{"id":1304,"date":"2022-04-18T10:27:27","date_gmt":"2022-04-18T10:27:27","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=1304"},"modified":"2024-09-27T11:00:44","modified_gmt":"2024-09-27T11:00:44","slug":"partial-quotient-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/partial-quotient","title":{"rendered":"Partial Quotient &#8211; Definition, Facts, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-cdd16d82-5434-4143-90da-d1a5df1de544\" 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\/division\/partial-quotient#0-what-is-a-partial-quotient>What Is a Partial Quotient?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/division\/partial-quotient#2-partial-quotient-definition>Partial Quotient Definition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/division\/partial-quotient#8-how-to-divide-decimals-using-partial-quotients>How to Divide Decimals Using Partial Quotients<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/division\/partial-quotient#11-solved-examples-on-partial-quotients>Solved Examples on Partial Quotients<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/division\/partial-quotient#12-practice-problems-on-partial-quotients>Practice Problems on Partial Quotients<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/division\/partial-quotient#13-frequently-asked-questions-about-partial-quotients>Frequently Asked Questions about Partial Quotients<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\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%\">\n<h2 class=\"wp-block-heading\" id=\"0-what-is-a-partial-quotient\">What Is a Partial Quotient?<\/h2>\n\n\n\n<p><strong>A partial quotient refers to a division strategy that uses repeated subtraction to perform the <\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/division\"><strong>division<\/strong><\/a><strong> of large numbers easily<\/strong>.<\/p>\n\n\n\n<p>The partial quotient method is used in <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/long-division\">long division<\/a> to break down a division problem into simpler, more manageable steps. It involves finding partial quotients for each part of the dividend. These partial quotients are then added together to obtain the final quotient.<\/p>\n\n\n\n<p>This approach is useful when dealing with large division problems since it makes division more understandable and less overwhelming for kids. The partial quotient method is also called the \u201cchunking method\u201d since it breaks down a large number into smaller parts.<\/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\/choose-the-correct-missing-part-of-division-equation\" 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\/mult_div_pv_miss_num_div_b_pt.png\" alt=\"Choose the Correct Missing Part of DIvision Equation 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\">Choose the Correct Missing Part of DIvision Equation 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\/complete-division-patterns-of-decimal-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\/dec_mul_div_complete_div_pattern_pt.png\" alt=\"Complete Division Patterns of Decimal 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\">Complete Division Patterns of Decimal 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\/complete-the-division-equation-by-filling-the-quotient-or-divisor\" 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\/mult_div_pv_miss_num_div_d_pt.png\" alt=\"Complete the Division Equation by FIlling the Quotient or Divisor 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\">Complete the Division Equation by FIlling the Quotient or Divisor 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\/complete-the-division-equation\" 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\/mult_div_pv_miss_num_div_e_pt.png\" alt=\"Complete the Division Equation 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\">Complete the Division Equation 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\/complete-the-division-expression-for-arrays\" 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\/mult_div_facts_rep_div_arr_pt.png\" alt=\"Complete the Division Expression for Arrays 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\">Complete the Division Expression for Arrays 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\/complete-the-division-expression-for-equal-groups\" 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\/mult_div_facts_rep_div_grp_pt.png\" alt=\"Complete the Division Expression for Equal Groups 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\">Complete the Division Expression for Equal Groups 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\/complete-the-division\" 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\/mult_div_pv_complete_div_1_pt.png\" alt=\"Complete the Division 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\">Complete the Division 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\/complete-the-division-patterns\" 