{"id":28013,"date":"2023-04-26T16:07:49","date_gmt":"2023-04-26T16:07:49","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=28013"},"modified":"2023-08-15T16:49:08","modified_gmt":"2023-08-15T16:49:08","slug":"proper-fraction-definition-examples-facts-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/proper-fraction","title":{"rendered":"Proper Fraction &#8211; Definition, Examples, Facts, 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-14dde3f8-ac02-4de6-823b-23c031db3807\" 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\/proper-fraction#0-what-is-a-proper-fraction-in-math>What Is a Proper Fraction in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/proper-fraction#11-proper-fraction-vs-improper-fraction>Proper Fraction vs. Improper Fraction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/proper-fraction#13-how-to-add-a-mixed-fraction-to-a-proper-fraction>How to Add a Mixed Fraction to a Proper Fraction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/proper-fraction#16-solved-examples-on-proper-fractions>Solved Examples on Proper Fractions<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/proper-fraction#17-practice-problems-on-proper-fractions>Practice Problems on Proper Fractions<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/proper-fraction#18-frequently-asked-questions-on-proper-fractions>Frequently Asked Questions on Proper Fractions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-proper-fraction-in-math\">What Is a Proper Fraction in Math?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>A proper fraction is a fraction whose numerator is less than the denominator. A proper fraction always lies between 0 and 1 since the denominator is larger than the numerator.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Proper Fraction Examples: $\\frac{1}{2},\\; \\frac{2}{5},\\; \\frac{3}{4},\\; \\frac{5}{7}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"390\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/proper-fraction-example.png\" alt=\"Proper fraction example\" class=\"wp-image-33055\" title=\"Proper fraction example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/proper-fraction-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/proper-fraction-example-300x189.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">What does fraction mean in math? A fraction represents a part of a whole. A fraction has two parts. The number on the top of the line is called the numerator. It tells us how many equal parts of the whole or collection are taken. The number below the line is called the denominator.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Fractions are categorized on the basis of the value of the numerator and the denominator as:<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Proper Fractions: <\/strong>Numerator $\\lt$ Denominator<\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>Improper Fractions: <\/strong>Numerator $\\ge$ Denominator<br><\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"396\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/numerator-and-denominator-of-a-proper-fraction-visual-model.png\" alt=\"Numerator and denominator of a proper fraction: visual model\" class=\"wp-image-33057\" title=\"Numerator and denominator of a proper fraction: visual model\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/numerator-and-denominator-of-a-proper-fraction-visual-model.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/numerator-and-denominator-of-a-proper-fraction-visual-model-300x192.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;Let\u2019s learn about proper fractions in detail.<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-definition-of-proper-fraction\">Definition of Proper Fraction<\/h3>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-ea3edd53-2472-455c-b2d1-135463ed38f9\">\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Fractions in which the numerator is less than the denominator are called proper fractions. The value of a proper fraction is always less than 1.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, $\\frac{18}{20},\\; \\frac{19}{40},\\; \\frac{60}{80},\\; \\frac{1}{4}, \\frac{1}{6}$, are proper fractions.<\/p>\n\n\n<\/div>\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"358\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/3_4-as-a-proper-fraction-since-3-is-less-than-4.png\" alt=\"\u00be as a proper fraction since 3 is less than 4\" class=\"wp-image-33058\" title=\"\u00be as a proper fraction since 3 is less than 4\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/3_4-as-a-proper-fraction-since-3-is-less-than-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/3_4-as-a-proper-fraction-since-3-is-less-than-4-300x173.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-decimal-fractions-using-equivalence\" 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\/decimals_convert_to_equi_frac_to_add_pt.png\" alt=\"Add Decimal Fractions Using Equivalence 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 Decimal Fractions Using Equivalence 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-fractions-using-models\" 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\/fractions_add_unlike_models_pt.png\" alt=\"Add Fractions using Models 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 Fractions using Models 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-fractions-with-the-aid-of-a-number-line\" 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\/fractions_add_like_frac_sum_greater_than_1_nl_pt.png\" alt=\"Add Fractions WIth the Aid of a Number LIne 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 Fractions WIth the Aid of a Number LIne 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-like-fractions\" 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\/fractions_add_like_frac_sum_upto_1_pt.png\" alt=\"Add Like Fractions 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 Like Fractions 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-like-fractions-greater-than-1\" 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\/fractions_find_sum_pt.png\" alt=\"Add