{"id":5052,"date":"2022-05-31T08:39:11","date_gmt":"2022-05-31T08:39:11","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=5052"},"modified":"2024-05-28T10:26:15","modified_gmt":"2024-05-28T10:26:15","slug":"naturals-numbers-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers","title":{"rendered":"What Are Natural Numbers? Definition, Properties, Types, and 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-3e3b496c-92e7-44ab-86a1-2b0dd20a8056\" 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\/natural-numbers#0-what-are-natural-numbers>What Are Natural Numbers?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers#1-definition-of-natural-numbers>Definition of Natural Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers#3-what-are-the-properties-of-natural-numbers>What Are the Properties of Natural Numbers?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers#12-solved-examples-on-natural-numbers>Solved Examples on Natural Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers#13-practice-problems-on-natural-numbers>Practice Problems on Natural Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers#14-frequently-asked-questions-about-natural-numbers>Frequently Asked Questions about Natural Numbers<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-natural-numbers\">What Are Natural Numbers?<\/h2>\n\n\n\n<p>Natural numbers are 1, 2, 3, 4, 5, 6, and go on till infinity. They are also called <strong>counting numbers,<\/strong> as they are used to count objects. Natural numbers do not include 0 or negative numbers. The symbol <strong>\u2115<\/strong> is used to represent the set of natural numbers.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"314\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/natural-numbers-on-a-number-line.png\" alt=\"Natural numbers on a number line\" class=\"wp-image-41798\" title=\"Natural numbers on a number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/natural-numbers-on-a-number-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/natural-numbers-on-a-number-line-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-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=\"wp-block-heading\" id=\"1-definition-of-natural-numbers\">Definition of Natural Numbers<\/h2>\n\n\n\n<p>Natural numbers are all positive integers from 1 to infinity. They are also called counting numbers as they are used to count objects. Natural numbers do not include 0 or negative numbers.&nbsp;<\/p>\n\n\n\n<p>We need numbers in our everyday lives, be it for counting objects, telling time, numbering houses, etc. Numbers that help us count and represent quantities are called natural numbers. These include 1, 2, 3, 4, 5, 6, and go on until infinity.&nbsp;<\/p>\n\n\n\n<p>Here we can see that 1 is the smallest natural number and each subsequent natural number is exactly one more than the previous one. Thus, the numbers that come in between these numbers are not natural numbers like fractions, decimals etc.&nbsp;<\/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\/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 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class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"2-types-of-natural-numbers\">Types of Natural Numbers<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Odd Natural Numbers<\/li>\n<\/ol>\n\n\n\n<p>The odd natural numbers are the positive numbers not divisible by 2.<\/p>\n\n\n\n<p>For example: 29, 677, 89901 etc.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"500\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/list-of-odd-numbers-within-100.png\" alt=\"List of odd numbers within 100\" class=\"wp-image-41799\" title=\"List of odd numbers within 100\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/list-of-odd-numbers-within-100.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/list-of-odd-numbers-within-100-300x242.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>Even Natural Numbers<\/li>\n<\/ol>\n\n\n\n<p>The even natural numbers are the positive numbers that are divisible by 2.&nbsp;<\/p>\n\n\n\n<p>For example: 28, 456, 6022 etc.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"441\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/list-of-even-natural-numbers-within-100.png\" alt=\"List of even natural numbers within 100\" class=\"wp-image-41800\" title=\"List of even natural numbers within 100\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/list-of-even-natural-numbers-within-100.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/list-of-even-natural-numbers-within-100-300x213.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-what-are-the-properties-of-natural-numbers\">What Are the Properties of Natural Numbers?<\/h2>\n\n\n\n<p><strong>Properties of natural numbers in mathematics are certain rules that can be applied or the characteristics of natural numbers that can be used when we perform arithmetic operations on them.<\/strong><\/p>\n\n\n\n<p>The four basic properties of natural numbers are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Closure Property\u00a0<\/li>\n\n\n\n<li>Associative Property<\/li>\n\n\n\n<li>Commutative Property\u00a0<\/li>\n\n\n\n<li>Distributive Property<\/li>\n<\/ul>\n\n\n\n<p>The basic operations of addition, subtraction, multiplication, and division give rise to four main properties of natural numbers.