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\/mult_div_facts_div_pattern2_pt.png\" alt=\"Complete the Division Patterns 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\">Complete the Division Patterns 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\/complete-the-division-solution\" 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\/mult_div_pv_div_2_to_5_d_pt.png\" alt=\"Complete the Division Solution 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\">Complete the Division Solution 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\/complete-the-division-solution-where-dividend-is-between-6-9\" 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\/mult_div_pv_div_6_to_9_b_pt.png\" alt=\"Complete the Division Solution Where Dividend is Between 6-9 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\">Complete the Division Solution Where Dividend is Between 6-9 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\" id=\"1-what-is-a-quotient\">What Is a Quotient?<\/h2>\n\n\n\n<p><strong>The<\/strong> <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/quotient\"><strong>quotient<\/strong><\/a><strong> is the number we obtain when dividing one number (<\/strong><a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/dividend\"><strong>dividend<\/strong><\/a><strong>) by another (divisor).<\/strong> Note that the quotient is always smaller than the dividend.<\/p>\n\n\n\n<p><strong>Example:<\/strong> $8 \\div 4 = 2$<\/p>\n\n\n\n<p>Here, 8 is the dividend, and 4 is the divisor.&nbsp;<\/p>\n\n\n\n<p>The result of the division is 2.<\/p>\n\n\n\n<p>Thus, 2 is the quotient.<\/p>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-d5cfc09f-5e0f-4a99-8c08-234cb35deac8\">\n\n\n<p><strong>NOTE<\/strong>: In this example, we are dealing with small numbers. So, it is very easy to check the times tables, recall the multiplication facts, and work out the quotient. It would be challenging to identify the quotient when the numbers are large. That\u2019s where the partial quotients come into the picture.<\/p>\n\n\n<\/div>\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\/apply-division-in-everyday-life\" 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\/apply-division-in-everyday-life.jpeg\" alt=\"Apply Division in Everyday Life 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\/check-the-estimated-quotients\" 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\/check-the-estimated-quotients.jpeg\" alt=\"Check the Estimated Quotients 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\/choose-the-best-estimate-of-the-quotients\" 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\/choose-the-best-estimate-of-the-quotients.jpeg\" alt=\"Choose the Best Estimate of the Quotients 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\/choose-the-better-estimate-of-the-quotient\" 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\/choose-the-better-estimate-of-the-quotient.jpeg\" alt=\"Choose the Better Estimate of the Quotient 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\/compare-division-expressions\" 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\/compare-division-expressions.jpeg\" alt=\"Compare Division Expressions 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\/compare-division-situations\" 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\/compare-division-situations.jpeg\" alt=\"Compare Division Situations 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\/compare-the-division-expressions\" 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\/compare-the-division-expressions.jpeg\" alt=\"Compare the Division Expressions 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\/complete-multiplication-and-division-sentences\" 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\/complete-multiplication-and-division-sentences.jpeg\" alt=\"Complete Multiplication and Division Sentences 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\/complete-the-division-facts\" 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\/complete-the-division-facts.jpeg\" alt=\"Complete the Division Facts 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\/complete-the-division-sentence\" 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\/complete-the-division-sentence.jpeg\" alt=\"Complete the Division Sentence Worksheet\">\r\n\t    <\/div>\r\n\t\t<div class=\"worksheet-card-container-inner\" >\r\n\t\t<\/div><\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/worksheets\">More Worksheets<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-worksheets-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".worksheet-card-container-outer\");\n            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\" id=\"2-partial-quotient-definition\">Partial Quotient Definition<\/h2>\n\n\n\n<p>Partial quotient is a division method that breaks down a dividend into smaller parts, enabling easier subtraction of multiples of the divisor until the remainder is smaller than the divisor.