{"id":23326,"date":"2026-10-03T06:32:18","date_gmt":"2026-10-03T06:32:18","guid":{"rendered":"https:\/\/oratrics.com\/blogs\/?p=23326"},"modified":"2026-10-03T07:29:30","modified_gmt":"2026-10-03T07:29:30","slug":"vedic-math-techniques-multiply-large-numbers","status":"publish","type":"post","link":"https:\/\/oratrics.com\/blogs\/math-explorer-program\/vedic-math-techniques-multiply-large-numbers\/","title":{"rendered":"Vedic Math Techniques to Multiply Large Numbers: 4 Methods with Step-by-Step Examples"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"23326\" class=\"elementor elementor-23326\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2043075 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"2043075\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0c4568b\" data-id=\"0c4568b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-34f95c6\" data-id=\"34f95c6\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-95c98cd elementor-widget elementor-widget-heading\" data-id=\"95c98cd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Vedic Math Techniques to Multiply Large Numbers: 4 Methods with Step-by-Step Examples\n<\/h1>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-51ff264 elementor-widget elementor-widget-text-editor\" data-id=\"51ff264\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Try multiplying 4,568 by 9,999 on paper. By the third row of partial products, most people are squinting at their own handwriting and hoping they didn&#8217;t slip somewhere. Vedic math techniques multiply large numbers with far less writing, and some problems you can finish in one line. Below are four methods, each with examples you can follow along with a pen.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d8d694e elementor-align-center elementor-widget elementor-widget-button\" data-id=\"d8d694e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/demo.oratrics.com\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Book a Free Demo Today<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a85aed2 elementor-widget elementor-widget-image\" data-id=\"a85aed2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"647\" src=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Vedic-Math_-Multiply-Large-Numbers-Fast-1024x647.webp\" class=\"attachment-large size-large wp-image-23491\" alt=\"Vedic Math techniques to multiply large numbers quickly using simple mental math methods\" srcset=\"https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Vedic-Math_-Multiply-Large-Numbers-Fast-1024x647.webp 1024w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Vedic-Math_-Multiply-Large-Numbers-Fast-300x190.webp 300w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Vedic-Math_-Multiply-Large-Numbers-Fast-768x486.webp 768w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Vedic-Math_-Multiply-Large-Numbers-Fast-1536x971.webp 1536w, https:\/\/blog.oratrics.com\/wp-content\/uploads\/2026\/10\/Vedic-Math_-Multiply-Large-Numbers-Fast.webp 1577w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4a7658f\" data-id=\"4a7658f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-31ed9f4 elementor-widget elementor-widget-html\" data-id=\"31ed9f4\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t\t<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\r\n<link href=\"https:\/\/fonts.googleapis.com\/css2?family=Poppins:wght@400;500;600;700&display=swap\" rel=\"stylesheet\">\r\n\r\n<div class=\"toc-wrapper\">\r\n    \r\n    \r\n    <div class=\"custom-toc\" id=\"custom-toc\">\r\n        <div class=\"toc-title\">\r\n            \u2630 Table of Contents\r\n        <\/div>\r\n        <ul class=\"toc-list\" id=\"toc-list\"><\/ul>\r\n    <\/div>\r\n    \r\n<\/div>\r\n\r\n<style>\r\n\/* Parent Fixed Wrapper holding both components together *\/\r\n.toc-wrapper {\r\n    position: fixed;\r\n    top: 150px; 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\r\n        overflow-y: visible;\r\n    }\r\n\r\n    .custom-toc .toc-title {\r\n        font-size: 25px;\r\n    }\r\n\r\n    .custom-toc .toc-list a {\r\n        font-size: 14px;\r\n    }\r\n}\r\n<\/style>\r\n\r\n<script>\r\ndocument.addEventListener(\"DOMContentLoaded\", function () {\r\n    const tocList = document.getElementById(\"toc-list\");\r\n    const h1 = document.querySelector(\"h1\");\r\n    const h2s = document.querySelectorAll(\"h2\");\r\n\r\n    function createId(text) {\r\n        return text.toLowerCase().replace(\/[^a-z0-9]+\/g, '-');\r\n    }\r\n\r\n    if (h1) {\r\n        if (!h1.id) {\r\n            h1.id = createId(h1.innerText);\r\n        }\r\n        const li = document.createElement(\"li\");\r\n        li.innerHTML = `<a href=\"#${h1.id}\">${h1.innerText}<\/a>`;\r\n        tocList.appendChild(li);\r\n    }\r\n\r\n    h2s.forEach(h2 => {\r\n        if (!h2.id) {\r\n            h2.id = createId(h2.innerText);\r\n        }\r\n        const li = document.createElement(\"li\");\r\n        li.classList.add(\"toc-h2\");\r\n        li.innerHTML = `<a href=\"#${h2.id}\">${h2.innerText}<\/a>`;\r\n        tocList.appendChild(li);\r\n    });\r\n});\r\n<\/script>\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-bbb9821 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"bbb9821\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-06397d1\" data-id=\"06397d1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-3acf78e\" data-id=\"3acf78e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-be7f3a3 elementor-widget elementor-widget-heading\" data-id=\"be7f3a3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">What Is Vedic Math?