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"521\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/properties-of-natural-numbers-closure-associative-commutative-distributive.png\" alt=\"Properties of natural numbers: closure, associative, commutative, distributive\" class=\"wp-image-41801\" title=\"Properties of natural numbers: closure, associative, commutative, distributive\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/properties-of-natural-numbers-closure-associative-commutative-distributive.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/05\/properties-of-natural-numbers-closure-associative-commutative-distributive-300x252.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>The image shown above gives a quick overview of each property. Let\u2019s understand each property in detail with examples.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-properties-of-natural-numbers\">Properties of Natural Numbers<\/h2>\n\n\n\n<p>Here are the significant properties of natural numbers:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Closed under addition and multiplication<\/li>\n\n\n\n<li>Follows the associative property of addition and multiplication<\/li>\n\n\n\n<li>Follows the distributive property of multiplication over addition and subtraction<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"5-closure-property-of-addition-and-multiplication\">Closure Property of Addition and Multiplication<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Closure property of addition: <\/strong>When you add two natural numbers, the result will always be a natural number.\u00a0<\/li>\n<\/ul>\n\n\n\n<p>Examples of closure property of addition: 2 + 2 = 4, 3 + 4 = 7, 5 + 5 = 10&nbsp;<\/p>\n\n\n\n<p>In each case, the result of the addition of natural numbers is a natural number.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Closure property of multiplication: <\/strong>When you multiply two natural numbers, the result will always be a natural number.\u00a0<\/li>\n<\/ul>\n\n\n\n<p>Examples of closure property of multiplication: 2 \u00d7 2 = 4, 3 \u00d7 2 = 6, 5 \u00d7 5 = 25\u00a0<\/p>\n\n\n\n<p>In each case, the result of the multiplication of natural numbers is a natural number.&nbsp;<\/p>\n\n\n\n<p>Thus, we say that the natural numbers are closed under addition and multiplication.<\/p>\n\n\n\n<p>The question remains: Are natural numbers closed under division and subtraction? In case of division and subtraction, the closure property does not hold true. Subtracting or dividing two natural numbers will not always give us a natural number.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Examples of subtraction: 4 \u2013 6 = \u20132, 5 \u2013 3 = 2, 6 \u2013 9 = \u20133\u00a0<\/li>\n<\/ul>\n\n\n\n<p>The second case resulted in a natural number, but the first and third examples did not.&nbsp;&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Examples of division: 10 \u00f7 3 = 3.33, 9 \u00f7 3 = 3, 15 \u00f7 4 = 3.75\u00a0<\/li>\n<\/ul>\n\n\n\n<p>The first and third cases did not result in natural numbers.&nbsp;&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"6-associative-property-of-addition-and-multiplication\">Associative Property of Addition and Multiplication<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Associative property of addition: <\/strong>The sum of natural numbers remains unchanged even if the grouping of numbers is changed. It is expressed as an equation as <strong>a + (b + c) = (a + b) + c.<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Examples of associative property of addition: 2 + (5 + 6) = 13 and (2 + 5) + 6 = 13&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Associative property of multiplication: <\/strong>The product of natural numbers remains unchanged even if the grouping of numbers is changed. It is expressed as an equation as <strong>a \u00d7<\/strong> <strong>(b \u00d7<\/strong> <strong>c) = (a \u00d7<\/strong> <strong>b) \u00d7<\/strong> <strong>c.<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Examples of associative property of multiplication: 2 \u00d7 (3 \u00d7 4) = 24 and (2 \u00d7 3) \u00d7 4 = 24\u00a0<\/p>\n\n\n\n<p><strong>The associative property does not hold for subtraction and division.<\/strong><\/p>\n\n\n\n<p><strong>a \u2212 (b \u2212 c) <strong>\u2260<\/strong><\/strong> <strong>(a \u2212 b) \u2212 c\u00a0<\/strong><\/p>\n\n\n\n<p><strong>a \u00f7<\/strong> <strong>(b \u00f7<\/strong> <strong>c) \u2260<\/strong> <strong>(a \u00f7<\/strong> <strong>b) \u00f7<\/strong> <strong>c<\/strong><\/p>\n\n\n\n<p>Examples of subtraction: 4 -(10 \u2212 2) = \u2212 4 and (4 \u2212 10) \u2212 2 = \u2212 8\u00a0<\/p>\n\n\n\n<p>Examples of division: 5 \u00f7 (6 \u00f7 3) = 2.5 and (5 \u00f7 6) \u00f7 3 = 0.27<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"7-commutative-property-of-addition-and-multiplication\">Commutative Property of Addition and Multiplication<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Commutative Property of Addition:<\/strong> If we change the order of natural numbers in addition, the result does not change.\u00a0<\/li>\n<\/ul>\n\n\n\n<p>Examples of commutative property of addition: 6 + 5 = 11 and 5 + 6 = 11<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Commutative Property of Multiplication: <\/strong>If we change the order of natural numbers in multiplication, the result does not change.\u00a0<\/li>\n<\/ul>\n\n\n\n<p>Examples of commutative property of multiplication: 2 \u00d7 4 = 8 and 4 \u00d7 2 = 8&nbsp;<\/p>\n\n\n\n<p>The commutative property does not apply to subtraction and division of natural numbers.