{"id":36145,"date":"2023-11-15T21:17:00","date_gmt":"2023-11-15T21:17:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=36145"},"modified":"2023-11-21T04:45:31","modified_gmt":"2023-11-21T04:45:31","slug":"rational-numbers-between-two-rational-numbers-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers-between-two-rational-numbers","title":{"rendered":"Rational Numbers Between Two Rational Numbers &#8211; Examples, FAQs"},"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-5b7df791-811a-4322-b9ee-c70b3d927661\" 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-between-two-rational-numbers#0-what-are-rational-numbers-between-two-rational-numbers>What Are Rational Numbers between Two Rational Numbers?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers-between-two-rational-numbers#1-how-to-find-rational-numbers-between-two-rational-numbers>How to Find Rational Numbers between Two Rational Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers-between-two-rational-numbers#2-arithmetic-mean-method-to-find-rational-numbers-between-two-rational-numbers>Arithmetic Mean Method to Find Rational Numbers between Two Rational Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers-between-two-rational-numbers#5-solved-examples-on-rational-numbers-between-two-rational-numbers>Solved Examples on Rational Numbers between Two Rational Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers-between-two-rational-numbers#6-practice-problems-on-rational-numbers-between-two-rational-numbers>Practice Problems on Rational Numbers between Two Rational Numbers<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers-between-two-rational-numbers#7-frequently-asked-questions-about-rational-numbers-between-two-rational-numbers>Frequently Asked Questions about Rational Numbers between Two Rational Numbers<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-are-rational-numbers-between-two-rational-numbers\">What Are Rational Numbers between Two Rational Numbers?<\/h2>\n\n\n\n<p>There are infinitely many <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers\">rational numbers<\/a> between any two distinct rational numbers.<\/p>\n\n\n\n<p>If you consider any two natural numbers, there will be only a finite number of natural numbers between them. For example, between the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/natural-numbers\">natural numbers<\/a> 8 and 14, there are only five natural numbers, which are 9, 10, 11, 12, and 13.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"379\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/natural-numbers-between-two-natural-numbers.png\" alt=\"Natural numbers between two natural numbers\" class=\"wp-image-36148\" title=\"Natural numbers between two natural numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/natural-numbers-between-two-natural-numbers.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/natural-numbers-between-two-natural-numbers-300x183.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>However, that\u2019s not the case with rational numbers.<\/p>\n\n\n\n<p>Rational numbers are numbers that can be written in the form $\\frac{p}{q}$, where p and q are integers, and $q \\neq 0$. The set of rational numbers include <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/integers\">integers<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/fraction\">fractions<\/a>, <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/terminating-decimal\">terminating decimals<\/a>, and non-terminating repeating decimals.&nbsp;<\/p>\n\n\n\n<p>If you take any two rational numbers, you can divide the segment on the number line joining these two numbers into infinitely many parts and get infinitely many numbers of the form $\\frac{p}{q}$, where p and q are integers, and $q \\neq 0$.&nbsp;<\/p>\n\n\n\n<p><strong>Example:<\/strong> Consider two rational numbers $\\frac{1}{4}$ and $\\frac{1}{2}$.<\/p>\n\n\n\n<p>Let\u2019s plot them on a number line. Divide the segment joining $\\frac{1}{4}$ and $\\frac{1}{2}$ into two equal parts, we get $\\frac{3}{8}$ as the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/midpoint\">midpoint<\/a>. Dividing each small segment, we get more and more such rational numbers. Same goes for the rational numbers between 0 and $\\frac{1}{4}$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"682\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-numbers-between-two-rational-numbers.png\" alt=\"Rational numbers between two rational numbers\" class=\"wp-image-36149\" title=\"Rational numbers between two rational numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-numbers-between-two-rational-numbers.