{"id":2150,"date":"2022-04-26T12:09:58","date_gmt":"2022-04-26T12:09:58","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test-new\/?page_id=2150"},"modified":"2024-03-14T08:07:21","modified_gmt":"2024-03-14T08:07:21","slug":"partial-product-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/partial-product","title":{"rendered":"Partial Product"},"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\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=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-85b9aea0-6354-41a3-a187-b19ac30c93a0\" 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\/multiplication\/partial-product#0-what-is-a-partial-product>What is a Partial Product?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/partial-product#1-partial-product-definition>Partial Product Definition<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/partial-product#2-distributive-property-of-multiplication>Distributive Property of Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/partial-product#8-solved-examples>Solved Examples<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/partial-product#9-practice-problems>Practice Problems<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/partial-product#10-frequently-asked-questions>Frequently Asked Questions<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-a-partial-product\">What is a Partial Product?<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">Partial means something that is incomplete or exists only in parts.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Suppose you take a pizza and cut it into slices. Each of the slices will be a partial part of the pizza.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"352\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/slices-of-a-pizza-to-represent-parts.png\" alt=\"Slices of a pizza to represent parts\" class=\"wp-image-40928\" title=\"Slices of a pizza to represent parts\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/slices-of-a-pizza-to-represent-parts.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/slices-of-a-pizza-to-represent-parts-300x170.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">So, what does partial product mean in math? When we say partial product, we mean breaking down large numbers into parts to find their product easily.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let&#8217;s say you are asked to find the product of 2 and 4. You can easily say that it is 8. But if you are asked to find the product of 32 and 54, you may have to carry out some calculations. A partial product helps you multiply such numbers easily by breaking them into parts.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s get familiar with partial products and how to multiply two numbers using this method.<\/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\/area-word-problems-on-product-of-fractions\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_real_life_prob_area_pt.png\" alt=\"Area Word Problems on Product of Fractions Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Area Word Problems on Product of Fractions Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-correct-product-for-the-multiplication-expressions\" 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_mult_match_4dby1d_fluently_pt.png\" alt=\"Choose the Correct Product for the Multiplication Expressions 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 Product for the Multiplication Expressions 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\/choose-the-missing-digit-in-the-product\" 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_find_missing_diff_arngment_pt.png\" alt=\"Choose the Missing Digit in the Product 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 Missing Digit in the Product 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\/choose-the-missing-number-in-the-multiplication-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_find_missing_2dby1d_pt.png\" alt=\"Choose the Missing Number in the Multiplication 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\">Choose the Missing Number in the Multiplication 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\/choose-the-multiplication-expression-representing-fraction-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_represent_mult_unit_by_whole_pt.png\" alt=\"Choose the Multiplication Expression Representing Fraction Models Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Choose the Multiplication Expression Representing Fraction Models Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/choose-the-product-for-the-multiplication-questions\" 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_find_product_4dby1d_1_pt.png\" alt=\"Choose the Product for the Multiplication Questions 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 Product for the Multiplication Questions 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\/choose-to-complete-each-of-the-multiplication-expressions\" 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_mult_match_3dby1d_fluently_pt.png\" alt=\"Choose to Complete each