\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0ecfcb6 elementor-widget elementor-widget-text-editor\" data-id=\"0ecfcb6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Vedic math is a collection of mental calculation shortcuts popularised by Bharati Krishna Tirthaji in his 1965 book <\/span><i><span style=\"font-weight: 400;\">Vedic Mathematics<\/span><\/i><span style=\"font-weight: 400;\">. It&#8217;s organised around 16 sutras, which are short rules. Each one suits a particular kind of problem.<\/span><\/p><p><span style=\"font-weight: 400;\">One honest point: historians haven&#8217;t found these sutras in the ancient Vedic texts, and many doubt the connection. That doesn&#8217;t change the maths. The shortcuts are correct and they work, so use them as extra tools next to the standard method, not instead of it.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f87ea8a\" data-id=\"f87ea8a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-840c51e elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"840c51e\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-55730b8\" data-id=\"55730b8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c643a30\" data-id=\"c643a30\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7515685 elementor-widget elementor-widget-heading\" data-id=\"7515685\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">How Do I Multiply Large Numbers Using Vedic Math Techniques?\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-146eb8e elementor-widget elementor-widget-text-editor\" data-id=\"146eb8e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Look at the numbers before you start. Five seconds of looking usually tells you which method to use.<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Both numbers sit near 100, 1,000, 10,000 or another power of 10? Use <\/span><b>Nikhilam<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Numbers look random? Use <\/span><b>Urdhva Tiryagbhyam<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">One number is all 9s, like 999 or 99,999? Use <\/span><b>Ekanyunena Purvena<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Numbers sit near 50, 500 or 5,000? Use <\/span><b>Anurupyena<\/b><span style=\"font-weight: 400;\">, the working base method.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">These are the Vedic math methods for multiplying big numbers quickly. Let&#8217;s take them one by one.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-711261d\" data-id=\"711261d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-cf451c6 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"cf451c6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-1d362db\" data-id=\"1d362db\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9f5c093\" data-id=\"9f5c093\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6430764 elementor-widget elementor-widget-heading\" data-id=\"6430764\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Method 1: Nikhilam Sutra (Subtract from the Base)\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e39ad13 elementor-widget elementor-widget-text-editor\" data-id=\"e39ad13\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>Works best when:<\/b><span style=\"font-weight: 400;\"> both numbers are close to 100, 1,000, 10,000, 100,000 and so on.<\/span><\/p><p><i><span style=\"font-weight: 400;\">Nikhilam Navatashcaramam Dashatah<\/span><\/i><span style=\"font-weight: 400;\"> is usually translated as &#8220;all from 9 and the last from 10.&#8221; You don&#8217;t need to remember that. What matters is the idea: measure how far each number is from the base, and work with those small gaps instead of the big numbers.<\/span><\/p><h4><b>Example 1: 998 \u00d7 997<\/b><\/h4><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The base is 1,000.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The gaps are 1,000 \u2212 998 = 2 and 1,000 \u2212 997 = 3.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Subtract one gap from the <\/span><i><span style=\"font-weight: 400;\">other<\/span><\/i><span style=\"font-weight: 400;\"> number: 998 \u2212 3 = 995. (Try 997 \u2212 2 and you get 995 again, which is a handy built-in check.)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply the gaps: 2 \u00d7 3 = 6. The base has three zeros, so the right side needs three digits. Write 006.