{"id":4219,"date":"2022-05-20T13:25:14","date_gmt":"2022-05-20T13:25:14","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=4219"},"modified":"2023-10-12T12:56:41","modified_gmt":"2023-10-12T12:56:41","slug":"rational-numbers-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers","title":{"rendered":"Rational Numbers &#8211; Definition, Operations, Examples, FAQs"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-88899a7b-ed1d-4fbf-9408-e3dec3178739\" 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\/rational-numbers#0-what-are-rational-numbers>What Are Rational Numbers?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers#3-operations-on-rational-numbers->Operations on Rational Numbers&nbsp;<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers#4-solved-examples%C2%A0on-rational-numbers>Solved Examples\u00a0On Rational Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers#5-practice-problems-on-rational-numbers>Practice Problems On Rational Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers#6-frequently-asked-questions-on-rational-numbers>Frequently Asked Questions On Rational Numbers<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<p class=\"eplus-wrapper\">The 101 to mastering any subject is the knowledge of its lexicon. The way we combine the letters of the alphabet to make a word and then arrange words in sentences to convey our thoughts is like a natural instinct to us only because we have the knowledge of the English alphabet. So, what should be the 101 for making maths a natural instinct? The knowledge of its rudimentary unit: numbers. We teach counting using whole numbers, but one of the most important aspect of the mathematical numbers system is rational numbers, or simply put, numbers between numbers.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-are-rational-numbers\">What Are Rational Numbers?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Rational numbers are numbers that can be written in the form pq, where p and q are integers and q\u22600. The difference between rational numbers and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/fraction\" title=\"\">fractions<\/a> lies in the fact that fractions cannot have negative numerator or denominator. Hence, the numerator and denominator of a fraction are whole numbers (denominator \u2260 0), whereas in the case of rational numbers, the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/numerator\" title=\"\">numerator<\/a> and <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/denominator\" title=\"\">denominator<\/a> are integers.<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_make_10_pt.png\" alt=\"Add 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-and-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_2d_1d_match_pt.png\" alt=\"Add 2-Digit and 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit and 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-numbers-by-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_2d_2d_vertical_pt.png\" alt=\"Add 2-Digit Numbers By Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit Numbers By Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_pt.png\" alt=\"Add 3 Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-in-any-order\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_shifty_bridges_4_gm.png\" alt=\"Add 3 Numbers in Any Order Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers in Any Order Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-groups-of-objects\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_using_model_pt.png\" alt=\"Add 3 Numbers Using Groups of Objects Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers Using Groups of Objects Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_using_models_pt.png\" alt=\"Add 3 Numbers using Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers using Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-digit-and-1-digit-numbers-and-match\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_3d_1d_match_g3_pt.png\" alt=\"Add 3-Digit and 1-Digit Numbers and Match Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3-Digit and 1-Digit Numbers and Match Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-digit-and-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_3d_1d_vertical_pt.png\" alt=\"Add 3-Digit and 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3-Digit and 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-digit-and-1-digit-numbers-with-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_3d_1d_vertical_pt.png\" alt=\"Add 3-Digit and 1-Digit Numbers with Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3-Digit and 1-Digit Numbers with Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-examples-of-rational-numbers\">Examples of Rational Numbers<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\\frac{4}{5}$, $\\frac{-10}{15}$, $\\frac{9}{-17}$, $\\frac{-2}{-7}$<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Zero is a rational number as it can be written as&nbsp; $\\frac{0}{10}$, $\\frac{0}{2}$, $\\frac{0}{-15}$, $\\frac{0}{27}$, etc.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">So, zero can be expressed as a fraction with a non-zero denominator.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Every natural number is a rational number.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">1 = $\\frac{1}{1}$, 5 = $\\frac{5}{1}$, 8 = $\\frac{8}{1}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, every natural number can be expressed as a fraction with 1 as the denominator.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Every integer number is a rational number.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">-7 = $\\frac{-7}{1}$, -13 = $\\frac{-13}{1}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, every integer number can be expressed as a fraction with 1 as the denominator.