of the Multiplication Expressions 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 to Complete each of the Multiplication Expressions 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-decimal-multiplication-pattern\" 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_mul_pattern_pt.png\" alt=\"Complete the Decimal Multiplication Pattern 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 Decimal Multiplication Pattern 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-multiplication-between-fractions-and-whole-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\/fractions_complete_multiplication_pt.png\" alt=\"Complete the Multiplication Between Fractions and Whole 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 the Multiplication Between Fractions and Whole 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-multiplication-expression-using-the-fraction-models\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/fractions_multiply_models_unit_by_whole_pt.png\" alt=\"Complete the Multiplication Expression Using the Fraction Models Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Complete the Multiplication Expression Using the Fraction Models Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"1-partial-product-definition\">Partial Product Definition<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">A partial product is a product of two numbers obtained when we break the numbers into parts, multiply the parts separately and then add them together.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Partial product method is applied to multiply numbers larger than 10. In this method, we first break the numbers into parts and then multiply the parts. We add the multiplication results to find the final product.<\/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\/addition-and-multiplication-expression-for-array\" 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\/addition-and-multiplication-expression-for-array.jpeg\" alt=\"Addition and Multiplication Expression for Array 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\/addition-and-multiplication-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\/addition-and-multiplication-expressions.jpeg\" alt=\"Addition and Multiplication 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\/apply-multiplication-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-multiplication-in-everyday-life.jpeg\" alt=\"Apply Multiplication 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\/break-the-multiplication-expression\" 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\/break-the-multiplication-expression.jpeg\" alt=\"Break the Multiplication Expression 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-your-own-multiplication-strategy\" 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-your-own-multiplication-strategy.jpeg\" alt=\"Choose Your own Multiplication Strategy 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\/commutative-property-of-multiplication\" 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\/commutative-property-of-multiplication.jpeg\" alt=\"Commutative Property of Multiplication 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-fraction-products\" 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-fraction-products.jpeg\" alt=\"Compare Fraction Products 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-multiplication-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-multiplication-expressions.jpeg\" alt=\"Compare the Multiplication 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\/comparing-multiplication-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\/comparing-multiplication-expressions.jpeg\" alt=\"Comparing Multiplication 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\" 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slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading eplus-wrapper\" id=\"2-distributive-property-of-multiplication\">Distributive Property of Multiplication<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">The distributive property of multiplication says that for three numbers a, b, and c, the sum of a and b, when multiplied by c, gives the same result as a and b individually multiplied by c, and then the products are added together to find the result.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $\\text{a} \\times (\\text{b} + \\text{c}) = \\text{a} \\times \\text{b} + \\text{a} \\times \\text{c}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">When we find the product of two numbers using partial products, we follow a similar process of breaking the numbers and then finding the product.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"292\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distributive-property-of-multiplication.png\" alt=\"Distributive property of multiplication\" class=\"wp-image-40929\" title=\"Distributive property of multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distributive-property-of-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/distributive-property-of-multiplication-300x141.