&nbsp;<\/p>\n\n\n\n<p>Examples for subtraction and division:<\/p>\n\n\n\n<p><strong>a \u2212 b <strong>\u2260<\/strong><\/strong> <strong>b \u2212 a\u00a0\u00a0<\/strong><\/p>\n\n\n\n<p><strong>a \u00f7<\/strong> <strong>b <strong>\u2260<\/strong><\/strong> <strong>b \u00f7 a<\/strong><\/p>\n\n\n\n<p>Examples for subtraction: 5 \u2212 3 = 2 and 3 \u2212 5 = \u2212 2<\/p>\n\n\n\n<p>Examples for division: 6 \u00f7 3 = 2 and 3 \u00f7 6 = 0.5&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"8-distributive-property\">Distributive Property<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Distributive property of multiplication over addition:<\/strong> According to the distributive property of multiplication over addition, if we multiply the total of two addends by a number or multiply each addend individually and then add them, the result will be the same.\u00a0<\/li>\n<\/ul>\n\n\n\n<p><strong>Distributive property of multiplication over addition:<\/strong> <strong>a(b + c) = (a \u00d7<\/strong> <strong>b) + (a \u00d7<\/strong> <strong>c)<\/strong><\/p>\n\n\n\n<p>Example: 2 \u00d7 (5 + 3) = 16<\/p>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(2 \u00d7 5) + (2 \u00d7 3) = 16<\/p>\n\n\n\n<p>This property also holds in the case of multiplication over subtraction.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Distributive property of multiplication over subtraction: a(b \u2212 c) = (a \u00d7<\/strong> <strong>b) \u2212 (a \u00d7<\/strong> <strong>c)<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Example: 2 \u00d7 (5 \u2013 3) = 4<\/p>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0(2 \u00d7 5) \u2013 (2 \u00d7 3) = 4<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-history-of-natural-numbers-\">History of Natural Numbers&nbsp;<\/h2>\n\n\n\n<p>It is widely accepted that natural numbers (starting from one) arose from the practical need to count objects. This development is tied to early human societies across the world as they began to manage resources, trade, and keep records.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-fun-facts-about-natural-numbers\">Fun Facts about Natural Numbers<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>There are an infinite number of natural numbers. There is no largest natural number. Natural numbers go on forever. The smallest natural number is 1.\u00a0<\/li>\n\n\n\n<li>You will get the next natural number by simply adding 1 to a given natural number.<\/li>\n\n\n\n<li>\u00a0For the natural number 1, there is no \u201cpredecessor\u201d or a previous natural number.<\/li>\n\n\n\n<li>\u00a0(1 = 0 + 1, but we know that 0 is not a natural number).<\/li>\n\n\n\n<li>Natural numbers are also called counting numbers, as they are used to count objects.<\/li>\n\n\n\n<li>The properties of natural numbers do not hold true in the case of division and\u00a0<\/li>\n\n\n\n<li>subtraction.<\/li>\n\n\n\n<li>Negative numbers, fractions, and decimals are neither natural numbers nor whole numbers.<\/li>\n\n\n\n<li>Even natural numbers = E = {2, 4, 6, 8, 10, \u2026}<\/li>\n\n\n\n<li>Odd natural numbers = O = {1, 3, 5, 7, 9, 11, \u2026}<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about natural numbers and its properties. These properties make the natural number set unique. In this process, we also understand that the division and subtraction of natural numbers is not guaranteed to be a natural number but that there are incidences where the result is a natural number. Now, let&#8217;s apply this knowledge to solve some examples.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-solved-examples-on-natural-numbers\">Solved Examples on Natural Numbers<\/h2>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify natural numbers from the following list.\u00a0<\/strong><\/li>\n<\/ol>\n\n\n\n<p>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a010, $\\frac{1}{6}$, 4.66, 22, 1564, \u20136.\u00a0<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The natural numbers are 10, 22, and 1564. Negative numbers, decimal numbers, and fractions are not considered natural numbers.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li><strong>List the first ten natural numbers.\u00a0<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>&nbsp;<\/strong>The answer is 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, as the natural numbers start from 1.&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>What is the difference between any two consecutive natural numbers?<\/strong><strong>\u00a0<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The difference between any two consecutive natural numbers is always 1.<\/p>\n\n\n\n<p><strong>4. Which of the following numbers are natural numbers?&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>2, 18, \u20135, 25.5, 1, \u201320.\u00a0<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Natural numbers are given by 1, 2, 3, 4, 5, \u2026 and so on.<\/p>\n\n\n\n<p>The numbers 2, 18, and 1 are natural numbers.<\/p>\n\n\n\n<p>The numbers -5 and -20&nbsp; are not natural numbers because they are negative.<\/p>\n\n\n\n<p>25.5 is not a natural number because it is a decimal.<\/p>\n\n\n\n<p><strong>5. State whether each of the given statements is True or False.<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>There is always a natural number between two consecutive natural numbers.<\/strong><\/li>\n\n\n\n<li><strong>Subtraction of two natural numbers is always a natural number.