{"id":1322,"date":"2022-04-18T12:25:56","date_gmt":"2022-04-18T12:25:56","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1322"},"modified":"2024-02-18T15:32:17","modified_gmt":"2024-02-18T15:32:17","slug":"decomposing-fractions-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/decomposing-fractions","title":{"rendered":"Decompose Fractions"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-da7cd8c6-6a76-4bcc-a756-9e89c1ae9e43\" 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\/fractions\/decomposing-fractions#0-decompose-fractions-introduction>Decompose Fractions &#8211; Introduction<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/decomposing-fractions#1-what-is-decomposing-fractions>What Is Decomposing Fractions?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/decomposing-fractions#2-how-to-decompose-fractions>How to Decompose Fractions?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/decomposing-fractions#5-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/decomposing-fractions#6-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/decomposing-fractions#7-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-decompose-fractions-introduction\">Decompose Fractions &#8211; Introduction<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">\u201cDecompose\u201d means to separate or break something apart. We can decompose numbers as well as geometric shapes. Decomposing numbers involves breaking a larger number into smaller numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, consider breaking the number 10 into parts. We can decompose ten into five, three, and two. Alternatively, we can compose the number ten by putting together five, four, and one. There is often more than one way to decompose a number.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We all know that fractions are part of a whole. But just like whole numbers, we can compose and decompose fractions. Does that sound interesting? Let\u2019s dive in and learn more about decomposing fractions.&nbsp;<\/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\/are-the-fractions-equivalent\" 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_identify_equi_visual_model_pt.png\" alt=\"Are the Fractions Equivalent 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\">Are the Fractions Equivalent 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\/area-word-problems-on-product-of-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_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of 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\">Area Word Problems on Product of 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                    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-what-is-decomposing-fractions\">What Is Decomposing Fractions?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A fraction represents a part of a whole.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">To decompose a fraction means breaking it into smaller parts.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Combining or adding all the smaller or decomposed parts must result in the initial fraction.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For instance, the fraction $\\frac{3}{4}$ means we have three out of four equal parts. We can split this fraction into even smaller parts!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"465\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decomposing-fractions-to-unit-fractions.png\" alt=\"Decomposing fractions to unit fractions\" class=\"wp-image-40052\" title=\"Decomposing fractions to unit fractions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decomposing-fractions-to-unit-fractions.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decomposing-fractions-to-unit-fractions-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We can decompose the fraction $\\frac{3}{4}$&nbsp; into three one-fourths. When we add these parts together, we get the fraction $\\frac{3}{4}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">What happens when we decompose a fraction into a sum of smaller fractions? We break the numerator into parts. Unlike partitioning, where we usually consider the fractional concept of dividing shapes into equal parts, decomposing does not need to be of equivalent size.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s look at other decompositions of $\\frac{3}{4}$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"465\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decomposing-fractions.png\" alt=\"Decomposing fractions\" class=\"wp-image-40053\" title=\"Decomposing fractions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decomposing-fractions.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decomposing-fractions-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{3}{4} = \\frac{1}{4} + \\frac{2}{4}$<\/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-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-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\" 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id=\"2-how-to-decompose-fractions\">How to Decompose Fractions?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Decomposition of fractions can be done in two ways: unit fractions or non-unit fractions.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>How to Decompose Fractions into Unit Fractions?