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"3-product-of-two-numbers-using-the-partial-product-method\">Product of Two Numbers Using the Partial Product Method<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We will discuss partial product examples with two cases:&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">One-digit number with a two-digit number&nbsp;<\/li>\n\n\n\n<li class=\"eplus-wrapper\">Two-digit number with a two-digit number&nbsp;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"4-multiplication-of-a-two-digit-number-with-an-one-digit-number-\"><strong>Multiplication of a Two-Digit Number with an One-Digit Number<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper\">Using the partial products method, we can multiply a $1-$digit number with a $2-$digit number. Here, too, we apply the distributive property of multiplication.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We use the property $\\text{a} \\times (\\text{b} + \\text{c}) = \\text{a} \\times \\text{b} + \\text{a} \\times \\text{c}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Suppose we have to find the product of 8 and 73.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We first expand 73 as $70 + 3$.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Now, we find the product as follows:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$8 \\times (70 + 3) = 8 \\times 70 + 8 \\times 3 = 560 + 24 = 584$<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"5-multiplication-of-a-two-digit-number-with-a-two-digit-number-\"><strong>Multiplication of a Two-Digit Number with a Two-Digit Number<\/strong><\/h3>\n\n\n\n<p class=\"eplus-wrapper\">When we look at the expression $(\\text{a} + \\text{b}) \\times \\text{c} = \\text{a} \\times \\text{c} + \\text{b} \\times \\text{c}$<strong>, <\/strong>we can use this to find the product of a $1-$digit number and a $2-$digit number. What if you have to find the product of two numbers with 2 digits each. What can we do?<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s take this expression itself&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(\\text{a} + \\text{b}) \\times \\text{c} = \\text{a} \\times \\text{c} + \\text{b} \\times \\text{c}$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s replace \u201c<em>c<\/em>\u201d with $(\\text{p} +\\text{q})$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(\\text{a} + \\text{b}) \\times (\\text{p} + \\text{q}) = \\text{a} \\times (\\text{p} + \\text{q}) + \\text{b} \\times (\\text{p} + \\text{q})$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Now we can see that we can apply distributive property in <\/strong>$\\text{a} \\times (\\text{p} + \\text{q})$ and $\\text{b} \\times (\\text{p} + \\text{q})$<strong> separately and add all of them to get the result.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(a + b) \\times (p + q) = (a \\times p) + (a \\times q) + (b \\times p) + (b \\times q)$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"219\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/2-digit-with-2-digit-multiplication.png\" alt=\"2-digit with 2-digit multiplication\" class=\"wp-image-40930\" title=\"2-digit with 2-digit multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/2-digit-with-2-digit-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/2-digit-with-2-digit-multiplication-300x106.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">We can follow the given steps to multiply $2-$digit numbers using the partial product method:<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 1:<\/strong> We take the numbers we want to multiply and expand or break them into parts based on their place value.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Let\u2019s<strong> <\/strong>suppose we want to multiply 12 by 34. We first break each number into parts based on its place value.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $12 = 10 + 2$ and $34 = 30 + 4$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 2:<\/strong> We multiply each part of the expanded form of a number with each part of the expanded form of the other number. Here, each part maintains its place.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Just like we do it in the area model of multiplication, we break the numbers into smaller parts and multiply each part with each other.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Continuing with our example,<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$12 \\times 34 = (10 + 2) \\times (30 + 4)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We multiply the expanded parts of the number, as shown in the image:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"315\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/example-of-partial-product-of-two-numbers.png\" alt=\"Example of partial product of two numbers\" class=\"wp-image-40931\" title=\"Example of partial product of two numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/example-of-partial-product-of-two-numbers.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/example-of-partial-product-of-two-numbers-300x152.