{"id":537,"date":"2022-03-11T13:01:52","date_gmt":"2022-03-11T13:01:52","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test\/?page_id=537"},"modified":"2023-04-03T07:22:46","modified_gmt":"2023-04-03T07:22:46","slug":"number-properties-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-properties","title":{"rendered":"Number Properties &#8211; Definition, Types, Chart"},"content":{"rendered":"<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-80bc5358-5d19-4b37-bb7f-792c443ab2ca\" 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\/number-sense\/number-properties#1-what-are-number-properties-in-math>What Are Number Properties in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-properties#12-formula-chart-of-basic-number-properties>Formula Chart of Basic Number Properties<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-properties#15-solved-examples-of-number-properties>Solved Examples of Number Properties<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-properties#16-practice-problems-of-number-properties>Practice Problems of Number Properties<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-properties#17-frequently-asked-questions-of-number-properties>Frequently Asked Questions of Number Properties<\/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-number-properties-introduction\">Number Properties &#8211; Introduction<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">Number properties are certain rules that can be applied and characteristics that numbers follow when we perform arithmetic operations on them. In mathematics, we use numbers to express mathematical facts and ideas logically. But what are <strong>number properties<\/strong>? Why do you need to learn them? We know that everything around us has certain properties, such as shape, size, weight, etc. Like these things, numbers also have some properties. Knowing the properties will help you solve <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/equation\" target=\"_blank\" rel=\"noopener\" title=\"\">equations<\/a> easily.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Come, let\u2019s explore the <strong>properties of numbers<\/strong> in detail.<\/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\/10-and-100-more-than-the-same-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_1_10_100_more_same_num_pt.png\" alt=\"10 and 100 More than the Same Number 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\">10 and 100 More than the Same Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-1-digit-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\/add_sub_facts_add_make_10_pt.png\" alt=\"Add 1-Digit 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\">Add 1-Digit 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\/add-10-to-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_10_number_pt.png\" alt=\"Add 10 to a 3-Digit Number 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 10 to a 3-Digit Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-100-to-a-3-digit-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_100_horizontal_pt.png\" alt=\"Add 100 to a 3-Digit Number 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 100 to a 3-Digit Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-and-1-digit-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\/add_sub_pv_add_2d_1d_match_pt.png\" alt=\"Add 2-Digit and 1-Digit 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\">Add 2-Digit and 1-Digit 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\/add-2-digit-numbers-by-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_2d_2d_vertical_pt.png\" alt=\"Add 2-Digit Numbers By Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit Numbers By Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-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\/add_sub_facts_add_3_no_pt.png\" alt=\"Add 3 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\">Add 3 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\/add-3-numbers-in-any-order\" 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_shifty_bridges_4_gm.png\" alt=\"Add 3 Numbers in Any Order 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 3 Numbers in Any Order Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-groups-of-objects\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_using_model_pt.png\" alt=\"Add 3 Numbers Using Groups of Objects 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 3 Numbers Using Groups of Objects Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_using_models_pt.png\" alt=\"Add 3 Numbers using Model 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 3 Numbers using Model 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-are-number-properties-in-math\">What Are Number Properties in Math?<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Number properties refer to the properties that help to express the basic characteristics or features of real numbers<\/strong>. There are four basic properties in math:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/commutative-property\" target=\"_blank\" rel=\"noopener\" title=\"\">Commutative Property<\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property\" target=\"_blank\" rel=\"noopener\" title=\"\">Associative Property<\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/distributive-property\" target=\"_blank\" rel=\"noopener\" title=\"\">Distributive Property<\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\">Identity Property<\/li>\n<\/ul>\n\n\n\n<p class=\" eplus-wrapper\"><br>We apply these properties while doing <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/addition\" target=\"_blank\" rel=\"noopener\" title=\"\">addition<\/a> and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplication\" target=\"_blank\" rel=\"noopener\" title=\"\">multiplication<\/a> operations. \u00a0<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/10-and-100-more-than-a-3-digit-number\" 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\/10-and-100-more-than-a-3-digit-number.jpeg\" alt=\"10 