{"id":26793,"date":"2023-03-24T09:41:50","date_gmt":"2023-03-24T09:41:50","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26793"},"modified":"2023-03-25T18:29:21","modified_gmt":"2023-03-25T18:29:21","slug":"properties-of-whole-numbers-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/properties-of-whole-numbers","title":{"rendered":"Properties of Whole Numbers: Definition with Examples"},"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-b26f54e1-b5e9-4308-b951-dd9e347b8d82\" 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\/properties-of-whole-numbers#0-what-are-the-properties-of-whole-numbers>What Are the Properties of Whole Numbers?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/properties-of-whole-numbers#1-what-are-whole-numbers>What Are Whole Numbers?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/properties-of-whole-numbers#2-list-of-properties-of-whole-numbers>List of Properties of Whole Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/properties-of-whole-numbers#10-solved-examples-on-properties-of-whole-numbers>Solved Examples On Properties of Whole Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/properties-of-whole-numbers#11-practice-problems-on-properties-of-whole-numbers>Practice Problems On Properties of Whole Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/properties-of-whole-numbers#12-frequently-asked-questions-on-properties-of-whole-numbers>Frequently Asked Questions on Properties of Whole Numbers<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"0-what-are-the-properties-of-whole-numbers\">What Are the Properties of Whole Numbers?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Properties of whole numbers include certain rules or facts that help us perform basic arithmetic operations like addition and multiplication. Using the properties of whole numbers, one can calculate mathematical expressions and solve them quickly.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Properties of whole numbers make it easier to perform basic arithmetic operations like addition, subtraction, and multiplication on the whole numbers. Using these properties, we can simplify calculations and solve math problems in less time.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-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-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 class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-digit-and-1-digit-numbers-and-match\" 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_3d_1d_match_g3_pt.png\" alt=\"Add 3-Digit and 1-Digit Numbers and Match 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-Digit and 1-Digit Numbers and Match 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-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_3d_1d_vertical_pt.png\" alt=\"Add 3-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 3-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-3-digit-and-1-digit-numbers-with-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_3d_1d_vertical_pt.png\" alt=\"Add 3-Digit and 1-Digit Numbers with 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 3-Digit and 1-Digit Numbers with 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><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=\"eplus-wrapper wp-block-heading\" id=\"1-what-are-whole-numbers\">What Are Whole Numbers?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A set of whole numbers include natural numbers and zero (0).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A set of whole numbers is represented by the letter W.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$W = \\left\\{0, 1, 2, 3, 4,\u2026\\right\\}$.\u00a0<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Whole numbers do not include fractions, decimals, or negative integers. We can also describe whole numbers as the union of the natural numbers (or positive integers) and 0.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"304\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-1.png\" alt=\"Whole numbers and natural numbers on the number line\" class=\"wp-image-26821\" title=\"Whole numbers and natural numbers on the number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-1-300x147.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-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\" >\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-place-value\" 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-place-value.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Place Value\">\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-numbers-and-teen-numbers-horizontal-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-1-digit-numbers-and-teen-numbers-horizontal-addition.jpeg\" alt=\"Add 1-Digit Numbers and Teen Numbers: Horizontal 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\/add-1-digit-numbers-and-teen-numbers-missing-digits\" 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-numbers-and-teen-numbers-missing-digits.jpeg\" alt=\"Add 1-Digit Numbers and Teen Numbers: Missing Digits 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-numbers-and-teen-numbers-missing-numbers\" 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  });\n    <\/script><h2 class=\"eplus-wrapper wp-block-heading\" id=\"2-list-of-properties-of-whole-numbers\">List of Properties of Whole Numbers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Properties of whole numbers are as follows:<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">Closure Property<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Commutative Property of Addition and Multiplication<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Associative Property of Addition and Multiplication<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Distributive Property of Multiplication over Addition<\/li>\n\n\n\n<li class=\" eplus-wrapper\">Identity Property<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The chart of properties of whole numbers summarizes these properties as shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"664\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-2.png\" alt=\"Properties of whole numbers chart\" class=\"wp-image-26822\" title=\"Properties of whole numbers chart\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-2-280x300.png 280w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, let\u2019s discuss the properties of whole numbers with examples.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"3-closure-property\">Closure Property<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The closure property of whole numbers states that the addition or multiplication of two whole numbers will always give us a whole number. In other words, whole numbers are closed under multiplication and addition.