Like Fractions Greater than 1 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 Like Fractions Greater than 1 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-like-fractions-to-get-a-sum-greater-than-1\" 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\/fractions_add_like_frac_sum_greater_than_1_pt.png\" alt=\"Add Like Fractions to Get a Sum Greater than 1 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 Like Fractions to Get a Sum Greater than 1 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-like-fractions-using-number-lines\" 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\/fractions_add_like_frac_sum_upto_1_nl_pt.png\" alt=\"Add Like Fractions using Number Lines 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 Like Fractions using Number Lines 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-the-fraction-to-the-mixed-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_add_mixed_num_and_frac_pt.png\" alt=\"Add the Fraction to the Mixed Number Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add the Fraction to the Mixed Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-the-mixed-number-and-the-fraction-on-a-number-line\" 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\/fractions_add_nl_pt.png\" alt=\"Add the Mixed Number and the Fraction on a Number Line 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 the Mixed Number and the Fraction on a Number Line 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-unlike-fractions\" 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\/fractions_add_unlike_pt.png\" alt=\"Add Unlike Fractions 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 Unlike Fractions 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                    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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-proper-fractions-on-a-number-line\">Proper Fractions on a Number Line<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A proper fraction has a value between 0 and 1. It is a fraction that lies between 0 and 1 on a number line.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example:<\/strong> Represent the proper fraction $\\frac{1}{4}$ on a number line.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To represent a proper fraction on the number line, we first look at the denominator.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This number tells us the number of parts the interval between 0 and 1 is to be divided into.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the denominator is 4. Thus, we divide the segment joining 0 and 1 into 4 equal parts.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"334\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/the-segment-joining-0-and-1-divided-into-4-equal-parts.png\" alt=\"The segment joining 0 and 1 divided into 4 equal parts\" class=\"wp-image-33059\" title=\"The segment joining 0 and 1 divided into 4 equal parts\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/the-segment-joining-0-and-1-divided-into-4-equal-parts.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/the-segment-joining-0-and-1-divided-into-4-equal-parts-300x162.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The numerator tells us where we place the dot or the mark to represent the given fraction. Here, the numerator is 1. Thus, we represent $\\frac{1}{4}$ on the first marking.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"427\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/representing-the-proper-fraction-14-on-a-number-line.png\" alt=\"Representing the proper fraction 14 on a number line\" class=\"wp-image-33060\" title=\"Representing the proper fraction 14 on a number line\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/representing-the-proper-fraction-14-on-a-number-line.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/representing-the-proper-fraction-14-on-a-number-line-300x207.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-decimal-fractions-to-write-decimal-number\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-decimal-fractions-to-write-decimal-number.jpeg\" alt=\"Add Decimal Fractions to Write Decimal Number 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-fractions-using-area-models\" 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-fractions-using-area-models.jpeg\" alt=\"Add Fractions using Area Models 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-fractions-using-fraction-models\" 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-fractions-using-fraction-models.jpeg\" alt=\"Add Fractions Using Fraction Models 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-fractions-using-visual-models\" 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-fractions-using-visual-models.jpeg\" alt=\"Add Fractions Using Visual Models 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-like-fractions-using-area-models\" 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-like-fractions-using-area-models.jpeg\" alt=\"Add Like Fractions using Area Models 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-mixed-numbers-and-fractions-using-area-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    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Mixed Numbers and Fractions using Models 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-the-numbers-using-commutative-property-of-addition\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-the-numbers-using-commutative-property-of-addition.jpeg\" alt=\"Add the Numbers Using Commutative Property of Addition\">\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\/adding-fractions-mixed-numbers-word-problems\" 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\/adding-fractions-mixed-numbers-word-problems.jpeg\" alt=\"Adding Fractions & Mixed Numbers Word Problems 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\/adding-fractions-using-fraction-models\" 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\/adding-fractions-using-fraction-models.jpeg\" alt=\"Adding Fractions Using Fraction Models 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       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((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=\"3-visualize-proper-fractions\">Visualize Proper Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Suppose you cut a pizza in equal parts, you can express each slice in the form of a fraction.