and 100 More than a 3-digit Number\">\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\/100-more-and-100-less-than-a-3-digit-number\" 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\/100-more-and-100-less-than-a-3-digit-number.jpeg\" alt=\"100 More and 100 Less than a 3-digit Number\">\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\/100-more-than-a-3-digit-number\" 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\/100-more-than-a-3-digit-number.jpeg\" alt=\"100 More than a 3-digit Number\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-subtract-ones-2-digit-numbers\" 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-subtract-ones-2-digit-numbers.jpeg\" alt=\"Add & Subtract Ones & 2-Digit Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-and-find-the-sum\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-and-find-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Find the Sum\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-and-match-the-sum\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-and-match-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Match the Sum\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-addition-tables\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-addition-tables.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Addition Tables\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-addition-wheel\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-addition-wheel.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Addition Wheel\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-number-charts\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-number-charts.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Number Charts\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" 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container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-commutative-property\">Commutative Property<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">To commute means to move from one place to another. Let\u2019s understand how it relates to the number properties.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"3-commutative-property-of-addition-\"><strong>Commutative Property of Addition<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\"><strong>This property says that when we add two numbers, the order in which we add the numbers makes no difference to the answer<\/strong>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Suppose we have to add 3 and 5.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We can write $3 + 5 = 8$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Similarly, we can also write it as $5 + 3 = 8$.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus,<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$3 + 5 = 5 + 3 = 8$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"438\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-1.png\" alt=\"Commutative property of addition\" class=\"wp-image-23298\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-1-300x212.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/commutative-property-of-addition\" target=\"_blank\" rel=\"noopener\" title=\"\">commutative property of addition<\/a> for any two real numbers a and b is given as:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a + b = b + a$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-commutative-property-of-multiplication-\"><strong>Commutative Property of Multiplication<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\"><strong>This property says that when we multiply two numbers, the order in which we multiply the numbers makes no difference to the answer<\/strong>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s multiply 4 and 5. We get $4 \\times 5 = 20$. Now, if we reverse the order of the numbers and multiply, we get $5 \\times 4 = 20$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"426\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-2.png\" alt=\"Commutative property of multiplication\" class=\"wp-image-23299\" title=\"Commutative property of multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-2-300x206.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the <a href=\"http:\/\/Commutative Property of Multiplication\" target=\"_blank\" rel=\"noopener\" title=\"\">commutative property of multiplication<\/a> for any two real numbers a and b is given as:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a \\times b = b \\times a$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-associative-property\">Associative Property<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">The word \u201cassociative\u201d refers to combining or collaborating. Let\u2019s understand the property.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-associative-property-of-addition-\"><strong>Associative Property of Addition<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\"><strong>This property says that when we add three or more numbers, the order in which the numbers are grouped has no impact on the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/sum\" target=\"_blank\" rel=\"noopener\" title=\"\">sum<\/a><\/strong>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Suppose we have to add 3, 4, and 5. We first group 3 and 4 as $(3 + 4)$ and add the sum to 5. Next, we take 3 and add it to the group of 4 and 5 as $(4 + 5)$. We get&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(3 + 4) + 5 = 3 + (4 + 5) = 12$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"462\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-3.png\" alt=\"Associative property of addition visual\" class=\"wp-image-23300\" title=\"Associative property of addition visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-3-300x224.