{"id":80,"date":"2022-04-12T04:44:21","date_gmt":"2022-04-12T04:44:21","guid":{"rendered":"http:\/\/4thclass.deltapublications.in\/?page_id=80"},"modified":"2025-11-06T09:12:38","modified_gmt":"2025-11-06T09:12:38","slug":"d-8-properties-of-multiplication","status":"publish","type":"page","link":"https:\/\/4thclass.deltapublications.in\/index.php\/d-8-properties-of-multiplication\/","title":{"rendered":"D.8 Properties of multiplication"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Properties of multiplication<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-ac2bc047fac346cd34a46d2a76287634\" style=\"color:#74008b;text-transform:capitalize\">key notes:<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u2705 <strong>Commutative Property<\/strong><\/h4>\n\n\n\n<p>\ud83d\udd39 <em>Order of numbers does not change the product.<\/em><br>\u2728 <strong>a \u00d7 b = b \u00d7 a<\/strong><br>\ud83e\uddee Example: <strong>4 \u00d7 6 = 6 \u00d7 4<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\ud83d\udd01 <strong>Associative Property<\/strong><\/h4>\n\n\n\n<p>\ud83d\udd39 <em>When multiplying 3 numbers, you can group them in any way.<\/em><br>\u2728 <strong>(a \u00d7 b) \u00d7 c = a \u00d7 (b \u00d7 c)<\/strong><br>\ud83e\uddee Example: <strong>(2 \u00d7 3) \u00d7 5 = 2 \u00d7 (3 \u00d7 5)<\/strong><br>\u27a1\ufe0f <strong>6 \u00d7 5 = 2 \u00d7 15<\/strong><br>\u27a1\ufe0f <strong>30 = 30<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\ud83d\udd22 <strong>Identity Property of Multiplication<\/strong><\/h4>\n\n\n\n<p>\ud83d\udd39 <em>Multiplying any number by <strong>1<\/strong> keeps the number the same.<\/em><br>\u2728 <strong>a \u00d7 1 = a<\/strong><br>\ud83e\uddee Example: <strong>9 \u00d7 1 = 9<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">\ud83c\udd7e\ufe0f <strong>Zero Property of Multiplication<\/strong><\/h4>\n\n\n\n<p>\ud83d\udd39 <em>Any number multiplied by <strong>0<\/strong> is always <strong>0<\/strong><\/em><br>\u2728 <strong>a \u00d7 0 = 0<\/strong><br>\ud83e\uddee Example: <strong>8 \u00d7 0 = 0<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\">\ud83e\udde0 <strong>Distributive Property<\/strong><\/h4>\n\n\n\n<p>\ud83d\udd39 <em>Break a big multiplication into smaller parts using addition.<\/em><br>\u2728 <strong>a \u00d7 (b + c) = a \u00d7 b + a \u00d7 c<\/strong><br>\ud83e\uddee Example:<br><strong>7 \u00d7 (3 + 2)<\/strong><br>= <strong>7 \u00d7 3 + 7 \u00d7 2<\/strong><br>= <strong>21 + 14 = 35<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83c\udfaf <strong>Why Learn These Properties?<\/strong><\/h3>\n\n\n\n<p>\ud83d\udca1 Makes multiplication easier<br>\ud83d\udcd0 Helps solve mental math quickly<br>\ud83e\udde0 Builds strong math skills<br>\ud83d\ude80 Saves time in calculations<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\">Learn with an example<\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#facccc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-2b4e7ab466a8c6d5eb341a5a02903b9f\" style=\"color:#b00012\">\u2708\ufe0f Which equation shows the commutative property of multiplication?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1 \u00d7 4 = 4<\/li>\n\n\n\n<li>8 \u00d7 2 + 8 \u00d7 1 = 8 \u00d7&nbsp;(2 + 1)<\/li>\n\n\n\n<li>7 \u00d7 2 = 2 + 2 + 2 + 2 + 2 + 2 + 2<\/li>\n\n\n\n<li>3 \u00d7 1 = 1 \u00d7 3<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 \u00d7 1 = 1 \u00d7 3<\/li>\n\n\n\n<li>This equation shows the commutative property. The order of the factors is changed.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#d4f2b9\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\u2708\ufe0f Which property of multiplication is shown?<\/p>\n\n\n\n<p>\u2708\ufe0f (7 \u00d7 3)&nbsp;\u00d7 6 = 7 \u00d7&nbsp;(3 \u00d7 6)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>associative<\/li>\n\n\n\n<li>zero<\/li>\n\n\n\n<li>commutative<\/li>\n\n\n\n<li>identity<br><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(7 \u00d7 3)&nbsp;\u00d7 6 = 7 \u00d7&nbsp;(3 \u00d7 6)<\/li>\n\n\n\n<li>This equation shows the <strong>associative<\/strong> property. The grouping of the factors is changed.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#a7e3e5\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-fde3b8d116c018e51a0f5a55c5f377c2\" style=\"color:#b00012\">\u2708\ufe0f Which equation shows the associative property of multiplication?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>7 \u00d7 3 \u2212 0 \u00d7 3 =&nbsp;(7 \u2212 0)&nbsp;\u00d7 3<\/li>\n\n\n\n<li>(5 \u00d7 1)&nbsp;\u00d7 9 = 5 \u00d7&nbsp;(1 \u00d7 9)<\/li>\n\n\n\n<li>7 \u00d7 9 + 1 = 63 + 1<\/li>\n\n\n\n<li>6 + 6 + 6 = 3 \u00d7 6<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(5 \u00d7 1)&nbsp;\u00d7 9 = 5 \u00d7&nbsp;(1 \u00d7 9)<\/li>\n\n\n\n<li>This equation shows the associative property. The grouping of the factors is changed.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/101391\/975\/959\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/4thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-200.png\" alt=\"\" class=\"wp-image-6870\" srcset=\"https:\/\/4thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-200.png 500w, https:\/\/4thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-200-300x300.png 300w, https:\/\/4thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-3-200-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/30317\/575\/584\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/4thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-191.png\" alt=\"\" class=\"wp-image-6873\" srcset=\"https:\/\/4thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-191.png 500w, https:\/\/4thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-191-300x300.png 300w, https:\/\/4thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-2-191-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Properties of multiplication key notes: \u2705 Commutative Property \ud83d\udd39 Order of numbers does not change the product.\u2728 a \u00d7 b = b \u00d7 a\ud83e\uddee Example: 4 \u00d7 6 = 6 \u00d7 4 \ud83d\udd01 Associative Property \ud83d\udd39 When multiplying 3 numbers, you can group them in any way.\u2728 (a \u00d7 b) \u00d7 c = a \u00d7<a class=\"more-link\" href=\"https:\/\/4thclass.deltapublications.in\/index.php\/d-8-properties-of-multiplication\/\">Continue reading <span class=\"screen-reader-text\">&#8220;D.8 Properties of multiplication&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-80","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/4thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/80","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/4thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/4thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/4thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/4thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=80"}],"version-history":[{"count":17,"href":"https:\/\/4thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/80\/revisions"}],"predecessor-version":[{"id":16687,"href":"https:\/\/4thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/80\/revisions\/16687"}],"wp:attachment":[{"href":"https:\/\/4thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=80"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}