{"id":84,"date":"2022-04-12T12:03:44","date_gmt":"2022-04-12T12:03:44","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=84"},"modified":"2025-02-22T15:49:22","modified_gmt":"2025-02-22T15:49:22","slug":"e-8-apply-addition-subtraction-multiplication-and-division-rules","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/e-8-apply-addition-subtraction-multiplication-and-division-rules\/","title":{"rendered":"E.8 Apply addition, subtraction, multiplication and division rules"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Apply addition, subtraction, multiplication and division rules<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-c18f78a0e63a8dec9ff68f9d95baaf7a\" style=\"color:#74008b\"><strong>Key notes<\/strong><\/p>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-cb3dc6694aa079ce3ba60aa0173b4297\" style=\"color:#000060\"><strong>Addition Rules<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\"><strong>Commutative Property<\/strong>: a + b = b + a (Order doesn&#8217;t change the sum)<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Associative Property<\/strong>: (a+b) + c = a + (b+c) (Grouping doesn&#8217;t affect the sum)<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Identity Property<\/strong>: a + 0 = a (Adding zero doesn\u2019t change a number)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-81d0b193a04538acbb475e656e81152e\" style=\"color:#000060\"><strong>Adding Positive and Negative Numbers<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Same sign \u2192 Add values and keep the sign.<\/li>\n\n\n\n<li>Different signs \u2192 Subtract smaller from larger and keep the sign of the larger number.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-d418a79c80fca29e310f9559a5abc112\" style=\"color:#000060\"><strong>Subtraction Rules<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\"><strong>Subtraction as Addition of the Opposite<\/strong>: a \u2212 b = a + (\u2212b)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-8c5116dc652d18ed063e852eb1291a80\" style=\"color:#000060\"><strong>Sign Change Rule<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Positive &#8211; Negative \u2192  a \u2212(\u2212b) = a + b<\/li>\n\n\n\n<li>Negative &#8211; Positive \u2192 \u2212a \u2212b = \u2212(a+b)<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>Order Matters<\/strong>: a\u2212b \u2260 b \u2212 a<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-519ff4e4f33ab01a6a697c5b209509c1\" style=\"color:#000060\"><strong>Multiplication Rules<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\"><strong>Commutative Property<\/strong>: a \u00d7 b = b \u00d7 a<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Associative Property<\/strong>: (a\u00d7b) \u00d7 c = a \u00d7 (b\u00d7c)<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Distributive Property<\/strong>: a \u00d7 (b + c) = a \u00d7 b + a \u00d7 c<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-9c20cd214c20c1653836675aa075be15\" style=\"color:#000060\"><strong>Multiplying Positive and Negative Numbers<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Positive \u00d7 Positive = Positive<\/li>\n\n\n\n<li>Negative \u00d7 Negative = Positive<\/li>\n\n\n\n<li>Positive \u00d7 Negative = Negative<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color wp-elements-cbf9c3f7f6050a20c37c513913190e29\" style=\"color:#000060\"><strong>Division Rules<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\"><strong>Dividing by 1<\/strong>: a \u00f7 1 = a<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Dividing by Itself<\/strong>: a \u00f7 a = 1 (except when a = 0)<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>Dividing by Zero is Undefined<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-a3f713d1b769f38dd71b061fdc8143d7\" style=\"color:#000060\"><strong>Sign Rules<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Positive \u00f7 Positive = Positive<\/li>\n\n\n\n<li>Negative \u00f7 Negative = Positive<\/li>\n\n\n\n<li>Positive \u00f7 Negative = Negative<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity is-style-wide\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-7063e56c9f3acd659e9e0231971b47e4\" style=\"color:#000060\"><strong>Order of Operations (PEMDAS\/BODMAS)<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li><strong>P<\/strong>: Parentheses (Brackets)<\/li>\n\n\n\n<li><strong>E<\/strong>: Exponents (Orders)<\/li>\n\n\n\n<li><strong>MD<\/strong>: Multiplication and Division (Left to Right)<\/li>\n\n\n\n<li><strong>AS<\/strong>: Addition and Subtraction (Left to Right)<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-0556e28c1c7a0fb7ae60f85726de602c\" style=\"color:#105000\">Learn with an example<\/p>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-7bbd2185e86ecef81bc743a10b1e14d2\" style=\"background-color:#fac3fc\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>The&nbsp;number line shows an unknown number,&nbsp;b.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/09\/Untitled-design-11.png\" alt=\"\" class=\"wp-image-2727\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/09\/Untitled-design-11.png 1000w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/09\/Untitled-design-11-300x60.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/09\/Untitled-design-11-768x154.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\">Is&nbsp;3b&nbsp;positive or&nbsp;negative?<\/p>\n<\/div><\/div>\n\n\n\n<p><strong>Determine&nbsp;if&nbsp;<\/strong>b<strong>&nbsp;is positive or&nbsp;negative.<\/strong><\/p>\n\n\n\n<p>The&nbsp;unknown number&nbsp;b&nbsp;is to the left of 0. So,&nbsp;b&nbsp;is&nbsp;negative.