multiplication-300x144.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Total bricks $=$ Number of rows $\\times$ Number of bricks in each row&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=&nbsp; 3 \\times 4$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= 12$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We have observed that interchanging the number of rows with the number of bricks in each row does not change the total bricks needed.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-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\" 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Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Apply Distributive Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/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 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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 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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\" 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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            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-what-is-multiplication\">What Is Multiplication?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Multiplication is nothing but repeated addition. It is denoted by \u2018*\u2019, \u2018.\u2019 and \u2018\u2715\u2019.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s see what is repeated addition with the help of given example:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: <\/strong>A monkey is jumping from one point to another. It covers one unit distance with every jump. How many units will it cover in 5 jumps?<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>From the above statement, we can say that 1 jump $= 1$ unit. Let\u2019s look at this image.&nbsp;<\/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\/finding-the-total-distance-travelled-using-a-number-line.png\" alt=\"Finding the total distance travelled using a number line\" class=\"wp-image-40256\" title=\"Finding the total distance travelled using a number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-distance-travelled-using-a-number-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-distance-travelled-using-a-number-line-300x142.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">So, we can see that monkey covers $1+1+1+1+1 = 5$ units<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can also write it as $1 \\times 5 = 5$ units.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, observe that for each step, we need to add \u201c1\u201d in the previous one. That\u2019s why we can say that multiplication is nothing but repeated addition.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s go through another example.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example: <\/strong>Robin wants to buy 3 bars of chocolate. Each bar costs $\\$$ 10. How much money Robin needs to buy 3 bars?<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can solve this problem using two different methods. Let\u2019s look at both methods.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"316\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-cost-of-the-chocolates-using-multiplication.png\" alt=\"Finding the total cost of the chocolates using multiplication\" class=\"wp-image-40257\" title=\"Finding the total cost of the chocolates using multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-cost-of-the-chocolates-using-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/finding-the-total-cost-of-the-chocolates-using-multiplication-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Method 1:&nbsp;&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Number of chocolates&nbsp; $\\times$ Cost of Each Chocolate&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 3$ $\\times $ $\\$$ 10<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$=$ $\\$$ 30<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Method 2 <\/strong>:&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Cost of Each Chocolate $\\times$ Number of chocolates<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$=$ $\\$$ 10&nbsp;$\\times$ $3$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;$=$ $\\$$ 30<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>We have observed that <\/strong><strong>&nbsp;the order in which we multiplied the number of chocolate bars and cost of each bar does not change the amount required.<\/strong><\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a 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adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-commutative-property-of-multiplication-\">Commutative Property of Multiplication&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">You must be familiar with tables up to 5. <\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"295\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/observing-the-commutative-property-of-multiplication-in-times-table.png\" alt=\"Observing the commutative property of multiplication in times table\" class=\"wp-image-40258\" title=\"Observing the commutative property of multiplication in times table\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/observing-the-commutative-property-of-multiplication-in-times-table.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/observing-the-commutative-property-of-multiplication-in-times-table-300x143.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Have you observed&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1 \\times 2&nbsp; = 2&nbsp; \\times 1 = 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2 \\times 4&nbsp; = 4&nbsp; \\times 2 = 8$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3 \\times 5&nbsp; = 5&nbsp; \\times 3 = 15$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, we can conclude that the order in which we multiply numbers does not change the final answer.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Do you know?<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If you remember tables up to 5, you can figure out the multiplication of bigger tables by using the commutative property.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>For example:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">If you know&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Five times eight, i.e., $5 \\times 8 =$ ?&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">You can also answer&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Eight times five, i.e., $8 \\times 5&nbsp; =$ ?&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Both are equal to 40.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-fact-to-remember\">Fact to Remember<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The commutative property applies only to addition and multiplication but not to subtraction and division.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s understand this with examples.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"302\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-holds-true-in-case-of-Addition.png\" alt=\"Commutative Property holds true in case of Addition\" class=\"wp-image-40259\" title=\"Commutative Property holds true in case of Addition\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-holds-true-in-case-of-Addition.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-holds-true-in-case-of-Addition-300x146.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"302\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-does-not-hold-true-in-case-of-subtraction.png\" alt=\"Commutative Property does not hold true in case of Subtraction\" class=\"wp-image-40260\" title=\"Commutative Property does not hold true in case of Subtraction\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-does-not-hold-true-in-case-of-subtraction.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-does-not-hold-true-in-case-of-subtraction-300x146.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Alt Tag: Commutative Property holds true in case of Multiplication<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"302\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-does-not-hold-true-in-case-of-division.png\" alt=\"Commutative Property does not hold true in case of Division\" class=\"wp-image-40261\" title=\"Commutative Property does not hold true in case of Division\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-does-not-hold-true-in-case-of-division.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/commutative-property-does-not-hold-true-in-case-of-division-300x146.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">So, we can conclude that commutative property applies to addition and multiplication, not to subtraction and division.