{"id":2204,"date":"2022-04-27T06:33:52","date_gmt":"2022-04-27T06:33:52","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=2204"},"modified":"2024-01-10T17:04:12","modified_gmt":"2024-01-10T17:04:12","slug":"equivalent-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/equivalent","title":{"rendered":"Equivalent &#8211; Definition with Examples"},"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-0e1126e2-0342-44c9-bafa-6da1cfe886e5\" 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\/number-sense\/equivalent#0-definition-of-equivalent->Definition of Equivalent<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/equivalent#1-what-is-the-meaning-of-equivalent-in-math>What Is the Meaning of Equivalent in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/equivalent#2-solved-examples->Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/equivalent#3-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/equivalent#4-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-definition-of-equivalent-\">Definition of Equivalent<br><\/h2>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"280\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/equivalent-explaination.png\" alt=\"Equivalent Explaination\" class=\"wp-image-37326\" title=\"Equivalent Explaination\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/equivalent-explaination.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/equivalent-explaination-300x135.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">The meaning of &#8216;equivalent&#8217; generally refers to two numbers, expressions, or quantities with the same value. There are many ways to express an equivalent quantity \u2013 it can be denoted either by a bar or an equivalent symbol. Children find this topic very interesting for several reasons as they can relate to it in their daily lives.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">The equivalent can also mean some common or logical equivalence between different values or quantities. Equivalence is similar but not the same as equality.&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\/10-and-100-more-than-the-same-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_1_10_100_more_same_num_pt.png\" alt=\"10 and 100 More than the Same 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\">10 and 100 More than the Same Number Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_make_10_pt.png\" alt=\"Add 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-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_number_pt.png\" alt=\"Add 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\">Add 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\/add-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_horizontal_pt.png\" alt=\"Add 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\">Add 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 class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-and-1-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_2d_1d_match_pt.png\" alt=\"Add 2-Digit and 1-Digit Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit and 1-Digit Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-2-digit-numbers-by-regrouping\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_pv_add_regrp_2d_2d_vertical_pt.png\" alt=\"Add 2-Digit Numbers By Regrouping Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 2-Digit Numbers By Regrouping Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_pt.png\" alt=\"Add 3 Numbers Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-in-any-order\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_shifty_bridges_4_gm.png\" alt=\"Add 3 Numbers in Any Order Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers in Any Order Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-groups-of-objects\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_using_model_pt.png\" alt=\"Add 3 Numbers Using Groups of Objects Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers Using Groups of Objects Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/add-3-numbers-using-model\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/add_sub_facts_add_3_no_using_models_pt.png\" alt=\"Add 3 Numbers using Model Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Add 3 Numbers using Model Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><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                    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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-what-is-the-meaning-of-equivalent-in-math\">What Is the Meaning of Equivalent in Math?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">There are two ways in which one can <strong>define<\/strong> an equivalent in math. This is because the term equivalent in mathematical theory is a notion that has multiple meanings. Equivalent means that different terms and expressions with a similar value are considered equal in mathematical form.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Equal Vs Equivalent<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">In math, equivalent is different from equal. Equal means same in all aspects, whereas equivalent means similar but not identical.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, 2 is said to be equal to 2 but equivalent to 1 + 1.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">In simple words we can say that two things or quantities are equal when they are exactly the same like \u00bd is equal to \u00bd but \u00bd is equivalent to 2\/4 as they represent the same value.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\" id=\"2-equivalent-expressions-\"><strong>Equivalent Expressions<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Two mathematical expressions are said to be equivalent if they yield the same result upon solving them.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>For example<\/strong>, let\u2019s solve the following numerical expressions:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">25 \u00d7 5 = 125<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Also, 10$^{2}$ + 5$^{2}$&nbsp; = 100 + 25  = 125<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Thus, the above two expressions are equivalent and can be written as:&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">25 \u00d7 5 = 10$^{2}$ + 5$^{2}$<br><br>Similarly, the two math expressions&nbsp; 2 \u00d7 (10 \u2013 8) and 4$^{2}$ \u00f7&nbsp; 4 are also equivalent as both can be simplified to 4.<\/p>\n\n\n\n<p class=\"eplus-wrapper\" id=\"2-equivalent-fractions-\"><strong>Equivalent Fractions<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Two fractions are equivalent if the value, proportion, or quantity they represent is the same. Equivalent fractions can have different numerators and denominators.