<\/strong><\/li>\n\n\n\n<li><strong>Natural numbers do not include 0.<\/strong><\/li>\n<\/ol>\n\n\n\n<p><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The statement is false. Between two consecutive natural numbers, there is no natural number.\u00a0<\/li>\n<\/ol>\n\n\n\n<p>For example, no natural number exists between 1 and 2, as 1.1, 1.2, 1.3, 1.7, 1.9, etc. are decimal numbers.<\/p>\n\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n<li>The statement is false. The natural numbers are not closed under subtraction. It means subtracting two natural numbers may or may not give a natural number.<\/li>\n\n\n\n<li>True. 0 is not a natural number. It is a whole number.<\/li>\n<\/ol>\n\n\n\n<p><strong>6. Solve the expression 2 (20 + 15) using the distributive property of multiplication over addition.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>According to distributive property, we have&nbsp;<\/p>\n\n\n\n<p>a(b + c) = (a \u00d7 b) + (a \u00d7 c)<\/p>\n\n\n\n<p>2 (20 + 15) = (2 \u00d7 20) + (2 \u00d7 15) = 40 + 30 = 70\u00a0<\/p>\n\n\n\n<p>Thus, 2 (20 + 15) = 70<\/p>\n\n\n\n<p><strong>7. Identify the properties of the natural numbers based on the expressions given below:<\/strong><\/p>\n\n\n\n<p><strong>a) 2 + (5 + 6) = (2 + 5) + 6<\/strong><\/p>\n\n\n\n<p><strong>b) (10 + 15) = (15 + 10)<\/strong><\/p>\n\n\n\n<p><strong>c) 4 \u00d7<\/strong> <strong>(6 \u00d7<\/strong> <strong>8) = (4 \u00d7<\/strong> <strong>6) \u00d7<\/strong> <strong>8\u00a0<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>a) 2 + (5 + 6) = (2 + 5) + 6&nbsp;<\/p>\n\n\n\n<p>This is an example of the associative property of addition.&nbsp;<\/p>\n\n\n\n<p>b) (10 + 15) = (15 + 10)&nbsp;<\/p>\n\n\n\n<p>This is an example of the commutative property of addition.<\/p>\n\n\n\n<p>c) 4 \u00d7 (6 \u00d7 8) = (4 \u00d7 6) \u00d7 8\u00a0<\/p>\n\n\n\n<p>This is an example of the associative property of multiplication.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-practice-problems-on-natural-numbers\">Practice Problems on Natural Numbers<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Natural Numbers<\/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\">Identify a natural number.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\u2013 1$<\/div><div class=\"spq_answer_block\" data-value=\"1\">1.0<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">0.1<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1.0<br\/>1.0 = 1<br>\r\n1 is a natural number.<br>\r\n(Don\u2019t get confused! 1.0 is just a decimal notation of the natural number 1.)<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">If m and n are two natural numbers, then:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$m + n = n + m$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$m \u2013 n = n \u2013 m$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$m \u00f7 n = n \u00f7 m$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of these<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $m + n = n + m$<br\/>The commutative property states that if we change the order of natural numbers during multiplication and addition, the result will not change. This property does not apply for subtraction and division.<\/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\">Which property of natural numbers holds for $2 + (5 + 6) = 13 and (2 + 5) + 6 = 13$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">associative property of multiplication<\/div><div class=\"spq_answer_block\" data-value=\"1\">associative property of subtraction<\/div><div class=\"spq_answer_block\" data-value=\"2\">associative property of addition<\/div><div class=\"spq_answer_block\" data-value=\"3\">closure property of addition<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: associative property of addition<br\/>The associative property of addition holds for the given problem. The property states that the sum of natural numbers remains unchanged even if their grouping is varied.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following examples correctly represents commutative property?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$6 + 5 = 11 and 5 + 6 = 11$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$2 + (5 + 6) = 13 and (2 + 5) + 6 = 13$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2 \u00d7 (5 + 3) = (2 x 5) + (2 x 3) = 16$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$4 \u2013 6 = \u20132$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $6 + 5 = 11 and 5 + 6 = 11$<br\/>The commutative property states that changing the order of natural numbers during multiplication and addition will not change the result.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">The smallest natural number is _______.<\/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\">2<\/div><div class=\"spq_answer_block\" data-value=\"3\">\u2013 1<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>The smallest natural number is 1.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">6<\/span><h3 class=\"sqp_question_text\">Natural numbers do not follow the closure property under _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">addition<\/div><div class=\"spq_answer_block\" data-value=\"1\">multiplication<\/div><div class=\"spq_answer_block\" data-value=\"2\">subtraction<\/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: subtraction<br\/>The subtraction of two natural numbers may not be a natural number. The natural numbers are not closed under subtraction.