{"id":48,"date":"2022-04-12T11:57:19","date_gmt":"2022-04-12T11:57:19","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=48"},"modified":"2025-09-02T02:47:22","modified_gmt":"2025-09-02T02:47:22","slug":"c-7-multiply-and-divide-integers","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/c-7-multiply-and-divide-integers\/","title":{"rendered":"C.7 Multiply and divide integers"},"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>Multiply and divide integers<\/strong><\/h2>\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\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwsF85hlY\/vFiRQEkEjnLEreY5q7oyGQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwsF85hlY&#x2F;vFiRQEkEjnLEreY5q7oyGQ&#x2F;watch?utm_content=DAGwsF85hlY&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">Multiply and Divide Integers<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" 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:#000060\"><tbody><tr><td><strong>\ud83d\udd39 What are Integers?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Integers are <strong>whole numbers<\/strong> and their opposites.<\/li>\n\n\n\n<li>Examples: <strong>\u2026, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, \u2026<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>\ud83d\udd39 Multiplication Rules for Integers<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Positive \u00d7 Positive = Positive<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: 3\u00d74=12<\/li>\n<\/ul>\n\n\n\n<p><strong>Negative \u00d7 Negative = Positive<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: (\u22123)\u00d7(\u22124)=12<\/li>\n<\/ul>\n\n\n\n<p><strong>Positive \u00d7 Negative = Negative<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: 3\u00d7(\u22124)=\u221212<\/li>\n<\/ul>\n\n\n\n<p><strong>Negative \u00d7 Positive = Negative<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: (\u22123)\u00d74=\u221212<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 <strong>Rule of Thumb:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the signs are <strong>same<\/strong>, the product is <strong>positive<\/strong>.<\/li>\n\n\n\n<li>If the signs are <strong>different<\/strong>, the product is <strong>negative<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong>\ud83d\udd39 Division Rules for Integers<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Positive \u00f7 Positive = Positive<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: 12\u00f73=4<\/li>\n<\/ul>\n\n\n\n<p><strong>Negative \u00f7 Negative = Positive<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: (\u221212)\u00f7(\u22123)=4<\/li>\n<\/ul>\n\n\n\n<p><strong>Positive \u00f7 Negative = Negative<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: 12\u00f7(\u22123)=\u22124<\/li>\n<\/ul>\n\n\n\n<p><strong>Negative \u00f7 Positive = Negative<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: (\u221212)\u00f73=\u22124<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udc49 <strong>Rule of Thumb:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the signs are <strong>same<\/strong>, the quotient is <strong>positive<\/strong>.<\/li>\n\n\n\n<li>If the signs are <strong>different<\/strong>, the quotient is <strong>negative<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong><strong>\ud83d\udd39 Important Properties<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Commutative Property (Multiplication):<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a\u00d7b=b\u00d7a<\/li>\n\n\n\n<li>Example: (\u22122)\u00d73=3\u00d7(\u22122)=\u22126<\/li>\n<\/ul>\n\n\n\n<p>\u274c Not true for division.<\/p>\n\n\n\n<p><strong>Associative Property (Multiplication):<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a\u00d7b)\u00d7c=a\u00d7(b\u00d7c)<\/li>\n\n\n\n<li>Example: (2\u00d7\u22123)\u00d74=2\u00d7(\u221212)=\u221224<\/li>\n<\/ul>\n\n\n\n<p><strong>Distributive Property:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a\u00d7(b+c)=(a\u00d7b)+(a\u00d7c)<\/li>\n\n\n\n<li>Example: 2\u00d7(3+\u22125)=(2\u00d73)+(2\u00d7\u22125)=6\u221210=\u22124<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39 Worked Examples<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(\u22127)\u00d7(\u22125)=35<\/li>\n\n\n\n<li>(\u221236)\u00f7(9)=\u22124<\/li>\n\n\n\n<li>(45)\u00f7(\u22129)=\u22125<\/li>\n\n\n\n<li>(\u22128)\u00d7(6)=\u221248<\/li>\n\n\n\n<li>(\u221210)\u00f7(\u22122)=5<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39  Word Problem<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong> A submarine descends 50 meters each minute. How far does it descend in 8 minutes?