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/associative-property-of-addition\" target=\"_blank\" rel=\"noopener\" title=\"\">associative property of addition<\/a> for three real numbers a, b, and c is:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(a + b) + c = a + (b + c)$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"7-associative-property-of-multiplication-\"><strong>Associative Property of Multiplication<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\"><strong>This property says that when we multiply three or more numbers, the order in which the numbers are grouped has no impact on the product<\/strong>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">We take the numbers 2, 3, and 5. We first group 2 and 3 as $(2 \\times 3)$ and multiply the product by 5.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We get $(2 \\times 3) \\times 5 = 6 \\times 5 = 30$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Next, we group 3 and 5 as $(3 \\times 5)$ and multiply by 2.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">So, 2 $(3 \\times 5) = 2 \\times 15 = 30$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus,<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(2 \\times 3) \\times 5 = 2 \\times (3 \\times 5) = 30$.&nbsp;&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"366\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-4.png\" alt=\"Associative property of multiplication\" class=\"wp-image-23301\" title=\"Associative property of multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-4.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-4-300x177.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/associative-property-of-multiplication\" target=\"_blank\" rel=\"noopener\" title=\"\">associative property of multiplication<\/a> for three real numbers a, b, and c is:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(a \\times b) \\times c = a \\times (b \\times c)$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"8-identity-property-of-addition-\"><strong>Identity Property of Addition<\/strong><\/h3>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-identity-property\">Identity Property<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>This property says that when we add 0 to any number, the sum is equal to the number itself. We call 0 the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/additive-identity-property-of-0\" target=\"_blank\" rel=\"noopener\" title=\"\">additive identity<\/a><\/strong>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s take the 5 and add 0 to it. We get $5 + 0 = 5$ or $0 + 5 = 5$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"457\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-5.png\" alt=\"Identity property of addition\" class=\"wp-image-23302\" title=\"Identity property of addition\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-5-300x221.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the identity property of addition for any real number a is:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a + 0 = 0 + a = a$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"10-identity-property-of-multiplication-\"><strong>Identity Property of Multiplication<\/strong><\/h3>\n\n\n\n<p class=\" eplus-wrapper\"><strong>This property says that when we multiply any number by 1, the product is equal to the number itself. We call 1 the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/multiplicative-identity-property-of-1\" target=\"_blank\" rel=\"noopener\" title=\"\">multiplicative identity<\/a><\/strong>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s take the 4 and multiply it by 1.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We get&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$4 \\times 1 = 4$ or $1 \\times 4 = 4$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"370\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-6.png\" alt=\"Identity property of multiplication\" class=\"wp-image-23303\" title=\"Identity property of multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-6-300x179.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the identity property of multiplication for any real number a is:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a \\times 1 = 1 \\times a = a$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-distributive-property-of-multiplication-over-addition\">Distributive Property of Multiplication Over Addition<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>The distributive property says that when you multiply a number by the sum of two or more <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/addend\" target=\"_blank\" rel=\"noopener\" title=\"\">addends<\/a>, the product is the same as the result of the multiplication of the number by each of the addends individually and then adding the products. This property specifies that multiplication distributes over addition<\/strong>.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Example:<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s multiply 3 by the sum of 4 and 5. We get $3 \\times (4 + 5) = 27$. Now we multiply 3 by 4 and 5 individually and then add the products. We get $(3 \\times 4) + (3 \\times 5) = 12 + 15 = 27$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus, $3 \\times (4 + 5) = (3 \\times 4) + (3 \\times 5) = 27$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Now, let\u2019s consider the expression $(2 + 3) \\times 7$. We get $(2 + 3) \\times 7 = 5 \\times 7 = 35$. When we multiply 2 and 3 individually with 7 and add the products, we get $2 \\times 7 + 3 \\times 7 = 14 + 21 = 35$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus, $(2 + 3) \\times 7 = (2 \\times 7) + (3 \\times 7) = 35$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">These two <strong>examples of<\/strong> <strong>math properties <\/strong>show how we can distribute an expression for easy computation. For $a \\times (b + c)$, we can expand the expression using the distributive property as:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"618\" height=\"443\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-7.png\" alt=\"Distributive Property of Multiplication Over Addition\" class=\"wp-image-23304\" title=\"Distributive Property of Multiplication Over