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Every fraction is a rational number.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{2}{3}$, $\\frac{18}{7}$, $\\frac{19}{11}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Where the numerator and denominator are whole numbers and the denominator is not equal to zero.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Positive rational numbers<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">A rational number is positive if its numerator and denominator have the same signs (either both positive or both negative).<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{-5}{-6}$, $\\frac{7}{12}$, $\\frac{-19}{-12}$, $\\frac{42}{85}$&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Negative rational numbers<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">A rational number is negative if its numerator and denominator have opposite signs (one of them is positive and the other is negative).<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{-32}{43}$, $\\frac{27}{-63}$, $\\frac{-12}{14}$, $\\frac{9}{-16}$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Decimals: 0.45, 0.5446, 0.01864. Since decimals can be written as fractions with denominator as 10, 100, 1000 \u2026 decimal numbers also considered rational numbers.<\/li>\n<\/ul>\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\" 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Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-numbers-and-teen-numbers-missing-numbers\" 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-numbers.jpeg\" alt=\"Add 1-Digit Numbers and Teen Numbers: Missing 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><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-non-examples-of-rational-number\">Non-Examples of Rational Number<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/square-and-square-roots\" title=\"\">square root<\/a>, cube roots, etc., of <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers\" title=\"\">natural numbers<\/a> if their exact value cannot be determined.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$\\sqrt{2}$, $\\sqrt{3}$, $\\sqrt[2]{8}$, $\\sqrt[3]{81}$, $\\sqrt[4]{27}$&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">$\\sqrt{3}$, &#8211; $\\sqrt{5}$, 8 + $\\sqrt{10}$, $\\sqrt{2}$ + $\\sqrt{3}$<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Standard Form of Rational Numbers<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">A rational number, $\\frac{p}{q}$,&nbsp; is said to be in standard form if the numerator and the denominator (p and q) have no common divisor (or factor) except 1 and the denominator \u201c<em>q<\/em><em>\u201d<\/em> is positive.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>How to convert a rational number into standard form:<\/strong><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Consider the rational number $\\frac{18}{\u201324}$;&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s see how we can convert this rational number into its <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/algebra\/standard-form\" title=\"\">standard form<\/a>.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 1: Make sure that the denominator is positive. If not, multiply the numerator and the denominator by \u201c\u20131\u201d to change the sign.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"325\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image50-1.png\" alt=\"multiply the numerator and the denominator by \u201c\u20131\u201d to change the sign\" class=\"wp-image-4221\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image50-1.png 260w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image50-1-240x300.png 240w\" sizes=\"auto, (max-width: 260px) 100vw, 260px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Step 2: Find all the common divisors of the numerator and the denominator.<br>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Here, 18 and 24 have common divisors 1, 2, 3, 6.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 3: Divide the numerator and the denominator by their <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/greatest-common-divisor-gcd\" title=\"\">greatest common divisor<\/a>. Like this:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"325\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image44-1.png\" alt=\"Divide the numerator and the denominator by their greatest common\" class=\"wp-image-4222\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image44-1.png 260w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image44-1-240x300.png 240w\" sizes=\"auto, (max-width: 260px) 100vw, 260px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">No Step 3 required! As you can see $\\frac{\u20133}{4}$&nbsp; is a standard rational number and is the standard form of $\\frac{18}{\u201324}$.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Consider the decimal number 0.5<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Step 1: To convert a decimal number into a standard rational number, we first convert it into a rational number.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"246\" height=\"141\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image51-1.png\" alt=\"convert a decimal number into a rational number\" class=\"wp-image-4224\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Step 2: Now follow the same steps for converting a rational number into its standard form as defined above and we get<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"246\" height=\"305\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image49-1.png\" alt=\"converting a rational number into its standard form\" class=\"wp-image-4223\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image49-1.png 246w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image49-1-242x300.png 242w\" sizes=\"auto, (max-width: 246px) 100vw, 246px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-operations-on-rational-numbers-\">Operations on Rational Numbers&nbsp;<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Addition of Rational Numbers:<\/strong><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the denominators of the given rational numbers are equal:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Add the numerators and keep the denominators the same.