{"id":2156,"date":"2022-04-26T12:13:46","date_gmt":"2022-04-26T12:13:46","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=2156"},"modified":"2024-01-01T15:27:59","modified_gmt":"2024-01-01T15:27:59","slug":"multiplication-property-of-equality-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication-property-of-equality","title":{"rendered":"Multiplication Property of Equality &#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-c62469e9-818c-4353-aa0a-527a041bc418\" 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\/multiplication-property-of-equality#0-multiplication-property-of-inequality-introduction>Multiplication Property of Inequality: Introduction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication-property-of-equality#1-multiplication-property-of-equality-definition>Multiplication Property of Equality: Definition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication-property-of-equality#2-what-is-the-property-of-equality>What Is the Property of Equality?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication-property-of-equality#8-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication-property-of-equality#9-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication-property-of-equality#10-frequently-asked-questions>Frequently Asked Questions<\/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 eplus-wrapper\" id=\"0-multiplication-property-of-inequality-introduction\">Multiplication Property of Inequality: Introduction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">An algebraic equation is a mathematical statement that has two sides (LHS and RHS) separated by the \u201cequal sign $(=)$.\u201d The multiplication property of equality states that equality holds when the both sides of an equation are multiplied by a common value.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Multiplication-Property-of-Equality-1.png\" alt=\"Multiplication property of equality\" class=\"wp-image-20619\" title=\"Multiplication property of equality\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Multiplication-Property-of-Equality-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Multiplication-Property-of-Equality-1-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-using-associative-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_together_we_flee_4_gm.png\" alt=\"Add Using Associative Property Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add Using Associative Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/apply-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/mult_div_facts_mul_dispro_exp1_pt.png\" alt=\"Apply Distributive Property Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Apply Distributive Property Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/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><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            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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-multiplication-property-of-equality-definition\">Multiplication Property of Equality: Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Multiplication property of equality states that if both the sides of an equation are multiplied by the same number, the expressions on the both sides of the equation remain equal to each other.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Consider the algebraic equation $a = b$, where a and b are real numbers.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s multiply both sides by the real number c.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">By the multiplication property of equality, we get<\/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\/2023\/01\/Multiplication-Property-of-Equality-2.png\" alt=\"\" class=\"wp-image-20620\" title=\"Example of multiplication property of equality\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Multiplication-Property-of-Equality-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/01\/Multiplication-Property-of-Equality-2-300x142.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-the-numbers-using-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-the-numbers-using-commutative-property-of-addition.jpeg\" alt=\"Add the Numbers Using Commutative Property of Addition\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expression-for-array\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expression-for-array.jpeg\" alt=\"Addition and Multiplication Expression for Array Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/addition-and-multiplication-expressions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/addition-and-multiplication-expressions.jpeg\" alt=\"Addition and Multiplication Expressions Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-commutative-property-of-addition.jpeg\" alt=\"Apply Commutative Property of Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-commutative-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-commutative-property.jpeg\" alt=\"Apply Commutative Property Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/apply-distributive-property-in-2-different-ways\" 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-distributive-property-in-2-different-ways.jpeg\" alt=\"Apply Distributive Property in 2 Different Ways 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\/apply-the-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/apply-the-commutative-property-of-addition.jpeg\" alt=\"Apply the Commutative Property of Addition Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/break-it-down-using-distributive-property\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/break-it-down-using-distributive-property.jpeg\" alt=\"Break it Down using Distributive 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class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-what-is-the-property-of-equality\">What Is the Property of Equality?