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">A fraction with one as a numerator is called a unit fraction. When a whole is divided into equal parts, the unit fraction represents one part of the whole\u2014for<strong> example<\/strong>, $\\frac{1}{2}, \\frac{1}{3}, \\frac{1}{4}, \\frac{1}{5}$, etc.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The most basic way to decompose a fraction is to break it into unit fractions.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example,&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"438\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/visual-representation-of-breaking-a-fraction-into-unit-fractions.png\" alt=\"Visual representation of breaking a fraction into unit fractions\" class=\"wp-image-40054\" title=\"Visual representation of breaking a fraction into unit fractions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/visual-representation-of-breaking-a-fraction-into-unit-fractions.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/visual-representation-of-breaking-a-fraction-into-unit-fractions-300x212.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We can see that $\\frac{5}{8}$ is the same as the five times the unit fraction $\\frac{1}{8}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{5}{8} = \\frac{1}{8} + \\frac{1}{8} + \\frac{1}{8} + \\frac{1}{8} + \\frac{1}{8}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">When you break a fraction into unit fractions, you split it into equal parts.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s take another example. Consider the fraction $\\frac{9}{5}$. We can divide the fraction as shown below.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"326\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/nine-one-fifths.png\" alt=\"Nine one-fifths\" class=\"wp-image-40055\" title=\"Nine one-fifths\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/nine-one-fifths.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/nine-one-fifths-300x158.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{9}{5} = \\frac{1}{5} + \\frac{1}{5} + \\frac{1}{5} + \\frac{1}{5} + \\frac{1}{5} + \\frac{1}{5} + \\frac{1}{5} + \\frac{1}{5} + \\frac{1}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>How to Decompose Fractions into Non-Unit Fractions?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">In this method, we decompose a fraction into different smaller like fractions. We can express a fraction as the sum of smaller fractions, which are not all unit fractions. Adding up all the decomposed fractions must result in the initial fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, in the figure below, $\\frac{7}{9}$&nbsp; of the circle is divided into four unequal parts.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"489\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decompose-like-fractions.png\" alt=\"Decompose like fractions\" class=\"wp-image-40056\" title=\"Decompose like fractions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decompose-like-fractions.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decompose-like-fractions-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{7}{9} = \\frac{3}{9} + \\frac{1}{9} + \\frac{1}{9} + \\frac{2}{9}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s take another example: How do we decompose $\\frac{12}{5}$?&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"278\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/break-an-improper-fraction.png\" alt=\"Break an improper fraction\" class=\"wp-image-40057\" title=\"Break an improper fraction\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/break-an-improper-fraction.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/break-an-improper-fraction-300x135.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We can break it down into $\\frac{5}{5} + \\frac{5}{5} + \\frac{2}{5} = 1 + 1 + \\frac{2}{5} = 2\\frac{2}{5}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">This gives us the mixed number form of the fraction $\\frac{12}{5}$.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-how-to-decompose-mixed-numbers\">How to Decompose Mixed Numbers?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A mixed fraction is a combination of a whole number and a proper fraction, a number between two consecutive whole numbers.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, $1\\frac{3}{4}$ is a mixed number between the whole numbers 1 and 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, let\u2019s understand how to decompose a mixed number.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"342\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decompose-mixed-numbers.png\" alt=\"Decompose mixed numbers\" class=\"wp-image-40058\" title=\"Decompose mixed numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decompose-mixed-numbers.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/02\/decompose-mixed-numbers-300x165.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Practicing how to decompose fractions can help children perform various operations with fractions. It will improve their simplifying skills and teach them different techniques to master concepts and work on fractions.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Decompose the fraction <\/strong>$\\frac{4}{7}$<strong> into unit fractions.