{"id":26776,"date":"2023-03-24T04:39:41","date_gmt":"2023-03-24T04:39:41","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=26776"},"modified":"2023-08-16T04:15:09","modified_gmt":"2023-08-16T04:15:09","slug":"adding-fractions-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/adding-fractions","title":{"rendered":"Adding Fractions &#8211;\u00a0 Definition With Examples"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-7c633e54-e65e-47bf-9b0e-21b91e06aa10\" 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\/adding-fractions#0-what-is-%E2%80%9Cadding-fractions%E2%80%9D>What is \u201cAdding Fractions\u201d?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/adding-fractions#2-how-to-add-fractions>How To Add Fractions?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/adding-fractions#10-formulas-for-adding-fractions>Formulas For Adding Fractions<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/adding-fractions#13-solved-examples-on-adding-fractions>Solved Examples On Adding Fractions<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/adding-fractions#14-practice-problems-on-adding-fractions>Practice Problems On Adding Fractions<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/adding-fractions#15-frequently-asked-questions-on-adding-fractions>Frequently Asked Questions On Adding Fractions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-%E2%80%9Cadding-fractions%E2%80%9D\">What is \u201cAdding Fractions\u201d?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Adding fractions can be discussed using two cases:&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Adding fractions with like denominators<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Adding fractions with unlike denominators<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">A fraction represents part of a whole. A fraction has two parts: a numerator and a denominator. A numerator represents the parts taken from a whole, written at the top; the denominator represents the number of equal parts the whole is divided into, written at the bottom.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, $\\frac{5}{6},\\; \\frac{4}{5},\\; \\frac{3}{10},\\; \\frac{8}{9}$, and $\\frac{1}{3}$. In the given image, the whole cake is cut into 8 equal pieces. If you take out 3 pieces, they represent the fraction $\\frac{3}{8}$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"293\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/fraction-of-a-cake.png\" alt=\"Fraction of a cake\" class=\"wp-image-33124\" title=\"Fraction of a cake\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/fraction-of-a-cake.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/fraction-of-a-cake-300x142.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The addition of fractions is the method of finding the sum of two fractions. To add two fractions, we first make their denominators same (by LCM method or by rationalization) and then add the numerators, keeping the new denominator common.<\/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-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-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 class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/adding-10-to-a-3-digit-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\/add_sub_pv_add_10_find_sum_pt.png\" alt=\"Adding 10 to a 3-Digit 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\">Adding 10 to a 3-Digit 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\/adding-100-to-a-3-digit-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\/add_sub_pv_add_100_vertical_pt.png\" alt=\"Adding 100 to a 3-Digit 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\">Adding 100 to a 3-Digit 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><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-adding-fractions-definition\">Adding Fractions: Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Adding fractions refers to finding the sum of two or more fractions with same or different denominators.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Adding fractions with the same denominator is simple. We add the numerators and keep the denominator the same.When the denominators are different, we first have to make the denominators same.<\/p>\n\n\n\n<div id=\"recommended-worksheets-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Worksheets<\/h4><div class=\"recommended-games-container-slides\"><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-3-numbers-by-adding-doubles\" 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-3-numbers-by-adding-doubles.jpeg\" alt=\"Add 3 Numbers By Adding Doubles\">\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-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    <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-mixed-numbers-and-fractions-using-area-models.jpeg\" alt=\"Add Mixed Numbers and 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-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-mixed-numbers-and-fractions-using-models.jpeg\" alt=\"Add 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\/adding-3-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/adding-3-numbers.jpeg\" alt=\"Adding 3 Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/adding-by-making-multiple-of-10\" data-vars-ga-category=\"splashlearn_vocab\" 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maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-how-to-add-fractions\">How To Add Fractions?