Addition\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-7.png 618w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-7-300x215.png 300w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">For $(b + c) \\times a$, we can expand the expression using the distributive property as:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"618\" height=\"443\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-8.png\" alt=\"Distributive property\" class=\"wp-image-23305\" title=\"Distributive property\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-8.png 618w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-8-300x215.png 300w\" sizes=\"auto, (max-width: 618px) 100vw, 618px\" \/><\/figure>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the distributive property of multiplication over addition for three real numbers a, b, and c is:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a \\times (b + c) = a \\times b + a \\times c$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-formula-chart-of-basic-number-properties\">Formula Chart of Basic Number Properties<\/h2>\n\n\n\n<p class=\" eplus-wrapper\">Here\u2019s a list of <strong>math properties <\/strong>shown in the chart below. It includes the formula for the four basic <strong>math properties of operations<\/strong> discussed above.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"405\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-9.png\" alt=\"Number properties: formula chart\" class=\"wp-image-23306\" title=\"Number properties: formula chart\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-9.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/What-is-Number-Properties-9-300x196.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">There is just one version of the distributive property for multiplication and addition. It doesn\u2019t have two individual rules for addition and multiplication.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">The commutative property derives its name from the commute, which means to travel or move around.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">The associative property derives its name from the term associate.<\/li>\n\n\n\n<li class=\" eplus-wrapper\">The identity property of addition is also known as the zero property of addition.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Number properties<\/strong> tell us how math operations relate to one another. By using <strong>the 4 properties of math<\/strong> mentioned above, you can simplify computation and strengthen your base for learning higher mathematical concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"15-solved-examples-of-number-properties\">Solved Examples of Number Properties<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><strong>1. Identify the number property used in the given equation.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/strong>$(12 \\times 9) \\times 4 = 12 \\times( 9 \\times 4)$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution<\/strong>:&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">The property used is the associative property of multiplication,&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$(a \\times b) \\times c = a \\times (b \\times c)$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">The product is not affected by the way we group the numbers.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>2. Is <\/strong>$3yz = 3zy$<strong>?<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution<\/strong>:<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Yes, $3yz = 3zy$.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">By the commutative property of multiplication, we have $a \\times b = b \\times a$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We can say that $3yz = 3zy$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>3. By the commutative property of addition, <\/strong>$n + 3 =$<strong> ?<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution<\/strong>:&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">By the commutative property of addition, we have<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a + b = b + a$; for any real numbers a and b<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Thus, $n + 3 = 3 + n$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">The order of numbers does not affect the sum.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>4. If <\/strong>$4m \\times 1 = 20$<strong>, find the value of m using the identity property of multiplication. &nbsp;<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution<\/strong>: &nbsp;The given expression is $4m \\times 1 = 20$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">As per the identity property of multiplication, $a \\times 1 = a$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">So,&nbsp; $4m = 20$<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$m = \\frac{20}{4}$&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$m = 5$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Hence, the value of m is 5.<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>5. Solve the given expression using the distributive property.<\/strong><\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <\/strong>$6 \\times (5 + 8)$<\/p>\n\n\n\n<p class=\" eplus-wrapper\"><strong>Solution<\/strong>: The distributive property for three real numbers a, b, and c is&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a \\times (b + c) = a \\times b + a \\times c$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Let\u2019s consider $a = 6, b = 5$, and $c = 8$, and substitute the values in the equation&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">$a \\times (b + c) = a \\times b + a \\times c$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">We get $6 \\times (5 + 8) = 6 \\times 5 + 6 \\times 8 = 30 + 48 = 78$.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">So, $6 \\times (5 + 8) = 78$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"16-practice-problems-of-number-properties\">Practice Problems of Number Properties<\/h2>\n\n\n\n<p class=\" eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Number Properties<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which property is used in the image below?