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example: $\\frac{1}{2}$ = $\\frac{2}{4}$ = $\\frac{3}{6}$ = $\\frac{4}{8}$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"611\" height=\"274\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/equivalent-fractions.png\" alt=\"Equivalent Fractions\" class=\"wp-image-37325\" title=\"Equivalent Fractions\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/equivalent-fractions.png 611w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/01\/equivalent-fractions-300x135.png 300w\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Equivalent Ratios<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">Equivalent ratios are those which can express a similar or the same relationship between numbers or values.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">They are similar in ratios and identical in value. These ratios can be multiplied or divided by their common factors, which can help simplify them. Equivalent ratios have different numbers in different forms, but their relationship is reflected only by their final value.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">For example, 1:2 and 2:4 are equivalent ratios.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Application<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">The use of the equivalent symbol (as three bars) is frequently used in Unicode programming for computers, as well as in Boolean algebra. Venn diagrams use the concept of logical equivalence to establish the relationship between two algebraic expressions and functions. The concept of equivalence is also used in explaining the structural similarity between the chemical compounds.<\/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\/10-and-100-more-than-a-3-digit-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\/10-and-100-more-than-a-3-digit-number.jpeg\" alt=\"10 and 100 More than a 3-digit Number\">\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\/100-more-and-100-less-than-a-3-digit-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\/100-more-and-100-less-than-a-3-digit-number.jpeg\" alt=\"100 More and 100 Less than a 3-digit Number\">\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\/100-more-than-a-3-digit-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\/100-more-than-a-3-digit-number.jpeg\" alt=\"100 More than a 3-digit Number\">\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-subtract-ones-2-digit-numbers\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-subtract-ones-2-digit-numbers.jpeg\" alt=\"Add & Subtract Ones & 2-Digit Numbers Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-and-find-the-sum\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-and-find-the-sum.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers and Find the Sum\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a 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alt=\"Add 1 Digit and 3 Digit Numbers Using Addition Wheel\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-number-charts\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"worksheets_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t    <div class=\"worksheet-card-container-inner-block\">\r\n\t        <img decoding=\"async\" class=\"worksheet-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/cms_assets\/s\/math-worksheets\/add-1-digit-and-3-digit-numbers-using-number-charts.jpeg\" alt=\"Add 1 Digit and 3 Digit Numbers Using Number Charts\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><div class=\"worksheet-card-container-outer\">\r\n\t<a 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document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    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     checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-solved-examples-\"><strong>Solved Examples<\/strong><\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Example 1: Two fractions, $\\frac{3}{5}$ and $\\frac{6}{x}$, are equivalent. Find the value of <em>x<\/em>.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution<\/strong>: Given, $\\frac{3}{5}$ = $\\frac{6}{x}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We know that equivalent fractions can be generated by multiplying the numerator and the denominator by the same number. So $\\frac{3}{5}$ = $\\frac{6}{10}$.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Hence, x = 10.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Example 2: Check whether 7 \u00d7 6 + 66 \u00f7 11 &#8211; 5 \u00d7 2 is equivalent to 7 \u00d7 3 + 24 \u00f7 2 + 9 \u00d7 3 or not.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong>&nbsp; In order to verify the equivalence of both the expressions, solve the and find the final values.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">7 \u00d7 6 + 66 \u00f7 11 &#8211; 5 \u00d7 2&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">= 42 + 6 &#8211; 10&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">= 38<\/p>\n\n\n\n<p class=\"eplus-wrapper\">7 \u00d7 3 + 24 \u00f7 2 + 9 \u00d7 3<\/p>\n\n\n\n<p class=\"eplus-wrapper\">= 21 + 12 + 27<\/p>\n\n\n\n<p class=\"eplus-wrapper\">= 60<\/p>\n\n\n\n<p class=\"eplus-wrapper\">38 \u2260 60<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the given expressions are not equivalent to each other.<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Example 3:<\/strong> Are $\\frac{4}{5}$ and $\\frac{16}{20}$ equivalent fractions?<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\frac{4\\times 4}{5\\times 4}$ = $\\frac{16}{20}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">If we multiply numerator and denominator of $\\frac{4}{5}$ by 4, we get $\\frac{16}{20}$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, the given fractions are equivalent.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-practice-problems\">Practice Problems<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Equivalent<\/h2><p style=\"display:none;\">Attend this Quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Choose the fractions equivalent to $\\frac{5}{3}$ from the list of fractions that are shown below.  <\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{4}{8}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{10}{6}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{9}{24}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{15}{12}$<\/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: $\\frac{10}{6}$<br\/>$\\frac{5\\times 2}{3\\times 2}$ = $\\frac{10}{6}$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Choose a fraction equivalent to \u2018five-sixths\u2019<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\frac{6}{5}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\frac{5}{6}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\frac{25}{30}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\frac{30}{25}$<\/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: $\\frac{25}{30}$<br\/>$\\frac{5\\times 5}{6\\times 5}$ = $\\frac{25}{30}$<\/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\">Two fractions $\\frac{4}{15}$ and $\\frac{12}{x}$ are equivalent. Find the value of x.