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-numbers-between-two-rational-numbers-273x300.png 273w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p><strong>Note:&nbsp;<\/strong><\/p>\n\n\n\n<p>The difference between rational numbers and fractions lies in the fact that fractions cannot have negative <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/numerator\">numerator<\/a> or <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/denominator\">denominator<\/a>. Hence, the numerator and denominator of a fraction are whole numbers (denominator \u2260 0), whereas in the case of rational numbers, the numerator and denominator are integers (denominator \u2260 0).<\/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                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Denominator<\/strong><\/p>\n\n\n\n<p>If the two rational numbers have the same denominator, identifying a few rational numbers between them is simple.<\/p>\n\n\n\n<p><strong>Step 1: <\/strong>Check the value of the numerators. Write all the natural numbers between these two numbers.&nbsp;<\/p>\n\n\n\n<p><strong>Step 2:<\/strong> Write all the rational numbers with these natural numbers as numerators and keep the same denominator. Write these rational numbers in the increasing order of the numerators for better understanding.<\/p>\n\n\n\n<p><strong>Example:<\/strong> Find the rational numbers between $\\frac{3}{5}$ and $\\frac{9}{5}$.&nbsp;<\/p>\n\n\n\n<p>Denominator of both rational numbers is the same, 5.<\/p>\n\n\n\n<p>Numerators are 3 and 9.<\/p>\n\n\n\n<p>Natural numbers between them are 4, 5, 6, 7, and 8.<\/p>\n\n\n\n<p>We can write find five rational numbers between $\\frac{3}{5}$ and $\\frac{9}{5}$ by choosing 4, 5, 6, 7, and 8 as numerators and keeping 5 as the denominator.<\/p>\n\n\n\n<p>Five rational numbers between $\\frac{3}{5}$ and $\\frac{9}{5}$ are $\\frac{4}{5}, \\frac{5}{5}, \\frac{6}{5}, \\frac{7}{5}$, and $\\frac{8}{5}$.&nbsp;<\/p>\n\n\n\n<p>What if we are asked to find more rational numbers between $\\frac{3}{5}$ and $\\frac{9}{5}$?&nbsp;<\/p>\n\n\n\n<p>Let\u2019s understand how we can do that.<\/p>\n\n\n\n<p>If we multiply and divide both the numbers by 10 (or , we will get their equivalent rational numbers. Equivalent rational numbers are the rational numbers that, when reduced to the simplest form, have the same value. They are located at the same point on the number line.&nbsp;<\/p>\n\n\n\n<p>Here, we get&nbsp;<\/p>\n\n\n\n<p>$\\frac{3 \\times 10}{5 \\times 10} = \\frac{30}{50}$ and $\\frac{9 \\times 10}{5 \\times 10} = \\frac{90}{50}$<\/p>\n\n\n\n<p>Note that $\\frac{3}{5} = \\frac{30}{50}$ and $\\frac{9}{5} = \\frac{90}{50}$.<\/p>\n\n\n\n<p>Now, we can easily write ten rational numbers between $\\frac{30}{50}$ and $\\frac{90}{50}$, such as<\/p>\n\n\n\n<p>&nbsp;$\\frac{31}{50}, \\frac{32}{50}, \\frac{37}{50}, \\frac{39}{50}, \\frac{45}{50}, \\frac{67}{50}, \\frac{68}{50}, \\frac{78}{50}, \\frac{84}{50}, \\frac{88}{50}$.<\/p>\n\n\n\n<p>We can go further and write them in their simplest form, if required.<\/p>\n\n\n\n<p>For example, $\\frac{45}{50} = \\frac{9}{10}$<\/p>\n\n\n\n<p>(<em>Do not forget that there are infinite rational numbers between two given rational numbers<\/em>. <em>We are only trying to list a few of them.<\/em>)<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"471\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-numbers-between-two-rational-numbers-.png\" alt=\"Rational numbers between two rational numbers\" class=\"wp-image-36150\" title=\"Rational numbers between two rational numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-numbers-between-two-rational-numbers-.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/rational-numbers-between-two-rational-numbers--300x228.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p><strong>Rational Numbers between two Rational Numbers with Different Denominators<\/strong><\/p>\n\n\n\n<p>When we have to find the rational numbers between two rational numbers with different denominators, we first make the denominators equal using the <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/least-common-multiple\">LCM<\/a> method.&nbsp;<\/p>\n\n\n\n<p>Once the denominators are equal, we can use the method we discussed earlier.<\/p>\n\n\n\n<p><strong>Example 1:<\/strong> Find five rational numbers between $\\frac{1}{3}$ and $\\frac{2}{7}$.