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Join the parts: <\/span><b>995,006<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ol><h4><b>Example 2, with 6-digit numbers: 999,988 \u00d7 999,994<\/b><\/h4><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The base is 1,000,000. The gaps are 12 and 6.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Cross subtract: 999,988 \u2212 6 = 999,982.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply the gaps: 12 \u00d7 6 = 72. The right side needs six digits, so write 000072.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The answer is <\/span><b>999,982,000,072<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ol><h4><b>When both numbers are above the base<\/b><\/h4><p><span style=\"font-weight: 400;\">Take 1,012 \u00d7 1,005. The extras over 1,000 are +12 and +5. This time you cross <\/span><i><span style=\"font-weight: 400;\">add<\/span><\/i><span style=\"font-weight: 400;\">: 1,012 + 5 = 1,017. Multiply the extras: 12 \u00d7 5 = 60, written as 060. The answer is <\/span><b>1,017,060<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><b>One thing that trips people up:<\/b><span style=\"font-weight: 400;\"> the right-hand part must have exactly as many digits as the base has zeros. If your gap product is too short, pad it with zeros on the left. If it&#8217;s too long, carry the extra digits over to the left part.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-169b8c1\" data-id=\"169b8c1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-897f476 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"897f476\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-07bdfef\" data-id=\"07bdfef\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-ccfbce9\" data-id=\"ccfbce9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-40c3577 elementor-widget elementor-widget-heading\" data-id=\"40c3577\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Method 2: Urdhva Tiryagbhyam (Vertically and Crosswise)\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-25a62cc elementor-widget elementor-widget-text-editor\" data-id=\"25a62cc\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>Works best when:<\/b><span style=\"font-weight: 400;\"> the numbers are ordinary and no base is nearby.<\/span><\/p><p><span style=\"font-weight: 400;\">Ask which Vedic sutras help with multiplying large multi-digit numbers, and this is the one most teachers mention first. The name means &#8220;vertically and crosswise.&#8221; You move from right to left, add up a small group of products at each step, and carry as you go.<\/span><\/p><h4><b>Example 1, with 3-digit numbers: 234 \u00d7 321<\/b><\/h4><p><span style=\"font-weight: 400;\">Write the digits as 2-3-4 and 3-2-1, then work from the right.<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Units:<\/b><span style=\"font-weight: 400;\"> 4 \u00d7 1 = 4. Write 4.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Tens:<\/b><span style=\"font-weight: 400;\"> (3 \u00d7 1) + (4 \u00d7 2) = 3 + 8 = 11. Write 1, carry 1.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Hundreds:<\/b><span style=\"font-weight: 400;\"> (2 \u00d7 1) + (4 \u00d7 3) + (3 \u00d7 2) = 2 + 12 + 6 = 20, plus the carried 1 is 21. Write 1, carry 2.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Thousands:<\/b><span style=\"font-weight: 400;\"> (2 \u00d7 2) + (3 \u00d7 3) = 4 + 9 = 13, plus the carried 2 is 15. Write 5, carry 1.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Ten-thousands:<\/b><span style=\"font-weight: 400;\"> 2 \u00d7 3 = 6, plus the carried 1 is 7. Write 7.<\/span><\/li><\/ol><p><span style=\"font-weight: 400;\">Read the digits you wrote from the last step back to the first: <\/span><b>75,114<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h4><b>Example 2, with 4-digit numbers: 1,234 \u00d7 5,678<\/b><\/h4><table><tbody><tr><td><p><b>Step<\/b><\/p><\/td><td><p><b>Products added<\/b><\/p><\/td><td><p><b>Total with carry<\/b><\/p><\/td><td><p><b>Write<\/b><\/p><\/td><td><p><b>Carry<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">1<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">4\u00d78<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">32<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">3<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">2<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">3\u00d78 + 4\u00d77<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">52 + 3 = 55<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">5<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">5<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">3<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2\u00d78 + 3\u00d77 + 4\u00d76<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">61 + 5 = 66<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">6<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">6<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">4<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">1\u00d78 + 2\u00d77 + 3\u00d76 + 4\u00d75<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">60 + 6 = 