{"id":785,"date":"2025-10-15T11:02:35","date_gmt":"2025-10-15T11:02:35","guid":{"rendered":"https:\/\/kapdec.com\/help\/?post_type=docs&#038;p=785"},"modified":"2026-04-10T10:43:54","modified_gmt":"2026-04-10T10:43:54","slug":"what-is-the-multiplication-of-large-numbers","status":"publish","type":"post","link":"https:\/\/kapdec.com\/help\/what-is-the-multiplication-of-large-numbers\/","title":{"rendered":"What is the Multiplication of Large Numbers?"},"content":{"rendered":"<p><b>Multiplication of Large Numbers<\/b><\/p>\n<p>&nbsp;<\/p>\n<p><b>Multiplication\u00a0<\/b>of two numbers is nothing but\u00a0<b>repeated addition<\/b>. It is equivalent to adding one of the numbers as many times as the value of the other.<\/p>\n<p>&nbsp;<\/p>\n<p><b>Examples-<\/b><\/p>\n<ol>\n<li>7 X 5 = 7 + 7 + 7 + 7 + 7 = 35<\/li>\n<\/ol>\n<ol>\n<li>9 X 3 = 9 + 9 + 9 = 27<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<p>Now, for\u00a0<b>example<\/b>\u00a0there are 72 students in a class and each student buys books and copies worth\u00a0$28. What was the total spending on books for all students?<\/p>\n<p>&nbsp;<\/p>\n<p>In this case, we multiply\u00a028\u00a0with 72 to find the total spending. But to find the final answer, we cannot add 72 times, the number\u00a028.<\/p>\n<p>&nbsp;<\/p>\n<p>So, similar to addition and subtraction, we have a method to multiply the two numbers.<\/p>\n<p>&nbsp;<\/p>\n<ul>\n<li>We multiply the first digit i.e. the unit digit of the number by each digit of the other number starting left and carrying wherever necessary.<\/li>\n<\/ul>\n<ul>\n<li>Then we multiply the second digit from each digit of the other number writing our product from tens place.<\/li>\n<li>We do the same for third starting writing our product from hundreds place and so on.<\/li>\n<li>We then add all the products to get the multiplied number.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p>Let us find the total spending on books using this method-<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-790\" src=\"https:\/\/kapdec.com\/help\/venture\/wp-content\/uploads\/2025\/10\/a1-1-300x88.png\" alt=\"\" width=\"300\" height=\"88\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>So, from the above table we can say that the total spending on books was\u00a0$2016.<\/p>\n<p>&nbsp;<\/p>\n<p>Let us have a look at a practical problem on multiplication of large numbers-<\/p>\n<p>&nbsp;<\/p>\n<p><b>Example-<\/b><\/p>\n<p>A factory produces 74650 toys in a week. How many toys will it produce in 2 years?<\/p>\n<p>&nbsp;<\/p>\n<p><b>Solution-<\/b><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-medium wp-image-791\" src=\"https:\/\/kapdec.com\/help\/venture\/wp-content\/uploads\/2025\/10\/a2-1-300x101.png\" alt=\"\" width=\"300\" height=\"101\" \/><\/p>\n<p>&nbsp;<\/p>\n<p>So, in two years the factory produces 7,763,600 toys.<\/p>\n<p><b>Properties of Multiplication<\/b><\/p>\n<p>&nbsp;<\/p>\n<p>It is important to know about the properties because it helps in making our multiplication easier if we know where to use them. Let us look at the properties-<\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li><b>Multiplicative Property of 0:<\/b>\u00a0If a number is multiplied by 0, the product is 0.<\/li>\n<\/ol>\n<p>Example: 71,542 X 0 = 0<\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li><b>Multiplicative Property of 1:<\/b>\u00a0If a number is multiplied by 1, the product is the number itself.<\/li>\n<\/ol>\n<p>Example: 149,632 X 1 = 149,632<\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li><b>Commutative Property of Multiplication:<\/b>\u00a0The product of two numbers does not change with a change in the order of the numbers.