<\/p>\n\n\n\n<p>LCM(3, 7) = 21<\/p>\n\n\n\n<p>$\\frac{1 \\times 7}{3 \\times 7} = \\frac{7}{21}$&nbsp;<\/p>\n\n\n\n<p>$\\frac{2 \\times 3}{7 \\times 3} = \\frac{6}{21}$<\/p>\n\n\n\n<p>Now, since the difference between the numerators is too less, let\u2019s find their equivalent rational numbers.<\/p>\n\n\n\n<p>Multiplying the numerator and denominator by 10, we get<\/p>\n\n\n\n<p>$\\frac{6 \\times 10}{21 \\times 10} = \\frac{60}{210}$ and<\/p>\n\n\n\n<p>$\\frac{7 \\times 10}{21 \\times 10} = \\frac{70}{210}$<\/p>\n\n\n\n<p>Five rational numbers between $\\frac{1}{3}$ and $\\frac{2}{7}$ are $\\frac{61}{120}, \\frac{65}{120}, \\frac{66}{120}, \\frac{67}{120}, \\frac{69}{120}$.&nbsp;<\/p>\n\n\n\n<p><strong>Example 2: Find three rational numbers between <\/strong>$\\frac{-3}{5}$ and $\\frac{-1}{3}$.<\/p>\n\n\n\n<p>Let\u2019s make the denominators equal.<\/p>\n\n\n\n<p>LCM(3, 5) = 15<\/p>\n\n\n\n<p>$\\frac{-3 \\times 3}{5 \\times 3} = \\frac{-9}{15}$&nbsp;<\/p>\n\n\n\n<p>$\\frac{-1 \\times 5}{3 \\times 5} = \\frac{-5}{15}$&nbsp;<\/p>\n\n\n\n<p>Thus, $\\frac{-3}{5} = \\frac{-9}{15}$ and $\\frac{-1}{3} = \\frac{-5}{15}$.<\/p>\n\n\n\n<p>We can write<\/p>\n\n\n\n<p>$\\frac{-9}{15} \\lt \\frac{-8}{15} \\lt \\frac{-7}{15} \\lt \\frac{-6}{15} \\lt \\frac{-5}{15}$<\/p>\n\n\n\n<p>&nbsp;Thus,&nbsp;<\/p>\n\n\n\n<p>$\\frac{-3}{5}\\lt \\frac{-8}{15} \\lt \\frac{-7}{15} \\lt \\frac{-6}{15} \\lt \\frac{-1}{3}$<\/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 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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-arithmetic-mean-method-to-find-rational-numbers-between-two-rational-numbers\">Arithmetic Mean Method to Find Rational Numbers between Two Rational Numbers<\/h2>\n\n\n\n<p>We know that the mean or average of two values is the central value. So, if we find the arithmetic mean of any two rational numbers, we will get a rational number that lies between them.&nbsp;<\/p>\n\n\n\n<p>Note that it doesn&#8217;t matter if the denominators are same or different when we use this method. It is applicable to any two rational numbers.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"621\" height=\"502\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/arithmetic-mean-method-to-find-rational-numbers-between-to-rational-numbers.png\" alt=\"Arithmetic mean method to find rational numbers between to rational numbers\" class=\"wp-image-36151\" title=\"Arithmetic mean method to find rational numbers between to rational numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/arithmetic-mean-method-to-find-rational-numbers-between-to-rational-numbers.png 621w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/11\/arithmetic-mean-method-to-find-rational-numbers-between-to-rational-numbers-300x243.png 300w\" sizes=\"auto, (max-width: 621px) 100vw, 621px\" \/><\/figure>\n\n\n\n<p><strong>Example: <\/strong>Find three rational numbers between $\\frac{1}{3}$ and $\\frac{2}{7}$.<\/p>\n\n\n\n<p>Rational number between $\\frac{1}{3}$ and $\\frac{2}{7} = \\frac{1}{2}(\\frac{1}{3} + \\frac{2}{7}) = \\frac{1}{2}(\\frac{7 + 6}{21}) = \\frac{13}{42}$<\/p>\n\n\n\n<p><strong>Finding the Next Rational Numbers:<\/strong><\/p>\n\n\n\n<p>Rational number between $\\frac{1}{3}$ and $\\frac{13}{42} = \\frac{1}{2}(\\frac{1}{3} + \\frac{13}{42}) = \\frac{1}{2}(\\frac{1}{4} + \\frac{13}{42}) = \\frac{27}{84}$<\/p>\n\n\n\n<p>Rational number between $\\frac{2}{7}$ and $\\frac{13}{42} = \\frac{1}{2}(\\frac{2}{7} + \\frac{13}{42}) = \\frac{1}{2}(\\frac{12 + 13}{42}) = \\frac{25}{84}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-facts-about-rational-numbers-between-two-rational-numbers\">Facts about Rational Numbers Between Two Rational 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>The arithmetic mean of two rational numbers is a rational number that lies between them.<\/li>\n\n\n\n<li>There are infinitely many rational numbers between any two rational numbers.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned how to find rational numbers between two rational numbers with the help of two cases: i) finding rational numbers between two rational numbers with same denominators, and ii) finding rational numbers between two rational numbers with different denominators. Let\u2019s solve a few examples and practice MCQs to revise and practice!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-solved-examples-on-rational-numbers-between-two-rational-numbers\">Solved Examples on Rational Numbers between Two Rational Numbers<\/h2>\n\n\n\n<p><strong>1. Find two rational numbers between <\/strong>$\\frac{1}{7}$<strong> and <\/strong>$\\frac{4}{7}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>The denominator of $\\frac{1}{7}$<strong> <\/strong>and $\\frac{4}{7}$<strong> <\/strong>is the same, 7.