{"id":35,"date":"2022-04-12T05:53:08","date_gmt":"2022-04-12T05:53:08","guid":{"rendered":"http:\/\/5thclass.deltapublications.in\/?page_id=35"},"modified":"2025-08-06T06:28:54","modified_gmt":"2025-08-06T06:28:54","slug":"b-6-properties-of-addition","status":"publish","type":"page","link":"https:\/\/5thclass.deltapublications.in\/index.php\/b-6-properties-of-addition\/","title":{"rendered":"B.6 Properties of addition"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Properties of addition<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">key notes :<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000020\"><tbody><tr><td>\ud83c\udf87<strong> Properties of Addition<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"wp-block-group has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p><strong>Commutative Property<\/strong><\/p>\n\n\n\n<p><strong>Definition<\/strong>: Changing the order of the numbers being added does not change the sum.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula<\/strong>: a+b=b+a<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example<\/strong>: 4+9=9+4 \u2192 Both equal 13.<\/li>\n<\/ul>\n\n\n\n<p><strong>Associative Property<\/strong><\/p>\n\n\n\n<p><strong>Definition<\/strong>: Changing the grouping of numbers being added does not change the sum.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula<\/strong>: (a+b)+c=a+(b+c)<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example<\/strong>: (2+3)+4=2+(3+4) \u2192 Both equal 9.<\/li>\n<\/ul>\n\n\n\n<p><strong>Identity Property (Additive Identity)<\/strong><\/p>\n\n\n\n<p><strong>Definition<\/strong>: The sum of any number and zero is the number itself.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula<\/strong>: a+0=a<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example<\/strong>: 7+0=7<\/li>\n<\/ul>\n\n\n\n<p><strong>Distributive Property<\/strong><em>(Related to Addition and Multiplication)<\/em><\/p>\n\n\n\n<p><strong>Definition<\/strong>: Multiplying a number by a sum is the same as multiplying each addend by the number and then adding the products.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula<\/strong>: a\u00d7(b+c)=(a\u00d7b)+(a\u00d7c)<\/li>\n<\/ul>\n\n\n\n<p><strong>Example<\/strong>: 3\u00d7(2+4)=(3\u00d72)+(3\u00d74) \u2192 Both equal 18.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000020\"><tbody><tr><td>\ud83e\udde8<strong>Properties of Subtraction<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Non-Commutative Property<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Definition<\/strong>: The order of numbers in subtraction matters; changing the order changes the result.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example<\/strong>: 9\u22125 is not the same as 5\u22129.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Explanation<\/strong>: 9\u22125=4, but 5\u22129 would result in \u22124, which is different.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Non-Associative Property<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Definition<\/strong>: Changing the grouping of numbers in subtraction will change the result.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example<\/strong>: (10\u22125)\u22122 is not the same as 10\u2212(5\u22122).<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Explanation<\/strong>: (10\u22125)\u22122=3, while 10\u2212(5\u22122)=7.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Identity Property of Subtraction<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Definition<\/strong>: Subtracting zero from any number leaves the number unchanged.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula<\/strong>: a\u22120=a<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example<\/strong>: 8\u22120=8<\/li>\n<\/ul>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Subtraction as the Inverse of Addition<\/strong><\/p>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Definition<\/strong>: Subtraction is the opposite of addition. If you add a number and then subtract the same number, you return to the original number.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula<\/strong>: a+b\u2212b=a<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example<\/strong>: 15+5\u22125=15<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#febbbb\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-normal-font-size\"><strong>Commutative property:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\">&nbsp;h&nbsp;+&nbsp;j&nbsp;=&nbsp;j&nbsp;+&nbsp;h<br>You can add numbers in any order and get the same sum.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\"><strong>Ex:  2 + 6 = 6 + 2<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#bdfff1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-normal-font-size\"><strong>Associative property:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">(f&nbsp;+&nbsp;g) +&nbsp;h&nbsp;=&nbsp;f&nbsp;+ (g&nbsp;+&nbsp;h)<br>You can group the addends with brackets and get the same sum.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\"><strong>Ex: 6 +&nbsp;(9 + 7)&nbsp;=&nbsp;(6 + 9)&nbsp;+ 7<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#a1c5f7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-align-center has-normal-font-size\"><strong>Identity property:<\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center\">&nbsp;t&nbsp;= 0 +&nbsp;t<br>Adding zero does not change a number.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\"><strong>Ex : 2 = 2 + 0<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#fdc0c0\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf Which property of addition is shown?<\/strong><\/p>\n\n\n\n<p>\ud83c\udfaf 3 = 3 + 0<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>associative<\/li>\n\n\n\n<li>commutative<\/li>\n\n\n\n<li>identity<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 = 3 + 0<\/li>\n\n\n\n<li>This equation shows the identity property. Adding zero does not change the sum.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#c5f9b2\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf Which equation shows the associative property of addition?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 + 7 = 7 + 5<\/li>\n\n\n\n<li>5 +&nbsp;(3 + 7)&nbsp;=&nbsp;(5 + 3)&nbsp;+ 7<\/li>\n\n\n\n<li>1 = 0 + 1<\/li>\n\n\n\n<li>3 = 3 + 0<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 +&nbsp;(3 + 7)&nbsp;=&nbsp;(5 + 3)&nbsp;+ 7<\/li>\n\n\n\n<li>This equation shows the associative property. The grouping of the addends is changed.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#c0b4f9\"><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\" style=\"color:#b00012\"><strong>\ud83c\udfaf Which property of addition is shown?<\/strong><\/p>\n\n\n\n<p>\ud83c\udfaf 9 + 3 = 3 + 9<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>associative<\/li>\n\n\n\n<li>commutative<\/li>\n\n\n\n<li>identity<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>9 + 3 = 3 + 9<\/li>\n\n\n\n<li>This equation shows the commutative property. The order of the addends 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!<\/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\/76409\/960\/171\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-2-69.png\" alt=\"\" class=\"wp-image-5795\" srcset=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-2-69.png 500w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-2-69-300x300.png 300w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-2-69-150x150.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\/33607\/136\/932\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-1-69.png\" alt=\"\" class=\"wp-image-5797\" srcset=\"https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-1-69.png 500w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-1-69-300x300.png 300w, https:\/\/5thclass.deltapublications.in\/wp-content\/uploads\/2023\/04\/Worksheet-1-1-1-69-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Properties of addition key notes : \ud83c\udf87 Properties of Addition Commutative Property Definition: Changing the order of the numbers being added does not change the sum. Associative Property Definition: Changing the grouping of numbers being added does not change the sum. Identity Property (Additive Identity) Definition: The sum of any number and zero is the<a class=\"more-link\" href=\"https:\/\/5thclass.deltapublications.in\/index.php\/b-6-properties-of-addition\/\">Continue reading <span class=\"screen-reader-text\">&#8220;B.6 Properties of addition&#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-35","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":20,"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/35\/revisions"}],"predecessor-version":[{"id":15452,"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/35\/revisions\/15452"}],"wp:attachment":[{"href":"https:\/\/5thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}