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: To decompose 47 into unit fractions, we can split the numerator four and express the fraction as the sum of 4 one-sevenths.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{4}{7} = \\frac{1}{7} + \\frac{1}{7} + \\frac{1}{7} + \\frac{1}{7}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2.<\/strong> <strong>Write the given fraction as the sum of two different fractions: <\/strong>$\\frac{3}{10}$<strong>.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: To express the fraction as the sum of two different fractions, we can decompose the numerator three into 1 and 2.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $\\frac{3}{10} = \\frac{1}{10} + \\frac{2}{10}$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3.<\/strong> <strong>Write the fraction <\/strong>$\\frac{6}{11}$<strong> as the sum of three equal fractions.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: To express the given fraction as the sum of three equal fractions, we can split the numerator six into three equal parts. $6 = 2 + 2 + 2$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $\\frac{6}{11} = \\frac{2}{11} + \\frac{2}{11} + \\frac{2}{11}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>4. Decompose the improper fraction <\/strong>$\\frac{7}{4}$<strong> and write the mixed number form of the fraction.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: To break down the improper fraction, we can split the numerator as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{7}{4} = \\frac{4}{4} + \\frac{3}{4} = 1 + \\frac{3}{4}= 1\\frac{3}{4}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Decompose Fractions<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Which of the following sum equals $\\frac{1}{2}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{1}{4}+\\frac{1}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{2}+\\frac{1}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{4}+\\frac{1}{2}$<\/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: $\\frac{1}{4}+\\frac{1}{4}$<br\/>$\\frac{1}{4} + \\frac{1}{4} = \\frac{2}{4} = \\frac{1}{2}$<\/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\">Select a fraction to complete the equation $\\frac{2}{8} + \\frac{3}{8} + \\frac{1}{8} + \\underline{} = \\frac{10}{8}$<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{4}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{3}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{2}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{8}$<\/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\/>Since $2 + 3 + 1 + 4 = 10, \\frac{2}{8} + \\frac{3}{8} + \\frac{1}{8} + \\frac{4}{8} = \\frac{10}{8}$<\/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 expression matches the model shown below?<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-3-4.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{4}{12} + \\frac{1}{12} + \\frac{6}{12}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{1}{10} + \\frac{1}{10} + \\frac{5}{10}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{4}{12} + \\frac{11}{2} + \\frac{5}{12}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{5}{10} + \\frac{5}{10}$<\/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: $\\frac{4}{12} + \\frac{11}{2} + \\frac{5}{12}$<br\/>The whole is divided into 12 equal parts. Blue parts represent $\\frac{4}{12}$ of the whole; the yellow part represents $\\frac{1}{12}$, and the pink parts represent $\\frac{5}{12}$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Which of the following is equivalent to $\\frac{1}{6} + \\frac{2}{6} + \\frac{2}{6}$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">A<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-a.png\" alt=\"A\"><\/div><div class=\"spq_answer_block\" data-value=\"1\">B<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-answer-b.png\" alt=\"B\"><\/div><div class=\"spq_answer_block\" data-value=\"2\">C<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-c.png\" alt=\"C\"><\/div><div class=\"spq_answer_block\" data-value=\"3\">D<img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-d.png\" alt=\"D\"><\/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: B<br\/>$\\frac{1}{6} + \\frac{2}{6} + \\frac{2}{6} = \\frac{5}{6}$<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-answer-b.png\"><\/div><\/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\">Select an expression that is more than $\\frac{8}{11}$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{2}{11} + \\frac{2}{11} + \\frac{2}{11}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{2}{11} + \\frac{3}{11} + \\frac{5}{11}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{1}{11} + \\frac{3}{11} + \\frac{3}{11}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{1}{11} + \\frac{1}{11} + \\frac{1}{11}$<\/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: $\\frac{2}{11} + \\frac{3}{11} + \\frac{5}{11}$<br\/>The sum of $\\frac{2}{11} + \\frac{3}{11} + \\frac{5}{11}$ is $\\frac{10}{11}$, greater than $\\frac{8}{11}$ .