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If you divide it in two equal parts, each part represents \u201chalf\u201d or the fraction $\\frac{1}{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If you divide it in four equal parts, each part represents \u201ca quarter\u201d or the fraction $\\frac{1}{4}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When we represent a proper fraction visually like this, notice that we never have enough slices to complete the whole pizza. Some slices are always missing.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"507\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-proper-fractions.png\" alt=\"Visualizing proper fractions\" class=\"wp-image-33061\" title=\"Visualizing proper fractions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-proper-fractions.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-proper-fractions-300x245.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">On the other hand, when we represent an improper fraction, we can always represent a whole and still some parts (slices) are left.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"318\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-the-improper-fraction-54.png\" alt=\"Visualizing the improper fraction 5\/4\" class=\"wp-image-33062\" title=\"Visualizing the improper fraction 5\/4\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-the-improper-fraction-54.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/visualizing-the-improper-fraction-54-300x154.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-adding-proper-fractions\">Adding Proper Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We consider two cases when we add two or more proper fractions.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Case 1: Denominators are the same.<\/strong><\/li>\n\n\n\n<li class=\"eplus-wrapper\"><strong>Case 2: Denominators are different<\/strong><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-case-1-denominators-are-same\">Case 1: Denominators Are Same<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When the denominators of two or more fractions are the same, we call them like fractions. Adding proper fractions with the same denominator is simple.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If denominators are the same, we simply add the numerators by keeping the denominator as it is.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 1:<\/strong> $\\frac{1}{4} + \\frac{2}{4} = \\frac{2 + 1}{4} = \\frac{3}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example 2:<\/strong> $\\frac{6}{10} + \\frac{2}{10} = \\frac{6 + 2}{10} = \\frac{8}{10}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"356\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-proper-fractions-with-same-denominators-visual-model.png\" alt=\"Adding proper fractions with same denominators visual model\" class=\"wp-image-33063\" title=\"Adding proper fractions with same denominators visual model\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-proper-fractions-with-same-denominators-visual-model.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-proper-fractions-with-same-denominators-visual-model-300x172.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"6-case-2-denominators-are-different\">Case 2: Denominators Are Different<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If denominators are different, we first take the LCM (Least Common Multiple) of the denominators and then rewrite the fractions as equivalent fractions using the LCM as the common denominator.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Once the denominators become the same, we add the numerators.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example:<\/strong> $\\frac{1}{2} + \\frac{1}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we will list the multiples of 2 and 4.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiples of 2: 2, 4, 6, 8, 10,\u2026<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiples of 4: 4, 8, 12, 16,\u2026<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">4 is the Lowest Common Multiple.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">LCM $(2,\\; 4) = 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We need to find a number which when multiplied to the top and bottom of 12, we get the LCM (4) as the new denominator.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{1\\times?}{2\\times?} = \\frac{?}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">As $2\\times2 = 4$ , we need to multiply the numerator and the denominator by 2.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{1\\times2}{2\\times2} = \\frac{2}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now we have, $\\frac{2}{4} + \\frac{1}{4} = \\frac{3}{4}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-subtracting-proper-fractions\">Subtracting Proper Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Subtraction of proper fractions is similar to addition of proper fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Case 1: <\/strong>If denominator is same, we simply find the difference between the numerators<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:&nbsp;$\\frac{5}{10} \\;-\\; \\frac{3}{10} = \\frac{5 \\;-\\; 3}{10} = \\frac{2}{10}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Case 2:<\/strong> If the denominators are not the same, we take the LCM of the denominators and when denominators become the same we find the difference between the numerators.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example:&nbsp; subtract $\\frac{6}{9} \\;-\\; \\frac{2}{4}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The LCM of 9 and 4 is 36.