66<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">6<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">6<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">5<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">1\u00d77 + 2\u00d76 + 3\u00d75<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">34 + 6 = 40<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">0<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">4<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">6<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">1\u00d76 + 2\u00d75<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">16 + 4 = 20<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">0<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">2<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">7<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">1\u00d75<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">5 + 2 = 7<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">7<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">0<\/span><\/p><\/td><\/tr><\/tbody><\/table><p><span style=\"font-weight: 400;\">Read the &#8220;Write&#8221; column from the bottom up: <\/span><b>7,006,652<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><h4><b>Fast ways in Vedic maths to multiply 6-digit or larger numbers<\/b><\/h4><p><span style=\"font-weight: 400;\">Bigger numbers don&#8217;t change the pattern, they just add more steps. Two numbers with <\/span><i><span style=\"font-weight: 400;\">n<\/span><\/i><span style=\"font-weight: 400;\"> digits each need 2n \u2212 1 steps, so a 6-digit by 6-digit problem has 11. The busiest step, right in the middle, adds six small products. It looks long, but you only keep one running line of carries instead of six rows of partial products, and that&#8217;s where the saving comes from.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-207278b\" data-id=\"207278b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8ef5332 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"8ef5332\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-75bfb55\" data-id=\"75bfb55\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-63628d2\" data-id=\"63628d2\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3a0e8c8 elementor-widget elementor-widget-heading\" data-id=\"3a0e8c8\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Method 3: Ekanyunena Purvena (Multiplying by 9s)\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6b38635 elementor-widget elementor-widget-text-editor\" data-id=\"6b38635\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>Works best when:<\/b><span style=\"font-weight: 400;\"> you&#8217;re multiplying by 9, 99, 999, 9,999 and so on.<\/span><\/p><p><span style=\"font-weight: 400;\">The name means &#8220;one less than the previous one,&#8221; and the rule is short.<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Subtract 1 from the number you&#8217;re multiplying. That&#8217;s the left part.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Subtract the left part from a row of 9s with the same number of digits. That&#8217;s the right part.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Put the two parts side by side.<\/span><\/li><\/ol><h4><b>Example 1: 4,568 \u00d7 9,999<\/b><\/h4><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Left part: 4,568 \u2212 1 = 4,567<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Right part: 9,999 \u2212 4,567 = 5,432<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Answer: <\/span><b>45,675,432<\/b><\/li><\/ul><h4><b>Example 2, with 6-digit numbers: 357,421 \u00d7 999,999<\/b><\/h4><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Left part: 357,421 \u2212 1 = 357,420<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Right part: 999,999 \u2212 357,420 = 642,579<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Answer: <\/span><b>357,420,642,579<\/b><\/li><\/ul><h4><b>When the number is shorter than the 9s<\/b><\/h4><p><span style=\"font-weight: 400;\">For 47 \u00d7 999, pad 47 to 047. The left part is 046 and the right part is 999 \u2212 46 = 953. The answer is <\/span><b>46,953<\/b><span style=\"font-weight: 400;\">.<\/span><\/p><p><span style=\"font-weight: 400;\">Once the rule sticks, this takes about ten seconds, which makes it the fastest method in this guide.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f5f8dac\" data-id=\"f5f8dac\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-799fe13 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"799fe13\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b82080a\" data-id=\"b82080a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e0b88f5\" data-id=\"e0b88f5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-9558fad elementor-widget elementor-widget-heading\" data-id=\"9558fad\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Method 4: Anurupyena (Working Base Method)\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5f50674 elementor-widget elementor-widget-text-editor\" data-id=\"5f50674\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><b>Works best when:<\/b><span style=\"font-weight: 400;\"> the numbers are near 50, 500, 5,000, 500,000 or similar half-way bases.