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let us look at the steps for adding two fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> Check whether the given fractions are like or unlike fractions. Find out whether the denominators are the same.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2: <\/strong>If the denominator is the same, find the sum of the numerators and place the sum over the common denominator. Simplify the final fraction if required.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: $\\frac{2}{5} + \\frac{1}{5} = \\frac{2 + 1}{5} = \\frac{3}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3:<\/strong> If the denominators are different, the fractions are unlike fractions. We will have to convert them into like fractions by making the denominators the same. We will learn different methods to do so later in the article.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-what-are-like-fractions-and-unlike-fractions\">What Are Like Fractions and Unlike Fractions?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The fractions that have the same denominator are called \u201clike fractions.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: $\\frac{2}{5},\\; \\frac{1}{5},\\; \\frac{3}{5},\\; \\frac{4}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The fractions that have different denominators are called \u201cunlike fractions.\u201d<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: $\\frac{2}{5},\\; \\frac{1}{4},\\; \\frac{1}{2},\\; \\frac{3}{7}$&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-adding-fractions-with-like-denominators\">Adding Fractions with Like Denominators<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Adding fractions is the easiest when the denominators of the fractions are the same. Hence, if denominators of two or more fractions are the same, we can directly add their numerators, and keep the denominator the same.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1:<\/strong> Add the fractions: $\\frac{3}{8}$ and $\\frac{1}{8}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since the denominators are like, therefore we can add the numerators directly.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3}{8} + \\frac{1}{8} = \\frac{3 + 1}{8} = \\frac{4}{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, simplify the fraction $\\frac{4}{8} = \\frac{1}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the sum of $\\frac{3}{8}$ and $\\frac{1}{8}$ is $\\frac{1}{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2:<\/strong> $\\frac{1}{5} + \\frac{2}{5} = \\frac{3}{5}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3:<\/strong> $\\frac{3}{4} + \\frac{1}{4} = \\frac{4}{4} = 1$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"494\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-like-fractions-visual.png\" alt=\"Adding like fractions: visual\" class=\"wp-image-33125\" title=\"Adding like fractions: visual\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-like-fractions-visual.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-like-fractions-visual-300x239.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-adding-fractions-with-unlike-denominators\">Adding Fractions with Unlike Denominators<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Now that we have learnt how to add like fractions, let us move on to the addition of unlike fractions. When we add two or more fractions with different denominators, then we cannot add the numerators directly.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s discuss methods we can use to convert the unlike fractions into like fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>LCM Method<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s solve $\\frac{2}{5} + \\frac{3}{7}$ using the LCM method.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, we are adding two fractions with different denominators.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Find the LCM of the denominators, 5 and 7.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">LCM of 5 and $7 = 35$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Multiply 25 by 77 so that the denominator becomes 35.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{2}{5} \\times \\frac{7}{7} = \\frac{14}{35}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, multiply $\\frac{3}{7}$ by $\\frac{5}{5}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3}{7} \\times \\frac{5}{5} = \\frac{15}{35}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The fractions $\\frac{14}{35}$ and $\\frac{15}{35}$ are like fractions.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, add the numerators and keep 35 as the denominator.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{14}{35} + \\frac{15}{35} = \\frac{29}{35}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We cannot simplify this further.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the sum of $\\frac{2}{5} + \\frac{3}{7} = \\frac{29}{35}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Cross Multiplication Method<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">This method works in all cases but when the numerators and denominators of the two unlike fractions are small numbers, the cross multiplication method is convenient to use.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: $\\frac{3}{7} + \\frac{2}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Adding simple fractions like these is much easier with the cross multiplication method.