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">7<\/span><h3 class=\"sqp_question_text\">The sum and product of two natural numbers are always natural numbers. This property is called the  ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">associative property<\/div><div class=\"spq_answer_block\" data-value=\"1\">closure property<\/div><div class=\"spq_answer_block\" data-value=\"2\">commutative 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: closure property<br\/>According to the closure property, the result will always be a natural number when you add or multiply two natural numbers.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">8<\/span><h3 class=\"sqp_question_text\">If a, b, and c are natural numbers, then $(a + b) + c = a + (b + c)$. This property is called ______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">associative property<\/div><div class=\"spq_answer_block\" data-value=\"1\">closure property<\/div><div class=\"spq_answer_block\" data-value=\"2\">commutative 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: associative property<br\/>According to associative property, the sum or product of natural numbers remains unchanged even if the grouping of numbers is changed. It is given in the form of equation as $(a + b) + c = a + (b + c)$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">9<\/span><h3 class=\"sqp_question_text\">Which of the following is an example of the commutative property of multiplication?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$2 \u00d7 4 = 4 \u00d7 \\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$2 \u00d7 2 = 4$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2 \u00d7 4 = 4 \u00d7 2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$2 \u00d7 (3 \u00d7 4) = (2 \u00d7 3) \u00d7 4$<\/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: $2 \u00d7 4 = 4 \u00d7 2$<br\/>According to the commutative property, if we change the order of natural numbers during multiplication, the result does not change.<br>\r\nThus, $2 \u00d7 4 = 4 \u00d7 2 = 8$<\/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\": \"Natural Numbers\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Natural Numbers\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Identify a natural number.\",\n                    \"text\": \"Identify a natural number.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"1.0 = 1<br>\r\n1 is a natural number.<br>\r\n(Don\u2019t get confused! 1.0 is just a decimal notation of the natural number 1.)\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\u2013 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"1.0 = 1<br>\r\n1 is a natural number.<br>\r\n(Don\u2019t get confused! 1.0 is just a decimal notation of the natural number 1.)\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"1.0 = 1<br>\r\n1 is a natural number.<br>\r\n(Don\u2019t get confused! 1.0 is just a decimal notation of the natural number 1.)\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"1.0 = 1<br>\r\n1 is a natural number.<br>\r\n(Don\u2019t get confused! 1.0 is just a decimal notation of the natural number 1.)\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1.0\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"1.0 = 1<br>\r\n1 is a natural number.<br>\r\n(Don\u2019t get confused! 1.0 is just a decimal notation of the natural number 1.)\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"1.0 = 1<br>\r\n1 is a natural number.<br>\r\n(Don\u2019t get confused! 1.0 is just a decimal notation of the natural number 1.)\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If m and n are two natural numbers, then:\",\n                    \"text\": \"If m and n are two natural numbers, then:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The commutative property states that if we change the order of natural numbers during multiplication and addition, the result will not change. This property does not apply for subtraction and division.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$m \u2013 n = n \u2013 m$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property states that if we change the order of natural numbers during multiplication and addition, the result will not change. This property does not apply for subtraction and division.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$m \u00f7 n = n \u00f7 m$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property states that if we change the order of natural numbers during multiplication and addition, the result will not change. This property does not apply for subtraction and division.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of these\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property states that if we change the order of natural numbers during multiplication and addition, the result will not change. This property does not apply for subtraction and division.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$m + n = n + m$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The commutative property states that if we change the order of natural numbers during multiplication and addition, the result will not change. This property does not apply for subtraction and division.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The commutative property states that if we change the order of natural numbers during multiplication and addition, the result will not change. This property does not apply for subtraction and division.