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The properties of equality describe the relation between two equal quantities. If any mathematical operation is applied on one side of an equation, then it must be applied on the other side of an equation to keep it balanced.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In other words, the properties that do not change the truth value of an equation or, the properties that do not impact the equality of two or more quantities are called the properties of equality.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Such properties of equality help in solving various algebraic equations and define an equivalence or balance relation.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-what-is-the-multiplicative-property-of-equality\">What Is the Multiplicative Property of Equality?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">According to this property, when we multiply the same real number on both the sides of an equation, then the two sides of the equation always remain equal.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can express the formula for this property as, for real numbers a, b, and c,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">if $a = b$, then $a \\times c = b \\times c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This fact is used in arithmetic to find the equal terms. In algebra, the multiplicative property of equality helps us to isolate an unknown term from an equation. This is because multiplication and division are inverses of each other.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1<\/strong>: Suppose that Lisa and Linda have the same amount of money, $\\$100$ each. If both of them triple their amount of money, that is both of them multiply their money by 3; they still have the same amount of money, $\\$300$ each.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can also use this property to solve equations.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2<\/strong>: $\\frac{x}{4} = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If we multiply both the sides by 4, the equality still holds and we get<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow \\frac{x}{4} \\times 4 = 5 \\times 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\Rightarrow x = 20$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To check we can substitute the value of $x$ in the original equation.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{20}{4} = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$5 = 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3<\/strong>: One-fourth of the kids who visited the amusement park \u201cJump &amp; Slide\u201d on holiday tried their new ride \u201cloop-O-loop.\u201d If 75 kids tried the ride, how many kids visited the park that day?<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let \u201ca\u201d be the number of kids who visited the park that day. One-fourth of this number is given to be 75. That is,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{a}{4} = 75$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We need to solve the equation for a.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">By the multiplication property of equality, if we multiply both sides by the same number, the equality still holds true. So, multiplying both sides by 4.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{a}{4} \\times 4 = 75 \\times 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$a = 300$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the 300 kids visited the park that day.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-converse-of-the-multiplication-property-of-equality\">Converse of the Multiplication Property of Equality<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Converse of the multiplication property of equality holds true. It can be stated mathematically as:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let $a,b$ and $c$ be real numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If $a \\neq b$, then $a \\times c \\neq b \\times c$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Or<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If &nbsp;$a \\times c = b \\times c$, then $a = b$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-multiplication-property-of-equality-with-fractions\">Multiplication Property of Equality with Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s understand the multiplication property of equality for fractions. For any non-zero number a, the multiplicative inverse is nothing but the reciprocal $\\frac{1}{a}$ such that $a. \\frac{1}{a} = 1$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"486\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/multiplicative-property-of-equality-with-fractions.png\" alt=\"Multiplicative property of equality with fractions\" class=\"wp-image-37045\" title=\"Multiplicative property of equality with fractions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/multiplicative-property-of-equality-with-fractions.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/multiplicative-property-of-equality-with-fractions-300x235.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The <strong>multiplicative inverse property<\/strong>, which states that any number, other than 0, multiplied by its reciprocal will give a result of 1.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s see an example of multiplicative property of equality.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3}{2} y = 9$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Eliminating the fraction by multiplying both the sides by the multiplicative inverse.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3}{2} \\times \\frac{2}{3} y = 9 \\times \\frac{2}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Using the multiplicative inverse will result in 1 on the left side.