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">Commutative property of addition<\/div><div class=\"spq_answer_block\" data-value=\"1\">Associative property of addition<\/div><div class=\"spq_answer_block\" data-value=\"2\">Identity property of addition<\/div><div class=\"spq_answer_block\" data-value=\"3\">Distributive property<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Associative property of addition<br\/>If we consider $a = 3$ yellow balls, $b = 6$ red balls, and $c = 2$ green balls, and substitute them in the equation, we get: $(a + b) + c  =  a + (b + c)$. This is the associative property of addition.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following is an example of identity property of addition?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$7 + 1 = 8$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$22 + 2 = 24$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$20 + 0 = 20$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$1 \u2013 1 = 0$<\/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: $20 + 0 = 20$<br\/>The identity property of addition is $a + 0 = a$. When we substitute 20 as the value of a in this expression, we get $20 + 0 = 20$.<\/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\">Select the number property that the given expression illustrates. $yz \\times 1 = yz$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Identity property of multiplication<\/div><div class=\"spq_answer_block\" data-value=\"1\">Associative property of multiplication<\/div><div class=\"spq_answer_block\" data-value=\"2\">Distributive Property<\/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: Identity property of multiplication<br\/>The identity property of multiplication is $a \\times 1 = a$. If we consider $a = yz$, we can express this property as $yz \\times 1 = yz$.<\/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\">Which expression is equal to $(7 \\times 3) \\times 9$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$7 \\times (3 + 9)$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$7 \\times (3 \\times 9)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$7 + (3 \\times 9)$<\/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: $7 \\times (3 \\times 9)$<br\/>According to the associative property of multiplication, $(a \\times b) \\times c = a \\times (b \\times c)$.<br>\r\nThus, $(7 \\times 3) \\times 9 = 7 \\times (3 \\times 9)$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">If you expand $5 \\times (9 + 1)$ using the distributive property, which expression will you get?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$5 \\times 10$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$5 + (9 \\times 1)$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$5 \\times 9 + 5 \\times 1$<\/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: $5 \\times 9 + 5 \\times 1$<br\/>The distributive property of multiplication over addition is $a \\times (b + c) = a \\times b + a \\times c$.<br>\r\nBy substituting $a = 5$, $b = 9$, and $c = 1$, we get the expression $5 \\times (9 +1) = 5 \\times 9 + 5 \\times 1$.<\/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\": \"Number Properties\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Number Properties\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which property is used in the image below?\",\n                    \"text\": \"Which property is used in the image below? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/02\/Practice-Problems-1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If we consider $$a = 3$$ yellow balls, $$b = 6$$ red balls, and $$c = 2$$ green balls, and substitute them in the equation, we get: $$(a + b) + c  =  a + (b + c)$$. This is the associative property of addition.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Commutative property of addition\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If we consider $$a = 3$$ yellow balls, $$b = 6$$ red balls, and $$c = 2$$ green balls, and substitute them in the equation, we get: $$(a + b) + c  =  a + (b + c)$$. This is the associative property of addition.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Identity property of addition\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If we consider $$a = 3$$ yellow balls, $$b = 6$$ red balls, and $$c = 2$$ green balls, and substitute them in the equation, we get: $$(a + b) + c  =  a + (b + c)$$. This is the associative property of addition.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Distributive property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If we consider $$a = 3$$ yellow balls, $$b = 6$$ red balls, and $$c = 2$$ green balls, and substitute them in the equation, we get: $$(a + b) + c  =  a + (b + c)$$. This is the associative property of addition.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Associative property of addition\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If we consider $$a = 3$$ yellow balls, $$b = 6$$ red balls, and $$c = 2$$ green balls, and substitute them in the equation, we get: $$(a + b) + c  =  a + (b + c)$$. This is the associative property of addition.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If we consider $$a = 3$$ yellow balls, $$b = 6$$ red balls, and $$c = 2$$ green balls, and substitute them in the equation, we get: $$(a + b) + c  =  a + (b + c)$$. This is the associative property of addition.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is an example of identity property of addition?\",\n                    \"text\": \"Which of the following is an example of identity property of addition?