&nbsp;<\/p>\n\n\n\n<p>The rational numbers between $\\frac{1}{7}$<strong> <\/strong>and $\\frac{4}{7}$<strong> <\/strong>are $\\frac{2}{7}$<strong> <\/strong>and $\\frac{3}{7}$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>2. What are the three rational numbers between 2 and 3?<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Rational number between 2 and 3 $= \\frac{1}{2}(2 + 3) = \\frac{5}{2}$<\/p>\n\n\n\n<p>Rational number between 2 and $\\frac{5}{2} = \\frac{1}{2}(2 + \\frac{5}{2}) = \\frac{1}{2} \\times \\frac{9}{2} = \\frac{9}{4}$<\/p>\n\n\n\n<p>Rational number between 3 and $\\frac{5}{2} = \\frac{1}{2}(3 + \\frac{5}{2}) = \\frac{1}{2} \\times \\frac{11}{2} = \\frac{11}{4}$<\/p>\n\n\n\n<p><strong>3. Find four rational numbers between <\/strong>$\\frac{2}{5}$<strong> and <\/strong>$\\frac{3}{8}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p>Denominators are different.<\/p>\n\n\n\n<p>LCM of 5 and 8 = 40<\/p>\n\n\n\n<p>$\\frac{2 \\times 8}{5 \\times 8} = \\frac{16}{40}$ and $\\frac{3 \\times 5}{8 \\times 5} = \\frac{15}{40}$<\/p>\n\n\n\n<p>$\\frac{16 \\times 10}{40 \\times 10} = \\frac{160}{400}$<strong> <\/strong>and $\\frac{15 \\times 10}{40 \\times 10} = \\frac{150}{400}$<\/p>\n\n\n\n<p>Four rational numbers between $\\frac{2}{5}$<strong> <\/strong>and<strong> <\/strong>$\\frac{3}{8}$<strong> <\/strong>are $\\frac{162}{400}, \\frac{164}{400}, \\frac{167}{400}$<strong>, <\/strong>and $\\frac{169}{400}$<strong>.&nbsp;<\/strong><\/p>\n\n\n\n<p>In simplest form, we can write them as $\\frac{81}{20}, \\frac{41}{10}, \\frac{167}{400}$<strong> <\/strong>and $\\frac{169}{400}$<\/p>\n\n\n\n<p><strong>4. Determine one rational numbers between <\/strong>$\\frac{9}{11}$<strong> and <\/strong>$\\frac{12}{13}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The arithmetic mean to rational numbers is a rational number that lies between them.<\/p>\n\n\n\n<p>Rational number between $\\frac{9}{11}$ and $\\frac{12}{13} = \\frac{1}{2}(\\frac{9}{11} + \\frac{12}{13})$<\/p>\n\n\n\n<p>$= \\frac{1}{2}(\\frac{(13 \\times 9) + (11 \\times 12)}{11 \\times 13})$<\/p>\n\n\n\n<p>$= \\frac{1}{2}(\\frac{117 + 132}{143})$<\/p>\n\n\n\n<p>$= \\frac{249}{286}$<\/p>\n\n\n\n<p><strong>5. Determine six rational numbers between <\/strong>$\\frac{1}{2}$<strong> and <\/strong>$\\frac{2}{3}$<strong>.<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>$\\frac{1 \\times 3}{2 \\times 3} = \\frac{3}{6}$ and $\\frac{2 \\times 2}{3 \\times 2} = \\frac{4}{6}$<\/p>\n\n\n\n<p>$\\frac{3 \\times 10}{6 \\times 10} = \\frac{30}{60}$ and $\\frac{4 \\times 10}{6 \\times 10} = \\frac{40}{60}$<\/p>\n\n\n\n<p>Six rational numbers between $\\frac{1}{2}$<strong> <\/strong>and<strong> <\/strong>$\\frac{2}{3}$<strong> <\/strong>are $\\frac{31}{60}, \\frac{33}{60}, \\frac{34}{60}, \\frac{35}{60}, \\frac{37}{60}$,<strong> <\/strong>and $\\frac{39}{60}$<strong>.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-practice-problems-on-rational-numbers-between-two-rational-numbers\">Practice Problems on Rational Numbers between Two Rational Numbers<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Rational Numbers Between Two Rational Numbers - Examples, FAQs<\/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\">Which of the following is not a rational number between $\\frac{3}{4}$ and $\\frac{3}{7}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{22}{28}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{9}{14}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{13}{28}$<\/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: $\\frac{22}{28}$<br\/>LCM of 4 and 7 = 28<br>\r\n$\\frac{3 \\times 7}{4 \\times 7} = \\frac{21}{28}$ and $\\frac{3 \\times 4}{7 \\times 4} = \\frac{12}{28}$<br>\r\n$\\frac{22}{28}$ will not lie between $\\frac{3}{4}$ and $\\frac{3}{7}$.<\/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 rational number between $\\frac{1}{9}$ and $\\frac{1}{5}$ is ____.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{2}{5}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{8}{45}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{2}{45}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{-8}{45}$<\/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: $\\frac{8}{45}$<br\/>$\\frac{1 \\times 5}{9 \\times 5} = \\frac{5}{45}$ and $\\frac{1 \\times 9}{5 \\times 9} = \\frac{9}{45}$<br>\r\nRational number between $\\frac{5}{45}$ and $\\frac{9}{45}$ are<br>\r\n$\\frac{6}{45} = \\frac{2}{15}; \\frac{7}{45}$ and $\\frac{8}{45}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">The rational number between \u2013 3 and \u2013 1 is ___.