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider a and b to be two whole numbers such that a, $b \\in W$, then,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a + b \\rightarrow W$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a \\times b \\rightarrow W$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The closure property does not apply over subtraction and division of whole numbers since the difference and division between two whole numbers might not give us a whole number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4\\;-\\;7 = \\;-3$, negative integer<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{4}{7} = 0.5714$, a decimal number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Also, division by the whole number zero $(0)$ gives us an undefined number.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"4-commutative-property-of-addition-and-multiplication\">Commutative Property of Addition and Multiplication<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The commutative property of whole numbers states that even if we change the order of the two whole numbers in addition and multiplication, the sum or the product stays the same. In other words, one can add or multiply two whole numbers in any order and will get the same answer.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider two whole numbers A and B, the commutative property states that:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">for all a, $b \\in W$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a + b = b + a$ \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u2026 addition<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">and<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u00a0$a \\times b = b \\times a$ \u2026 multiplication<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">in addition: $1 + 4 = 4 + 1 = 5$,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">and in multiplication: $2 \\times 4 = 4 \\times 2 =8$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The commutativity does not apply over subtraction and division of two whole numbers. The reason being, if we change the order of the numbers during subtraction, the resulting answer will change in sign.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4 \\;-\\; 2 = 2$ and $2 \\;-\\; 4 = \\;-2$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{4}{2} = 2$ and $\\frac{2}{4} = 0.5$<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"5-associative-property-of-addition-and-multiplication\">Associative Property of Addition and Multiplication<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Under the associative property, the sum or product obtained of three or more numbers remains the same even if we rearrange or regroup numbers in different order.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider three whole numbers a, b, and c. The associative property states that:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a+ \\left[b + c\\right]= \\left[a + b\\right] + c$ \u2026addition<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\left[a \\times b\\right] \\times c = a \\times \\left[b \\times c\\right]$ \u2026multiplication<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example:<\/strong><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">$3 + \\left[5 + 7\\right] = \\left[3 + 5\\right] + 7$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$3 + 12 = 8 + 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$15 = 15$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">$3 \\times \\left[5 \\times 7\\right] = \\left[3 \\times 5\\right] \\times 7$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$3\u00a0 \\times\u00a0 35 = 15\u00a0 \\times\u00a0 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$105 = 105$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Associative property does not apply over subtraction and division of two whole numbers.<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"6-distributive-property-of-multiplication-over-addition-and-subtraction\">Distributive Property of Multiplication Over Addition and Subtraction<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The distributive property of multiplication over addition states that multiplication is distributive over the sum of two or more whole numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Consider three whole numbers a, b, and c.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The associative property states that:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u00a0 $a \\times \\left[b + c\\right] = \\left[a \\times b\\right] + \\left[a \\times c\\right]$ \u2026multiplication over addition<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u00a0 $a \\times \\left[b \\;-\\; c\\right] = \\left[a \\times b\\right] \\;-\\; \\left[a \\times c\\right]$ \u2026multiplication over subtraction<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example of distributive property of multiplication over addition:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4 \\times \\left[6 + 8\\right] = \\left[4 \\times 6\\right] + \\left[4 \\times 8\\right]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4 \\times 14 = 24 + 32$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$56 = 56$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example of distributive property of multiplication over subtraction:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$5 \\times \\left[4 + 2\\right] = \\left[5 \\times 4\\right] + \\left[5 \\times 2\\right]$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$5 \\times 6 = 20 + 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$30 = 30$<\/p>\n\n\n\n<h3 class=\"eplus-wrapper wp-block-heading\" id=\"7-identity-property\">Identity Property<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Additive Identity:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This property states that when zero is added to a whole number, the result is the whole number itself. This makes zero the additive identity for the whole numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If a is a whole number, then<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$a + 0 = a = 0 + a$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example,&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$0 + 8 = 8 = 8 + 0$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Multiplicative Identity:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This property states that the product of a whole number and 1 results in the whole number itself. This makes 1 the multiplicative identity for whole numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If A is a whole number, then<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u00a0$a \\times 1 = a = 1 \\times a$.