{"id":669,"date":"2022-03-11T12:57:08","date_gmt":"2022-03-11T12:57:08","guid":{"rendered":"https:\/\/www.splashlearn.com\/article-test\/?page_id=669"},"modified":"2024-03-27T03:37:53","modified_gmt":"2024-03-27T03:37:53","slug":"long-multiplication-definition-with-examples","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/long-multiplication","title":{"rendered":"Long Multiplication: Definition with Examples"},"content":{"rendered":"\n<div class=\"wp-block-columns eplus-wrapper is-layout-flex wp-container-core-columns-is-layout-8f761849 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column eplus-wrapper is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\"><div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-6b728fa6-9ff4-4682-b156-716155185a6a\" 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\/long-multiplication#0-what-is-long-multiplication>What Is Long Multiplication?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/long-multiplication#2-how-to-multiply-using-long-multiplication>How to Multiply Using Long Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/long-multiplication#3-long-multiplication-column-method>Long Multiplication Column Method<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/long-multiplication#9-solved-examples-on-long-multiplication>Solved Examples on Long Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/long-multiplication#10-practice-problems-on-long-multiplication>Practice Problems on Long Multiplication<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/long-multiplication#11-frequently-asked-questions-on-long-multiplication>Frequently Asked Questions on Long Multiplication<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"0-what-is-long-multiplication\">What Is Long Multiplication?<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Long multiplication is a method of multiplying large numbers easily. It simplifies the process of multiplication of two numbers that are not otherwise easy to multiply.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>For example,<\/strong> we can easily find the product of $55 \\times 20$ by multiplying 55 by 2 and then adding a 0 at the rightmost place of the answer.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$55 \\times 2 = 110$ and $55 \\times 20 = 1100$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">However, sometimes, finding the product is not this easy. In such cases, we use the method of long multiplication. It is often termed as the long hand multiplication (long multiplication by hand).<\/p>\n\n\n\n<h3 class=\"wp-block-heading eplus-wrapper\" id=\"1-long-multiplication-definition\">Long Multiplication: Definition<\/h3>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Long multiplication is a method of multiplication using which multiplying two large numbers that have two or more digits becomes easier.<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, we can easily find the product of $55 \\times 20$ by multiplying 55 by 2 and then adding a 0 at the rightmost place of the answer.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$55 \\times 2 = 110$ and $55 \\times 20 = 1100$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">But how to multiply large numbers? Many times, finding the product is not this easy. In such cases, we use the long method of multiplication.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example: $47 \\times 63 =$ ?<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We can find the answer in simple steps using long multiplication. Let\u2019s discuss the method in detail in the next section.&nbsp;<\/p>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/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-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-long-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_6_to_9_d_pt.png\" alt=\"Complete the Long 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 Long 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-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 class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/complete-the-multiplication-fact-of-11\" 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_missing_num_pt.png\" alt=\"Complete the Multiplication Fact of 11 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 Fact of 11 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 = 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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-how-to-multiply-using-long-multiplication\">How to Multiply Using Long Multiplication<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s discuss the steps for multiplying a two-digit number by a two-digit number using the long multiplication method.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let us multiply 47 by 63 using the <strong>long multiplication method<\/strong>.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1: <\/strong>First, write the two numbers, one below the other, such that their place values are aligned. We generally write the bigger number on top and a multiplication sign on the left and draw a line below the numbers as shown below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-1.png\" alt=\"long multiplication step 1\" class=\"wp-image-41189\" title=\"long multiplication step 1\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-1.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-1-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Important Note:<\/strong>&nbsp;<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">In the long multiplication method, the number on the top (63) is called the <strong>multiplicand<\/strong>. The number by which it is multiplied, that is, the number at the bottom (47), is called the <strong>multiplier<\/strong>.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">If you write the small number on the top and perform the multiplication, the answer will still be the same since the order does not matter while multiplying two numbers.