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Multiply the numerator of the first fraction with the denominator of the second fraction.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$(3 \\times 5) = 15$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Multiply the denominator of the first fraction with the numerator of the second fraction.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$(7 \\times 2) = 14$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Add these products together and write the sum as the numerator. Multiply the denominators and write the product as the denominator of the final answer.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper\">$15 + 14 = 29$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$7 \\times 5 = 35$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus,&nbsp; $\\frac{3}{7} + \\frac{2}{5} = \\frac{29}{35}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can write all the steps together as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3}{7} + \\frac{2}{5} = \\frac{(3 \\times 5) + (7 \\times 2)}{7 \\times 5} = \\frac{15 + 14}{35} = \\frac{29}{35}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Adding unlike fractions can be represented visually as follows:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"300\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-unlike-fractions-visual-model.png\" alt=\"Adding unlike fractions: visual model\" class=\"wp-image-33126\" title=\"Adding unlike fractions: visual model\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-unlike-fractions-visual-model.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/adding-unlike-fractions-visual-model-300x145.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Note that when the denominators of two numbers are co-prime (HCF $= 1$, the denominators that do not have common factors, except 1), we can use the cross multiplication method.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-adding-fractions-with-co-prime-denominators\">Adding Fractions with Co-prime Denominators<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Co-prime or relatively prime numbers are numbers that have only 1 as a common factor. How to add fractions with co-prime denominators? Let\u2019s understand with an example.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Add the fractions $\\frac{5}{7}$ and $\\frac{3}{4}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We see that the denominators 7 and 4 are co-prime because they have only one common factor which is 1. Such fractions can be added easily using the cross multiplication method!<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{5}{7} + \\frac{3}{4} = \\frac{(5 \\times 4 )&nbsp; + ( 3 \\times 7)}{7 \\times 4} = \\frac{20 + 21}{28} = \\frac{41}{28}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-addition-of-a-fraction-and-a-whole-number\">Addition of a Fraction and a Whole Number<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let us learn how to add a fraction and a whole number with the below mentioned steps:<\/p>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Write the given whole number in the form of a fraction (for example $5 = \\frac{5}{1}$).<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Make the denominators the same.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Add the fractions.<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Simplify the sum.<\/li>\n<\/ol>\n\n\n\n<p class=\"eplus-wrapper\">For example: Add \\frac{5}{2} + 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $\\frac{5}{2}$ is a fraction and 3 is a whole number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can write 3 as $\\frac{3}{1}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now after making the denominators same, we get;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{5}{2}$ and $\\frac{3}{1} \\times \\frac{2}{2} = \\frac{6}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, add $\\frac{5}{2}$ and $\\frac{6}{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{5}{2} + \\frac{6}{2} = \\frac{11}{2} = 5\\frac{1}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the sum of $\\frac{5}{2}$ and 3 is $5\\frac{1}{2}$.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-adding-mixed-fractions\">Adding Mixed Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A mixed fraction is a fraction, which consists of a whole number and a fraction. To add two mixed fractions, first we can convert them into improper fractions and then add them together.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s look at an example to understand it better.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example: Add : $3\\frac{1}{4} + 2\\frac{3}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">First, convert the given mixed fractions into improper fractions as shown below.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3\\frac{1}{4}&nbsp; = \\frac{(4 \\times 3) + 1}{4} = \\frac{13}{4}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$2\\frac{3}{4} =&nbsp; \\frac{(4 \\times 2) + 3}{4} = \\frac{11}{4}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The fractions are like fractions.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{13}{4} + \\frac{11}{4} = \\frac{13 + 11}{4} = \\frac{24}{4} = 6$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the sum of $3\\frac{1}{4}$&nbsp; and $2\\frac{3}{4}$ is 6.