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The identity property of addition is $$a + 0 = a$$. When we substitute 20 as the value of a in this expression, we get $$20 + 0 = 20$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$7 + 1 = 8$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity property of addition is $$a + 0 = a$$. When we substitute 20 as the value of a in this expression, we get $$20 + 0 = 20$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$22 + 2 = 24$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity property of addition is $$a + 0 = a$$. When we substitute 20 as the value of a in this expression, we get $$20 + 0 = 20$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$1 \u2013 1 = 0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity property of addition is $$a + 0 = a$$. When we substitute 20 as the value of a in this expression, we get $$20 + 0 = 20$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$20 + 0 = 20$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The identity property of addition is $$a + 0 = a$$. When we substitute 20 as the value of a in this expression, we get $$20 + 0 = 20$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The identity property of addition is $$a + 0 = a$$. When we substitute 20 as the value of a in this expression, we get $$20 + 0 = 20$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Select the number property that the given expression illustrates. $$yz \\\\times 1 = yz$$\",\n                    \"text\": \"Select the number property that the given expression illustrates. $$yz \\\\times 1 = yz$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The identity property of multiplication is $$a \\\\times 1 = a$$. If we consider $$a = yz$$, we can express this property as $$yz \\\\times 1 = yz$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Associative property of multiplication\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity property of multiplication is $$a \\\\times 1 = a$$. If we consider $$a = yz$$, we can express this property as $$yz \\\\times 1 = yz$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Distributive Property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity property of multiplication is $$a \\\\times 1 = a$$. If we consider $$a = yz$$, we can express this property as $$yz \\\\times 1 = yz$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The identity property of multiplication is $$a \\\\times 1 = a$$. If we consider $$a = yz$$, we can express this property as $$yz \\\\times 1 = yz$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Identity property of multiplication\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The identity property of multiplication is $$a \\\\times 1 = a$$. If we consider $$a = yz$$, we can express this property as $$yz \\\\times 1 = yz$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The identity property of multiplication is $$a \\\\times 1 = a$$. If we consider $$a = yz$$, we can express this property as $$yz \\\\times 1 = yz$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which expression is equal to $$(7 \\\\times 3) \\\\times 9$$?\",\n                    \"text\": \"Which expression is equal to $$(7 \\\\times 3) \\\\times 9$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the associative property of multiplication, $$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$.<br>\r\nThus, $$(7 \\\\times 3) \\\\times 9 = 7 \\\\times (3 \\\\times 9)$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$7 \\\\times (3 + 9)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the associative property of multiplication, $$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$.<br>\r\nThus, $$(7 \\\\times 3) \\\\times 9 = 7 \\\\times (3 \\\\times 9)$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$7 + (3 \\\\times 9)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the associative property of multiplication, $$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$.<br>\r\nThus, $$(7 \\\\times 3) \\\\times 9 = 7 \\\\times (3 \\\\times 9)$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the associative property of multiplication, $$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$.<br>\r\nThus, $$(7 \\\\times 3) \\\\times 9 = 7 \\\\times (3 \\\\times 9)$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$7 \\\\times (3 \\\\times 9)$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the associative property of multiplication, $$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$.<br>\r\nThus, $$(7 \\\\times 3) \\\\times 9 = 7 \\\\times (3 \\\\times 9)$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the associative property of multiplication, $$(a \\\\times b) \\\\times c = a \\\\times (b \\\\times c)$$.<br>\r\nThus, $$(7 \\\\times 3) \\\\times 9 = 7 \\\\times (3 \\\\times 9)$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If you expand $$5 \\\\times (9 + 1)$$ using the distributive property, which expression will you get?\",\n                    \"text\": \"If you expand $$5 \\\\times (9 + 1)$$ using the distributive property, which expression will you get?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The distributive property of multiplication over addition is $$a \\\\times (b + c) = a \\\\times b + a \\\\times c$$.<br>\r\nBy substituting $$a = 5$$, $$b = 9$$, and $$c = 1$$, we get the expression $$5 \\\\times (9 +1) = 5 \\\\times 9 + 5 \\\\times 1$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$5 \\\\times 10$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distributive property of multiplication over addition is $$a \\\\times (b + c) = a \\\\times b + a \\\\times c$$.<br>\r\nBy substituting $$a = 5$$, $$b = 9$$, and $$c = 1$$, we get the expression $$5 \\\\times (9 +1) = 5 \\\\times 9 + 5 \\\\times 1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$5 + (9 \\\\times 1)$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distributive property of multiplication over addition is $$a \\\\times (b + c) = a \\\\times b + a \\\\times c$$.<br>\r\nBy substituting $$a = 5$$, $$b = 9$$, and $$c = 1$$, we get the expression $$5 \\\\times (9 +1) = 5 \\\\times 9 + 5 \\\\times 1$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The distributive property of multiplication over addition is $$a \\\\times (b + c) = a \\\\times b + a \\\\times c$$.