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2: <\/strong>Multiply the ones digit of the top number by the ones digit of the bottom number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Write the product as shown in the image. Don\u2019t forget the carryover that goes in the next place!<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-2.png\" alt=\"long multiplication step 2\" class=\"wp-image-41190\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-2.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-2-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 3: <\/strong>Multiply the tens digit of the top number by the ones digit of the bottom number. Add the carryover.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-3.png\" alt=\"long multiplication step 3\" class=\"wp-image-41192\" title=\"long multiplication step 3\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-3.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-3-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This is our first partial product which we got by multiplying the top number by the ones digit of the bottom number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 4:<\/strong> Now, we place a 0 below the ones digit as shown. This is because we will now be multiplying the digits of the top number by the tens digit of the bottom number.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-4.png\" alt=\"long multiplication step 4\" class=\"wp-image-41193\" title=\"long multiplication step 4\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-4.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-4-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 5:<\/strong> Multiply the ones digit of the top number by the tens digit of the bottom number.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-5.png\" alt=\"long multiplication step 5\" class=\"wp-image-41194\" title=\"long multiplication step 5\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-5.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-5-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 6: <\/strong>Multiply the tens digit of the top number by the tens digit of the bottom number.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-6.png\" alt=\"long multiplication step 6\" class=\"wp-image-41195\" title=\"long multiplication step 6\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-6.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-6-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">This is the second partial product obtained by multiplying the top number by the tens digit of the bottom number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 7: <\/strong>Now, add the two partial products.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-7.png\" alt=\"long multiplication step 7\" class=\"wp-image-41196\" title=\"long multiplication step 7\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-7.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-step-7-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s summarize.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"328\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-of-63-with-47.png\" alt=\"long multiplication of 63 with 47\" class=\"wp-image-41197\" title=\"long multiplication of 63 with 47\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-of-63-with-47.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-of-63-with-47-300x159.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">We follow the above <strong>long multiplication steps<\/strong> only for multiplying numbers greater than two digits.<\/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-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\" 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-multiplication-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-multiplication-sentence.jpeg\" alt=\"Complete Multiplication 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 eplus-wrapper\" id=\"3-long-multiplication-column-method\">Long Multiplication Column Method<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Long multiplication is also known as the column method of multiplication since we perform the multiplication vertically or column wise.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let\u2019s take another example to understand this better.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Multiply 321 by 23.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Take a look at the long multiplication chart that shows the long multiplication step by step. You can refer to it to avoid mistakes when solving long multiplication problems.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"782\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-column-method-example.png\" alt=\"Long multiplication column method example\" class=\"wp-image-41198\" title=\"Long multiplication column method example\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-column-method-example.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/long-multiplication-column-method-example-238x300.png 238w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"4-multiplying-decimals-using-long-multiplication\">Multiplying Decimals Using Long Multiplication<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let&#8217;s understand <strong>how to multiply<\/strong> decimals with the help of the <strong>long multiplication<\/strong> method.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: Multiply <\/strong>$3.6 \\times 5.5$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1<\/strong>: First, we place the smaller number out of the two on the right-hand side and change the decimal number to a fraction.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$5.5 \\times 3.6 = \\frac{55}{10} \\times \\frac{36}{10}$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2<\/strong>: Then, we multiply the numerators using the steps of the long multiplication method. We leave the denominator as it is for now.