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-adding-fractions-with-variables\">Adding Fractions with Variables<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">If the numerators of the given fractions have a variable coefficient, we can still add the fractions using the similar steps.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 1: <\/strong>Add $\\frac{x}{5} + \\frac{2x}{5}$, where \u201cx\u201d is the variable.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong> Let us learn how to add these fractions using the following steps:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1: <\/strong>The given fractions, $\\frac{x}{5} + \\frac{2x}{5}$ are like fractions since they have the same denominator and we can see that \u201cx\u201d is common.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2:<\/strong> We can take out the common factor and rewrite it as: $\\frac{x}{5} + \\frac{2x}{5} = (\\frac{1}{5} + \\frac{2}{5})x = \\frac{3x}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: <\/strong>Therefore, $\\frac{x}{5} + \\frac{2x}{5} = \\frac{3x}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 2: <\/strong>&nbsp;Add unlike fractions: $\\frac{x}{3} + \\frac{x}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Solution: Let us learn how to add the fractions using the following steps.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that the given fractions, $\\frac{x}{3} + \\frac{x}{5}$ are unlike fractions, we will take the LCM of the denominators and convert them into like fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Next, we need to take the common variable out and rewrite it as follows:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">LCM $(3,\\; 5) = 15$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{x}{3} = \\frac{x}{3} \\times \\frac{5}{5} = \\frac{5x}{15}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{x}{5} = \\frac{x}{5} \\times \\frac{3}{3} = \\frac{3x}{15}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We got two fractions with common denominators, $\\frac{5x}{15} + \\frac{3x}{15} = \\frac{5x + 3x}{15} = \\frac{8x}{15}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the sum of $\\frac{x}{2} + \\frac{x}{3} = \\frac{8x}{15}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Note: Different variables, like \u201cx\u201d and \u201cy\u201d are treated as unlike terms.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-formulas-for-adding-fractions\">Formulas For Adding Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s summarize the formulas we discussed for adding fractions.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Adding fractions with like denominators: $\\frac{a}{c} + \\frac{b}{c} = \\frac{a + b}{c}$<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Adding fractions with unlike denominators: $\\frac{a}{b} + \\frac{c}{d} = \\frac{ad + bc}{bd}$<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Adding a fraction and a whole number: $w + \\frac{a}{b} =  \\frac{a + wb}{b}$<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-fun-fact\">Fun Fact!<\/h2>\n\n\n\n<ol class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Subtracting fractions also uses the same set of rules as addition of fractions, only the operation is different.<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"12-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">In this article, we learned how to add fractions. We learned how to add like fractions, unlike fractions, mixed fractions, fractions and whole number addition, etc. Now let us solve a few examples on adding fractions along with practice problems to better understand the concepts.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"13-solved-examples-on-adding-fractions\">Solved Examples On Adding Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. What is the sum of <\/strong>$\\frac{5}{30}$<strong> and <\/strong>$\\frac{10}{30}$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Since, the denominators of the given fractions are equal, the fractions are like fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Add the numerators.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{5}{30} + \\frac{10}{30} = \\frac{5 + 10}{30} = \\frac{15}{30}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In the end, we have to simplify the fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{15}{30} = \\frac{1}{2}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the sum of $\\frac{5}{30}$ and $\\frac{10}{30}$ is $\\frac{1}{2}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. What is the sum of <\/strong>$\\frac{7}{10}$<strong> and <\/strong>$\\frac{4}{15}$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">First, we have to check if the given fractions are like fractions or unlike fractions. Since, the denominators of the given fractions are not equal, hence, the fractions are unlike fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, let us make the denominator equal by taking the LCM of 10 and 15.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The LCM of 10 and 15 is equal to 30.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now let us make both the denominators equal.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{7}{10} \\times \\frac{3}{3} = \\frac{21}{30}$ and,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{4}{15} \\times \\frac{2}{2} = \\frac{8}{30}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, let us add both the fractions<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{21}{30} + \\frac{8}{30} = \\frac{21 + 8}{30} = \\frac{29}{30}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore the sum of $\\frac{7}{10}$ and $\\frac{4}{15}$ is equal to $\\frac{29}{30}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. What is the sum of <\/strong>$\\frac{4}{5}$<strong> and 7?