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$1 y = 6 \\Rightarrow y = 6$&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">1. Another form of the property is if $a, b, c$, and d are real numbers such that&nbsp; $a = b, c = d$, then $ac = bd$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">2. Since division is the multiplication by the reciprocal if a,b and c are real numbers such that $a = b$ and $c \\neq 0$, then $a \\times \\frac{1}{c} = b \\times \\frac{1}{c}$ or $\\frac{a}{c} = \\frac{b}{c}$. This is also known as the division property of equality.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learnt about the multiplicative property of equality. Multiplicative property of equality states that if we multiply the same number on both sides of an equation, then the equation remains balanced.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Let <\/strong>$a$<strong> and <\/strong>$b$<strong> be real numbers such that <\/strong>$\\frac{z}{2} = 3 x$<strong> and <\/strong>$\\frac{z}{3} = 2 z$<strong>,&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>then show that <\/strong>$x = z$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> $\\frac{z}{2} = 3 x$<strong>,<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both the sides by 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{z}{2} \\times 2 = 3x \\times 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$z = 6 x$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Substituting the value of $z$ in $\\frac{z}{3} = 2 z$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{6x}{3} = 2 z$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2 x = 2 z$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. If&nbsp; <\/strong>$\\frac{3x}{4} = 36$<strong>, then find the value of <\/strong>$x$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> $\\frac{3x}{4} = 36$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both the sides by the multiplicative inverse of $\\frac{3}{4}$ i.e. $\\frac{4}{3}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3x}{4} \\times \\frac{4}{3} = 36 \\times \\frac{4}{3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$x = 48$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. If <\/strong>$2(m + 3) = 12$<strong>, then find the value of <\/strong>$m$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> $2(m + 3) = 12$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2(m + 3) = 2 \\times 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that if $ac = bc$, then $a = b$ if $c \\neq 0$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$m + 3 = 6 \\Rightarrow m = 6 \u2212 3 = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Solve for <\/strong>$y: \\frac{y + 8}{2} = \u2212 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> $\\frac{y + 8}{2} = \u2212 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both the sides by $2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">&nbsp;$2 \\times ( \\frac{y + 8}{2} ) = \u2212 7 \\times 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y + 8 = \u2212 14$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$y = \u2212 22$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. If&nbsp; <\/strong>$\\frac{3n + 5}{4} = 15$<strong>, then find the value of <\/strong>$n$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>$\\frac{3n + 5}{4} = 15$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiplying both the sides by $4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$4 \\times \\frac{3n + 5}{4} = 15 \\times 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3 n + 5 = 60$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3 n = 55$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$n = \\frac{55}{3} = 18\\frac{1}{3}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Multiplication Property of Equality - 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\">One seventh of the students in a class are boys. If the number of boys in the class is 21, then how many girls are there in the class?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">126<\/div><div class=\"spq_answer_block\" data-value=\"1\">139<\/div><div class=\"spq_answer_block\" data-value=\"2\">147<\/div><div class=\"spq_answer_block\" data-value=\"3\">158<\/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: 126<br\/>Let total number of students be $x$.<br>\r\n$\\frac{x}{7} = 21 \\Rightarrow x = 147$<br>\r\nNumber of girls $= 147 \u2013 21 = 126$<\/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\">Which property of equality can we use to solve the equation $\\frac{x}{3} = 16$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Additive property of equality<\/div><div class=\"spq_answer_block\" data-value=\"1\">Multiplicative property of equality<\/div><div class=\"spq_answer_block\" data-value=\"2\">Subtraction property of equality<\/div><div class=\"spq_answer_block\" data-value=\"3\">Division property of equality<\/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: Multiplicative property of equality<br\/>In order to solve for $x$, we will multiply both sides by 3.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If $a = b$, then which of the following is incorrect regarding the multiplicative property of equality?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$2 \\times a = 2 \\times b$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$3 a=3 b$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$a + 2 = b + 2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: $a + 2 = b + 2$<br\/>$a + 2 = b + 2$ shows the additive property of equality.<\/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\">Two-third of the total eggs are defective. If the number of non defective eggs is 24, then find the total number of eggs.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">36<\/div><div class=\"spq_answer_block\" data-value=\"1\">72<\/div><div class=\"spq_answer_block\" data-value=\"2\">108<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/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: 72<br\/>Let the total number of eggs be $x$.