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"489\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/55-multiplied-by-36-using-long-multiplication.png\" alt=\"55 multiplied by 36 using long multiplication\" class=\"wp-image-41199\" title=\"55 multiplied by 36 using long multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/55-multiplied-by-36-using-long-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/55-multiplied-by-36-using-long-multiplication-300x237.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 3<\/strong>: Now, we divide the answer (that we got in step 2) by the denominator to get the final answer.&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$\\frac{1980}{100} = 19.80$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"5-long-multiplication-using-the-horizontal-method\">Long Multiplication Using the Horizontal Method<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Let&#8217;s now understand how to use the horizontal method with the help of a long multiplication example. As the name suggests, we multiply the numbers horizontally but follow the same steps as we discussed earlier.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Example: Multiply 48 by 24.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 1<\/strong>: First, we write the numbers beside each other and place them horizontally.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$48 \\times 24$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 2<\/strong>: Now, we multiply the second number (number on the right side) with the ones digit of the first number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we multiply 24 with 8, since 8 is at the ones place in 48.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$24 \\times 8 = 192$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 3<\/strong>: Now, we multiply the second number with the tens digit of the first number.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Here, we multiply 24 with 40, since 4 is at the tens place in 48.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$24 \\times 40 = 960$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Step 4<\/strong>: Finally, we add the partial products obtained from steps 2 and 3 to get the final answer.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"317\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/addition-of-partial-products-in-long-multiplication.png\" alt=\"Addition of partial products in long multiplication\" class=\"wp-image-41200\" title=\"Addition of partial products in long multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/addition-of-partial-products-in-long-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/addition-of-partial-products-in-long-multiplication-300x153.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, $48 \\times 24 = 1152$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"6-long-multiplication-with-negative-numbers\">Long Multiplication with Negative Numbers<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The multiplication of negative numbers using the method of <strong>long multiplication <\/strong>follows the same steps as mentioned above.&nbsp;However, we have to carefully consider the signs of the two numbers in order to decide the sign of the product.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For instance, when we multiply two negative numbers with each other, the sign of the result remains positive. On the other hand, it becomes negative when a negative number and a positive number are multiplied.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The figure below shows how the sign changes upon multiplication with negative numbers:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"466\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/rules-for-multiplying-signed-numbers.png\" alt=\"Rules for multiplying signed numbers\" class=\"wp-image-41201\" title=\"Rules for multiplying signed numbers\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/rules-for-multiplying-signed-numbers.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/rules-for-multiplying-signed-numbers-300x225.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"7-fun-facts-about-long-multiplication\">Fun Facts about Long Multiplication<\/h2>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Long multiplication<\/strong> is also known as the column method of multiplication.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Whenever any number is multiplied by zero, the answer is also zero.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">When the number 9 is multiplied by any other number, the sum of digits in the product is always 9.<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, $9 \\times 25 = 225$ and $2 + 2 + 5 = 9$;&nbsp;<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$9 \\times 9 = 81$ and $8 + 1 = 9$.<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\"><strong>Long multiplication<\/strong> can also be referred to as repeated addition because multiplying any number is just an alternative to adding it repeatedly.<\/li>\n<\/ul>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Whenever any even number from 0 to 9 is multiplied by 6, the product has the same even number in the ones digit.&nbsp;<\/li>\n<\/ul>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">For example, $6 \\times 4 = 24,\\;&nbsp; 6 \\times 2 = 12$<\/p>\n\n\n\n<ul class=\"eplus-wrapper wp-block-list\">\n<li class=\"eplus-wrapper\">Whenever two large numbers (let\u2019s say three-digit or four-digit numbers) are multiplied, the process of long multiplication remains the same. For example:<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"388\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/112-multiplied-by-232-using-long-multiplication.png\" alt=\"112 multiplied by 232 using long multiplication\" class=\"wp-image-41202\" title=\"112 multiplied by 232 using long multiplication\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/112-multiplied-by-232-using-long-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/112-multiplied-by-232-using-long-multiplication-300x188.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Long multiplication<\/strong> is a method that simplifies the multiplication of large numbers, including two-digit, three-digit numbers, etc., with each other. Let\u2019s solve a few examples and practice problems based on long multiplication!