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-understanding-partial-quotients-as-a-division-strategy\">Understanding Partial Quotients as a Division Strategy<\/h2>\n\n\n\n<p>The division operation is defined as the process of <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/subtraction\/repeated-subtraction\">repeated subtraction<\/a>. It is exactly the opposite of multiplication. In the standard form of division, the divisor is used to determine how many times it can be subtracted from the dividend.<\/p>\n\n\n\n<p><strong>Example<\/strong>: $20 \\div 5$&nbsp;<\/p>\n\n\n\n<p>$20 &#8211; 5 = 15$<\/p>\n\n\n\n<p>$15 &#8211; 5 = 10$<\/p>\n\n\n\n<p>$10 &#8211; 5 = 5$<\/p>\n\n\n\n<p>$5 &#8211; 5 = 0$<\/p>\n\n\n\n<p>5 is subtracted 4 times to get the remainder of 0.<\/p>\n\n\n\n<p>$20 \\div 5 = 4$<\/p>\n\n\n\n<p>Here, we can easily identify that&nbsp;<\/p>\n\n\n\n<p>$5 \\times 4 =$ Four groups of $5 = 5 + 5 + 5 + 5 = 20$<\/p>\n\n\n\n<p>Thus, quotient $= 4$<\/p>\n\n\n\n<p>In the partial quotient division, we break the dividend into smaller parts by subtracting multiples of the divisor until the remainder is 0 or less than the divisor. The multipliers (numbers used to multiply the divisor to find these multiples) are the partial quotients, which are then summed to find the final quotient.<\/p>\n\n\n\n<p><strong>Example<\/strong>: $285 \\div 5$<\/p>\n\n\n\n<p>Using repeated subtraction, we will have to subtract 5 multiple times to find the quotient. It would be tedious. Instead, we can use the partial quotients.&nbsp;&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"536\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-using-partial-quotients-example.png\" alt=\"Division using partial quotients - example\" class=\"wp-image-40895\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-using-partial-quotients-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-using-partial-quotients-example-300x259.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Thus, 5 can be subtracted 57 times from 285. To reach the final quotient of 57, we preferred chunking the division process into smaller steps. The outcome is the same, no matter how many steps you choose. The numbers with which the divisor is multiplied during this process are called the partial quotients.<\/p>\n\n\n<div class=\"ub-styled-box ub-notification-box\" id=\"ub-styled-box-d82fec1a-dfe9-49aa-b20c-1588526061e2\">\n\n\n<p><strong>NOTE:<\/strong>&nbsp;The partial quotients method is not limited to a single correct sequence of steps. It&#8217;s more about breaking down the division into manageable steps by finding multiples of the divisor and subtracting them from the dividend until the problem is solved.&nbsp;<br><br>You can choose different multiples of the divisor to subtract from the dividend in each step, making the method adaptable to the specific problem you are trying to solve. The idea is to find multiples that make the computation easier and more understandable.<br><br>The goal is to help students understand the concept of division and place value while allowing for flexibility in their approach.<\/p>\n\n\n<\/div>\n\n\n<p>Here\u2019s how we can solve the same example using different partial quotients.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"540\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-285-by-5-using-partial-quotients.png\" alt=\"Dividing 285 by 5 using partial quotients\" class=\"wp-image-40897\" title=\"Dividing 285 by 5 using partial quotients\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-285-by-5-using-partial-quotients.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-285-by-5-using-partial-quotients-300x261.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-how-to-divide-using-the-partial-quotient-method\">How to Divide Using the Partial Quotient Method<\/h2>\n\n\n\n<p>Let\u2019s understand the steps to divide using the partial quotients with the help of an example.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Identify the dividend and the divisor: <\/strong>Understand the division problem, which consists of a dividend (the number to be divided) and a divisor (the number you&#8217;re dividing by).<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Estimate Partial Quotients: <\/strong>Choose a multiple of the divisor that is as close as possible to the dividend without exceeding it. The best approach would be to write simple multiplication facts of the divisor (such as multiples of 10).<\/li>\n<\/ul>\n\n\n\n<p>The multiplier of the divisor at every step of this division is the partial quotient. This multiple of the divisor should be as close as possible to the dividend, that is, less than or equal to the dividend.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Subtract: <\/strong>Subtract the multiple from the dividend to find the remainder.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Continue the process: <\/strong>If the remainder is not zero, repeat the process. Find another multiple of the divisor that can be subtracted from the remaining dividend to obtain the next partial quotient. Repeat this process until the remainder is 0 or less than the divisor.