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Here, $\\frac{4}{5}$ is a fraction and 7 is a whole number.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We can write 7 as $\\frac{7}{1}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, after making the denominators same, we get:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{7}{1} \\times \\frac{5}{5} = \\frac{35}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, add $\\frac{4}{5}$ and $\\frac{35}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{4}{5} + \\frac{35}{5} = \\frac{39}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, the sum of <strong>4<\/strong><strong>5<\/strong> and 7 is 395.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. What is the sum of <\/strong>$3\\frac{2}{5}$<strong> and <\/strong>$6\\frac{3}{7}$<strong> ?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">First, convert the given mixed fractions to improper fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$3\\frac{2}{5} = \\frac{17}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$6\\frac{3}{7} = \\frac{45}{7}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Make the denominators the same by taking LCM.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The LCM of 5 and 7 is 35.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{17}{5} \\times \\frac{7}{7} = \\frac{119}{35}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{45}{7} \\times \\frac{5}{5} = \\frac{225}{35}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now,&nbsp; add the numerators.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{119}{35} + \\frac{225}{35} = \\frac{119 + 225}{35} = \\frac{344}{35}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, the sum of $3\\frac{2}{5}$ and $6\\frac{3}{7}$ is $\\frac{344}{35}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>5. Add the fractions <\/strong>$\\frac{y}{5}$<strong> and <\/strong>$\\frac{3y}{5}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let us look at the steps to add the fractions:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 1: The given fractions, $\\frac{y}{5}$ + $\\frac{3y}{5}$ are like fractions since they have the same denominator and we can see that \u201cy\u201d is common.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 2: We can take out the common factor and rewrite it as: $\\frac{y}{5} + \\frac{3y}{5} = (\\frac{1}{5} + \\frac{3}{5})y = \\frac{4y}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Step 3: Therefore, the sum of $\\frac{y}{5} + \\frac{3y}{5} = \\frac{4y}{5}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"14-practice-problems-on-adding-fractions\">Practice Problems On Adding Fractions<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Adding Fractions -\u00a0 Definition With Examples<\/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\">What is the sum of $\\frac{17}{20}$ and $\\frac{3}{20}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>$\\frac{17}{20} + \\frac{3}{20} = \\frac{17 + 3}{20} = \\frac{20}{20} = 1$.<br>\r\nTherefore, the sum of $\\frac{17}{20}$ and $\\frac{3}{20}$ is 1.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What is the sum of $\\frac{12}{21}$ and $\\frac{3}{7}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1<\/div><div class=\"spq_answer_block\" data-value=\"1\">2<\/div><div class=\"spq_answer_block\" data-value=\"2\">3<\/div><div class=\"spq_answer_block\" data-value=\"3\">4<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 1<br\/>$\\frac{12}{21} \\times \\frac{1}{1} = \\frac{12}{21}$ and $\\frac{3}{7} \\times \\frac{3}{3} = \\frac{9}{21}$<br>\r\nNow let us add both the fractions.<br>\r\n$\\frac{12}{21} + \\frac{9}{21} = \\frac{12 + 9}{21} = \\frac{21}{21} = 1$<\/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\">What is the sum of $\\frac{9}{10}$ and 5?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{10}{59}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{59}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{56}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{59}{12}$<\/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: $\\frac{59}{10}$<br\/>Here, $\\frac{9}{10}$ is a fraction and 5 is a whole number.<br>\r\nWe can write 5 as $\\frac{5}{1}$.<br>\r\nNow after making the denominators same, we get;<br>\r\n$\\frac{9}{10}$ and $\\frac{5}{1} \\times \\frac{10}{10} = \\frac{50}{10}$<br>\r\nNow, add $\\frac{9}{10}$ and $\\frac{50}{10}$<br>\r\n$\\frac{9}{10} + \\frac{50}{10} = \\frac{59}{10}$<br>\r\nTherefore, the sum of $\\frac{9}{10}$ and 5 is $\\frac{59}{10}$.<\/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\">What is the sum of $4\\frac{2}{3}$ and $7\\frac{1}{3}$ ?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">11<\/div><div class=\"spq_answer_block\" data-value=\"1\">13<\/div><div class=\"spq_answer_block\" data-value=\"2\">12<\/div><div class=\"spq_answer_block\" data-value=\"3\">14<\/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: 12<br\/>First, convert the given mixed fractions to improper fractions.<br>\r\n$4\\frac{2}{3} = \\frac{14}{3}$<br>\r\n$7\\frac{1}{3} = \\frac{22}{3}$<br>\r\nWe see that the fractions are like fractions.