<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"9-solved-examples-on-long-multiplication\">Solved Examples on Long Multiplication<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>1.&nbsp;Multiply 38 by 91 using the column method.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong><br><\/strong><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"201\" height=\"264\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/91-multiplied-by-38-using-long-multiplication.png\" alt=\"91 multiplied by 38 using long multiplication\" class=\"wp-image-41183\" title=\"91 multiplied by 38 using long multiplication\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>2. Multiply 72 by 44 using the column method.<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong><br><\/strong><strong>Solution<\/strong>:&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"195\" height=\"266\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/72-multiplied-by-44-using-long-multiplication.png\" alt=\"72 multiplied by 44 using long multiplication\" class=\"wp-image-41184\" style=\"width:195px;height:266px\" title=\"72 multiplied by 44 using long multiplication\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>3. Multiply <\/strong><strong>&#8211;<\/strong><strong>58 by 30.<\/strong><strong><br><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><br>The sign of the product when we calculate $(\\;-\\;58) \\times (30)$ will be negative.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"194\" height=\"264\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/58-multiplied-by-30-using-long-multiplication.png\" alt=\"58 multiplied by 30 using long multiplication\" class=\"wp-image-41185\" title=\"58 multiplied by 30 using long multiplication\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since 58 has a negative sign, the final answer will be $<strong>&#8211;<\/strong>1740$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(\\;-\\;58) \\times (30) = \\;-\\;1740$<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>4. Alia bought 42 notebooks, each worth <\/strong>$\\$9.6$<strong>. How much did she spend?<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:<\/strong><br><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">To find the amount Alia spent, multiply 9.6 by 42.<br><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$9.6 \\times 42 = \\frac{96}{10} \\times 42$<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"197\" height=\"259\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/96-multiplied-by-42-using-long-multiplication.png\" alt=\"96 multiplied by 42 using long multiplication\" class=\"wp-image-41186\" title=\"96 multiplied by 42 using long multiplication\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Now, we divide 4032 by 10 to get the final answer, which is $403.2$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$9.6 \\times 42 = 403.2$<br><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Thus, Alia spent $403.2 on notebooks.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>5. Multiply <\/strong>$-70$<strong> and <\/strong>$-15$<strong>.<br><\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><br>Let\u2019s find $(70) \\times (15)$.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full eplus-wrapper\"><img loading=\"lazy\" decoding=\"async\" width=\"185\" height=\"264\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2024\/03\/70-multiplied-by-15-using-long-multiplication.png\" alt=\"70 multiplied by 15 using long multiplication\" class=\"wp-image-41187\" title=\"70 multiplied by 15 using long multiplication\"\/><\/figure>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Since both the numbers are negative, the final answer will remain positive, $1050$.<\/p>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\">$(70) \\times (15) = 1050$<\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"10-practice-problems-on-long-multiplication\">Practice Problems on Long Multiplication<\/h2>\n\n\n\n<p class=\"eplus-wrapper wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Long Multiplication: Definition with Examples<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">Multiply 95 by 13 using the column method.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">1125<\/div><div class=\"spq_answer_block\" data-value=\"1\">1235<\/div><div class=\"spq_answer_block\" data-value=\"2\">1545<\/div><div class=\"spq_answer_block\" data-value=\"3\">1425<\/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: 1235<br\/>$95\\times13 = 1235$<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problem-1.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Multiply the decimals 1.2 and 6.7.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">9.05<\/div><div class=\"spq_answer_block\" data-value=\"1\">13.5<\/div><div class=\"spq_answer_block\" data-value=\"2\">8.04<\/div><div class=\"spq_answer_block\" data-value=\"3\">6.08<\/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: 8.04<br\/>$6.7\\times1.2=\\frac{67}{10}\\times\\frac{12}{10}$<br>\r\nFirst, we multiply the numerators. Then, we divide their product with the denominators to reach the final answer.<\/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\">Multiply the negative numbers $(-\\;89)$ and $(-\\;61)$.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5429<\/div><div class=\"spq_answer_block\" data-value=\"1\">3489<\/div><div class=\"spq_answer_block\" data-value=\"2\">5299<\/div><div class=\"spq_answer_block\" data-value=\"3\">4529<\/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: 5429<br\/>Since both the numbers are negative, the final answer will remain positive.<br>\r\n$(-\\;89)\\times(-\\;61) = 5429$.<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/practice-problem-3.png\"><\/div><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">Multiply 45 by 21 using the horizontal method.