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we multiply both the fractions with such a number (in this case, 4 and 9 respectively) so that the denominators become equal.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{6\\times4}{9\\times4} \\;-\\; \\frac{2\\times9}{4\\times9} = \\frac{24}{36} \\;-\\; \\frac{18}{36} = \\frac{24 \\;-\\; 18}{36} = \\frac{6}{36} = \\frac{1}{6}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-multiplying-proper-fractions\">Multiplying Proper Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiplication and division of proper fractions is easier compared to addition and subtraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We simply multiply the given numerators, then multiply the denominators, and finally reduce the resultant fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example:&nbsp; $\\frac{3}{7}\\times\\frac{2}{4}&nbsp; = \\frac{3\\times2}{7\\times4} = \\frac{6}{28} =&nbsp; \\frac{3}{14}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-dividing-proper-fractions\">Dividing Proper Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To divide one fraction by another fraction, we multiply the fraction on the top (first fraction or the dividend) by the reciprocal of the fraction on the bottom (second fraction or the divisor).<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let&#8217;s take an example to understand the process of division.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example: $\\frac{3}{10} \\div \\frac{2}{3}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Reciprocal of $\\frac{2}{3} = \\frac{3}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{3}{10}\\div \\frac{2}{3} = \\frac{3}{10}\\times\\frac{3}{2} = \\frac{9}{20}$&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-proper-fraction-and-improper-fraction\">Proper Fraction and Improper Fraction<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A proper fraction is a fraction whose numerator is smaller than its denominator.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;$\\frac{5}{12},\\; \\frac{2}{10},\\; \\frac{1}{2}$ are a few examples of proper fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">An improper fraction is a fraction whose numerator is equal to or greater than its denominator. $\\frac{12}{5},\\; \\frac{10}{4},\\; \\frac{12}{11},\\; \\frac{5}{5}$ are a few examples of improper fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Improper fractions are often expressed as a mixed number. A mixed number has a whole number part and a fractional part. The fractional part of a mixed fraction is always a proper fraction.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Example: $\\frac{12}{5} = 2\\frac{2}{5}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-proper-fraction-vs-improper-fraction\">Proper Fraction vs. Improper Fraction<\/h2>\n\n\n\n<figure class=\"wp-block-table eplus-wrapper\"><table class=\"has-fixed-layout\"><thead><tr><th class=\"has-text-align-center\" data-align=\"center\"><strong>Proper Fraction<\/strong><\/th><th class=\"has-text-align-center\" data-align=\"center\"><strong>Improper Fraction<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-center\" data-align=\"center\">&nbsp; &nbsp; &nbsp; &nbsp; Numerator $\\lt$ Denominator<br>(Numerator is less than the denominator.)<\/td><td class=\"has-text-align-center\" data-align=\"center\">&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; Numerator $\\ge$Denominator<br>(Numerator is greater than or equal to the denominator.)<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">The value of the proper fraction is always between 0 and 1.<\/td><td class=\"has-text-align-center\" data-align=\"center\">The value of the improper fraction is greater than or equal to 1.<\/td><\/tr><tr><td class=\"has-text-align-center\" data-align=\"center\">Examples: $\\frac{5}{6},\\; \\frac{2}{7},\\; \\frac{1}{2}$<\/td><td class=\"has-text-align-center\" data-align=\"center\">Examples:&nbsp; $\\frac{12}{5},\\; \\frac{10}{9},\\; \\frac{12}{12}$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-improper-fractions-to-proper-fractions\">Improper Fractions to Proper Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We cannot convert an improper fraction to a proper fraction. Proper fractions lie between 0 and 1. They do not have any whole number part. Improper fractions are greater than 1. They have a whole number part and some fractional part. Thus, there is no equivalence.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">However, an improper fraction can be converted to a mixed fraction. A mixed fraction or a mixed number consists of a whole number and a proper fraction. Thus, note that we can basically convert an improper fraction to a mixed number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us convert $\\frac{25}{6}$ to mixed fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Divide 25 by 6.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$25\\div6 = 4\\; R\\; 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It means that the quotient is 4, with a remainder of 1.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Use the quotient = 4 as the whole number part of the mixed number, and place the remainder = 1 as the numerator over the original denominator.