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Step 3: <\/strong>We calculate the products of the parts and add them to find the final product of the multiplication problem.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">So, $(10 \\times 30) + (10 \\times 4) + (2 \\times 30) + (2 \\times 4) = 300 + 40 + 60 + 8 = 408$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-fun-fact\">Fun Fact!<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">While the word \u201cpartial\u201d indicates a part of something, it may not always do so. Partial is also used to indicate bias or favor of one side over another.<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper\">We learnt about the method of partial product to multiply two numbers easily along with definition, properties and fun facts. Learn and explore more at <a href=\"https:\/\/www.splashlearn.com\/?adCampaign=15938457564&amp;adGroup=136003246239&amp;adTag=splashlearn&amp;adID=619161893251&amp;ipad_blocker_disabled=1&amp;gclid=CjwKCAjwh4ObBhAzEiwAHzZYU4VryQTZ1ms3CSLgAjnCacyTAcRsEVCFQABO23d-kN50znThqws8hRoCJ4gQAvD_BwE\">SplashLearn<\/a>.&nbsp;<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-solved-examples\">Solved Examples<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><strong>1. Multiply 84 and 36 using the partial products multiplication method.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>Solution: <\/strong>We have to multiply 84 and 36.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We expand<strong> <\/strong>84 and 36.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$84 \\times 36 = (80 + 4) \\times (30 + 6)$&nbsp;&nbsp;&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We multiply each part of the expanded form by 84, with each part of the expanded form of 36.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= (80 \\times 30) + (80 \\times 6) + (4 \\times 30) + (4 \\times 6)$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">We calculate the products and add them.<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$= 2400 + 480 + 120 + 24 = 3024$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>2. The size of a banner is <\/strong>$30 \\times 40$<strong> feet. The banner is increased in size by 3 feet in both length and width. What would be the area of the banner?<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"278\" height=\"179\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/area-model-for-size-of-the-banner.png\" alt=\"Area model for size of the banner\" class=\"wp-image-40932\" title=\"Area model for size of the banner\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Area of the new banner $=$ Sum of partial products $= 1200 + 150 + 200 + 25 = 1575$<\/p>\n\n\n\n<p class=\"eplus-wrapper\"><strong>3. Find the missing numbers.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"278\" height=\"179\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/area-model-for-missing-number.png\" alt=\"Area model for missing number\" class=\"wp-image-40933\" title=\"Area model for missing number\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{A} = 20 \\times 70 = 1400$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{B} = 60 \\div 20 = 3$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{C} = 630 \\div 70 = 9$&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$\\text{D} = \\text{C} \\times \\text{B} = 9 \\times 3 = 27$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-practice-problems\">Practice Problems<\/h2>\n\n\n\n<p class=\"eplus-wrapper\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Partial Product<\/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\">Which of the following is the correct set of partial products for $15 \\times 51$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">200, 50, 15, 2<\/div><div class=\"spq_answer_block\" data-value=\"1\">50, 10, 5, 1<\/div><div class=\"spq_answer_block\" data-value=\"2\">500, 250, 10, 5<\/div><div class=\"spq_answer_block\" data-value=\"3\">250, 500, 25, 10<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 500, 250, 10, 5<br\/>$15 \\times 51 = (10 + 5) \\times (50 + 1)$<br>\r\n$= (10 \\times 50) + (10 \\times 1) + (5 \\times 50) + (5 \\times 1)$<br>\r\n$= 500 + 10 + 250 + 5$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">A carpet measures 11 feet $\\times$ 13 feet. The carpet is increased by adding new fabric and now measures 4 feet longer and 2 feet wider. What is the area of the new carpet?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">220 sq. feet<\/div><div class=\"spq_answer_block\" data-value=\"1\">221 sq. feet<\/div><div class=\"spq_answer_block\" data-value=\"2\">219 sq. feet<\/div><div class=\"spq_answer_block\" data-value=\"3\">201 sq. feet<\/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: 221 sq. feet<br\/>$13 \\times 17 = (10 + 3) \\times (10 + 7)$\r\n$= (10 \\times 10) + (10 \\times 7) + (3 \\times 10) + (3 \\times 7)$\r\n$= 100 + 70 + 30 + 21 = 221$ sq. feet<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">Find the missing numbers.