<br>\r\n$\\frac{14}{3} + \\frac{22}{3} = \\frac{14 + 22}{3} = \\frac{36}{3}$<br>\r\nThis is equal to 12 after simplification.<\/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\">What is the result after adding the fractions $\\frac{y}{10}$ and $\\frac{4y}{5}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{2y}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{9y}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{8y}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{7y}{10}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\frac{9y}{10}$<br\/>The given fractions, $\\frac{y}{10} + \\frac{4y}{5}$ are unlike fractions since they have different denominators and we can see that \u201cy\u201d is common.\r\nHere, $\\frac{4y}{5} \\times \\frac{2}{2} = \\frac{8y}{10}$\r\n$\\frac{y}{10} + \\frac{4y}{5} = (\\frac{1}{10} + \\frac{8}{10} ) y = \\frac{9y}{10}$<\/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\": \"Adding Fractions -\u00a0 Definition With Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Adding Fractions\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the sum of $$\\\\frac{17}{20}$$ and $$\\\\frac{3}{20}$$?\",\n                    \"text\": \"What is the sum of $$\\\\frac{17}{20}$$ and $$\\\\frac{3}{20}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{17}{20} + \\\\frac{3}{20} = \\\\frac{17 + 3}{20} = \\\\frac{20}{20} = 1$$.<br>\r\nTherefore, the sum of $$\\\\frac{17}{20}$$ and $$\\\\frac{3}{20}$$ is 1.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{17}{20} + \\\\frac{3}{20} = \\\\frac{17 + 3}{20} = \\\\frac{20}{20} = 1$$.<br>\r\nTherefore, the sum of $$\\\\frac{17}{20}$$ and $$\\\\frac{3}{20}$$ is 1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{17}{20} + \\\\frac{3}{20} = \\\\frac{17 + 3}{20} = \\\\frac{20}{20} = 1$$.<br>\r\nTherefore, the sum of $$\\\\frac{17}{20}$$ and $$\\\\frac{3}{20}$$ is 1.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{17}{20} + \\\\frac{3}{20} = \\\\frac{17 + 3}{20} = \\\\frac{20}{20} = 1$$.<br>\r\nTherefore, the sum of $$\\\\frac{17}{20}$$ and $$\\\\frac{3}{20}$$ is 1.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{17}{20} + \\\\frac{3}{20} = \\\\frac{17 + 3}{20} = \\\\frac{20}{20} = 1$$.<br>\r\nTherefore, the sum of $$\\\\frac{17}{20}$$ and $$\\\\frac{3}{20}$$ is 1.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{17}{20} + \\\\frac{3}{20} = \\\\frac{17 + 3}{20} = \\\\frac{20}{20} = 1$$.<br>\r\nTherefore, the sum of $$\\\\frac{17}{20}$$ and $$\\\\frac{3}{20}$$ is 1.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the sum of $$\\\\frac{12}{21}$$ and $$\\\\frac{3}{7}$$?\",\n                    \"text\": \"What is the sum of $$\\\\frac{12}{21}$$ and $$\\\\frac{3}{7}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{12}{21} \\\\times \\\\frac{1}{1} = \\\\frac{12}{21}$$ and $$\\\\frac{3}{7} \\\\times \\\\frac{3}{3} = \\\\frac{9}{21}$$<br>\r\nNow let us add both the fractions.<br>\r\n$$\\\\frac{12}{21} + \\\\frac{9}{21} = \\\\frac{12 + 9}{21} = \\\\frac{21}{21} = 1$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{12}{21} \\\\times \\\\frac{1}{1} = \\\\frac{12}{21}$$ and $$\\\\frac{3}{7} \\\\times \\\\frac{3}{3} = \\\\frac{9}{21}$$<br>\r\nNow let us add both the fractions.<br>\r\n$$\\\\frac{12}{21} + \\\\frac{9}{21} = \\\\frac{12 + 9}{21} = \\\\frac{21}{21} = 1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{12}{21} \\\\times \\\\frac{1}{1} = \\\\frac{12}{21}$$ and $$\\\\frac{3}{7} \\\\times \\\\frac{3}{3} = \\\\frac{9}{21}$$<br>\r\nNow let us add both the fractions.<br>\r\n$$\\\\frac{12}{21} + \\\\frac{9}{21} = \\\\frac{12 + 9}{21} = \\\\frac{21}{21} = 1$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{12}{21} \\\\times \\\\frac{1}{1} = \\\\frac{12}{21}$$ and $$\\\\frac{3}{7} \\\\times \\\\frac{3}{3} = \\\\frac{9}{21}$$<br>\r\nNow let us add both the fractions.<br>\r\n$$\\\\frac{12}{21} + \\\\frac{9}{21} = \\\\frac{12 + 9}{21} = \\\\frac{21}{21} = 1$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{12}{21} \\\\times \\\\frac{1}{1} = \\\\frac{12}{21}$$ and $$\\\\frac{3}{7} \\\\times \\\\frac{3}{3} = \\\\frac{9}{21}$$<br>\r\nNow let us add both the fractions.<br>\r\n$$\\\\frac{12}{21} + \\\\frac{9}{21} = \\\\frac{12 + 9}{21} = \\\\frac{21}{21} = 1$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{12}{21} \\\\times \\\\frac{1}{1} = \\\\frac{12}{21}$$ and $$\\\\frac{3}{7} \\\\times \\\\frac{3}{3} = \\\\frac{9}{21}$$<br>\r\nNow let us add both the fractions.<br>\r\n$$\\\\frac{12}{21} + \\\\frac{9}{21} = \\\\frac{12 + 9}{21} = \\\\frac{21}{21} = 1$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the sum of $$\\\\frac{9}{10}$$ and 5?\",\n                    \"text\": \"What is the sum of $$\\\\frac{9}{10}$$ and 5?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Here, $$\\\\frac{9}{10}$$ is a fraction and 5 is a whole number.<br>\r\nWe can write 5 as $$\\\\frac{5}{1}$$.<br>\r\nNow after making the denominators same, we get;<br>\r\n$$\\\\frac{9}{10}$$ and $$\\\\frac{5}{1} \\\\times \\\\frac{10}{10} = \\\\frac{50}{10}$$<br>\r\nNow, add $$\\\\frac{9}{10}$$ and $$\\\\frac{50}{10}$$<br>\r\n$$\\\\frac{9}{10} + \\\\frac{50}{10} = \\\\frac{59}{10}$$<br>\r\nTherefore, the sum of $$\\\\frac{9}{10}$$ and 5 is $$\\\\frac{59}{10}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{10}{59}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, $$\\\\frac{9}{10}$$ is a fraction and 5 is a whole number.<br>\r\nWe can write 5 as $$\\\\frac{5}{1}$$.