<br>\r\nBy substituting $$a = 5$$, $$b = 9$$, and $$c = 1$$, we get the expression $$5 \\\\times (9 +1) = 5 \\\\times 9 + 5 \\\\times 1$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$5 \\\\times 9 + 5 \\\\times 1$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The distributive property of multiplication over addition is $$a \\\\times (b + c) = a \\\\times b + a \\\\times c$$.<br>\r\nBy substituting $$a = 5$$, $$b = 9$$, and $$c = 1$$, we get the expression $$5 \\\\times (9 +1) = 5 \\\\times 9 + 5 \\\\times 1$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The distributive property of multiplication over addition is $$a \\\\times (b + c) = a \\\\times b + a \\\\times c$$.<br>\r\nBy substituting $$a = 5$$, $$b = 9$$, and $$c = 1$$, we get the expression $$5 \\\\times (9 +1) = 5 \\\\times 9 + 5 \\\\times 1$$.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"17-frequently-asked-questions-of-number-properties\">Frequently Asked Questions of Number Properties<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-cbb8b36b-4174-4191-a24d-b0083f435619\" 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-cbb8b36b-4174-4191-a24d-b0083f435619\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cbb8b36b-4174-4191-a24d-b0083f435619\"><strong>What are real 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-0-cbb8b36b-4174-4191-a24d-b0083f435619\">\n\n<p class=\" eplus-wrapper\">Real numbers include <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/fraction\" target=\"_blank\" rel=\"noopener\" title=\"\">fractions<\/a>, positive <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/integers\" target=\"_blank\" rel=\"noopener\" title=\"\">integers<\/a>, negative integers, and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number\/irrational-numbers\" target=\"_blank\" rel=\"noopener\" title=\"\">irrational numbers<\/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-cbb8b36b-4174-4191-a24d-b0083f435619\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cbb8b36b-4174-4191-a24d-b0083f435619\"><strong>Do decimal numbers follow the math properties mentioned above?<\/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-cbb8b36b-4174-4191-a24d-b0083f435619\">\n\n<p class=\" eplus-wrapper\">Yes, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/decimals\/decimal\" target=\"_blank\" rel=\"noopener\" title=\"\">decimal<\/a> numbers follow the math properties mentioned above.<\/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-cbb8b36b-4174-4191-a24d-b0083f435619\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cbb8b36b-4174-4191-a24d-b0083f435619\"><strong>Can we use the commutative property for subtraction?<\/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-cbb8b36b-4174-4191-a24d-b0083f435619\">\n\n<p class=\" eplus-wrapper\">No, we can\u2019t. This is because the commutative property doesn\u2019t hold for <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/subtraction\/subtract\" target=\"_blank\" rel=\"noopener\" title=\"\">subtraction<\/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-3-cbb8b36b-4174-4191-a24d-b0083f435619\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cbb8b36b-4174-4191-a24d-b0083f435619\"><strong>Is <\/strong>$-1$<strong> a multiplicative identity?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-cbb8b36b-4174-4191-a24d-b0083f435619\">\n\n<p class=\" eplus-wrapper\">No, $\u2212 1$ isn\u2019t a multiplicative identity. This is because if we multiply any real number by $\u2212 1$, the sign of the number changes. For example, $9 \\times \u2212 1 = \u2212 9$. Also, $\u2212 9 \\times \u2212 1 = 9$.<\/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-cbb8b36b-4174-4191-a24d-b0083f435619\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-cbb8b36b-4174-4191-a24d-b0083f435619\"><strong>What is the additive identity of <\/strong>$\u2212 1<strong>?<\/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-cbb8b36b-4174-4191-a24d-b0083f435619\">\n\n<p class=\" eplus-wrapper\">The additive identity of $\u2212 1$ is 0.<\/p>\n\n<\/div><\/div>\n<\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"18-related-articles\">Related Articles<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number\"><strong>Number System<\/strong><\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/commutative-property\"><strong>Commutative Property<\/strong><\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/distributive-property\"><strong>Distributive Property<\/strong><\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/addition\/properties-of-addition\"><strong>Properties of addition<\/strong><\/a><\/li>\n\n\n\n<li class=\" eplus-wrapper\"><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/properties-of-multiplication\"><strong>Properties of multiplication<\/strong><\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Number Properties &#8211; Introduction Number properties are certain rules that can be applied and characteristics that numbers follow when we perform arithmetic operations on them. In mathematics, we use numbers to express mathematical facts and ideas logically. But what are number properties? Why do you need to learn them? We know that everything around us &#8230; <a title=\"Number Properties &#8211; Definition, Types, Chart\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/number-properties\" aria-label=\"More on Number Properties &#8211; Definition, Types, Chart\">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-537","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\/537","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=537"}],"version-history":[{"count":29,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/537\/revisions"}],"predecessor-version":[{"id":27135,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/537\/revisions\/27135"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=537"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=537"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=537"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}