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$- \\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$- \\frac{5}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$2$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{2}$<\/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: $- \\frac{5}{2}$<br\/>Rational number between \u2013 3 and \u2013 1 is  \u2013 2.<br>\r\nIt is not mentioned in the options. Let\u2019s find one more.<br>\r\nRational number between \u2013 3 and \u2013 2 $=  \\frac{1}{2}(- 3 -2)= \\frac{-5}{2}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following is not a rational number between $\\frac{3}{8}$ and $\\frac{1}{7}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{9}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{5}{28}$<\/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: $\\frac{1}{3}$<br\/>$\\frac{3 \\times 7}{8 \\times 7} = \\frac{21}{56}$ and $\\frac{1 \\times 8}{7 \\times 8} = \\frac{8}{56}$<br>\r\nRational numbers between $\\frac{3}{8}$ and $\\frac{1}{7}$ are<br>\r\n$\\frac{9}{56}; \\frac{10}{56} = \\frac{5}{28}; \\frac{11}{56}; \\frac{12}{56} = \\frac{6}{28}; \\frac{13}{56}; \\frac{14}{56} = \\frac{1}{4}; \\frac{15}{56}; \\frac{16}{56} = \\frac{2}{7}; \\frac{17}{56}; \\frac{18}{56} = \\frac{9}{28}; \\frac{19}{56}$ and $\\frac{20}{56} = \\frac{5}{14}$<\/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 rational numbers between 0.45 and 0.49 is:<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{5}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{12}{25}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{21}{25}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{2}{5}$<\/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: $\\frac{12}{25}$<br\/>0.45 $= \\frac{45}{100}$ and 0.49 $= \\frac{49}{100}$<br>\r\nRational numbers between 0.45 and 0.49<br>\r\n$\\frac{46}{100}; \\frac{47}{100}$; and $\\frac{48}{100} = \\frac{12}{25}$<\/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 Between Two Rational Numbers - Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Rational Numbers Between Two Rational Numbers\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is not a rational number between $$\\\\frac{3}{4}$$ and $$\\\\frac{3}{7}$$?\",\n                    \"text\": \"Which of the following is not a rational number between $$\\\\frac{3}{4}$$ and $$\\\\frac{3}{7}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"LCM of 4 and 7 = 28<br>\r\n$$\\\\frac{3 \\\\times 7}{4 \\\\times 7} = \\\\frac{21}{28}$$ and $$\\\\frac{3 \\\\times 4}{7 \\\\times 4} = \\\\frac{12}{28}$$<br>\r\n$$\\\\frac{22}{28}$$ will not lie between $$\\\\frac{3}{4}$$ and $$\\\\frac{3}{7}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{9}{14}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCM of 4 and 7 = 28<br>\r\n$$\\\\frac{3 \\\\times 7}{4 \\\\times 7} = \\\\frac{21}{28}$$ and $$\\\\frac{3 \\\\times 4}{7 \\\\times 4} = \\\\frac{12}{28}$$<br>\r\n$$\\\\frac{22}{28}$$ will not lie between $$\\\\frac{3}{4}$$ and $$\\\\frac{3}{7}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCM of 4 and 7 = 28<br>\r\n$$\\\\frac{3 \\\\times 7}{4 \\\\times 7} = \\\\frac{21}{28}$$ and $$\\\\frac{3 \\\\times 4}{7 \\\\times 4} = \\\\frac{12}{28}$$<br>\r\n$$\\\\frac{22}{28}$$ will not lie between $$\\\\frac{3}{4}$$ and $$\\\\frac{3}{7}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{13}{28}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"LCM of 4 and 7 = 28<br>\r\n$$\\\\frac{3 \\\\times 7}{4 \\\\times 7} = \\\\frac{21}{28}$$ and $$\\\\frac{3 \\\\times 4}{7 \\\\times 4} = \\\\frac{12}{28}$$<br>\r\n$$\\\\frac{22}{28}$$ will not lie between $$\\\\frac{3}{4}$$ and $$\\\\frac{3}{7}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{22}{28}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"LCM of 4 and 7 = 28<br>\r\n$$\\\\frac{3 \\\\times 7}{4 \\\\times 7} = \\\\frac{21}{28}$$ and $$\\\\frac{3 \\\\times 4}{7 \\\\times 4} = \\\\frac{12}{28}$$<br>\r\n$$\\\\frac{22}{28}$$ will not lie between $$\\\\frac{3}{4}$$ and $$\\\\frac{3}{7}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"LCM of 4 and 7 = 28<br>\r\n$$\\\\frac{3 \\\\times 7}{4 \\\\times 7} = \\\\frac{21}{28}$$ and $$\\\\frac{3 \\\\times 4}{7 \\\\times 4} = \\\\frac{12}{28}$$<br>\r\n$$\\\\frac{22}{28}$$ will not lie between $$\\\\frac{3}{4}$$ and $$\\\\frac{3}{7}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The rational number between $$\\\\frac{1}{9}$$ and $$\\\\frac{1}{5}$$ is ____.