<\/span><\/p><p><i><span style=\"font-weight: 400;\">Anurupyena<\/span><\/i><span style=\"font-weight: 400;\"> means &#8220;proportionally.&#8221; You pick a base that&#8217;s easy to work with, like 5,000 (half of 10,000), do the same cross step as in Nikhilam, and then multiply by that base.<\/span><\/p><h4><b>Example 1: 4,985 \u00d7 4,990<\/b><\/h4><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The working base is 5,000. The gaps are \u221215 and \u221210.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Cross subtract: 4,985 \u2212 10 = 4,975.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply by the base: 4,975 \u00d7 5,000 = 24,875,000. (Quick route: half of 4,975 is 2,487.5, and times 10,000 gives the same thing.)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply the gaps: (\u221215) \u00d7 (\u221210) = +150.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Add: 24,875,000 + 150 = <\/span><b>24,875,150<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ol><h4><b>Example 2, with 6-digit numbers: 499,985 \u00d7 500,012<\/b><\/h4><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">The working base is 500,000. The gaps are \u221215 and +12.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Cross add: 499,985 + 12 = 499,997.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply by the base: 499,997 \u00d7 500,000 = 249,998,500,000.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Multiply the gaps: (\u221215) \u00d7 (+12) = \u2212180.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Subtract: 249,998,500,000 \u2212 180 = <\/span><b>249,998,499,820<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ol><p><span style=\"font-weight: 400;\">Mind the signs. If one gap is negative and the other positive, the gap product is negative, so you subtract it.<\/span><\/p><h3><b>Which Method Should You Use?<\/b><\/h3><table><tbody><tr><td><p><b>Method<\/b><\/p><\/td><td><p><b>Best when<\/b><\/p><\/td><td><p><b>Difficulty<\/b><\/p><\/td><td><p><b>Speed<\/b><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Nikhilam<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Both numbers near a power of 10<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Easy<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Very fast<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Urdhva Tiryagbhyam<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Any numbers<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Medium<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Fast<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Ekanyunena Purvena<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">One number is all 9s<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Very easy<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Very fast<\/span><\/p><\/td><\/tr><tr><td><p><span style=\"font-weight: 400;\">Anurupyena<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Numbers near 50, 500, 5,000&#8230;<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Medium<\/span><\/p><\/td><td><p><span style=\"font-weight: 400;\">Fast<\/span><\/p><\/td><\/tr><\/tbody><\/table><p><span style=\"font-weight: 400;\">If a shortcut fits, use it. If nothing fits, Urdhva Tiryagbhyam will handle whatever you throw at it.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-1e81922\" data-id=\"1e81922\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7c7125f elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"7c7125f\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-5f05c3e\" data-id=\"5f05c3e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-e81a5e8\" data-id=\"e81a5e8\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-98bb93c elementor-widget elementor-widget-heading\" data-id=\"98bb93c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Step-by-Step Vedic Multiplication for Large Numbers: A Simple Routine\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7a9d89c elementor-widget elementor-widget-text-editor\" data-id=\"7a9d89c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Here&#8217;s an order that keeps your work tidy while you&#8217;re still learning.<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Scan<\/b><span style=\"font-weight: 400;\"> both numbers. Are they near a base? Is one all 9s?<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Pick<\/b><span style=\"font-weight: 400;\"> the matching method from the table.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Write carries<\/b><span style=\"font-weight: 400;\"> in a small row above your work so none go missing.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Check<\/b><span style=\"font-weight: 400;\"> the answer with the digit-sum test below.<\/span><\/li><\/ol><h4><b>The digit-sum check<\/b><\/h4><p><span style=\"font-weight: 400;\">Add the digits of each number until you&#8217;re down to one digit. Multiply those two single digits and reduce the product to one digit as well. It should match the single-digit sum of your answer.