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which property of natural numbers holds for $$2 + (5 + 6) = 13 and (2 + 5) + 6 = 13$$?\",\n                    \"text\": \"Which property of natural numbers holds for $$2 + (5 + 6) = 13 and (2 + 5) + 6 = 13$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The associative property of addition holds for the given problem. The property states that the sum of natural numbers remains unchanged even if their grouping is varied.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"associative property of multiplication\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property of addition holds for the given problem. The property states that the sum of natural numbers remains unchanged even if their grouping is varied.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"associative property of subtraction\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property of addition holds for the given problem. The property states that the sum of natural numbers remains unchanged even if their grouping is varied.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"closure property of addition\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The associative property of addition holds for the given problem. The property states that the sum of natural numbers remains unchanged even if their grouping is varied.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"associative property of addition\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The associative property of addition holds for the given problem. The property states that the sum of natural numbers remains unchanged even if their grouping is varied.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The associative property of addition holds for the given problem. The property states that the sum of natural numbers remains unchanged even if their grouping is varied.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following examples correctly represents commutative property?\",\n                    \"text\": \"Which of the following examples correctly represents commutative property?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The commutative property states that changing the order of natural numbers during multiplication and addition will not change the result.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2 + (5 + 6) = 13 and (2 + 5) + 6 = 13$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property states that changing the order of natural numbers during multiplication and addition will not change the result.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2 \u00d7 (5 + 3) = (2 x 5) + (2 x 3) = 16$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property states that changing the order of natural numbers during multiplication and addition will not change the result.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$4 \u2013 6 = \u20132$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The commutative property states that changing the order of natural numbers during multiplication and addition will not change the result.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$6 + 5 = 11 and 5 + 6 = 11$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The commutative property states that changing the order of natural numbers during multiplication and addition will not change the result.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The commutative property states that changing the order of natural numbers during multiplication and addition will not change the result.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The smallest natural number is _______.\",\n                    \"text\": \"The smallest natural number is _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The smallest natural number is 1.\"\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\": \"The smallest natural number is 1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The smallest natural number is 1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"\u2013 1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The smallest natural number is 1.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The smallest natural number is 1.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The smallest natural number is 1.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Natural numbers do not follow the closure property under _______.\",\n                    \"text\": \"Natural numbers do not follow the closure property under _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The subtraction of two natural numbers may not be a natural number. The natural numbers are not closed under subtraction.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"addition\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The subtraction of two natural numbers may not be a natural number. The natural numbers are not closed under subtraction.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"multiplication\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The subtraction of two natural numbers may not be a natural number. The natural numbers are not closed under subtraction.\"\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 subtraction of two natural numbers may not be a natural number. The natural numbers are not closed under subtraction.