\",\n                    \"text\": \"The rational number between $$\\\\frac{1}{9}$$ and $$\\\\frac{1}{5}$$ is ____.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{1 \\\\times 5}{9 \\\\times 5} = \\\\frac{5}{45}$$ and $$\\\\frac{1 \\\\times 9}{5 \\\\times 9} = \\\\frac{9}{45}$$<br>\r\nRational number between $$\\\\frac{5}{45}$$ and $$\\\\frac{9}{45}$$ are<br>\r\n$$\\\\frac{6}{45} = \\\\frac{2}{15}; \\\\frac{7}{45}$$ and $$\\\\frac{8}{45}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1 \\\\times 5}{9 \\\\times 5} = \\\\frac{5}{45}$$ and $$\\\\frac{1 \\\\times 9}{5 \\\\times 9} = \\\\frac{9}{45}$$<br>\r\nRational number between $$\\\\frac{5}{45}$$ and $$\\\\frac{9}{45}$$ are<br>\r\n$$\\\\frac{6}{45} = \\\\frac{2}{15}; \\\\frac{7}{45}$$ and $$\\\\frac{8}{45}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{45}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1 \\\\times 5}{9 \\\\times 5} = \\\\frac{5}{45}$$ and $$\\\\frac{1 \\\\times 9}{5 \\\\times 9} = \\\\frac{9}{45}$$<br>\r\nRational number between $$\\\\frac{5}{45}$$ and $$\\\\frac{9}{45}$$ are<br>\r\n$$\\\\frac{6}{45} = \\\\frac{2}{15}; \\\\frac{7}{45}$$ and $$\\\\frac{8}{45}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{-8}{45}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1 \\\\times 5}{9 \\\\times 5} = \\\\frac{5}{45}$$ and $$\\\\frac{1 \\\\times 9}{5 \\\\times 9} = \\\\frac{9}{45}$$<br>\r\nRational number between $$\\\\frac{5}{45}$$ and $$\\\\frac{9}{45}$$ are<br>\r\n$$\\\\frac{6}{45} = \\\\frac{2}{15}; \\\\frac{7}{45}$$ and $$\\\\frac{8}{45}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{8}{45}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{1 \\\\times 5}{9 \\\\times 5} = \\\\frac{5}{45}$$ and $$\\\\frac{1 \\\\times 9}{5 \\\\times 9} = \\\\frac{9}{45}$$<br>\r\nRational number between $$\\\\frac{5}{45}$$ and $$\\\\frac{9}{45}$$ are<br>\r\n$$\\\\frac{6}{45} = \\\\frac{2}{15}; \\\\frac{7}{45}$$ and $$\\\\frac{8}{45}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{1 \\\\times 5}{9 \\\\times 5} = \\\\frac{5}{45}$$ and $$\\\\frac{1 \\\\times 9}{5 \\\\times 9} = \\\\frac{9}{45}$$<br>\r\nRational number between $$\\\\frac{5}{45}$$ and $$\\\\frac{9}{45}$$ are<br>\r\n$$\\\\frac{6}{45} = \\\\frac{2}{15}; \\\\frac{7}{45}$$ and $$\\\\frac{8}{45}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The rational number between \u2013 3 and \u2013 1 is ___.\",\n                    \"text\": \"The rational number between \u2013 3 and \u2013 1 is ___.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Rational number between \u2013 3 and \u2013 1 is  \u2013 2.<br>\r\nIt is not mentioned in the options. Let\u2019s find one more.<br>\r\nRational number between \u2013 3 and \u2013 2 $$=  \\\\frac{1}{2}(- 3 -2)= \\\\frac{-5}{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$- \\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Rational number between \u2013 3 and \u2013 1 is  \u2013 2.<br>\r\nIt is not mentioned in the options. Let\u2019s find one more.<br>\r\nRational number between \u2013 3 and \u2013 2 $$=  \\\\frac{1}{2}(- 3 -2)= \\\\frac{-5}{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$2$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Rational number between \u2013 3 and \u2013 1 is  \u2013 2.<br>\r\nIt is not mentioned in the options. Let\u2019s find one more.<br>\r\nRational number between \u2013 3 and \u2013 2 $$=  \\\\frac{1}{2}(- 3 -2)= \\\\frac{-5}{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Rational number between \u2013 3 and \u2013 1 is  \u2013 2.<br>\r\nIt is not mentioned in the options. Let\u2019s find one more.<br>\r\nRational number between \u2013 3 and \u2013 2 $$=  \\\\frac{1}{2}(- 3 -2)= \\\\frac{-5}{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$- \\\\frac{5}{2}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Rational number between \u2013 3 and \u2013 1 is  \u2013 2.<br>\r\nIt is not mentioned in the options. Let\u2019s find one more.<br>\r\nRational number between \u2013 3 and \u2013 2 $$=  \\\\frac{1}{2}(- 3 -2)= \\\\frac{-5}{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Rational number between \u2013 3 and \u2013 1 is  \u2013 2.<br>\r\nIt is not mentioned in the options. Let\u2019s find one more.<br>\r\nRational number between \u2013 3 and \u2013 2 $$=  \\\\frac{1}{2}(- 3 -2)= \\\\frac{-5}{2}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is not a rational number between $$\\\\frac{3}{8}$$ and $$\\\\frac{1}{7}$$?