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{25}{6} =&nbsp; 4\\frac{1}{6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, 4 is the whole number and $\\frac{1}{6}$ is the proper fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can convert this mixed number back to the improper fraction form:<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$4\\frac{1}{6} = \\frac{(6\\times4) + 1}{6} = \\frac{24 + 1}{6} = \\frac{25}{6}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-how-to-add-a-mixed-fraction-to-a-proper-fraction\">How to Add a Mixed Fraction to a Proper Fraction<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To add a mixed fraction to a proper fraction we convert the mixed fraction to an improper fraction. Then we add the two fractions in the usual way. After finding the answers we again convert the result into a mixed fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us look at an example:&nbsp; $3\\frac{1}{5} + \\frac{1}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Convert mixed fraction into improper fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$3\\frac{1}{5} = \\frac{16}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{16}{5} + \\frac{1}{4} = \\frac{16\\times4}{5\\times4} + \\frac{1\\times5}{4\\times5}$ \u2026since LCM$(4,\\; 5) = 20$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$= \\frac{64}{20} + \\frac{5}{20}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$= \\frac{64 + 5}{20}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$= \\frac{69}{20}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we also can convert improper fraction into mixed fraction which will be $3\\frac{9}{20}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-facts-about-proper-fractions\">Facts about Proper Fractions<\/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-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The word fraction is acquired from the Latin word \u201cfractus,\u201d which implies \u201cbroken.\u201d<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Every whole number can be written as a fraction. For example, 2 can be written as $\\frac{2}{1}$.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">A proper fraction is one where the numerator is less than the denominator.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The NUMERATOR tells how many pieces of the whole the fraction represents.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">The DENOMINATOR tells how many equal pieces the whole is divided into.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Proper fractions are used with whole numbers to denote a sum that is greater than 1.&nbsp;<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"15-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">In this article, we have learned about proper fractions, their addition, multiplication, subtraction, and division. Let&#8217;s solve some examples to understand the concept better.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"16-solved-examples-on-proper-fractions\">Solved Examples on Proper Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1. Identify whether the following are proper fractions.<\/strong><br>a) $\\frac{10}{12}$ &nbsp; &nbsp; &nbsp; &nbsp; b) $\\frac{15}{11}$                      c) $\\frac{18}{18}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<br><\/strong>a) $\\frac{10}{12}$ is a proper fraction as the numerator is less than the denominator.<br>b) $\\frac{15}{11}$ is not a proper fraction as the numerator is greater than the denominator. It is an improper fraction.<br>c) $\\frac{18}{18}$ is not a proper fraction because in this case the numerator is equal to the denominator. It is an improper fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Add the proper fractions: <\/strong>$\\frac{10}{20} + \\frac{15}{20}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">If denominators are the same, we simply add the numerators.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{10}{20} + \\frac{15}{20}&nbsp; =&nbsp; \\frac{10 + 15}{20} = \\frac{25}{20}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">It can also be reduce or simplified further as $\\frac{25\\div5}{20\\div5} = \\frac{5}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $\\frac{10}{20} + \\frac{15}{20} = \\frac{25}{20} = \\frac{5}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Solve <\/strong>$\\frac{6}{20}\\div \\frac{1}{2}$<strong> .<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiply the first fraction by the reciprocal of the second fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{6}{20}\\div\\frac{1}{2} = \\frac{6}{20}\\times \\frac{2}{1} =&nbsp; \\frac{6\\times2}{20\\times1} = \\frac{12}{20}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{12}{20}$ can be further reduced as $\\frac{12\\div4}{20\\div4} = \\frac{3}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $\\frac{6}{20}\\div\\frac{1}{2} =&nbsp;\\frac{3}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Subtract&nbsp; <\/strong>$\\frac{2}{5} \\;-\\; \\frac{1}{4}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, the denominators are not the same, so we take the LCM of the denominators and when denominators become the same we find the difference between the numerators.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The LCM of 5 and 4 is 20.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we multiply both the fractions with such a number (in this case, 5 and 4 respectively) so that the denominators become equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{2\\times4}{5\\times4} \\;-\\; \\frac{1\\times5}{4\\times5} =&nbsp; \\frac{8}{20} \\;-\\; \\frac{5}{20}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=&nbsp; \\frac{8 \\;-\\; 5}{20}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$=&nbsp; \\frac{3}{20}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore, $\\frac{2}{5} \\;-\\; \\frac{1}{4} = &nbsp;\\frac{3}{20}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. Add <\/strong>$2\\frac{3}{6} + \\frac{3}{8}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we first convert a mixed fraction into an improper fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;$2\\frac{3}{6} = \\frac{15}{6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we add the two fractions $\\frac{15}{6}$ and $\\frac{3}{8}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;$\\frac{15}{6} + \\frac{3}{8} = \\frac{15\\times4}{6\\times4} + \\frac{3\\times3}{8\\times3}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{60}{24} + \\frac{9}{24}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$= \\frac{69}{24}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This can be further reduced as $\\frac{69\\div3}{24\\div3} = \\frac{23}{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Expressing it as mixed fraction $\\frac{23}{8} =&nbsp; 2\\frac{7}{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Therefore,&nbsp; $2\\frac{3}{6} + \\frac{3}{8} =&nbsp; 2\\frac{7}{8}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"17-practice-problems-on-proper-fractions\">Practice Problems on Proper Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Proper Fraction - Definition, Examples, Facts, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">The fraction representation of the shaded portion is _________.