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Combine Partial Quotients<\/strong>: Keep finding partial quotients and subtracting them until the remainder is zero or less than the divisor. Then, add all the partial quotients together to obtain the final quotient.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Check your answer: <\/strong>Verify that your answer is correct by multiplying the divisor by the quotient and adding any remaining remainder. It should equal the original dividend.<\/li>\n<\/ul>\n\n\n\n<p><strong>Example 1: <\/strong>Divide 378 by 6 using partial quotients.<\/p>\n\n\n\n<p>Dividend $= 378$<\/p>\n\n\n\n<p>Divisor $= 6$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"626\" height=\"598\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-378-by-6-using-the-partial-quotients-method.png\" alt=\"Dividing 378 by 6 using the partial quotients method\" class=\"wp-image-40914\" title=\"Dividing 378 by 6 using the partial quotients method\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-378-by-6-using-the-partial-quotients-method.png 626w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-378-by-6-using-the-partial-quotients-method-300x287.png 300w\" sizes=\"auto, (max-width: 626px) 100vw, 626px\" \/><\/figure>\n\n\n\n<p><strong>Example 2:<\/strong> Let\u2019s consider an example where the remainder is not 0.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"617\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-partial-quotients-involving-non-zero-remainder.png\" alt=\"Division by partial quotients involving non-zero remainder\" class=\"wp-image-40898\" title=\"Division by partial quotients involving non-zero remainder\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-partial-quotients-involving-non-zero-remainder.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-partial-quotients-involving-non-zero-remainder-300x300.png 300w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-partial-quotients-involving-non-zero-remainder-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-partial-quotients-involving-non-zero-remainder-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-partial-quotients-involving-non-zero-remainder-120x120.png 120w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p>Adding the partial quotients, we get<\/p>\n\n\n\n<p>$10 + 2 + 2 = 14$<\/p>\n\n\n\n<p>We also have a remainder of 1.&nbsp;<\/p>\n\n\n\n<p>Thus, $57 \\div 4 = 14$ R 1<\/p>\n\n\n\n<p>We can also write this using mixed fractions as&nbsp;<\/p>\n\n\n\n<p>$57 \\div 4 = 14 \\frac{1}{4}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-how-to-use-partial-quotients-to-divide-by-one-digit-numbers\">How to Use Partial Quotients to Divide by One-Digit Numbers<\/h2>\n\n\n\n<p>The steps are the same. Let\u2019s consider an example. Let\u2019s divide 78 by 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"697\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-single-digit-numbers-using-partial-quotients.png\" alt=\"Division by single-digit numbers using partial quotients\" class=\"wp-image-40899\" title=\"Division by single-digit numbers using partial quotients\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-single-digit-numbers-using-partial-quotients.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-single-digit-numbers-using-partial-quotients-267x300.png 267w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-how-to-use-partial-quotients-to-divide-by-two-digit-numbers\">How to Use Partial Quotients to Divide by Two-Digit Numbers<\/h2>\n\n\n\n<p>The process discussed earlier stays the same regardless of the number of digits in the divisor.<\/p>\n\n\n\n<p><strong>Example<\/strong>: $1275 \\div 15$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"484\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-two-digit-numbers-using-partial-quotients.png\" alt=\"Division by two-digit numbers using partial quotients\" class=\"wp-image-40900\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-two-digit-numbers-using-partial-quotients.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-by-two-digit-numbers-using-partial-quotients-300x234.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-partial-quotients-using-area-model\">Partial Quotients Using Area Model<\/h2>\n\n\n\n<p>The<a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/area-model-division\"> area model division<\/a> method visually represents division using rectangles, where the partial quotients and the divisor determine the length and width of these rectangles. Each partial quotient corresponds to the length of one rectangle. The combined area of these rectangles equals the dividend of the division equation.<\/p>\n\n\n\n<p><strong>Example<\/strong>: $275 \\div 25$<\/p>\n\n\n\n<p>Dividend $= 275$<\/p>\n\n\n\n<p>Divisor $= 25$<\/p>\n\n\n\n<p>We can choose as many rectangles as we choose the number of partial quotients.