\u00a0<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example,<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$23 \\times 1 = 23 = 1 \\times 23$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"429\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-3.png\" alt=\"Identity property of multiplication and addition\" class=\"wp-image-26823\" title=\"Identity property of multiplication and addition\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/03\/Properties-of-Whole-Numbers-3-300x208.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"8-fun-facts\">Fun Facts!<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">The closure, associative, and commutative properties do not satisfy subtraction and division in whole numbers.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\" eplus-wrapper\">When zero is subtracted from any number, we obtain that number itself. But if we subtract any number from zero, we obtain its additive inverse.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"9-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we learned about what whole numbers are and looked at some of the properties that whole numbers offer over addition, subtraction, multiplication and division.<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"10-solved-examples-on-properties-of-whole-numbers\">Solved Examples On Properties of Whole Numbers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Which of the following expressions express the multiplicative and additive identity property?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>(i) \u00a0 <\/strong>$7 \\times 1 = 7$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>(ii)\u00a0 <\/strong>$0 \\times 3 = 3 \\times 0 = 0$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>(iii) <\/strong>$0 + 90 = 90$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>(iv) <\/strong>$34 \\times \\frac{1}{34} = 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(i)\u00a0 $a \\times 1 = 1 \\times a = a$, where $a = 7$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It represents multiplicative identity property.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">(iv) $a + 0 = 0 + a = a$, where $a = 90$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It represents additive identity property.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. By using properties of whole numbers, fill in the blanks in the following expression: <\/strong>$165 \\times 78 \\times 12 = \\underline{} \\times 12 \\times 165$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The commutative property of multiplication states that the order of the multiplication operation does not change the product.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $165 \\times 78 \\times 12 = 78 \\times 12 \\times 165$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. By using properties of whole numbers, fill in the blanks in the following expression: <\/strong>$49 + (43 + 23) = (49 + \\underline{}) + 23$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The associative property of addition states that the sum of numbers does not change regardless how we group the numbers.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $49 + (43 + 23) = (49 + 43) + 23$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Find the addition of <\/strong>$10 \\times (15 + 1)$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">By distributive property, we have<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$10 \\times (15 + 1) = (10 \\times 15) + (101)$\u00a0<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/strong>$= 150 + 10$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0$= 160$<\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"11-practice-problems-on-properties-of-whole-numbers\">Practice Problems On Properties of Whole Numbers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Properties of Whole Numbers: Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following expressions uses the commutative property of addition:<br>(i)$7 \\times 5 = 5 \\times 7 = 35$<br>(ii)$4 + 1 = 1 + 4 = 5$<br>(iii)$1 \\times 5 = 5 \\times 1 = 5$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Statement (i)<\/div><div class=\"spq_answer_block\" data-value=\"1\">Statement (ii)<\/div><div class=\"spq_answer_block\" data-value=\"2\">Statement (iii)<\/div><div class=\"spq_answer_block\" data-value=\"3\">All 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: Statement (ii)<br\/>The commutative property of addition states that, for any two whole numbers a and b, $a + b = b + a$.<br>\r\nThus,  $4 + 1 = 1 + 4 = 5$ uses the commutative property of addition.<\/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\">Fill in the blanks: $235 \\times ? = 235$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$0$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$1$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$-1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$11$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $1$<br\/>$235 \\times 1 = 235$<\/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\">The commutative property is not applicable over<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Addition and Multiplication<\/div><div class=\"spq_answer_block\" data-value=\"1\">Addition and Subtraction<\/div><div class=\"spq_answer_block\" data-value=\"2\">Subtraction and Division<\/div><div class=\"spq_answer_block\" data-value=\"3\">Addition and Division<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Subtraction and Division<br\/>The commutative property is not applicable over subtraction and division.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Properties of Whole Numbers: Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Properties of Whole Numbers\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following expressions uses the commutative property of addition:<br>(i)$$7 \\\\times 5 = 5 \\\\times 7 = 35$$<br>(ii)$$4 + 1 = 1 + 4 = 5$$<br>(iii)$$1 \\\\times 5 = 5 \\\\times 1 = 5$$\",\n                    \"text\": \"Which of the following expressions uses the commutative property of addition:<br>(i)$$7 \\\\times 5 = 5 \\\\times 7 = 35$$<br>(ii)$$4 + 1 = 1 + 4 = 5$$<br>(iii)$$1 \\\\times 5 = 5 \\\\times 1 = 5$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The commutative property of addition states that, for any two whole numbers a and b, $$a + b = b + a$$.<br>\r\nThus,  $$4 + 1 = 1 + 4 = 5$$ uses the commutative property of addition.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Statement (i)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property of addition states that, for any two whole numbers a and b, $$a + b = b + a$$.