<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        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$$\\\\frac{1}{2}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{1}{4} + \\\\frac{1}{4} = \\\\frac{2}{4} = \\\\frac{1}{2}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{2}+\\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1}{4} + \\\\frac{1}{4} = \\\\frac{2}{4} = \\\\frac{1}{2}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{4}+\\\\frac{1}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1}{4} + \\\\frac{1}{4} = \\\\frac{2}{4} = \\\\frac{1}{2}$$\"\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\": \"$$\\\\frac{1}{4} + \\\\frac{1}{4} = \\\\frac{2}{4} = \\\\frac{1}{2}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{1}{4}+\\\\frac{1}{4}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{1}{4} + \\\\frac{1}{4} = \\\\frac{2}{4} = \\\\frac{1}{2}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{1}{4} + \\\\frac{1}{4} = \\\\frac{2}{4} = \\\\frac{1}{2}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Select a fraction to complete the equation $$\\\\frac{2}{8} + \\\\frac{3}{8} + \\\\frac{1}{8} + \\\\underline{} = \\\\frac{10}{8}$$\",\n                    \"text\": \"Select a fraction to complete the equation $$\\\\frac{2}{8} + \\\\frac{3}{8} + \\\\frac{1}{8} + \\\\underline{} = \\\\frac{10}{8}$$\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Since $$2 + 3 + 1 + 4 = 10, \\\\frac{2}{8} + \\\\frac{3}{8} + \\\\frac{1}{8} + \\\\frac{4}{8} = \\\\frac{10}{8}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{3}{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since $$2 + 3 + 1 + 4 = 10, \\\\frac{2}{8} + \\\\frac{3}{8} + \\\\frac{1}{8} + \\\\frac{4}{8} = \\\\frac{10}{8}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since $$2 + 3 + 1 + 4 = 10, \\\\frac{2}{8} + \\\\frac{3}{8} + \\\\frac{1}{8} + \\\\frac{4}{8} = \\\\frac{10}{8}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{8}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since $$2 + 3 + 1 + 4 = 10, \\\\frac{2}{8} + \\\\frac{3}{8} + \\\\frac{1}{8} + \\\\frac{4}{8} = \\\\frac{10}{8}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{4}{8}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Since $$2 + 3 + 1 + 4 = 10, \\\\frac{2}{8} + \\\\frac{3}{8} + \\\\frac{1}{8} + \\\\frac{4}{8} = \\\\frac{10}{8}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Since $$2 + 3 + 1 + 4 = 10, \\\\frac{2}{8} + \\\\frac{3}{8} + \\\\frac{1}{8} + \\\\frac{4}{8} = \\\\frac{10}{8}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which expression matches the model shown below?\",\n                    \"text\": \"Which expression matches the model shown below? <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-3-4.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The whole is divided into 12 equal parts. Blue parts represent $$\\\\frac{4}{12}$$ of the whole; the yellow part represents $$\\\\frac{1}{12}$$, and the pink parts represent $$\\\\frac{5}{12}$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{4}{12} + \\\\frac{1}{12} + \\\\frac{6}{12}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The whole is divided into 12 equal parts. Blue parts represent $$\\\\frac{4}{12}$$ of the whole; the yellow part represents $$\\\\frac{1}{12}$$, and the pink parts represent $$\\\\frac{5}{12}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{10} + \\\\frac{1}{10} + \\\\frac{5}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The whole is divided into 12 equal parts. Blue parts represent $$\\\\frac{4}{12}$$ of the whole; the yellow part represents $$\\\\frac{1}{12}$$, and the pink parts represent $$\\\\frac{5}{12}$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{5}{10} + \\\\frac{5}{10}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The whole is divided into 12 equal parts. Blue parts represent $$\\\\frac{4}{12}$$ of the whole; the yellow part represents $$\\\\frac{1}{12}$$, and the pink parts represent $$\\\\frac{5}{12}$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{4}{12} + \\\\frac{11}{2} + \\\\frac{5}{12}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The whole is divided into 12 equal parts. Blue parts represent $$\\\\frac{4}{12}$$ of the whole; the yellow part represents $$\\\\frac{1}{12}$$, and the pink parts represent $$\\\\frac{5}{12}$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The whole is divided into 12 equal parts. Blue parts represent $$\\\\frac{4}{12}$$ of the whole; the yellow part represents $$\\\\frac{1}{12}$$, and the pink parts represent $$\\\\frac{5}{12}$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is equivalent to $$\\\\frac{1}{6} + \\\\frac{2}{6} + \\\\frac{2}{6}$$?\",\n                    \"text\": \"Which of the following is equivalent to $$\\\\frac{1}{6} + \\\\frac{2}{6} + \\\\frac{2}{6}$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{1}{6} + \\\\frac{2}{6} + \\\\frac{2}{6} = \\\\frac{5}{6}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"A <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-a.png\\\"\/>\",\n                                \n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1}{6} + \\\\frac{2}{6} + \\\\frac{2}{6} = \\\\frac{5}{6}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"C <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-c.png\\\"\/>\",\n                                \n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1}{6} + \\\\frac{2}{6} + \\\\frac{2}{6} = \\\\frac{5}{6}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"D <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-d.png\\\"\/>\",\n                                \n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{1}{6} + \\\\frac{2}{6} + \\\\frac{2}{6} = \\\\frac{5}{6}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"B\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{1}{6} + \\\\frac{2}{6} + \\\\frac{2}{6} = \\\\frac{5}{6}$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-answer-b.