<\/span><\/p><p><span style=\"font-weight: 400;\">Try 234 \u00d7 321 = 75,114. The digits of 234 add to 9, and 321 gives 6. Then 9 \u00d7 6 = 54, and 5 + 4 = 9. For the answer, 7 + 5 + 1 + 1 + 4 = 18, and 1 + 8 = 9. They match. The test isn&#8217;t perfect (swapped digits slip past it), but it catches most slips in seconds.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-bcc3c2b\" data-id=\"bcc3c2b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a722a2a elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"a722a2a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-353d226\" data-id=\"353d226\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-c186556\" data-id=\"c186556\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-569da3b elementor-widget elementor-widget-heading\" data-id=\"569da3b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Common Mistakes to Avoid\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-477f1f1 elementor-widget elementor-widget-text-editor\" data-id=\"477f1f1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Wrong digit count on the right side.<\/b><span style=\"font-weight: 400;\"> In Nikhilam, the right part needs as many digits as the base has zeros.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Dropping carries<\/b><span style=\"font-weight: 400;\"> in the crosswise method. Write them down until it becomes a habit.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Mixing up signs<\/b><span style=\"font-weight: 400;\"> in the working base method. Check whether each number is above or below the base.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>Quitting too soon.<\/b><span style=\"font-weight: 400;\"> These methods feel awkward at first. Most learners settle in after 10 to 15 problems of each type.<\/span><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-9393129\" data-id=\"9393129\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-231fdc7 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"231fdc7\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-f6ec5ea\" data-id=\"f6ec5ea\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-882f8dd\" data-id=\"882f8dd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3d5124b elementor-widget elementor-widget-heading\" data-id=\"3d5124b\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Practice Questions\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cd3b9be elementor-widget elementor-widget-text-editor\" data-id=\"cd3b9be\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Try these by hand before looking at the answers.<\/span><\/p><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">9,997 \u00d7 9,994 (Nikhilam)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">312 \u00d7 245 (Urdhva Tiryagbhyam)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">8,265 \u00d7 9,999 (Ekanyunena Purvena)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">5,008 \u00d7 4,996 (Anurupyena, base 5,000)<\/span><\/li><\/ol><p><b>Answers:<\/b><\/p><ol><li style=\"list-style-type: none;\"><ol><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Gaps are 3 and 6. Cross: 9,997 \u2212 6 = 9,991. Gap product: 18, written as 0018. Answer: <\/span><b>99,910,018<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>76,440<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Left part: 8,264. Right part: 9,999 \u2212 8,264 = 1,735. Answer: <\/span><b>82,641,735<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Cross: 5,008 \u2212 4 = 5,004. Then 5,004 \u00d7 5,000 = 25,020,000. The gaps are +8 and \u22124, giving \u221232. Answer: <\/span><b>25,019,968<\/b><span style=\"font-weight: 400;\">.<\/span><\/li><\/ol><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-38d64ee\" data-id=\"38d64ee\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-84808e1 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"84808e1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-937a670\" data-id=\"937a670\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-0621d6f\" data-id=\"0621d6f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e7bcb07 elementor-widget elementor-widget-heading\" data-id=\"e7bcb07\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Conclusion<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-63df499 elementor-widget elementor-widget-text-editor\" data-id=\"63df499\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Long multiplication isn&#8217;t going away, but when the numbers cooperate, vedic math techniques multiply large numbers with much less effort. Start with Nikhilam and the 9s method because they&#8217;re the easiest. Add Urdhva Tiryagbhyam as your everyday method, and bring in the working base method when numbers sit near 50, 500 or 5,000. A few problems a day, plus the digit-sum check, and the speed comes on its own.