<br>\r\nThus,  $$4 + 1 = 1 + 4 = 5$$ uses the commutative property of addition.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Statement (iii)\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property of addition states that, for any two whole numbers a and b, $$a + b = b + a$$.<br>\r\nThus,  $$4 + 1 = 1 + 4 = 5$$ uses the commutative property of addition.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"All of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property of addition states that, for any two whole numbers a and b, $$a + b = b + a$$.<br>\r\nThus,  $$4 + 1 = 1 + 4 = 5$$ uses the commutative property of addition.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Statement (ii)\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The commutative property of addition states that, for any two whole numbers a and b, $$a + b = b + a$$.<br>\r\nThus,  $$4 + 1 = 1 + 4 = 5$$ uses the commutative property of addition.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The commutative property of addition states that, for any two whole numbers a and b, $$a + b = b + a$$.<br>\r\nThus,  $$4 + 1 = 1 + 4 = 5$$ uses the commutative property of addition.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Fill in the blanks: $$235 \\\\times ? = 235$$\",\n                    \"text\": \"Fill in the blanks: $$235 \\\\times ? = 235$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$235 \\\\times 1 = 235$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$0$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$235 \\\\times 1 = 235$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$-1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$235 \\\\times 1 = 235$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$11$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$235 \\\\times 1 = 235$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$1$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$235 \\\\times 1 = 235$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$235 \\\\times 1 = 235$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The commutative property is not applicable over\",\n                    \"text\": \"The commutative property is not applicable over\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The commutative property is not applicable over subtraction and division.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Addition and Multiplication\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property is not applicable over subtraction and division.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Addition and Subtraction\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property is not applicable over subtraction and division.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Addition and Division\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property is not applicable over subtraction and division.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Subtraction and Division\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The commutative property is not applicable over subtraction and division.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The commutative property is not applicable over subtraction and division.\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"eplus-wrapper wp-block-heading\" id=\"12-frequently-asked-questions-on-properties-of-whole-numbers\">Frequently Asked Questions on Properties of Whole Numbers<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-8803603b-8b5f-4ca2-b702-02a47f19fcbd\" 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-0-8803603b-8b5f-4ca2-b702-02a47f19fcbd\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8803603b-8b5f-4ca2-b702-02a47f19fcbd\"><strong>What is an additive inverse?<\/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-0-8803603b-8b5f-4ca2-b702-02a47f19fcbd\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Additive inverse is a number which when added to the original number, results in zero. Under addition, the additive inverse of a whole number \u201ca\u201d will be \u201c-a.\u201d<\/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-1-8803603b-8b5f-4ca2-b702-02a47f19fcbd\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8803603b-8b5f-4ca2-b702-02a47f19fcbd\"><strong>What is a multiplicative inverse?<\/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-1-8803603b-8b5f-4ca2-b702-02a47f19fcbd\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiplicative inverse is a number that, when multiplied by the original number, will give 1 as the result. Under multiplication, the multiplicative inverse of an element \u201ca\u201d will be $a^{-1}$.<\/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-2-8803603b-8b5f-4ca2-b702-02a47f19fcbd\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8803603b-8b5f-4ca2-b702-02a47f19fcbd\"><strong>What are rational 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-2-8803603b-8b5f-4ca2-b702-02a47f19fcbd\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Rational numbers are numbers of the form $\\frac{p}{q}$, where p,q are integers and $q \\neq 0$.<\/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-3-8803603b-8b5f-4ca2-b702-02a47f19fcbd\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8803603b-8b5f-4ca2-b702-02a47f19fcbd\"><strong>Do whole numbers include negative integers?<\/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-3-8803603b-8b5f-4ca2-b702-02a47f19fcbd\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Whole numbers only include natural numbers and 0.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are the Properties of Whole Numbers? Properties of whole numbers include certain rules or facts that help us perform basic arithmetic operations like addition and multiplication. Using the properties of whole numbers, one can calculate mathematical expressions and solve them quickly. Properties of whole numbers make it easier to perform basic arithmetic operations like &#8230; <a title=\"Properties of Whole Numbers: Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/properties-of-whole-numbers\" aria-label=\"More on Properties of Whole Numbers: 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-26793","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\/26793","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=26793"}],"version-history":[{"count":9,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26793\/revisions"}],"predecessor-version":[{"id":26827,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26793\/revisions\/26827"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26793"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26793"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26793"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}