<br>\r\nNow after making the denominators same, we get;<br>\r\n$$\\\\frac{9}{10}$$ and $$\\\\frac{5}{1} \\\\times \\\\frac{10}{10} = \\\\frac{50}{10}$$<br>\r\nNow, add $$\\\\frac{9}{10}$$ and $$\\\\frac{50}{10}$$<br>\r\n$$\\\\frac{9}{10} + \\\\frac{50}{10} = \\\\frac{59}{10}$$<br>\r\nTherefore, the sum of $$\\\\frac{9}{10}$$ and 5 is $$\\\\frac{59}{10}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{56}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, $$\\\\frac{9}{10}$$ is a fraction and 5 is a whole number.<br>\r\nWe can write 5 as $$\\\\frac{5}{1}$$.<br>\r\nNow after making the denominators same, we get;<br>\r\n$$\\\\frac{9}{10}$$ and $$\\\\frac{5}{1} \\\\times \\\\frac{10}{10} = \\\\frac{50}{10}$$<br>\r\nNow, add $$\\\\frac{9}{10}$$ and $$\\\\frac{50}{10}$$<br>\r\n$$\\\\frac{9}{10} + \\\\frac{50}{10} = \\\\frac{59}{10}$$<br>\r\nTherefore, the sum of $$\\\\frac{9}{10}$$ and 5 is $$\\\\frac{59}{10}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{59}{12}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Here, $$\\\\frac{9}{10}$$ is a fraction and 5 is a whole number.<br>\r\nWe can write 5 as $$\\\\frac{5}{1}$$.<br>\r\nNow after making the denominators same, we get;<br>\r\n$$\\\\frac{9}{10}$$ and $$\\\\frac{5}{1} \\\\times \\\\frac{10}{10} = \\\\frac{50}{10}$$<br>\r\nNow, add $$\\\\frac{9}{10}$$ and $$\\\\frac{50}{10}$$<br>\r\n$$\\\\frac{9}{10} + \\\\frac{50}{10} = \\\\frac{59}{10}$$<br>\r\nTherefore, the sum of $$\\\\frac{9}{10}$$ and 5 is $$\\\\frac{59}{10}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{59}{10}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Here, $$\\\\frac{9}{10}$$ is a fraction and 5 is a whole number.<br>\r\nWe can write 5 as $$\\\\frac{5}{1}$$.<br>\r\nNow after making the denominators same, we get;<br>\r\n$$\\\\frac{9}{10}$$ and $$\\\\frac{5}{1} \\\\times \\\\frac{10}{10} = \\\\frac{50}{10}$$<br>\r\nNow, add $$\\\\frac{9}{10}$$ and $$\\\\frac{50}{10}$$<br>\r\n$$\\\\frac{9}{10} + \\\\frac{50}{10} = \\\\frac{59}{10}$$<br>\r\nTherefore, the sum of $$\\\\frac{9}{10}$$ and 5 is $$\\\\frac{59}{10}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Here, $$\\\\frac{9}{10}$$ is a fraction and 5 is a whole number.<br>\r\nWe can write 5 as $$\\\\frac{5}{1}$$.<br>\r\nNow after making the denominators same, we get;<br>\r\n$$\\\\frac{9}{10}$$ and $$\\\\frac{5}{1} \\\\times \\\\frac{10}{10} = \\\\frac{50}{10}$$<br>\r\nNow, add $$\\\\frac{9}{10}$$ and $$\\\\frac{50}{10}$$<br>\r\n$$\\\\frac{9}{10} + \\\\frac{50}{10} = \\\\frac{59}{10}$$<br>\r\nTherefore, the sum of $$\\\\frac{9}{10}$$ and 5 is $$\\\\frac{59}{10}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the sum of $$4\\\\frac{2}{3}$$ and $$7\\\\frac{1}{3}$$ ?\",\n                    \"text\": \"What is the sum of $$4\\\\frac{2}{3}$$ and $$7\\\\frac{1}{3}$$ ?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"First, convert the given mixed fractions to improper fractions.<br>\r\n$$4\\\\frac{2}{3} = \\\\frac{14}{3}$$<br>\r\n$$7\\\\frac{1}{3} = \\\\frac{22}{3}$$<br>\r\nWe see that the fractions are like fractions.<br>\r\n$$\\\\frac{14}{3} + \\\\frac{22}{3} = \\\\frac{14 + 22}{3} = \\\\frac{36}{3}$$<br>\r\nThis is equal to 12 after simplification.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"11\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"First, convert the given mixed fractions to improper fractions.<br>\r\n$$4\\\\frac{2}{3} = \\\\frac{14}{3}$$<br>\r\n$$7\\\\frac{1}{3} = \\\\frac{22}{3}$$<br>\r\nWe see that the fractions are like fractions.<br>\r\n$$\\\\frac{14}{3} + \\\\frac{22}{3} = \\\\frac{14 + 22}{3} = \\\\frac{36}{3}$$<br>\r\nThis is equal to 12 after simplification.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"13\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"First, convert the given mixed fractions to improper fractions.<br>\r\n$$4\\\\frac{2}{3} = \\\\frac{14}{3}$$<br>\r\n$$7\\\\frac{1}{3} = \\\\frac{22}{3}$$<br>\r\nWe see that the fractions are like fractions.<br>\r\n$$\\\\frac{14}{3} + \\\\frac{22}{3} = \\\\frac{14 + 22}{3} = \\\\frac{36}{3}$$<br>\r\nThis is equal to 12 after simplification.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"First, convert the given mixed fractions to improper fractions.<br>\r\n$$4\\\\frac{2}{3} = \\\\frac{14}{3}$$<br>\r\n$$7\\\\frac{1}{3} = \\\\frac{22}{3}$$<br>\r\nWe see that the fractions are like fractions.<br>\r\n$$\\\\frac{14}{3} + \\\\frac{22}{3} = \\\\frac{14 + 22}{3} = \\\\frac{36}{3}$$<br>\r\nThis is equal to 12 after simplification.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"12\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"First, convert the given mixed fractions to improper fractions.<br>\r\n$$4\\\\frac{2}{3} = \\\\frac{14}{3}$$<br>\r\n$$7\\\\frac{1}{3} = \\\\frac{22}{3}$$<br>\r\nWe see that the fractions are like fractions.<br>\r\n$$\\\\frac{14}{3} + \\\\frac{22}{3} = \\\\frac{14 + 22}{3} = \\\\frac{36}{3}$$<br>\r\nThis is equal to 12 after simplification.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"First, convert the given mixed fractions to improper fractions.<br>\r\n$$4\\\\frac{2}{3} = \\\\frac{14}{3}$$<br>\r\n$$7\\\\frac{1}{3} = \\\\frac{22}{3}$$<br>\r\nWe see that the fractions are like fractions.<br>\r\n$$\\\\frac{14}{3} + \\\\frac{22}{3} = \\\\frac{14 + 22}{3} = \\\\frac{36}{3}$$<br>\r\nThis is equal to 12 after simplification.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What is the result after adding the fractions $$\\\\frac{y}{10}$$ and $$\\\\frac{4y}{5}$$?\",\n                    \"text\": \"What is the result after adding the fractions $$\\\\frac{y}{10}$$ and $$\\\\frac{4y}{5}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The given fractions, $$\\\\frac{y}{10} + \\\\frac{4y}{5}$$ are unlike fractions since they have different denominators and we can see that \u201cy\u201d is common.