&nbsp;<\/p>\n\n\n\n<p>Suppose we choose two partial quotients, 10 and 1.<\/p>\n\n\n\n<p><strong>Division Step i)<\/strong>&nbsp;<\/p>\n\n\n\n<p>$25 \\times 10 = 250$&nbsp;<\/p>\n\n\n\n<p>$275 &#8211; 250 = 25$<\/p>\n\n\n\n<p><strong>Division Step ii)<\/strong>&nbsp;<\/p>\n\n\n\n<p>$25 \\times 1 = 25$&nbsp;<\/p>\n\n\n\n<p>$25 &#8211; 25 = 0$<\/p>\n\n\n\n<p>Consider two rectangles, both having a width equal to the value of the divisor, 25.<\/p>\n\n\n\n<p>Divisor $= 25 =$ Width of the rectangles<\/p>\n\n\n\n<p>Length of one rectangle $= 25$ \u2026partial quotient<\/p>\n\n\n\n<p>Length of the other rectangle $= 1$ \u2026partial quotient<\/p>\n\n\n\n<p>Sum of partial quotients $= 10 + 1 = 11 =$ Length of the big rectangle<\/p>\n\n\n\n<p>Sum of areas of two rectangles $= 250 + 25 = 275$ square units = Dividend<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"617\" height=\"375\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/partial-quotient-using-the-area-model.png\" alt=\"partial quotient using the area model\" class=\"wp-image-40911\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/partial-quotient-using-the-area-model.png 617w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/partial-quotient-using-the-area-model-300x182.png 300w\" sizes=\"auto, (max-width: 617px) 100vw, 617px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-how-to-divide-decimals-using-partial-quotients\">How to Divide Decimals Using Partial Quotients<\/h2>\n\n\n\n<p>Let\u2019s understand how to divide decimals using partial quotients. The process is similar, but we must consider the decimal point at every step.<\/p>\n\n\n\n<p><strong>Example:<\/strong> $9.7 \\div 4 = 2.425$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"604\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-decimals-using-partial-quotients-97-divided-by-4.png\" alt=\"Dividing decimals using partial quotients (9.7 divided by 4)\" class=\"wp-image-40901\" title=\"Dividing decimals using partial quotients (9.7 divided by 4)\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-decimals-using-partial-quotients-97-divided-by-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-decimals-using-partial-quotients-97-divided-by-4-300x292.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-facts-about-partial-quotients\">Facts about Partial Quotients<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-8cf370e7 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The partial quotient division approach makes long division easier. It offers flexibility, allowing students to adjust the amount they subtract at each step based on their preferred calculation method.<\/li>\n\n\n\n<li>The partial quotient strategy may be more time-consuming than traditional division methods due to its potential for more steps, particularly when dealing with larger numbers.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-conclusion\">Conclusion<\/h2>\n\n\n\n<p>In this article, we learned about the partial quotient division method. We discussed how to divide numbers and decimals easily using partial quotients. Let\u2019s solve a few examples for better comprehension.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-solved-examples-on-partial-quotients\">Solved Examples on Partial Quotients<\/h2>\n\n\n\n<p><strong>1. Solve <\/strong><strong>112 \u00f7 4&nbsp; <\/strong><strong>using partial quotients.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let\u2019s use the partial quotients method.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"195\" height=\"225\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/04\/dividing-112-by-4-using-partial-quotients.png\" alt=\"Dividing 112 by 4 using partial quotients\" class=\"wp-image-42179\" title=\"Dividing 112 by 4 using partial quotients\"\/><\/figure>\n\n\n\n<p>Quotient $= 25 + 2 + 1 = 28$<\/p>\n\n\n\n<p>Thus, $112 \\div 4 = 28$<\/p>\n\n\n\n<p><strong>2. Solve 108 \u00f7 3 using partial quotients.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let\u2019s use the partial quotient method.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"195\" height=\"225\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/division-of-108-by-3-using-partial-quotients.png\" alt=\"Division of 108 by 3 using partial quotients\" class=\"wp-image-40903\" title=\"Division of 108 by 3 using partial quotients\"\/><\/figure>\n\n\n\n<p>Final quotient $= 30 + 5 +&nbsp; 1 =&nbsp; 36$<\/p>\n\n\n\n<p>Thus, $108 \\div 3 = 36$<\/p>\n\n\n\n<p><strong>3. Find partial quotients and the final quotient.