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, we can add two rational numbers 2\/8 and \u215c like this:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"458\" height=\"303\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image47-1.png\" alt=\"Add the numerators and keep the denominators the same.\" class=\"wp-image-4225\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image47-1.png 458w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image47-1-300x198.png 300w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the denominators of given numbers are unequal:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">For example, to add the rational numbers \u2156 and \u00be&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 1: Find the LCM of the denominator of the given rational numbers. Here, the LCM of 4 and 5 is 20.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 2: Convert each rational number into an equivalent rational number with the LCM as the new denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"741\" height=\"381\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image45-2.png\" alt=\"Convert rational number into an equivalent rational number with the LCM \" class=\"wp-image-4226\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image45-2.png 741w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image45-2-300x154.png 300w\" sizes=\"auto, (max-width: 741px) 100vw, 741px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Step 3: For these new rational numbers, add the numerators and keep the denominators the same and that will be the final answer.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"432\" height=\"270\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image48-1.png\" alt=\"add the numerators and keep the denominators the same \" class=\"wp-image-4227\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image48-1.png 432w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image48-1-300x188.png 300w\" sizes=\"auto, (max-width: 432px) 100vw, 432px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, \u2156 + \u00be = 23\/20.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Subtraction of Rational Numbers:<\/strong><\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the denominators of the given numbers are equal:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">Subtract the numerators and keep the denominator the same.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"432\" height=\"270\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image39-1.png\" alt=\"Subtract the numerators and keep the denominator the same.\" class=\"wp-image-4228\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image39-1.png 432w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image39-1-300x188.png 300w\" sizes=\"auto, (max-width: 432px) 100vw, 432px\" \/><\/figure>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the denominators of the given numbers are unequal:<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">For example, to subtract \u2153 from \u00bd&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 1: Find the LCM of the denominator of the given rational numbers. In this case, the LCM of 2 and 3 is 6.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 2: Convert each rational number into an equivalent rational number with the LCM as the new denominator.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"676\" height=\"340\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image43-2.png\" alt=\"Convert rational number into an equivalent rational number with the LCM\" class=\"wp-image-4230\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image43-2.png 676w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image43-2-300x151.png 300w\" sizes=\"auto, (max-width: 676px) 100vw, 676px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Step 3: Follow the steps of subtraction of rational numbers with equal denominators.<\/p>\n\n\n\n<figure class=\"wp-block-image is-style-default eplus-wrapper\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/m4XNsiW1omjskNms-05QPNnwqUXFluL9OBBo9kRlNDk64SxLFbObVDiu6ByDrc0ko1OVoT_i5WbiYld91fORP_GTSfepBVveDbDrPgd7qM41qfTebjhRPAYPy85NZorw_POBUKo\" alt=\"subtraction of rational numbers with equal denominators.\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, \u00bd \u2013 \u2153 = \u2159&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Multiplication of Rational Numbers:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">This is perhaps the easiest operation on rational numbers.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To multiply two rational numbers, simply multiply the numerator and denominator of the first rational number with the numerator and denominator of the second rational number respectively.<br><br>For example, to multiply the rational numbers \u2156 and \u00be,&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"797\" height=\"341\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image42-1.png\" alt=\"multiply the numerator and denominator\" class=\"wp-image-4232\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image42-1.png 797w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image42-1-300x128.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image42-1-768x329.png 768w\" sizes=\"auto, (max-width: 797px) 100vw, 797px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-solved-examples%C2%A0on-rational-numbers\">Solved Examples\u00a0On Rational Numbers<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: Express <\/strong>$\\frac{25}{40}$<strong> in standard form.