\r\nHere, $$\\\\frac{4y}{5} \\\\times \\\\frac{2}{2} = \\\\frac{8y}{10}$$\r\n$$\\\\frac{y}{10} + \\\\frac{4y}{5} = (\\\\frac{1}{10} + \\\\frac{8}{10} ) y = \\\\frac{9y}{10}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2y}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The given fractions, $$\\\\frac{y}{10} + \\\\frac{4y}{5}$$ are unlike fractions since they have different denominators and we can see that \u201cy\u201d is common.\r\nHere, $$\\\\frac{4y}{5} \\\\times \\\\frac{2}{2} = \\\\frac{8y}{10}$$\r\n$$\\\\frac{y}{10} + \\\\frac{4y}{5} = (\\\\frac{1}{10} + \\\\frac{8}{10} ) y = \\\\frac{9y}{10}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{8y}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The given fractions, $$\\\\frac{y}{10} + \\\\frac{4y}{5}$$ are unlike fractions since they have different denominators and we can see that \u201cy\u201d is common.\r\nHere, $$\\\\frac{4y}{5} \\\\times \\\\frac{2}{2} = \\\\frac{8y}{10}$$\r\n$$\\\\frac{y}{10} + \\\\frac{4y}{5} = (\\\\frac{1}{10} + \\\\frac{8}{10} ) y = \\\\frac{9y}{10}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{7y}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The given fractions, $$\\\\frac{y}{10} + \\\\frac{4y}{5}$$ are unlike fractions since they have different denominators and we can see that \u201cy\u201d is common.\r\nHere, $$\\\\frac{4y}{5} \\\\times \\\\frac{2}{2} = \\\\frac{8y}{10}$$\r\n$$\\\\frac{y}{10} + \\\\frac{4y}{5} = (\\\\frac{1}{10} + \\\\frac{8}{10} ) y = \\\\frac{9y}{10}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{9y}{10}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The given fractions, $$\\\\frac{y}{10} + \\\\frac{4y}{5}$$ are unlike fractions since they have different denominators and we can see that \u201cy\u201d is common.\r\nHere, $$\\\\frac{4y}{5} \\\\times \\\\frac{2}{2} = \\\\frac{8y}{10}$$\r\n$$\\\\frac{y}{10} + \\\\frac{4y}{5} = (\\\\frac{1}{10} + \\\\frac{8}{10} ) y = \\\\frac{9y}{10}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The given fractions, $$\\\\frac{y}{10} + \\\\frac{4y}{5}$$ are unlike fractions since they have different denominators and we can see that \u201cy\u201d is common.\r\nHere, $$\\\\frac{4y}{5} \\\\times \\\\frac{2}{2} = \\\\frac{8y}{10}$$\r\n$$\\\\frac{y}{10} + \\\\frac{4y}{5} = (\\\\frac{1}{10} + \\\\frac{8}{10} ) y = \\\\frac{9y}{10}$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"15-frequently-asked-questions-on-adding-fractions\">Frequently Asked Questions On Adding Fractions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-24c989be-aece-413b-ade6-1bcfc09b8e4a\" 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-0-24c989be-aece-413b-ade6-1bcfc09b8e4a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-24c989be-aece-413b-ade6-1bcfc09b8e4a\"><strong>What are equivalent 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-0-24c989be-aece-413b-ade6-1bcfc09b8e4a\">\n\n<p class=\"eplus-wrapper\">Fractions that have different numerators and denominators but still represent the same value are called equivalent fractions. Example: $\\frac{1}{2},\\; \\frac{2}{4}$<\/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-1-24c989be-aece-413b-ade6-1bcfc09b8e4a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-24c989be-aece-413b-ade6-1bcfc09b8e4a\"><strong>What is 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-1-24c989be-aece-413b-ade6-1bcfc09b8e4a\">\n\n<p class=\"eplus-wrapper\">Proper fractions are fractions in which the numerator is less than the denominator. The decimal value of a proper fraction is always less 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-2-24c989be-aece-413b-ade6-1bcfc09b8e4a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-24c989be-aece-413b-ade6-1bcfc09b8e4a\"><strong>How do we multiply 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-2-24c989be-aece-413b-ade6-1bcfc09b8e4a\">\n\n<p class=\"eplus-wrapper\">To multiply any two fractions, we first multiply the numerators, then multiply the denominators. Finally, we simplify the resultant fraction. For example, $\\frac{3}{5} \\times \\frac{7}{9} = \\frac{21}{45} = \\frac{7}{15}$<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What is \u201cAdding Fractions\u201d? Adding fractions can be discussed using two cases:&nbsp; A fraction represents part of a whole. A fraction has two parts: a numerator and a denominator. A numerator represents the parts taken from a whole, written at the top; the denominator represents the number of equal parts the whole is divided into, &#8230; <a title=\"Adding Fractions &#8211;\u00a0 Definition With Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/adding-fractions\" aria-label=\"More on Adding Fractions &#8211;\u00a0 Definition With Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-26776","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\/26776","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=26776"}],"version-history":[{"count":12,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26776\/revisions"}],"predecessor-version":[{"id":33127,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/26776\/revisions\/33127"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=26776"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=26776"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=26776"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}