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"112\" height=\"262\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/identifying-final-quotient-using-the-partial-quotient-strategy.png\" alt=\"Identifying final quotient using the partial quotient strategy\" class=\"wp-image-40904\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Dividend $= 654$<\/p>\n\n\n\n<p>Divisor $= 3$<\/p>\n\n\n\n<p>1st partial quotient $= 200$ since $200 \\times 3 = 600$<\/p>\n\n\n\n<p>2nd partial quotient $= 10$ since $10 \\times 3 = 30$<\/p>\n\n\n\n<p>3rd partial quotient $= 8$ since $8 \\times 3 = 24$<\/p>\n\n\n\n<p>Final quotient = Sum of partial quotients $= 200 + 10 + 8 = 218$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"290\" height=\"291\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-653-by-3-using-the-partial-quotient-method.png\" alt=\"Dividing 653 by 3 using the partial quotient method\" class=\"wp-image-40905\" title=\"Dividing 653 by 3 using the partial quotient method\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-653-by-3-using-the-partial-quotient-method.png 290w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-653-by-3-using-the-partial-quotient-method-150x150.png 150w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-653-by-3-using-the-partial-quotient-method-250x250.png 250w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/dividing-653-by-3-using-the-partial-quotient-method-120x120.png 120w\" sizes=\"auto, (max-width: 290px) 100vw, 290px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"12-practice-problems-on-partial-quotients\">Practice Problems on Partial Quotients<\/h2>\n\n\n\n<div class=\"spq_wrapper\"><h2 style=\"display:none;\">Partial Quotient<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What is the first step when dividing a number using the partial quotient method?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Multiply the divisor by a whole number to get the product equal to the dividend.<\/div><div class=\"spq_answer_block\" data-value=\"1\">Subtract the divisor from the dividend.<\/div><div class=\"spq_answer_block\" data-value=\"2\">Find a multiplier of the divisor to get a product as close to the dividend as possible.<\/div><div class=\"spq_answer_block\" data-value=\"3\">Bring down the next digit from the dividend.<\/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: Find a multiplier of the divisor to get a product as close to the dividend as possible.<br\/>In the first step, we multiply the divisor by a number to reach a friendly number closer to the dividend.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">What are partial quotients?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">The products obtained by multiplying the divisor by whole numbers<\/div><div class=\"spq_answer_block\" data-value=\"1\">The remainders in the division process<\/div><div class=\"spq_answer_block\" data-value=\"2\">The numbers you get when you divide one number by another.<\/div><div class=\"spq_answer_block\" data-value=\"3\">Multipliers of the divisor<\/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: Multipliers of the divisor<br\/>The multipliers of the divisor (the numbers you multiply the divisor by) we use in the division process are called partial products.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">In the partial quotients method, what do you do after finding the partial quotient for each step?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Add them all together to get the final quotient.<\/div><div class=\"spq_answer_block\" data-value=\"1\">Multiply them together to get the final quotient.<\/div><div class=\"spq_answer_block\" data-value=\"2\">Subtract them to get the remainder.<\/div><div class=\"spq_answer_block\" data-value=\"3\">Divide the dividend by the divisor.<\/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: Add them all together to get the final quotient.<br\/>In the final step, we add them all to get the quotient.<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": 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\"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Multiply the divisor by a whole number to get the product equal to the dividend.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the first step, we multiply the divisor by a number to reach a friendly number closer to the dividend.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Subtract the divisor from the dividend.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the first step, we multiply the divisor by a number to reach a friendly number closer to the dividend.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Bring down the next digit from the dividend.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the first step, we multiply the divisor by a number to reach a friendly number closer to the dividend.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": 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problem\",\n                    \"name\": \"What are partial quotients?\",\n                    \"text\": \"What are partial quotients?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The multipliers of the divisor (the numbers you multiply the divisor by) we use in the division process are called partial products.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"The products obtained by multiplying the divisor by whole numbers\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The multipliers of the divisor 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},\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Multiply them together to get the final quotient.