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Greatest divisor of 25 and 40 = 5<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-style-default eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"241\" height=\"341\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image46-1.png\" alt=\"Express 2540 in standard form.\" class=\"wp-image-4233\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image46-1.png 241w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/05\/image46-1-212x300.png 212w\" sizes=\"auto, (max-width: 241px) 100vw, 241px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: Add:&nbsp; <\/strong>$\\frac{2}{11}+\\frac{7}{11}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{2}{11}+\\frac{7}{11}= \\frac{2+7}{11}=\\frac{9}{11}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3: Subtract <\/strong>$\\frac{5}{7}$<strong> from<\/strong> $\\frac{9}{7}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{9}{7}\u2013\\frac{5}{7}= \\frac{9\u20135}{7}=\\frac{2}{7}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-practice-problems-on-rational-numbers\">Practice Problems On Rational Numbers<\/h2>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"wj-table-class\"><tbody><tr><td><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Rational Numbers<\/h2><p style=\"display:none;\">Attend this Quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The number 398 can be expressed as a rational number as:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">398\/1<\/div><div class=\"spq_answer_block\" data-value=\"1\">0\/398<\/div><div class=\"spq_answer_block\" data-value=\"2\">1\/398<\/div><div class=\"spq_answer_block\" data-value=\"3\">398 is not a rational number.<\/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: 398\/1<br\/>Whole numbers can be expressed as rational numbers with denominator 1. <br>\r\n398 = $\\frac{398}{1}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">The number 0.7 can be expressed as a rational number as:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{10}{7}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{7}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{0.7}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">0.7 is not a rational number<\/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: $\\frac{7}{10}$<br\/>Removing the decimal point we can represent $\\frac{7}{10}$ as 0.7<\/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\">Standard form of the number $\\frac{\u201320}{15}$ is:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{2}{5}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{-10}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{3}{-10}$<\/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: $\\frac{-10}{3}$<br\/>Greatest common divisor of 20 and 15 is 5; so dividing both the numerator and denominator in \u201320\/15 by 5 gives us \u201310\/3.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Product of $\\frac{8}{9}$ with $\\frac{9}{8}$ is:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{64}{81}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">1<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{72}{81}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">0<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>$\\frac{8}{9}\\times \\frac{9}{8}=\\frac{8\u00d79}{9\u00d78}= \\frac{72}{72}$ = 1<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this Quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Rational Numbers\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Rational Numbers\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The number 398 can be expressed as a rational number as:\",\n                    \"text\": \"The number 398 can be expressed as a rational number as:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Whole numbers can be expressed as rational numbers with denominator 1. <br>\r\n398 = $$\\\\frac{398}{1}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\/398\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Whole numbers can be expressed as rational numbers with denominator 1. <br>\r\n398 = $$\\\\frac{398}{1}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\/398\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Whole numbers can be expressed as rational numbers with denominator 1. <br>\r\n398 = $$\\\\frac{398}{1}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"398 is not a rational number.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Whole numbers can be expressed as rational numbers with denominator 1. <br>\r\n398 = $$\\\\frac{398}{1}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"398\/1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Whole numbers can be expressed as rational numbers with denominator 1. <br>\r\n398 = $$\\\\frac{398}{1}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Whole numbers can be expressed as rational numbers with denominator 1. <br>\r\n398 = $$\\\\frac{398}{1}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The number 0.7 can be expressed as a rational number as:\",\n                    \"text\": \"The number 0.7 can be expressed as a rational number as:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Removing the decimal point we can represent $$\\\\frac{7}{10}$$ as 0.7\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{10}{7}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Removing the decimal point we can represent $$\\\\frac{7}{10}$$ as 0.7\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{0.7}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Removing the decimal point we can represent $$\\\\frac{7}{10}$$ as 0.7\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.7 is not a rational number\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Removing the decimal point we can represent $$\\\\frac{7}{10}$$ as 0.7\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{7}{10}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Removing the decimal point we can represent $$\\\\frac{7}{10}$$ as 0.7\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Removing the decimal point we can represent $$\\\\frac{7}{10}$$ as 0.7\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Standard form of the number $$\\\\frac{\u201320}{15}$$ is:\",\n                    \"text\": \"Standard form of the number $$\\\\frac{\u201320}{15}$$ is:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Greatest common divisor of 20 and 15 is 5; so dividing both the numerator and denominator in \u201320\/15 by 5 gives us \u201310\/3.