<br>\r\n$x \u2212 \\frac{2x}{3} = 24 \\Rightarrow \\frac{x}{3} = 24$<br>\r\nMultiplying both the sides by 3, we get<br>\r\n$x = 72$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Find the value of $x$ if $\\frac{x}{6} = 12$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">2<\/div><div class=\"spq_answer_block\" data-value=\"1\">18<\/div><div class=\"spq_answer_block\" data-value=\"2\">24<\/div><div class=\"spq_answer_block\" data-value=\"3\">72<\/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: 72<br\/>$\\frac{x}{6} = 12$<br>\r\nMultiplying both the sides by 6, we get<br>\r\n$\\frac{x}{6} \\times 6 = 12 \\times 6 \\Rightarrow x = 72$<\/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\": \"Multiplication Property of Equality - Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Multiplication Property of Equality - Definition with Examples\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"One seventh of the students in a class are boys. 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126$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"147\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let total number of students be $$x$$.<br>\r\n$$\\\\frac{x}{7} = 21 \\\\Rightarrow x = 147$$<br>\r\nNumber of girls $$= 147 \u2013 21 = 126$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"158\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let total number of students be $$x$$.<br>\r\n$$\\\\frac{x}{7} = 21 \\\\Rightarrow x = 147$$<br>\r\nNumber of girls $$= 147 \u2013 21 = 126$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"126\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let total number of students be $$x$$.<br>\r\n$$\\\\frac{x}{7} = 21 \\\\Rightarrow x = 147$$<br>\r\nNumber of girls $$= 147 \u2013 21 = 126$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let total number of students be $$x$$.<br>\r\n$$\\\\frac{x}{7} = 21 \\\\Rightarrow x = 147$$<br>\r\nNumber of girls $$= 147 \u2013 21 = 126$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which property of equality can we use to solve the equation $$\\\\frac{x}{3} = 16$$?\",\n                    \"text\": \"Which property of equality can we use to solve the equation $$\\\\frac{x}{3} = 16$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In order to solve for $$x$$, we will multiply both sides by 3.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Additive property of equality\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In order to solve for $$x$$, we will multiply both sides by 3.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Subtraction property of equality\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In order to solve for $$x$$, we will multiply both sides by 3.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Division property of equality\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In order to solve for $$x$$, we will multiply both sides by 3.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Multiplicative property of equality\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In order to solve for $$x$$, we will multiply both sides by 3.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In order to solve for $$x$$, we will multiply both sides by 3.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If $$a = b$$, then which of the following is incorrect regarding the multiplicative property of equality?\",\n                    \"text\": \"If $$a = b$$, then which of the following is incorrect regarding the multiplicative property of equality?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$a + 2 = b + 2$$ shows the additive property of equality.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2 \\\\times a = 2 \\\\times b$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$a + 2 = b + 2$$ shows the additive property of equality.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$3 a=3 b$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$a + 2 = b + 2$$ shows the additive property of equality.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$a + 2 = b + 2$$ shows the additive property of equality.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$a + 2 = b + 2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$a + 2 = b + 2$$ shows the additive property of equality.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$a + 2 = b + 2$$ shows the additive property of equality.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Two-third of the total eggs are defective. If the number of non defective eggs is 24, then find the total number of eggs.\",\n                    \"text\": \"Two-third of the total eggs are defective. If the number of non defective eggs is 24, then find the total number of eggs.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Let the total number of eggs be $$x$$.<br>\r\n$$x \u2212 \\\\frac{2x}{3} = 24 \\\\Rightarrow \\\\frac{x}{3} = 24$$<br>\r\nMultiplying both the sides by 3, we get<br>\r\n$$x = 72$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"36\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let the total number of eggs be $$x$$.<br>\r\n$$x \u2212 \\\\frac{2x}{3} = 24 \\\\Rightarrow \\\\frac{x}{3} = 24$$<br>\r\nMultiplying both the sides by 3, we get<br>\r\n$$x = 72$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"108\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let the total number of eggs be $$x$$.<br>\r\n$$x \u2212 \\\\frac{2x}{3} = 24 \\\\Rightarrow \\\\frac{x}{3} = 24$$<br>\r\nMultiplying both the sides by 3, we get<br>\r\n$$x = 72$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Let the total number of eggs be $$x$$.<br>\r\n$$x \u2212 \\\\frac{2x}{3} = 24 \\\\Rightarrow \\\\frac{x}{3} = 24$$<br>\r\nMultiplying both the sides by 3, we get<br>\r\n$$x = 72$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"72\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Let the total number of eggs be $$x$$.<br>\r\n$$x \u2212 \\\\frac{2x}{3} = 24 \\\\Rightarrow \\\\frac{x}{3} = 24$$<br>\r\nMultiplying both the sides by 3, we get<br>\r\n$$x = 72$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Let the total number of eggs be $$x$$.