\",\n                    \"text\": \"Which of the following is not a rational number between $$\\\\frac{3}{8}$$ and $$\\\\frac{1}{7}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{3 \\\\times 7}{8 \\\\times 7} = \\\\frac{21}{56}$$ and $$\\\\frac{1 \\\\times 8}{7 \\\\times 8} = \\\\frac{8}{56}$$<br>\r\nRational numbers between $$\\\\frac{3}{8}$$ and $$\\\\frac{1}{7}$$ are<br>\r\n$$\\\\frac{9}{56}; \\\\frac{10}{56} = \\\\frac{5}{28}; \\\\frac{11}{56}; \\\\frac{12}{56} = \\\\frac{6}{28}; \\\\frac{13}{56}; \\\\frac{14}{56} = \\\\frac{1}{4}; \\\\frac{15}{56}; \\\\frac{16}{56} = \\\\frac{2}{7}; \\\\frac{17}{56}; \\\\frac{18}{56} = \\\\frac{9}{28}; \\\\frac{19}{56}$$ and $$\\\\frac{20}{56} = \\\\frac{5}{14}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{9}{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{3 \\\\times 7}{8 \\\\times 7} = \\\\frac{21}{56}$$ and $$\\\\frac{1 \\\\times 8}{7 \\\\times 8} = \\\\frac{8}{56}$$<br>\r\nRational numbers between $$\\\\frac{3}{8}$$ and $$\\\\frac{1}{7}$$ are<br>\r\n$$\\\\frac{9}{56}; \\\\frac{10}{56} = \\\\frac{5}{28}; \\\\frac{11}{56}; \\\\frac{12}{56} = \\\\frac{6}{28}; \\\\frac{13}{56}; \\\\frac{14}{56} = \\\\frac{1}{4}; \\\\frac{15}{56}; \\\\frac{16}{56} = \\\\frac{2}{7}; \\\\frac{17}{56}; \\\\frac{18}{56} = \\\\frac{9}{28}; \\\\frac{19}{56}$$ and $$\\\\frac{20}{56} = \\\\frac{5}{14}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{3 \\\\times 7}{8 \\\\times 7} = \\\\frac{21}{56}$$ and $$\\\\frac{1 \\\\times 8}{7 \\\\times 8} = \\\\frac{8}{56}$$<br>\r\nRational numbers between $$\\\\frac{3}{8}$$ and $$\\\\frac{1}{7}$$ are<br>\r\n$$\\\\frac{9}{56}; \\\\frac{10}{56} = \\\\frac{5}{28}; \\\\frac{11}{56}; \\\\frac{12}{56} = \\\\frac{6}{28}; \\\\frac{13}{56}; \\\\frac{14}{56} = \\\\frac{1}{4}; \\\\frac{15}{56}; \\\\frac{16}{56} = \\\\frac{2}{7}; \\\\frac{17}{56}; \\\\frac{18}{56} = \\\\frac{9}{28}; \\\\frac{19}{56}$$ and $$\\\\frac{20}{56} = \\\\frac{5}{14}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{5}{28}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{3 \\\\times 7}{8 \\\\times 7} = \\\\frac{21}{56}$$ and $$\\\\frac{1 \\\\times 8}{7 \\\\times 8} = \\\\frac{8}{56}$$<br>\r\nRational numbers between $$\\\\frac{3}{8}$$ and $$\\\\frac{1}{7}$$ are<br>\r\n$$\\\\frac{9}{56}; \\\\frac{10}{56} = \\\\frac{5}{28}; \\\\frac{11}{56}; \\\\frac{12}{56} = \\\\frac{6}{28}; \\\\frac{13}{56}; \\\\frac{14}{56} = \\\\frac{1}{4}; \\\\frac{15}{56}; \\\\frac{16}{56} = \\\\frac{2}{7}; \\\\frac{17}{56}; \\\\frac{18}{56} = \\\\frac{9}{28}; \\\\frac{19}{56}$$ and $$\\\\frac{20}{56} = \\\\frac{5}{14}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{3 \\\\times 7}{8 \\\\times 7} = \\\\frac{21}{56}$$ and $$\\\\frac{1 \\\\times 8}{7 \\\\times 8} = \\\\frac{8}{56}$$<br>\r\nRational numbers between $$\\\\frac{3}{8}$$ and $$\\\\frac{1}{7}$$ are<br>\r\n$$\\\\frac{9}{56}; \\\\frac{10}{56} = \\\\frac{5}{28}; \\\\frac{11}{56}; \\\\frac{12}{56} = \\\\frac{6}{28}; \\\\frac{13}{56}; \\\\frac{14}{56} = \\\\frac{1}{4}; \\\\frac{15}{56}; \\\\frac{16}{56} = \\\\frac{2}{7}; \\\\frac{17}{56}; \\\\frac{18}{56} = \\\\frac{9}{28}; \\\\frac{19}{56}$$ and $$\\\\frac{20}{56} = \\\\frac{5}{14}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{3 \\\\times 7}{8 \\\\times 7} = \\\\frac{21}{56}$$ and $$\\\\frac{1 \\\\times 8}{7 \\\\times 8} = \\\\frac{8}{56}$$<br>\r\nRational numbers between $$\\\\frac{3}{8}$$ and $$\\\\frac{1}{7}$$ are<br>\r\n$$\\\\frac{9}{56}; \\\\frac{10}{56} = \\\\frac{5}{28}; \\\\frac{11}{56}; \\\\frac{12}{56} = \\\\frac{6}{28}; \\\\frac{13}{56}; \\\\frac{14}{56} = \\\\frac{1}{4}; \\\\frac{15}{56}; \\\\frac{16}{56} = \\\\frac{2}{7}; \\\\frac{17}{56}; \\\\frac{18}{56} = \\\\frac{9}{28}; \\\\frac{19}{56}$$ and $$\\\\frac{20}{56} = \\\\frac{5}{14}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The rational numbers between 0.45 and 0.49 is:\",\n                    \"text\": \"The rational numbers between 0.45 and 0.49 is:\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"0.45 $$= \\\\frac{45}{100}$$ and 0.49 $$= \\\\frac{49}{100}$$<br>\r\nRational numbers between 0.45 and 0.49<br>\r\n$$\\\\frac{46}{100}; \\\\frac{47}{100}$$; and $$\\\\frac{48}{100} = \\\\frac{12}{25}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"0.45 $$= \\\\frac{45}{100}$$ and 0.49 $$= \\\\frac{49}{100}$$<br>\r\nRational numbers between 0.45 and 0.49<br>\r\n$$\\\\frac{46}{100}; \\\\frac{47}{100}$$; and $$\\\\frac{48}{100} = \\\\frac{12}{25}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{21}{25}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"0.45 $$= \\\\frac{45}{100}$$ and 0.49 $$= \\\\frac{49}{100}$$<br>\r\nRational numbers between 0.45 and 0.49<br>\r\n$$\\\\frac{46}{100}; \\\\frac{47}{100}$$; and $$\\\\frac{48}{100} = \\\\frac{12}{25}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"0.45 $$= \\\\frac{45}{100}$$ and 0.49 $$= \\\\frac{49}{100}$$<br>\r\nRational numbers between 0.45 and 0.49<br>\r\n$$\\\\frac{46}{100}; \\\\frac{47}{100}$$; and $$\\\\frac{48}{100} = \\\\frac{12}{25}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{12}{25}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"0.45 $$= \\\\frac{45}{100}$$ and 0.49 $$= \\\\frac{49}{100}$$<br>\r\nRational numbers between 0.45 and 0.49<br>\r\n$$\\\\frac{46}{100}; \\\\frac{47}{100}$$; and $$\\\\frac{48}{100} = \\\\frac{12}{25}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"0.45 $$= \\\\frac{45}{100}$$ and 0.49 $$= \\\\frac{49}{100}$$<br>\r\nRational numbers between 0.45 and 0.49<br>\r\n$$\\\\frac{46}{100}; \\\\frac{47}{100}$$; and $$\\\\frac{48}{100} = \\\\frac{12}{25}$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-frequently-asked-questions-about-rational-numbers-between-two-rational-numbers\">Frequently Asked Questions about Rational Numbers between Two Rational Numbers<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-46b3954e-9ee0-4290-a2f9-dcb238d15063\" 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-0-46b3954e-9ee0-4290-a2f9-dcb238d15063\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-46b3954e-9ee0-4290-a2f9-dcb238d15063\"><strong>What are irrational numbers?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-46b3954e-9ee0-4290-a2f9-dcb238d15063\">\n\n<p>Irrational numbers are the numbers which can not be expressed in the form of $\\frac{p}{q}$ where p and q are integers and $q \\neq 0$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-46b3954e-9ee0-4290-a2f9-dcb238d15063\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-46b3954e-9ee0-4290-a2f9-dcb238d15063\"><strong>Is the sum of two or more rational numbers always a rational 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-1-46b3954e-9ee0-4290-a2f9-dcb238d15063\">\n\n<p>Yes, the sum of two or more rational numbers is always a rational number. Thus, the rational numbers are closed under the addition operation.<\/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-2-46b3954e-9ee0-4290-a2f9-dcb238d15063\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-46b3954e-9ee0-4290-a2f9-dcb238d15063\"><strong>How do you find the standard form of a rational 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-2-46b3954e-9ee0-4290-a2f9-dcb238d15063\">\n\n<p>For finding the standard form of a rational number, we divide the numerator and denominator by the GCD of the numerator and denominator.<\/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-3-46b3954e-9ee0-4290-a2f9-dcb238d15063\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-46b3954e-9ee0-4290-a2f9-dcb238d15063\"><strong>Can we find rational numbers between two irrational 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-3-46b3954e-9ee0-4290-a2f9-dcb238d15063\">\n\n<p>Yes, we can find rational numbers between two irrational numbers.<br>Consider irrational numbers $\\sqrt{2} = 1.4142$\u2026and $\\sqrt{3} = 1.73$\u2026<br>Rational number between $\\sqrt{2}$ and $\\sqrt{3}$ is 1.534.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Are Rational Numbers between Two Rational Numbers? There are infinitely many rational numbers between any two distinct rational numbers. If you consider any two natural numbers, there will be only a finite number of natural numbers between them. For example, between the natural numbers 8 and 14, there are only five natural numbers, which &#8230; <a title=\"Rational Numbers Between Two Rational Numbers &#8211; Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/rational-numbers-between-two-rational-numbers\" aria-label=\"More on Rational Numbers Between Two Rational Numbers &#8211; 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-36145","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\/36145","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=36145"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36145\/revisions"}],"predecessor-version":[{"id":36163,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/36145\/revisions\/36163"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=36145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=36145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=36145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}