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{1}{6} + \\\\frac{2}{6} + \\\\frac{2}{6} = \\\\frac{5}{6}$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-4-answer-b.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Select an expression that is more than $$\\\\frac{8}{11}$$.\",\n                    \"text\": \"Select an expression that is more than $$\\\\frac{8}{11}$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The sum of $$\\\\frac{2}{11} + \\\\frac{3}{11} + \\\\frac{5}{11}$$ is $$\\\\frac{10}{11}$$, greater than $$\\\\frac{8}{11}$$ .\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{2}{11} + \\\\frac{2}{11} + \\\\frac{2}{11}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of $$\\\\frac{2}{11} + \\\\frac{3}{11} + \\\\frac{5}{11}$$ is $$\\\\frac{10}{11}$$, greater than $$\\\\frac{8}{11}$$ .\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{11} + \\\\frac{3}{11} + \\\\frac{3}{11}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of $$\\\\frac{2}{11} + \\\\frac{3}{11} + \\\\frac{5}{11}$$ is $$\\\\frac{10}{11}$$, greater than $$\\\\frac{8}{11}$$ .\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{1}{11} + \\\\frac{1}{11} + \\\\frac{1}{11}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The sum of $$\\\\frac{2}{11} + \\\\frac{3}{11} + \\\\frac{5}{11}$$ is $$\\\\frac{10}{11}$$, greater than $$\\\\frac{8}{11}$$ .\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{2}{11} + \\\\frac{3}{11} + \\\\frac{5}{11}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The sum of $$\\\\frac{2}{11} + \\\\frac{3}{11} + \\\\frac{5}{11}$$ is $$\\\\frac{10}{11}$$, greater than $$\\\\frac{8}{11}$$ .\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The sum of $$\\\\frac{2}{11} + \\\\frac{3}{11} + \\\\frac{5}{11}$$ is $$\\\\frac{10}{11}$$, greater than $$\\\\frac{8}{11}$$ .\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-8474ab94-36d6-4cc7-b907-70070f874bd9\" 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-0-8474ab94-36d6-4cc7-b907-70070f874bd9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8474ab94-36d6-4cc7-b907-70070f874bd9\"><strong>Can we decompose fractions using operations other than addition?<\/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-0-8474ab94-36d6-4cc7-b907-70070f874bd9\">\n\n<p>No, when we decompose a fraction, we write it as the sum of smaller fractions. To decompose a fraction means breaking it into smaller parts. Combining all the decomposed parts must result in the initial fraction.&nbsp;<\/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-1-8474ab94-36d6-4cc7-b907-70070f874bd9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8474ab94-36d6-4cc7-b907-70070f874bd9\"><strong>Can we decompose a unit 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-1-8474ab94-36d6-4cc7-b907-70070f874bd9\">\n\n<p class=\"eplus-wrapper\">To decompose a unit fraction, we can decompose the fraction equivalent to a unit fraction. For example, $\\frac{1}{3}$ is a unit fraction. $\\frac{1}{3}$ is equal to $\\frac{2}{6}$, so we can write it as $\\frac{2}{6}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{2}{6} = \\frac{1}{6} + \\frac{1}{6}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Therefore, $\\frac{1}{3} = \\frac{1}{6} + \\frac{1}{6}$<\/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-2-8474ab94-36d6-4cc7-b907-70070f874bd9\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8474ab94-36d6-4cc7-b907-70070f874bd9\"><strong>Can we decompose fractions into their 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-2-8474ab94-36d6-4cc7-b907-70070f874bd9\">\n\n<p class=\"eplus-wrapper\">Equivalent fractions have different numerators and denominators but are equal to the same value. Decomposing a fraction means writing it as the sum of smaller fractions. Since equivalent fractions are of equal value, we cannot decompose a fraction into an equivalent fraction. For example, $\\frac{3}{6}$ cannot be decomposed into $\\frac{1}{2}$ because $\\frac{3}{6} =&nbsp;\\frac{1}{2}$.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Decompose Fractions &#8211; Introduction \u201cDecompose\u201d means to separate or break something apart. We can decompose numbers as well as geometric shapes. Decomposing numbers involves breaking a larger number into smaller numbers.&nbsp; For example, consider breaking the number 10 into parts. We can decompose ten into five, three, and two. Alternatively, we can compose the number &#8230; <a title=\"Decompose Fractions\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/fractions\/decomposing-fractions\" aria-label=\"More on Decompose Fractions\">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-1322","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\/1322","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=1322"}],"version-history":[{"count":18,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1322\/revisions"}],"predecessor-version":[{"id":40059,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1322\/revisions\/40059"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1322"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1322"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1322"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}