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design-removebg-preview-2.png\" alt=\"\" class=\"wp-image-10878\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design-removebg-preview-2.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design-removebg-preview-2-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p><strong>Determine&nbsp;if&nbsp;<\/strong>3b<strong>&nbsp;is positive or&nbsp;negative.<\/strong><\/p>\n\n\n\n<p>In&nbsp;the expression&nbsp;3b,&nbsp;3&nbsp;is positive and&nbsp;b&nbsp;is negative. The product of a positive number and a negative number is negative. So,&nbsp;3b&nbsp;is&nbsp;negative.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-ffa213de3a9c621e8b1ed56820c62494\" style=\"background-color:#c2f8b5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>The&nbsp;number line shows an unknown number,&nbsp;v.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"200\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/09\/Untitled-design-12.png\" alt=\"\" class=\"wp-image-2733\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/09\/Untitled-design-12.png 1000w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/09\/Untitled-design-12-300x60.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2022\/09\/Untitled-design-12-768x154.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Is&nbsp;5v&nbsp;positive or&nbsp;negative?<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p><strong>Determine&nbsp;if&nbsp;<\/strong>v<strong>&nbsp;is positive or&nbsp;negative.<\/strong><\/p>\n\n\n\n<p>The&nbsp;unknown number&nbsp;v&nbsp;is to the right of 0. So,&nbsp;v&nbsp;is&nbsp;positive.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__1_-removebg-preview-1-1.png\" alt=\"\" class=\"wp-image-10879\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__1_-removebg-preview-1-1.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__1_-removebg-preview-1-1-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p><strong>Determine&nbsp;if&nbsp;<\/strong>5v<strong>&nbsp;is positive or&nbsp;negative.<\/strong><\/p>\n\n\n\n<p>In&nbsp;the expression&nbsp;5v,&nbsp;5&nbsp;is positive and&nbsp;v&nbsp;is positive. The product of two positive numbers is positive. So,&nbsp;5v&nbsp;is&nbsp;positive.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#fcf7d2\"><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-88ac572bc06174e98bc34c3104e78329\" style=\"color:#b00012\"><strong>The number line shows an unknown number, u.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-2.png\" alt=\"\" class=\"wp-image-10881\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-2.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-2-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-d14d996f28275861ce151740aa0d5cf2\" style=\"color:#b00012\"><strong>Is&nbsp;3u&nbsp;positive or&nbsp;negative?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-primary-color has-text-color has-link-color wp-elements-5fb3e76dfa020a713634fe1d01ac5694\">positive<\/li>\n\n\n\n<li>negative<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Determine if u is positive or negative.<\/p>\n\n\n\n<p>The unknown number u is to the left of 0. So, u is negative.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__2_-removebg-preview-1.png\" alt=\"\" class=\"wp-image-10882\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__2_-removebg-preview-1.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__2_-removebg-preview-1-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n\n\n\n<p><strong>Determine if 3u is positive or negative.<\/strong><\/p>\n\n\n\n<p>In the expression 3u, 3 is positive and u is negative. The product of a positive number and a negative number is negative. So, 3u is negative.<\/p>\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\/80687\/784\/855\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-289.png\" alt=\"\" class=\"wp-image-9547\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-289.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-289-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-289-150x150.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\/85130\/315\/198\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-296.png\" alt=\"\" class=\"wp-image-9548\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-296.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-296-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-296-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Apply addition, subtraction, multiplication and division rules Key notes Addition Rules Commutative Property: a + b = b + a (Order doesn&#8217;t change the sum) Associative Property: (a+b) + c = a + (b+c) (Grouping doesn&#8217;t affect the sum) Identity Property: a + 0 = a (Adding zero doesn\u2019t change a number) Adding Positive and<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/e-8-apply-addition-subtraction-multiplication-and-division-rules\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.8 Apply addition, subtraction, multiplication and division rules&#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-84","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_hostinger_reach_plugin_has_subscription_block":false,"_hostinger_reach_plugin_is_elementor":false,"_links":{"self":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/84","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=84"}],"version-history":[{"count":19,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/84\/revisions"}],"predecessor-version":[{"id":19915,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/84\/revisions\/19915"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=84"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}