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">12<\/div><div class=\"spq_answer_block\" data-value=\"1\">15<\/div><div class=\"spq_answer_block\" data-value=\"2\">45<\/div><div class=\"spq_answer_block\" data-value=\"3\">60<\/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: 45<br\/>$\\frac{4\\times 3}{15\\times 3}$ = $\\frac{12}{45}$<\/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                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                   },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{6}{5}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{5\\\\times 5}{6\\\\times 5}$$ = $$\\\\frac{25}{30}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{5}{6}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{5\\\\times 5}{6\\\\times 5}$$ = $$\\\\frac{25}{30}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\frac{30}{25}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{5\\\\times 5}{6\\\\times 5}$$ = $$\\\\frac{25}{30}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\frac{25}{30}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{5\\\\times 5}{6\\\\times 5}$$ = $$\\\\frac{25}{30}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{5\\\\times 5}{6\\\\times 5}$$ = $$\\\\frac{25}{30}$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Two fractions $$\\\\frac{4}{15}$$ and $$\\\\frac{12}{x}$$ are equivalent. Find the value of x.\",\n                    \"text\": \"Two fractions $$\\\\frac{4}{15}$$ and $$\\\\frac{12}{x}$$ are equivalent. Find the value of x.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\frac{4\\\\times 3}{15\\\\times 3}$$ = $$\\\\frac{12}{45}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{4\\\\times 3}{15\\\\times 3}$$ = $$\\\\frac{12}{45}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"15\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{4\\\\times 3}{15\\\\times 3}$$ = $$\\\\frac{12}{45}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"60\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\frac{4\\\\times 3}{15\\\\times 3}$$ = $$\\\\frac{12}{45}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"45\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\frac{4\\\\times 3}{15\\\\times 3}$$ = $$\\\\frac{12}{45}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\frac{4\\\\times 3}{15\\\\times 3}$$ = $$\\\\frac{12}{45}$$\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We have learned about the equivalent and its properties and properties with different examples. We have also solved a few problems that have helped us grasp the concept of equivalent. Hopefully, this will help the kids master the concept to solve different mathematical problems.<br>Teaching math concepts can be challenging, especially when the students are young kids. So, to make parents&#8217; and teachers\u2019 lives easy, <a href=\"https:\/\/www.splashlearn.com\/\">SplashLearn<\/a> has brought some courses specifically designed for students from K-8. After all, it should be fun to learn!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-f255669e-09c3-4327-a2b7-8ef2c79b838a\" 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-f255669e-09c3-4327-a2b7-8ef2c79b838a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f255669e-09c3-4327-a2b7-8ef2c79b838a\"><strong>What are some examples of equivalent values?<\/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-f255669e-09c3-4327-a2b7-8ef2c79b838a\">\n\n<p>Some examples of equivalent values would be fractions like $\\frac{1}{2}$ and $\\frac{2}{4}$. They are both simplified at 0.5 each. An example of an equivalent ratio would be 1:5 and 2:10, as, after simplification, they would both have the same value, making them equivalent.&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-f255669e-09c3-4327-a2b7-8ef2c79b838a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f255669e-09c3-4327-a2b7-8ef2c79b838a\"><strong>Are equivalent fractions and equivalent ratios the same?<\/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-f255669e-09c3-4327-a2b7-8ef2c79b838a\">\n\n<p>Yes, equivalent fractions are the same as they are two different ways of representing the same concept. Equivalent ratios, sometimes known as equivalent fractions, are ratios that have the same proportion to each other when put in simplest form.&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-2-f255669e-09c3-4327-a2b7-8ef2c79b838a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f255669e-09c3-4327-a2b7-8ef2c79b838a\"><strong>How do we find 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-f255669e-09c3-4327-a2b7-8ef2c79b838a\">\n\n<p>To find equiavlent fractions, we multiply the numerator and denominator by the same number.&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-3-f255669e-09c3-4327-a2b7-8ef2c79b838a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-f255669e-09c3-4327-a2b7-8ef2c79b838a\"><strong>What are some real-life examples of 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-3-f255669e-09c3-4327-a2b7-8ef2c79b838a\">\n\n<p>For example, let&#8217;s say we are making a recipe that requires 1\/2 cup of butter. But we only have 1\/4 cups in the kitchen. Can we still make the recipe? Yes! Because 1\/2 is equivalent to 2\/4. So, we can use two 1\/4 cups of butter instead of one 1\/2 cup.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Definition of Equivalent The meaning of &#8216;equivalent&#8217; generally refers to two numbers, expressions, or quantities with the same value. There are many ways to express an equivalent quantity \u2013 it can be denoted either by a bar or an equivalent symbol. Children find this topic very interesting for several reasons as they can relate to &#8230; <a title=\"Equivalent &#8211; Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/number-sense\/equivalent\" aria-label=\"More on Equivalent &#8211; 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-2204","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\/2204","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=2204"}],"version-history":[{"count":18,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2204\/revisions"}],"predecessor-version":[{"id":37327,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2204\/revisions\/37327"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=2204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=2204"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=2204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}