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Greatest common divisor of 20 and 15 is 5; so dividing both the numerator and denominator in \u201320\/15 by 5 gives us \u201310\/3.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Greatest common divisor of 20 and 15 is 5; so dividing both the numerator and denominator in \u201320\/15 by 5 gives us \u201310\/3.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{3}{-10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Greatest common divisor of 20 and 15 is 5; so dividing both the numerator and denominator in \u201320\/15 by 5 gives us \u201310\/3.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{-10}{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Greatest common divisor of 20 and 15 is 5; so dividing both the numerator and denominator in \u201320\/15 by 5 gives us \u201310\/3.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Greatest common divisor of 20 and 15 is 5; so dividing both the numerator and denominator in \u201320\/15 by 5 gives us \u201310\/3.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Product of $$\\\\frac{8}{9}$$ with $$\\\\frac{9}{8}$$ is:\",\n                    \"text\": \"Product of $$\\\\frac{8}{9}$$ with $$\\\\frac{9}{8}$$ is:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{8}{9}\\\\times \\\\frac{9}{8}=\\\\frac{8\u00d79}{9\u00d78}= \\\\frac{72}{72}$$ = 1\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{64}{81}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{8}{9}\\\\times \\\\frac{9}{8}=\\\\frac{8\u00d79}{9\u00d78}= \\\\frac{72}{72}$$=1\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{72}{81}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{8}{9}\\\\times \\\\frac{9}{8}=\\\\frac{8\u00d79}{9\u00d78}= \\\\frac{72}{72}$$=1\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{8}{9}\\\\times \\\\frac{9}{8}=\\\\frac{8\u00d79}{9\u00d78}= \\\\frac{72}{72}$$=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\": \"$$\\\\frac{8}{9}\\\\times \\\\frac{9}{8}=\\\\frac{8\u00d79}{9\u00d78}= \\\\frac{72}{72}$$=1\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{8}{9}\\\\times \\\\frac{9}{8}=\\\\frac{8\u00d79}{9\u00d78}= \\\\frac{72}{72}$$=1\"\n                      }\n                    } \n\n                    }]}<\/script><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-frequently-asked-questions-on-rational-numbers\">Frequently Asked Questions On Rational Numbers<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-f63585fd-2f51-4fe4-8e15-da0dced7cefe\" 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-f63585fd-2f51-4fe4-8e15-da0dced7cefe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f63585fd-2f51-4fe4-8e15-da0dced7cefe\"><strong>Is 1 a rational number<\/strong>?<\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap left\"><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-f63585fd-2f51-4fe4-8e15-da0dced7cefe\">\n\n<p>Yes, 1 is a rational number as it can be expressed in the form of a fraction as $\\frac{1}{1}$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-f63585fd-2f51-4fe4-8e15-da0dced7cefe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f63585fd-2f51-4fe4-8e15-da0dced7cefe\"><strong>How do you identify a rational number?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap left\"><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-f63585fd-2f51-4fe4-8e15-da0dced7cefe\">\n\n<p>Any number that can be expressed in the form of a fraction is a rational number. Note that the denominator of a rational number cannot be 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-f63585fd-2f51-4fe4-8e15-da0dced7cefe\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f63585fd-2f51-4fe4-8e15-da0dced7cefe\"><strong>How to find the standard form of rational number?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap left\"><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-f63585fd-2f51-4fe4-8e15-da0dced7cefe\">\n\n<p>Divide the numerator and denominator with their greatest common divisor.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>The 101 to mastering any subject is the knowledge of its lexicon. The way we combine the letters of the alphabet to make a word and then arrange words in sentences to convey our thoughts is like a natural instinct to us only because we have the knowledge of the English alphabet. So, what should &#8230; <a title=\"Rational Numbers &#8211; Definition, Operations, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers\" aria-label=\"More on Rational Numbers &#8211; Definition, Operations, Examples, FAQs\">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-4219","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\/4219","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=4219"}],"version-history":[{"count":19,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/4219\/revisions"}],"predecessor-version":[{"id":34865,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/4219\/revisions\/34865"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=4219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=4219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=4219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}