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the final step, we add them all to get the quotient.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Subtract them to get the remainder.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the final step, we add them all to get the quotient.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Divide the dividend by the divisor.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In the final step, we add them all to get the quotient.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Add them all together to get the final quotient.\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In the final step, we add them all to get the quotient.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In the final step, we add them all to get the quotient.\"\n                      }\n                    } \n\n                    }]}<\/script>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"13-frequently-asked-questions-about-partial-quotients\">Frequently Asked Questions about Partial Quotients<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-b2f17e97-6265-4a9e-a347-47117a2f0d7d\" 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-b2f17e97-6265-4a9e-a347-47117a2f0d7d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2f17e97-6265-4a9e-a347-47117a2f0d7d\"><strong>What is the significance of partial quotients?<\/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-b2f17e97-6265-4a9e-a347-47117a2f0d7d\">\n\n<p>Partial quotients provide the simple transition from a visual approach to division to a more abstract one, addressing a gap in understanding. It helps students to simplify the long division process into smaller and easy-to-understand steps.<\/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-b2f17e97-6265-4a9e-a347-47117a2f0d7d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2f17e97-6265-4a9e-a347-47117a2f0d7d\"><strong>Are partial quotients unique?<\/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-b2f17e97-6265-4a9e-a347-47117a2f0d7d\">\n\n<p>Partial quotients in division are not unique; they can vary depending on the way you choose to approach a particular division problem. The flexibility of the partial quotients method is one of its advantages, as it allows for different approaches that suit the problem and the student&#8217;s understanding.<\/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-b2f17e97-6265-4a9e-a347-47117a2f0d7d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2f17e97-6265-4a9e-a347-47117a2f0d7d\"><strong>Which value should necessarily be less than the divisor?<\/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-b2f17e97-6265-4a9e-a347-47117a2f0d7d\">\n\n<p>The remainder should necessarily be less than the divisor.<\/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-b2f17e97-6265-4a9e-a347-47117a2f0d7d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2f17e97-6265-4a9e-a347-47117a2f0d7d\"><strong>How do you define division?<\/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-b2f17e97-6265-4a9e-a347-47117a2f0d7d\">\n\n<p>Division is the process of repeated subtraction, where we determine how many times the divisor can be subtracted from the dividend until the remainder is 0 or less than the divisor.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-4-b2f17e97-6265-4a9e-a347-47117a2f0d7d\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-b2f17e97-6265-4a9e-a347-47117a2f0d7d\"><strong>What is the division formula?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-4-b2f17e97-6265-4a9e-a347-47117a2f0d7d\">\n\n<p><em>Dividend = (Divisor \u00d7<\/em> <em>Quotient) + Remainder<\/em><\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Is a Partial Quotient? A partial quotient refers to a division strategy that uses repeated subtraction to perform the division of large numbers easily. The partial quotient method is used in long division to break down a division problem into simpler, more manageable steps. It involves finding partial quotients for each part of the &#8230; <a title=\"Partial Quotient &#8211; Definition, Facts, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/division\/partial-quotient\" aria-label=\"More on Partial Quotient &#8211; Definition, Facts, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1304","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\/1304","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=1304"}],"version-history":[{"count":19,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1304\/revisions"}],"predecessor-version":[{"id":42180,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/1304\/revisions\/42180"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=1304"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=1304"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=1304"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}