<\/h3><\/span><div class=\"spq_question_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-3-1.png\"><\/div><div class=\"spq_answer_block\" data-value=\"0\">$\\text{A} = 9$, $\\text{B} = 10$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\text{A} = 9$, $\\text{B} = 9$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\text{A} = 10$, $\\text{B} = 7$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\text{A} = 10$, $\\text{B} = 9$<\/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: $\\text{A} = 10$, $\\text{B} = 9$<br\/>$\\text{A} = 200 \\div 20 = 10$<br>\r\n$\\text{B} = 180 \\div 20 = 9$ <\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Partial Product\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Partial Product\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which of the following is the correct set of partial products for $$15 \\\\times 51$$?\",\n                    \"text\": \"Which of the following is the correct set of partial products for $$15 \\\\times 51$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$15 \\\\times 51 = (10 + 5) \\\\times (50 + 1)$$<br>\r\n$$= (10 \\\\times 50) + (10 \\\\times 1) + (5 \\\\times 50) + (5 \\\\times 1)$$<br>\r\n$$= 500 + 10 + 250 + 5$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"200, 50, 15, 2\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$15 \\\\times 51 = (10 + 5) \\\\times (50 + 1)$$<br>\r\n$$= (10 \\\\times 50) + (10 \\\\times 1) + (5 \\\\times 50) + (5 \\\\times 1)$$<br>\r\n$$= 500 + 10 + 250 + 5$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"50, 10, 5, 1\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$15 \\\\times 51 = (10 + 5) \\\\times (50 + 1)$$<br>\r\n$$= (10 \\\\times 50) + (10 \\\\times 1) + (5 \\\\times 50) + (5 \\\\times 1)$$<br>\r\n$$= 500 + 10 + 250 + 5$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"250, 500, 25, 10\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$15 \\\\times 51 = (10 + 5) \\\\times (50 + 1)$$<br>\r\n$$= (10 \\\\times 50) + (10 \\\\times 1) + (5 \\\\times 50) + (5 \\\\times 1)$$<br>\r\n$$= 500 + 10 + 250 + 5$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"500, 250, 10, 5\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$15 \\\\times 51 = (10 + 5) \\\\times (50 + 1)$$<br>\r\n$$= (10 \\\\times 50) + (10 \\\\times 1) + (5 \\\\times 50) + (5 \\\\times 1)$$<br>\r\n$$= 500 + 10 + 250 + 5$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$15 \\\\times 51 = (10 + 5) \\\\times (50 + 1)$$<br>\r\n$$= (10 \\\\times 50) + (10 \\\\times 1) + (5 \\\\times 50) + (5 \\\\times 1)$$<br>\r\n$$= 500 + 10 + 250 + 5$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"A carpet measures 11 feet $$\\\\times$$ 13 feet. The carpet is increased by adding new fabric and now measures 4 feet longer and 2 feet wider. What is the area of the new carpet?\",\n                    \"text\": \"A carpet measures 11 feet $$\\\\times$$ 13 feet. The carpet is increased by adding new fabric and now measures 4 feet longer and 2 feet wider. What is the area of the new carpet?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$13 \\\\times 17 = (10 + 3) \\\\times (10 + 7)$$\r\n$$= (10 \\\\times 10) + (10 \\\\times 7) + (3 \\\\times 10) + (3 \\\\times 7)$$\r\n$$= 100 + 70 + 30 + 21 = 221$$ sq. feet\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"220 sq. feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$13 \\\\times 17 = (10 + 3) \\\\times (10 + 7)$$\r\n$$= (10 \\\\times 10) + (10 \\\\times 7) + (3 \\\\times 10) + (3 \\\\times 7)$$\r\n$$= 100 + 70 + 30 + 21 = 221$$ sq. feet\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"219 sq. feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$13 \\\\times 17 = (10 + 3) \\\\times (10 + 7)$$\r\n$$= (10 \\\\times 10) + (10 \\\\times 7) + (3 \\\\times 10) + (3 \\\\times 7)$$\r\n$$= 100 + 70 + 30 + 21 = 221$$ sq. feet\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"201 sq. feet\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$13 \\\\times 17 = (10 + 3) \\\\times (10 + 7)$$\r\n$$= (10 \\\\times 10) + (10 \\\\times 7) + (3 \\\\times 10) + (3 \\\\times 7)$$\r\n$$= 100 + 70 + 30 + 21 = 221$$ sq. feet\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"221 sq. feet\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$13 \\\\times 17 = (10 + 3) \\\\times (10 + 7)$$\r\n$$= (10 \\\\times 10) + (10 \\\\times 7) + (3 \\\\times 10) + (3 \\\\times 7)$$\r\n$$= 100 + 70 + 30 + 21 = 221$$ sq. feet\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$13 \\\\times 17 = (10 + 3) \\\\times (10 + 7)$$\r\n$$= (10 \\\\times 10) + (10 \\\\times 7) + (3 \\\\times 10) + (3 \\\\times 7)$$\r\n$$= 100 + 70 + 30 + 21 = 221$$ sq. feet\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Find the missing numbers.\",\n                    \"text\": \"Find the missing numbers. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/Practice-Problems-3-1.png\\\"\/>\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$\\\\text{A} = 200 \\\\div 20 = 10$$<br>\r\n$$\\\\text{B} = 180 \\\\div 20 = 9$$ \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\text{A} = 9$$, $$\\\\text{B} = 10$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\text{A} = 200 \\\\div 20 = 10$$<br>\r\n$$\\\\text{B} = 180 \\\\div 20 = 9$$ \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\text{A} = 9$$, $$\\\\text{B} = 9$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\text{A} = 200 \\\\div 20 = 10$$<br>\r\n$$\\\\text{B} = 180 \\\\div 20 = 9$$ \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\text{A} = 10$$, $$\\\\text{B} = 7$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$\\\\text{A} = 200 \\\\div 20 = 10$$<br>\r\n$$\\\\text{B} = 180 \\\\div 20 = 9$$ \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\text{A} = 10$$, $$\\\\text{B} = 9$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$\\\\text{A} = 200 \\\\div 20 = 10$$<br>\r\n$$\\\\text{B} = 180 \\\\div 20 = 9$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$\\\\text{A} = 200 \\\\div 20 = 10$$<br>\r\n$$\\\\text{B} = 180 \\\\div 20 = 9$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-frequently-asked-questions\">Frequently Asked Questions<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-7542e455-8d3a-4b64-92e6-5bed9b2b0d74\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n\n<div style=\"border-color:#f1f1f1\" class=\"wp-block-ub-content-toggle-panel wp-block-ub-content-toggle-accordion\"><div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" style=\"background-color:#f1f1f1\"><span class=\"wp-block-ub-content-toggle-accordion-title\" style=\"color:#000000\"><strong>Why do we need to know place value to learn partial products?<\/strong><\/span><span class=\"wp-block-ub-content-toggle-accordion-state-indicator dashicons dashicons-arrow-right-alt2 \"><\/span><\/div><div style=\"height:0;padding-top:0;padding-bottom:0\" class=\"wp-block-ub-content-toggle-accordion-content-wrap\">\n<p class=\"eplus-wrapper\">Place value helps us understand each digit\u2019s position in a number and expand them to break down numbers. Example: $27 = 20 + 7, 358 = 300 + 50 + 8$<\/p>\n<\/div><\/div>\n\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-1-7542e455-8d3a-4b64-92e6-5bed9b2b0d74\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7542e455-8d3a-4b64-92e6-5bed9b2b0d74\"><strong>Can we use the partial products method to multiply two algebraic expressions?<\/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-1-7542e455-8d3a-4b64-92e6-5bed9b2b0d74\">\n\n<p class=\"eplus-wrapper\">Yes. Let\u2019s take an example:&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$(2x + 3y) \u00d7 (3x + 7y) = (2x \\times 3x) + (2x \\times 7y) + (3y \\times 3x) + (3y \\times 7y),$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">where all the four individual products are the partial products.<\/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-2-7542e455-8d3a-4b64-92e6-5bed9b2b0d74\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-7542e455-8d3a-4b64-92e6-5bed9b2b0d74\"><strong>Can we use the partial products method to find the product of three-digit and four-digit numbers?<\/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-2-7542e455-8d3a-4b64-92e6-5bed9b2b0d74\">\n\n<p class=\"eplus-wrapper\">Yes, the partial products method can be used to find the product of three-digit and four-digit numbers as well. We break the numbers according to place value and follow the same steps. Let\u2019s take an example of multiplying 315 and 241:<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$315 = 300 + 10 + 5$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$241 = 200 + 40 + 1$<\/p>\n\n\n\n<p class=\"eplus-wrapper\">Using the area model,&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"283\" height=\"230\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2022\/11\/FAQs-3.png\" alt=\"Multiplication of 3-digit numbers\" class=\"wp-image-13823\" title=\"Multiplication of 3-digit numbers\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper\">Product of $315$ and $241 =$ Sum of partial products&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper\">$315 \\times 241 = 60000 + 12000 + 300 + 2000 + 400 + 10 + 1000 + 200 + 5 = 75,915$<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What is a Partial Product? Partial means something that is incomplete or exists only in parts. Suppose you take a pizza and cut it into slices. Each of the slices will be a partial part of the pizza. So, what does partial product mean in math? When we say partial product, we mean breaking down &#8230; <a title=\"Partial Product\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/partial-product\" aria-label=\"More on Partial Product\">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-2150","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\/2150","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=2150"}],"version-history":[{"count":20,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2150\/revisions"}],"predecessor-version":[{"id":40934,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/2150\/revisions\/40934"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=2150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=2150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=2150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}