<\/li>\n\n\n\n<li>\ud83d\udc49 \u221250\u00d78=\u2212400<\/li>\n\n\n\n<li><strong>Answer:<\/strong> The submarine descends <strong>400 meters below sea level<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>\ud83d\udd39 Quick Tips<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>\u2705 Multiplying\/Dividing integers with <strong>same sign \u2192 Positive<\/strong><br>\u2705 Multiplying\/Dividing integers with <strong>different sign \u2192 Negative<\/strong><br>\u2705 Zero times any integer = <strong>0<\/strong><br>\u2705 Division by zero is <strong>not defined<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>\ud83d\udccc <strong>Summary:<\/strong><\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiplication and division of integers follow sign rules.<\/li>\n\n\n\n<li>Same signs = positive result.<\/li>\n\n\n\n<li>Different signs = negative result.<\/li>\n\n\n\n<li>Properties like commutative, associative, and distributive help in simplifying problems.<\/li>\n<\/ul>\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:#d2e5ff\"><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-text-color has-background has-link-color wp-elements-dfc2ad89960d158a5492ea94286cc556\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\u27a1\ufe0f Multiply:<\/p>\n\n\n\n<p>-4 \u00d7 4 =&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>First, ignore any negatives and multiply:<\/p>\n\n\n\n<p>4 \u00d7 4 = 16<\/p>\n\n\n\n<p>Now find the sign of the result. Since you multiply a negative number, \u20134, by a positive number, 4, the result should be negative: \u201316.<\/p>\n\n\n\n<p>So, \u20134 \u00d7 4 = \u201316.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#e3c8fe\"><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-text-color has-background has-link-color wp-elements-922280fa2f82dd5ee8e683f4090f5fa3\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\u27a1\ufe0f Multiply:<\/p>\n\n\n\n<p>-9 \u00d7 3 =&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>First, ignore any negatives and multiply:<\/p>\n\n\n\n<p>9 \u00d7 3 = 27<\/p>\n\n\n\n<p>Now find the sign of the result. Since you multiply a negative number,&nbsp;-9, by a positive number, 3, the result should be negative:&nbsp;-27.<\/p>\n\n\n\n<p>So, \u20139 \u00d7 3 = \u201327.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#ceffdc\"><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-text-color has-background has-link-color wp-elements-469dbaed2b465340fad72d0f293bf2d0\" style=\"color:#b00012\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\u27a1\ufe0f Multiply:<\/p>\n\n\n\n<p>-2 \u00d7&nbsp;-1 =&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>First, ignore any negatives and multiply:<\/p>\n\n\n\n<p>2 \u00d7 1 = 2<\/p>\n\n\n\n<p>Now find the sign of the result. Since you multiply a negative number, \u20132, by a negative number, \u20131, the result should be positive: 2.<\/p>\n\n\n\n<p>So, \u20132 \u00d7 \u20131 = 2.<\/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\/76325\/477\/994\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-228.png\" alt=\"\" class=\"wp-image-9329\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-228.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-228-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-228-150x150.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\/33811\/901\/309\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-234.png\" alt=\"\" class=\"wp-image-9330\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-234.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-234-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-234-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply and divide integers Multiply and Divide Integers by Delta publications Key Notes : \ud83d\udd39 What are Integers? \ud83d\udd39 Multiplication Rules for Integers Positive \u00d7 Positive = Positive Negative \u00d7 Negative = Positive Positive \u00d7 Negative = Negative Negative \u00d7 Positive = Negative \ud83d\udc49 Rule of Thumb: \ud83d\udd39 Division Rules for Integers Positive \u00f7 Positive<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/c-7-multiply-and-divide-integers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;C.7 Multiply and divide integers&#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-48","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\/48","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=48"}],"version-history":[{"count":26,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/48\/revisions"}],"predecessor-version":[{"id":21362,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/48\/revisions\/21362"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=48"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}