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">645<\/div><div class=\"spq_answer_block\" data-value=\"1\">745<\/div><div class=\"spq_answer_block\" data-value=\"2\">845<\/div><div class=\"spq_answer_block\" data-value=\"3\">945<\/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: 945<br\/>$21\\times5=105$  \t\t\t__(i)<br>\r\n$21\\times4=84$  \t\t\t__(ii)<br>\r\nAdding (i) and (ii), we get<br>\r\n$105\\;+\\;84=945$.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Multiply 530 by 22.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">12600<\/div><div class=\"spq_answer_block\" data-value=\"1\">13550<\/div><div class=\"spq_answer_block\" data-value=\"2\">11660<\/div><div class=\"spq_answer_block\" data-value=\"3\">14650<\/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: 11660<br\/>$530\\times22 = 11660$<\/span><div class=\"spq_explanation_image\"><img decoding=\"async\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/practice-problem-5.png\"><\/div><\/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\": \"Long Multiplication: Definition with Examples\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Long Multiplication\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Multiply 95 by 13 using the column method.\",\n                    \"text\": \"Multiply 95 by 13 using the column method.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$95\\\\times13 = 1235$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1125\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$95\\\\times13 = 1235$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1545\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$95\\\\times13 = 1235$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"1425\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$95\\\\times13 = 1235$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"1235\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$95\\\\times13 = 1235$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problem-1.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$95\\\\times13 = 1235$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/Practice-Problem-1.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Multiply the decimals 1.2 and 6.7.\",\n                    \"text\": \"Multiply the decimals 1.2 and 6.7.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$6.7\\\\times1.2=\\\\frac{67}{10}\\\\times\\\\frac{12}{10}$$<br>\r\nFirst, we multiply the numerators. Then, we divide their product with the denominators to reach the final answer.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"9.05\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$6.7\\\\times1.2=\\\\frac{67}{10}\\\\times\\\\frac{12}{10}$$<br>\r\nFirst, we multiply the numerators. Then, we divide their product with the denominators to reach the final answer.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"13.5\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$6.7\\\\times1.2=\\\\frac{67}{10}\\\\times\\\\frac{12}{10}$$<br>\r\nFirst, we multiply the numerators. Then, we divide their product with the denominators to reach the final answer.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"6.08\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$6.7\\\\times1.2=\\\\frac{67}{10}\\\\times\\\\frac{12}{10}$$<br>\r\nFirst, we multiply the numerators. Then, we divide their product with the denominators to reach the final answer.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8.04\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$6.7\\\\times1.2=\\\\frac{67}{10}\\\\times\\\\frac{12}{10}$$<br>\r\nFirst, we multiply the numerators. Then, we divide their product with the denominators to reach the final answer.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$6.7\\\\times1.2=\\\\frac{67}{10}\\\\times\\\\frac{12}{10}$$<br>\r\nFirst, we multiply the numerators. Then, we divide their product with the denominators to reach the final answer.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Multiply the negative numbers $$(-\\\\;89)$$ and $$(-\\\\;61)$$.\",\n                    \"text\": \"Multiply the negative numbers $$(-\\\\;89)$$ and $$(-\\\\;61)$$.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"Since both the numbers are negative, the final answer will remain positive.<br>\r\n$$(-\\\\;89)\\\\times(-\\\\;61) = 5429$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"3489\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since both the numbers are negative, the final answer will remain positive.<br>\r\n$$(-\\\\;89)\\\\times(-\\\\;61) = 5429$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5299\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since both the numbers are negative, the final answer will remain positive.<br>\r\n$$(-\\\\;89)\\\\times(-\\\\;61) = 5429$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4529\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"Since both the numbers are negative, the final answer will remain positive.<br>\r\n$$(-\\\\;89)\\\\times(-\\\\;61) = 5429$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"5429\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"Since both the numbers are negative, the final answer will remain positive.<br>\r\n$$(-\\\\;89)\\\\times(-\\\\;61) = 5429$$. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/practice-problem-3.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"Since both the numbers are negative, the final answer will remain positive.<br>\r\n$$(-\\\\;89)\\\\times(-\\\\;61) = 5429$$. <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/practice-problem-3.png\\\"\/>\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Multiply 45 by 21 using the horizontal method.\",\n                    \"text\": \"Multiply 45 by 21 using the horizontal method.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$21\\\\times5=105$$  \t\t\t__(i)<br>\r\n$$21\\\\times4=84$$  \t\t\t__(ii)<br>\r\nAdding (i) and (ii), we get<br>\r\n$$105\\\\;+\\\\;84=945$$.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"645\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$21\\\\times5=105$$  \t\t\t__(i)<br>\r\n$$21\\\\times4=84$$  \t\t\t__(ii)<br>\r\nAdding (i) and (ii), we get<br>\r\n$$105\\\\;+\\\\;84=945$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"745\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$21\\\\times5=105$$  \t\t\t__(i)<br>\r\n$$21\\\\times4=84$$  \t\t\t__(ii)<br>\r\nAdding (i) and (ii), we get<br>\r\n$$105\\\\;+\\\\;84=945$$.