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problems-1-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{2}{3}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{2}{6}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{1}{2}$<br\/>The whole is divided into 2 parts. So the shaded part is $\\frac{1}{2}$ .<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Which of the following is a proper fraction ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{7}{9}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{5}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{3}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{5}{2}$<\/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: $\\frac{7}{9}$<br\/>A fraction is called a proper fraction if its numerator is less than its denominator. Thus, $\\frac{7}{9}$ is a proper fraction.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Which of the following is NOT a proper fraction ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{3}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{11}{3}$<\/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: $\\frac{11}{3}$<br\/>A fraction is called a proper fraction if its numerator is less than its denominator. An improper fraction is a fraction whose numerator is equal to or greater than its denominator. As 11 is greater than $3,\\; \\frac{11}{3}$ is an improper fraction.<\/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\">$\\frac{1}{3} + \\frac{2}{3} =$ _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">3<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">1<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>If denominators are the same, we simply add the numerators by keeping the denominator as it is. Thus, $\\frac{1}{3} + \\frac{2}{3} = \\frac{1 + 2}{3} = \\frac{3}{3} = 1$<\/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\">Find the sum of fractions.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problems-5-2.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{3}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{4}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{2}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{4}{8}$<br\/>$\\frac{1}{8} + \\frac{3}{8} = \\frac{4}{8}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Proper Fraction - Definition, Examples, Facts, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Proper Fraction\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"The fraction representation of the shaded portion is _________.\",\n                    \"text\": \"The fraction representation of the shaded portion is _________. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problems-1-1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The whole is divided into 2 parts. 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As 11 is greater than $$3,\\\\; \\\\frac{11}{3}$$ is an improper fraction.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{4}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A fraction is called a proper fraction if its numerator is less than its denominator. An improper fraction is a fraction whose numerator is equal to or greater than its denominator. 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As 11 is greater than $$3,\\\\; \\\\frac{11}{3}$$ is an improper fraction.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{11}{3}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A fraction is called a proper fraction if its numerator is less than its denominator. An improper fraction is a fraction whose numerator is equal to or greater than its denominator. As 11 is greater than $$3,\\\\; \\\\frac{11}{3}$$ is an improper fraction.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A fraction is called a proper fraction if its numerator is less than its denominator. An improper fraction is a fraction whose numerator is equal to or greater than its denominator. As 11 is greater than $$3,\\\\; \\\\frac{11}{3}$$ is an improper fraction.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"$$\\\\frac{1}{3} + \\\\frac{2}{3} =$$ _______.\",\n                    \"text\": \"$$\\\\frac{1}{3} + \\\\frac{2}{3} =$$ _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"If denominators are the same, we simply add the numerators by keeping the denominator as it is. Thus, $$\\\\frac{1}{3} + \\\\frac{2}{3} = \\\\frac{1 + 2}{3} = \\\\frac{3}{3} = 1$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If denominators are the same, we simply add the numerators by keeping the denominator as it is. Thus, $$\\\\frac{1}{3} + \\\\frac{2}{3} = \\\\frac{1 + 2}{3} = \\\\frac{3}{3} = 1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If denominators are the same, we simply add the numerators by keeping the denominator as it is. Thus, $$\\\\frac{1}{3} + \\\\frac{2}{3} = \\\\frac{1 + 2}{3} = \\\\frac{3}{3} = 1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"If denominators are the same, we simply add the numerators by keeping the denominator as it is. Thus, $$\\\\frac{1}{3} + \\\\frac{2}{3} = \\\\frac{1 + 2}{3} = \\\\frac{3}{3} = 1$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"If denominators are the same, we simply add the numerators by keeping the denominator as it is. Thus, $$\\\\frac{1}{3} + \\\\frac{2}{3} = \\\\frac{1 + 2}{3} = \\\\frac{3}{3} = 1$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"If denominators are the same, we simply add the numerators by keeping the denominator as it is. Thus, $$\\\\frac{1}{3} + \\\\frac{2}{3} = \\\\frac{1 + 2}{3} = \\\\frac{3}{3} = 1$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the sum of fractions.\",\n                    \"text\": \"Find the sum of fractions. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problems-5-2.