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"subtraction\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The subtraction of two natural numbers may not be a natural number. The natural numbers are not closed under subtraction.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The subtraction of two natural numbers may not be a natural number. The natural numbers are not closed under subtraction.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The sum and product of two natural numbers are always natural numbers. This property is called the  ______.\",\n                    \"text\": \"The sum and product of two natural numbers are always natural numbers. This property is called the  ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the closure property, the result will always be a natural number when you add or multiply two natural numbers.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"associative property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the closure property, the result will always be a natural number when you add or multiply two natural numbers.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"commutative property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the closure property, the result will always be a natural number when you add or multiply two natural numbers.\"\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 closure property, the result will always be a natural number when you add or multiply two natural numbers.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"closure property\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the closure property, the result will always be a natural number when you add or multiply two natural numbers.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the closure property, the result will always be a natural number when you add or multiply two natural numbers.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If a, b, and c are natural numbers, then $$(a + b) + c = a + (b + c)$$. This property is called ______.\",\n                    \"text\": \"If a, b, and c are natural numbers, then $$(a + b) + c = a + (b + c)$$. This property is called ______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to associative property, the sum or product of natural numbers remains unchanged even if the grouping of numbers is changed. It is given in the form of equation as $$(a + b) + c = a + (b + c)$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"closure property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to associative property, the sum or product of natural numbers remains unchanged even if the grouping of numbers is changed. It is given in the form of equation as $$(a + b) + c = a + (b + c)$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"commutative property\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to associative property, the sum or product of natural numbers remains unchanged even if the grouping of numbers is changed. It is given in the form of equation as $$(a + b) + c = a + (b + c)$$\"\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 associative property, the sum or product of natural numbers remains unchanged even if the grouping of numbers is changed. It is given in the form of equation as $$(a + b) + c = a + (b + c)$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"associative property\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to associative property, the sum or product of natural numbers remains unchanged even if the grouping of numbers is changed. It is given in the form of equation as $$(a + b) + c = a + (b + c)$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to associative property, the sum or product of natural numbers remains unchanged even if the grouping of numbers is changed. It is given in the form of equation as $$(a + b) + c = a + (b + c)$$\"\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 the commutative property of multiplication?\",\n                    \"text\": \"Which of the following is an example of the commutative property of multiplication?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"According to the commutative property, if we change the order of natural numbers during multiplication, the result does not change.<br>\r\nThus, $$2 \u00d7 4 = 4 \u00d7 2 = 8$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2 \u00d7 4 = 4 \u00d7 \\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the commutative property, if we change the order of natural numbers during multiplication, the result does not change.<br>\r\nThus, $$2 \u00d7 4 = 4 \u00d7 2 = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2 \u00d7 2 = 4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the commutative property, if we change the order of natural numbers during multiplication, the result does not change.<br>\r\nThus, $$2 \u00d7 4 = 4 \u00d7 2 = 8$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2 \u00d7 (3 \u00d7 4) = (2 \u00d7 3) \u00d7 4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"According to the commutative property, if we change the order of natural numbers during multiplication, the result does not change.<br>\r\nThus, $$2 \u00d7 4 = 4 \u00d7 2 = 8$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$2 \u00d7 4 = 4 \u00d7 2$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"According to the commutative property, if we change the order of natural numbers during multiplication, the result does not change.