<\/li>\n<\/ol>\n<p>Example: 18,257 X 9 = 164,313<\/p>\n<p>9 X 18,257 = 164,313<\/p>\n<p>18,257 X 9 = 9 X 18,257<\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li><b>Associative Property of Multiplication:<\/b>\u00a0Regrouping and changing the order of the numbers does not change the product of the numbers.<\/li>\n<\/ol>\n<p>Example: 60 X 8 X 100 = (60 X 8) X 100 = 480 X 100 = 48000<\/p>\n<p>60 X 8 X 100 = 60 X (8 X 100) = 600 X 800 = 48000<\/p>\n<p>60 X 8 X 100 = (60 X 100) X 8 = 6000 X 8 = 48000<\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li><b>Distributive Property of Multiplication:<\/b>\u00a0Bigger numbers can be divided into smaller numbers to multiply easily.<\/li>\n<\/ol>\n<p>Examples:<\/p>\n<ol>\n<li>18 X 98 = 18 X (100 &#8211; 2)<\/li>\n<\/ol>\n<p>= (18 X 100) \u2013 (18 X 2)<\/p>\n<p>= 1800-36<\/p>\n<p>=1764<\/p>\n<ol>\n<li>24 X 125 = 24 X (100 + 20 + 5)<\/li>\n<\/ol>\n<p>= 24 X 100 + 24 X 20 + 24 X 5<\/p>\n<p>= 2400 + 480 + 120<\/p>\n<p>= 3000<\/p>\n<p>&nbsp;<\/p>\n<p><b>Multiplication of a number by 10, 100, 1000, 10000<\/b><\/p>\n<p>&nbsp;<\/p>\n<ol>\n<li>When a number is multiplied by 10, 20, 30, 40, .. , 90; we multiply the number by 1, 2, 3,.., 9 respectivelyand add a zero at the end of the multiplied number.<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<ol>\n<li>When a number is multiplied by 100, 200, 300, 400, .. , 900; we multiply the number by 1, 2, 3,.., 9 respectivelyand add 2 zeroes at the end of the multiplied number.<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<ol>\n<li>When a number is multiplied by 1000, 2000, 3000, 4000, .. , 9000; we multiply the number by 1, 2, 3,.., 9 respectivelyand add 3 zeroes at the end of the multiplied number.<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<ol>\n<li>When a number is multiplied by 10000, 20000, 30000, 40000, .. , 90000; we multiply the number by 1, 2, 3,.., 9 respectivelyand add 4 zeroes at the end of the multiplied number.<\/li>\n<\/ol>\n<p><b>Examples-<\/b><\/p>\n<ol>\n<li>7 X 20 = (7 X 2) X 10 = 14 X 10 = 140<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<ol>\n<li>12 X 5000 = (12 X 5) X 1000 = 60 X 1000 = 60000<\/li>\n<\/ol>\n<p>&nbsp;<\/p>\n<p><b>Fun Fact<\/b><\/p>\n<p>111,111,111 \u00d7 111,111,111 = 12,345,678,987,654,321<\/p>\n<p>It also works for smaller numbers: 111 \u00d7 111 = 12321.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Multiplication of Large Numbers &nbsp; Multiplication\u00a0of two numbers is nothing but\u00a0repeated addition. It is equivalent to adding one of the numbers as many times as the value of the other. &nbsp; Examples- 7 X 5 = 7 + 7 + 7 + 7 + 7 = 35 9 X 3 = 9 + 9 + [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[590],"tags":[595],"class_list":["post-785","post","type-post","status-publish","format-standard","hentry","category-grade-5","tag-grade-5-mathematics"],"_links":{"self":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/785","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/comments?post=785"}],"version-history":[{"count":1,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/785\/revisions"}],"predecessor-version":[{"id":1556,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/posts\/785\/revisions\/1556"}],"wp:attachment":[{"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/media?parent=785"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/categories?post=785"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kapdec.com\/help\/wp-json\/wp\/v2\/tags?post=785"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}