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{1}{8} + \\\\frac{3}{8} = \\\\frac{4}{8}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{3}{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1}{8} + \\\\frac{3}{8} = \\\\frac{4}{8}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1}{8} + \\\\frac{3}{8} = \\\\frac{4}{8}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1}{8} + \\\\frac{3}{8} = \\\\frac{4}{8}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{4}{8}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{1}{8} + \\\\frac{3}{8} = \\\\frac{4}{8}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{1}{8} + \\\\frac{3}{8} = \\\\frac{4}{8}$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"18-frequently-asked-questions-on-proper-fractions\">Frequently Asked Questions on Proper Fractions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-80180edc-ba74-4894-a978-d2ab3103a03a\" 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-0-80180edc-ba74-4894-a978-d2ab3103a03a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-80180edc-ba74-4894-a978-d2ab3103a03a\"><strong>Is 1 a fraction?<\/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-0-80180edc-ba74-4894-a978-d2ab3103a03a\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">When numerator equals denominator, a fraction becomes 1. It is considered as an improper fraction.<\/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-1-80180edc-ba74-4894-a978-d2ab3103a03a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-80180edc-ba74-4894-a978-d2ab3103a03a\"><strong>What are mixed fractions?<\/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-1-80180edc-ba74-4894-a978-d2ab3103a03a\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Mixed fractions consist of a whole number and a proper fraction. Since mixed fractions are combinations of whole numbers and a fraction, mixed fractions are always greater than 1.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-80180edc-ba74-4894-a978-d2ab3103a03a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-80180edc-ba74-4894-a978-d2ab3103a03a\"><strong>Why is it preferable to simplify fractions down to their lowest possible form?<\/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-2-80180edc-ba74-4894-a978-d2ab3103a03a\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We simplify fractions because it is always easy to work or calculate when the fractions are in the simplest form. Simplified or lowest form or reduced form of a fraction makes the calculation easier.<\/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-3-80180edc-ba74-4894-a978-d2ab3103a03a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-80180edc-ba74-4894-a978-d2ab3103a03a\"><strong>What are like and unlike fractions?<\/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-3-80180edc-ba74-4894-a978-d2ab3103a03a\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Fractions with the same denominators are called \u201clike\u201d fractions. For example, $\\frac{2}{4}$ and $\\frac{3}{4}$.Fractions with different denominators are called \u201cunlike\u201d fractions. For example, $\\frac{1}{2}$ and $\\frac{2}{3}$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-80180edc-ba74-4894-a978-d2ab3103a03a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-80180edc-ba74-4894-a978-d2ab3103a03a\"><strong>Can a proper fraction be negative ?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-80180edc-ba74-4894-a978-d2ab3103a03a\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Yes, the proper fraction can be negative or positive. A negative proper fraction will have a negative sign either in numerator or denominator. For example, $\\frac{-3}{4}$.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-5-80180edc-ba74-4894-a978-d2ab3103a03a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-80180edc-ba74-4894-a978-d2ab3103a03a\"><strong>Why is an improper to proper fraction conversion not possible?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-5-80180edc-ba74-4894-a978-d2ab3103a03a\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A proper fraction is always less than 1, while an improper fraction is always greater than 1. Thus, we cannot express a proper fraction in the form of an improper fraction. Similarly, mixed fraction to proper fraction conversion is also not possible. However, we can convert an improper fraction to a mixed number and vice-versa.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-6-80180edc-ba74-4894-a978-d2ab3103a03a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-80180edc-ba74-4894-a978-d2ab3103a03a\"><strong>Is <\/strong>$\\frac{4}{3}$<strong> a proper fraction?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-6-80180edc-ba74-4894-a978-d2ab3103a03a\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{4}{3}$ is not a proper fraction. The numerator is greater than the denominator. Thus, $\\frac{4}{3}$ is an improper fraction.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is a Proper Fraction in Math? A proper fraction is a fraction whose numerator is less than the denominator. A proper fraction always lies between 0 and 1 since the denominator is larger than the numerator. Proper Fraction Examples: $\\frac{1}{2},\\; \\frac{2}{5},\\; \\frac{3}{4},\\; \\frac{5}{7}$ What does fraction mean in math? A fraction represents a part &#8230; <a title=\"Proper Fraction &#8211; Definition, Examples, Facts, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/proper-fraction\" aria-label=\"More on Proper Fraction &#8211; Definition, Examples, Facts, 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-28013","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\/28013","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=28013"}],"version-history":[{"count":10,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28013\/revisions"}],"predecessor-version":[{"id":33064,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/28013\/revisions\/33064"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=28013"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=28013"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=28013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}