<br>\r\nThus, $$2 \u00d7 4 = 4 \u00d7 2 = 8$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"According to the commutative property, if we change the order of natural numbers during multiplication, the result does not change.<br>\r\nThus, $$2 \u00d7 4 = 4 \u00d7 2 = 8$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"14-frequently-asked-questions-about-natural-numbers\">Frequently Asked Questions about Natural Numbers<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" 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-0-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\"><strong>Is zero a natural number?<\/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-0-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\">\n\n<p>No, 0 is not a natural number. It is neither positive nor negative. Natural numbers are a subset of real numbers that only include positive integers 1, 2, 3, 4, 5, 6, and so on, while excluding negative numbers, zero, decimals, and fractions. They do not comprise negative numbers or 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-1-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\"><strong>Are natural numbers whole numbers?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\">\n\n<p>All natural numbers are whole numbers. Whole numbers include natural numbers and 0.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\"><strong>Why are natural numbers named so?<\/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-2-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\">\n\n<p>Natural numbers are used to count objects in the most natural and instinctive manner. If you can count them on your fingers, the numbers can be deemed natural.<\/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-3-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\"><strong>Is -1 a natural number?<\/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-3-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\">\n\n<p>The set of natural numbers in mathematics is {1, 2, 3, &#8230;}. Since <strong>&#8211;<\/strong>1 is a negative number, it is not a natural number.<\/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-4-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\"><strong>What are cardinal 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-4-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\">\n\n<p>Cardinal numbers are natural numbers or positive integers used for counting. The smallest cardinal number is 1. Examples of cardinal numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, and so on.<\/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-5-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\"><strong>Is associative property true for subtraction and division of natural 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-5-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\">\n\n<p>The associative property applies to the addition and multiplication of natural numbers.<br>But for subtraction and division of natural numbers, the associative property does not hold.<br>For example,\u00a0 $5 &#8211; (3 &#8211; 2 ) = 4$\u00a0 and\u00a0 $(5 &#8211; 3) &#8211; 2 = 0$<br>$30 \\div (10 \\div 5 ) = 15$ and\u00a0$(30 \\div 10) 5 = \\frac{3}{5}$<\/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-6-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\"><strong>Is a square of a natural number also a natural number?<\/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-6-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\">\n\n<p>A square of a natural number is a natural number multiplied by itself. Since natural numbers follow the closure property, the square of a natural number is also a natural number. For example, $5^{2} = 5 \\times 5 = 25$, and\u00a0 25 is a natural number.<\/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-7-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\"><strong>Is the square root of a natural number always a natural number?<\/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-7-6535b772-3ea7-46ee-9b03-bc70c66ebcc5\">\n\n<p>The square root of a natural number may or may not be a natural number.<br>For example, the square root of 9 is 3, square root of 16 is 4, which are natural numbers, but the square root of 6 is approximately 2.449, which is not a natural number.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Natural Numbers? Natural numbers are 1, 2, 3, 4, 5, 6, and go on till infinity. They are also called counting numbers, as they are used to count objects. Natural numbers do not include 0 or negative numbers. The symbol \u2115 is used to represent the set of natural numbers.&nbsp; Recommended Games Add &#8230; <a title=\"What Are Natural Numbers? Definition, Properties, Types, and Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers\" aria-label=\"More on What Are Natural Numbers? Definition, Properties, Types, and 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-5052","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\/5052","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=5052"}],"version-history":[{"count":19,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/5052\/revisions"}],"predecessor-version":[{"id":41827,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/5052\/revisions\/41827"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=5052"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=5052"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=5052"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}