<\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-3ac9ce4\" data-id=\"3ac9ce4\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4c27c50 elementor-section-full_width elementor-section-height-default elementor-section-height-default\" data-id=\"4c27c50\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-4b68dbd\" data-id=\"4b68dbd\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-83fef82\" data-id=\"83fef82\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-26e2bf3 elementor-widget elementor-widget-heading\" data-id=\"26e2bf3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Frequently Asked Questions\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fe481c6 elementor-widget elementor-widget-accordion\" data-id=\"fe481c6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"accordion.default\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion\">\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2661\" class=\"elementor-tab-title\" data-tab=\"1\" role=\"button\" aria-controls=\"elementor-tab-content-2661\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Is Vedic math faster than the usual method?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2661\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"1\" role=\"region\" aria-labelledby=\"elementor-tab-title-2661\"><p><span style=\"font-weight: 400;\">For numbers near a base or made of 9s, yes, by a lot. For random numbers, the crosswise method is usually quicker and neater than long multiplication once you&#8217;ve practised it.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2662\" class=\"elementor-tab-title\" data-tab=\"2\" role=\"button\" aria-controls=\"elementor-tab-content-2662\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Can children learn these techniques?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2662\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"2\" role=\"region\" aria-labelledby=\"elementor-tab-title-2662\"><p><span style=\"font-weight: 400;\">Yes. If a child is comfortable with place value and tables, Nikhilam and the 9s method are good starting points. The crosswise method can come after.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2663\" class=\"elementor-tab-title\" data-tab=\"3\" role=\"button\" aria-controls=\"elementor-tab-content-2663\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Do they work with decimals?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2663\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"3\" role=\"region\" aria-labelledby=\"elementor-tab-title-2663\"><p><span style=\"font-weight: 400;\">They do. Ignore the decimal points, multiply as whole numbers, then count the total decimal places in the original numbers and put the point back in your answer.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-accordion-item\">\n\t\t\t\t\t<div id=\"elementor-tab-title-2664\" class=\"elementor-tab-title\" data-tab=\"4\" role=\"button\" aria-controls=\"elementor-tab-content-2664\" aria-expanded=\"false\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon elementor-accordion-icon-left\" aria-hidden=\"true\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-closed\"><svg class=\"e-font-icon-svg e-fas-plus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H272V64c0-17.67-14.33-32-32-32h-32c-17.67 0-32 14.33-32 32v144H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h144v144c0 17.67 14.33 32 32 32h32c17.67 0 32-14.33 32-32V304h144c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t<span class=\"elementor-accordion-icon-opened\"><svg class=\"e-font-icon-svg e-fas-minus\" viewBox=\"0 0 448 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M416 208H32c-17.67 0-32 14.33-32 32v32c0 17.67 14.33 32 32 32h384c17.67 0 32-14.33 32-32v-32c0-17.67-14.33-32-32-32z\"><\/path><\/svg><\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t\t\t<a class=\"elementor-accordion-title\" tabindex=\"0\">Will they help in competitive exams?<\/a>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<div id=\"elementor-tab-content-2664\" class=\"elementor-tab-content elementor-clearfix\" data-tab=\"4\" role=\"region\" aria-labelledby=\"elementor-tab-title-2664\"><p><span style=\"font-weight: 400;\">They can save time in calculation-heavy sections. Still, learn the standard method first, because exams also test whether you understand the working.<\/span><\/p><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t\t\t<script type=\"application\/ld+json\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Is Vedic math faster than the usual method?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">For numbers near a base or made of 9s, yes, by a lot. For random numbers, the crosswise method is usually quicker and neater than long multiplication once you&#8217;ve practised it.<\\\/span><\\\/p>\"}},{\"@type\":\"Question\",\"name\":\"Can children learn these techniques?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"<p><span style=\\\"font-weight: 400;\\\">Yes. If a child is comfortable with place value and tables, Nikhilam and the 9s method are good starting points. 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