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"845\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$21\\\\times5=105$$  \t\t\t__(i)<br>\r\n$$21\\\\times4=84$$  \t\t\t__(ii)<br>\r\nAdding (i) and (ii), we get<br>\r\n$$105\\\\;+\\\\;84=945$$.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"945\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$21\\\\times5=105$$  \t\t\t__(i)<br>\r\n$$21\\\\times4=84$$  \t\t\t__(ii)<br>\r\nAdding (i) and (ii), we get<br>\r\n$$105\\\\;+\\\\;84=945$$.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$21\\\\times5=105$$  \t\t\t__(i)<br>\r\n$$21\\\\times4=84$$  \t\t\t__(ii)<br>\r\nAdding (i) and (ii), we get<br>\r\n$$105\\\\;+\\\\;84=945$$.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Multiply 530 by 22.\",\n                    \"text\": \"Multiply 530 by 22.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"$$530\\\\times22 = 11660$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"12600\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$530\\\\times22 = 11660$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"13550\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$530\\\\times22 = 11660$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"14650\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"$$530\\\\times22 = 11660$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"11660\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"$$530\\\\times22 = 11660$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/practice-problem-5.png\\\"\/>\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"$$530\\\\times22 = 11660$$ <img src=\\\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/04\/practice-problem-5.png\\\"\/>\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading eplus-wrapper\" id=\"11-frequently-asked-questions-on-long-multiplication\">Frequently Asked Questions on Long Multiplication<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-8b0e85fd-231c-4781-af09-4606b76f2f22\" 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-0-8b0e85fd-231c-4781-af09-4606b76f2f22\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b0e85fd-231c-4781-af09-4606b76f2f22\"><strong>What are negative 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-0-8b0e85fd-231c-4781-af09-4606b76f2f22\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Negative numbers are those whose value is less than zero and thus have a negative sign (-) before them.<\/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-1-8b0e85fd-231c-4781-af09-4606b76f2f22\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b0e85fd-231c-4781-af09-4606b76f2f22\"><strong>What are positive 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-1-8b0e85fd-231c-4781-af09-4606b76f2f22\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Positive numbers are those whose value is greater than zero.<\/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-2-8b0e85fd-231c-4781-af09-4606b76f2f22\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b0e85fd-231c-4781-af09-4606b76f2f22\"><strong>What is a decimal?<\/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-2-8b0e85fd-231c-4781-af09-4606b76f2f22\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">A decimal number represents the number that separates a whole number from a fractional number. It is represented by a dot (.) sign.<\/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-3-8b0e85fd-231c-4781-af09-4606b76f2f22\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b0e85fd-231c-4781-af09-4606b76f2f22\"><strong>What is the meaning of the horizontal method of multiplication?<\/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-3-8b0e85fd-231c-4781-af09-4606b76f2f22\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The horizontal method refers to a method wherein numbers are arranged in a horizontal line from left to right.<\/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-4-8b0e85fd-231c-4781-af09-4606b76f2f22\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b0e85fd-231c-4781-af09-4606b76f2f22\"><strong>What is the meaning of the column method of multiplication?<\/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-4-8b0e85fd-231c-4781-af09-4606b76f2f22\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">The column method refers to a method wherein numbers are placed one below the other from top to bottom.<\/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-5-8b0e85fd-231c-4781-af09-4606b76f2f22\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-8b0e85fd-231c-4781-af09-4606b76f2f22\"><strong>What is short multiplication?<\/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-5-8b0e85fd-231c-4781-af09-4606b76f2f22\">\n\n<p class=\"eplus-wrapper wp-block-paragraph\">Short multiplication is the method of multiplication commonly used when multiplying a three-digit or larger number with a single-digit number.<\/p>\n\n<\/div><\/div>\n<\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>What Is Long Multiplication? Long multiplication is a method of multiplying large numbers easily. It simplifies the process of multiplication of two numbers that are not otherwise easy to multiply. For example, we can easily find the product of $55 \\times 20$ by multiplying 55 by 2 and then adding a 0 at the rightmost &#8230; <a title=\"Long Multiplication: Definition with Examples\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/multiplication\/long-multiplication\" aria-label=\"More on Long Multiplication: Definition with Examples\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-669","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\/669","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=669"}],"version-history":[{"count":33,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/669\/revisions"}],"predecessor-version":[{"id":41203,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/669\/revisions\/41203"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}