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In conclusion, we can say that<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Multiplication is nothing but the repeated addition.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Commutative property means the end result will not change if we change the order.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Multiplication and addition follows commutative property.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: Fill in the blanks.&nbsp;<\/strong><\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$4 \\times 5 = 5 \\times \\underline{}$<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solution: &nbsp; <\/strong>$4&nbsp; \\times&nbsp; 5&nbsp; =&nbsp; 5 \\times&nbsp; 4$<\/p>\n\n\n\n<ol start=\"2\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$3 \\times = 6 \\times \\underline{}$<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp; <\/strong>$3 \\times \\underline{} $6$ \\underline{} = 6 \\times 3$<\/p>\n\n\n\n<ol start=\"3\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$2&nbsp; \\times&nbsp; 1&nbsp; = 1&nbsp; \\times \\underline{}$<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp; <\/strong>$2&nbsp; \\times&nbsp; 1&nbsp; = 1&nbsp; \\times&nbsp; 2$<\/p>\n\n\n\n<ol start=\"4\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$3 \\times 6 \\times \\underline{} =&nbsp; 3 \\times 2 \\times 6$<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Solution:&nbsp; <\/strong>$3 \\times 6 \\times 2 =&nbsp; 3 \\times 2 \\times 6$<strong>&nbsp;<\/strong><\/p>\n\n\n\n<ol start=\"5\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$16 \\times 2 \\times&nbsp; 4 =&nbsp; 2 \\times \\underline{} \\times&nbsp; 4$<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp; <\/strong>$16 \\times 2 \\times 4 =&nbsp; 2 \\times 16&nbsp; \\times&nbsp; 4$<\/p>\n\n\n\n<ol start=\"6\" class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$9 \\times \\underline{} \\times&nbsp; 2&nbsp; = &nbsp; 8 \\times \\underline{} \\times 2$&nbsp;<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<strong>Solution<\/strong>: $9 \\times \\underline{} 8 \\underline{} \\times 2&nbsp; = &nbsp; 8 \\times 9 \\times 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: Complete the following statement:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>The commutative property says that the order of numbers in _________ and _________ does not change the result.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The commutative property says that the order of numbers in <strong>multiplication<\/strong> and <strong>addition<\/strong> does not change the result.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Only multiplication and addition follow the commutative property.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Communicative 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=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which expression is the same as $6 \\times 4 \\times 5$ according to the commutative property?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$5 \\times 6 \\times 4$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$645$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$6+4+5$<\/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: $5 \\times 6 \\times 4$<br\/>Explanation: According to the commutative property of multiplication, if the order of numbers is changed, the product will remain the same.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">A $\\times$ B = B $\\times$ A is the<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Commutative property under addition<\/div><div class=\"spq_answer_block\" data-value=\"1\">Commutative property under multiplication<\/div><div class=\"spq_answer_block\" data-value=\"2\">Associative property under multiplication<\/div><div class=\"spq_answer_block\" data-value=\"3\">Associative property under addition<\/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: Commutative property under multiplication<br\/>Explanation: According to the commutative property of multiplication, if the order of numbers is changed, the product will remain the same.<\/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\">$A + B = B + A$ is the<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Commutative property under addition<\/div><div class=\"spq_answer_block\" data-value=\"1\">Commutative property under multiplication<\/div><div class=\"spq_answer_block\" data-value=\"2\">Associative property under multiplication<\/div><div class=\"spq_answer_block\" data-value=\"3\">Associative property under addition<\/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: Commutative property under addition<br\/>Explanation: According to the commutative property of addition, if the order of numbers  is changed, the addition will remain the same.<\/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 expression is the same as $6 + 4 +  5$ according to the commutative property?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$6 \\times 4 \\times 5$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$645$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$6 + 5 +  4$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$546$<\/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: $6 + 5 +  4$<br\/>Explanation: According to the commutative property of addition, if the order of numbers  is changed, the addition will remain the same.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n   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id=\"7-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-9cf4ce03-5755-45ef-9355-c035873705a3\" 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-0-9cf4ce03-5755-45ef-9355-c035873705a3\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9cf4ce03-5755-45ef-9355-c035873705a3\"><strong>Which operations do not follow commutative property?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-9cf4ce03-5755-45ef-9355-c035873705a3\">\n\n<p>Subtraction and division do not follow the commutative 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-1-9cf4ce03-5755-45ef-9355-c035873705a3\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9cf4ce03-5755-45ef-9355-c035873705a3\"><strong>Can we apply the commutative property for the multiplication of 4 numbers?<\/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-1-9cf4ce03-5755-45ef-9355-c035873705a3\">\n\n<p>Yes, we can apply commutative property for the multiplication of 4 numbers.<\/p>\n\n\n\n<p>For example, $4 \\times 5 \\times 6 \\times 7 = 7 \\times 5 \\times 6 \\times 4$<\/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-2-9cf4ce03-5755-45ef-9355-c035873705a3\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-9cf4ce03-5755-45ef-9355-c035873705a3\"><strong>What is the difference between the associative and commutative 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-2-9cf4ce03-5755-45ef-9355-c035873705a3\">\n\n<p>The associative feature of multiplication asserts that when the grouping of the numbers is altered, the product of the numbers remains the same. $(\\text{A B})$ $\\text{C} = \\text{A}$ $(\\text{B C})$ is how the associative property of multiplication is expressed.<\/p>\n\n\n\n<p>The commutative property of multiplication asserts that even if the order of the numbers is changed, the product of two or more integers remains the same. Multiplication\u2019s commutative property is represented as $\\text{A B C} = \\text{C B A}$.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Is the Commutative Property of Multiplication in Math?&nbsp; Commutative comes from the word \u201ccommute\u201d, which can be defined as moving around or traveling. According to the commutative property of multiplication, changing the order of the numbers we are multiplying does not change the product.&nbsp;&nbsp; Let\u2019s understand this with an example. Example of Commutative Property &#8230; <a title=\"Commutative Property of Multiplication &#8211; Definition With Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/commutative-property-of-multiplication\" aria-label=\"More on Commutative 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-2104","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\/2104","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=2104"}],"version-history":[{"count":62,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2104\/revisions"}],"predecessor-version":[{"id":40262,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2104\/revisions\/40262"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=2104"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=2104"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=2104"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}