<br>\r\n$$x \u2212 \\\\frac{2x}{3} = 24 \\\\Rightarrow \\\\frac{x}{3} = 24$$<br>\r\nMultiplying both the sides by 3, we get<br>\r\n$$x = 72$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the value of $$x$$ if $$\\\\frac{x}{6} = 12$$\",\n                    \"text\": \"Find the value of $$x$$ if $$\\\\frac{x}{6} = 12$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{x}{6} = 12$$<br>\r\nMultiplying both the sides by 6, we get<br>\r\n$$\\\\frac{x}{6} \\\\times 6 = 12 \\\\times 6 \\\\Rightarrow x = 72$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{x}{6} = 12$$<br>\r\nMultiplying both the sides by 6, we get<br>\r\n$$\\\\frac{x}{6} \\\\times 6 = 12 \\\\times 6 \\\\Rightarrow x = 72$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"18\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{x}{6} = 12$$<br>\r\nMultiplying both the sides by 6, we get<br>\r\n$$\\\\frac{x}{6} \\\\times 6 = 12 \\\\times 6 \\\\Rightarrow x = 72$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"24\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{x}{6} = 12$$<br>\r\nMultiplying both the sides by 6, we get<br>\r\n$$\\\\frac{x}{6} \\\\times 6 = 12 \\\\times 6 \\\\Rightarrow x = 72$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"72\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{x}{6} = 12$$<br>\r\nMultiplying both the sides by 6, we get<br>\r\n$$\\\\frac{x}{6} \\\\times 6 = 12 \\\\times 6 \\\\Rightarrow x = 72$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{x}{6} = 12$$<br>\r\nMultiplying both the sides by 6, we get<br>\r\n$$\\\\frac{x}{6} \\\\times 6 = 12 \\\\times 6 \\\\Rightarrow x = 72$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-653713cc-b59d-48a2-a0a7-b5d5839b399f\" 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-0-653713cc-b59d-48a2-a0a7-b5d5839b399f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-653713cc-b59d-48a2-a0a7-b5d5839b399f\"><strong>How is the multiplicative property of equality different from the 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-0-653713cc-b59d-48a2-a0a7-b5d5839b399f\">\n\n<p class=\"eplus-wrapper\">According to multiplicative property of equality, if $a = b$, then $ac = bc$ where $a,b,c$ are real numbers. On the other hand, according to the commutative property of multiplication, $a \\times b = b \\times a$.<\/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-1-653713cc-b59d-48a2-a0a7-b5d5839b399f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-653713cc-b59d-48a2-a0a7-b5d5839b399f\"><strong>What is the difference between the multiplicative property of equality and division property of equality?<\/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-1-653713cc-b59d-48a2-a0a7-b5d5839b399f\">\n\n<p class=\"eplus-wrapper\">According to multiplicative property of equality, if $a = b$, then $ac = bc$ where $a,b,c$ are real numbers and $c \\neq 0$. On the other hand, division property of equality states that if $a = b$, then $\\frac{a}{c} = \\frac{b}{c}$ where $a,b,c$ are real numbers and $c \\neq 0$.<\/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-2-653713cc-b59d-48a2-a0a7-b5d5839b399f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-653713cc-b59d-48a2-a0a7-b5d5839b399f\"><strong>What is the multiplicative property of inequality?<\/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-2-653713cc-b59d-48a2-a0a7-b5d5839b399f\">\n\n<p class=\"eplus-wrapper\">If $a \\lt b$ and if $c$ is a positive number, then $a \\times c \\lt b \\times c$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If a $\\lt$ b and if c is a negative number, then $a \\times c \\gt b \\times c$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">When a and b are multiplied by the same negative number, the inequality reverses.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-653713cc-b59d-48a2-a0a7-b5d5839b399f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-653713cc-b59d-48a2-a0a7-b5d5839b399f\"><strong>How is the multiplicative property of identity different from the multiplicative property of equality?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-653713cc-b59d-48a2-a0a7-b5d5839b399f\">\n\n<p class=\"eplus-wrapper\">According to the multiplicative property of identity, any number multiplied by 1 gives the same result as the number itself. Whereas, according to multiplicative property of equality, if $a = b$, then $ac = bc$ where $a,b,c$ are real numbers.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-653713cc-b59d-48a2-a0a7-b5d5839b399f\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-653713cc-b59d-48a2-a0a7-b5d5839b399f\"><strong>Why can\u2019t <\/strong>$c = 0$<strong> in the multiplicative property of equality?<\/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-4-653713cc-b59d-48a2-a0a7-b5d5839b399f\">\n\n<p class=\"eplus-wrapper\">Well, $c \\neq 0$<strong> <\/strong>in the multiplicative property of equality because multiplying by zero can change the truth of an equation. It can take a false equation to a true equation.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiplication Property of Inequality: Introduction An algebraic equation is a mathematical statement that has two sides (LHS and RHS) separated by the \u201cequal sign $(=)$.\u201d The multiplication property of equality states that equality holds when the both sides of an equation are multiplied by a common value.&nbsp; Recommended Games Add Using Associative Property Game Play &#8230; <a title=\"Multiplication Property of Equality &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication-property-of-equality\" aria-label=\"More on Multiplication Property of Equality &#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-2156","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\/2156","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=2156"}],"version-history":[{"count":21,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2156\/revisions"}],"predecessor-version":[{"id":37046,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2156\/revisions\/37046"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=2156"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=2156"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=2156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}