{"id":58,"date":"2022-04-12T09:25:39","date_gmt":"2022-04-12T09:25:39","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=58"},"modified":"2025-08-07T11:27:55","modified_gmt":"2025-08-07T11:27:55","slug":"c-7-multiply-and-divide-integers","status":"publish","type":"page","link":"https:\/\/7thclass.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\" style=\"color:#00056d;text-transform:uppercase\"><strong>Multiply and divide integers<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/08\/C.7-Multiply-and-divide-integers.mp4\"><\/video><\/figure>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\"><strong>Key Notes:<\/strong><\/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>What Are Integers?<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Integers include:<br>\u2705 <strong>Positive whole numbers<\/strong> (1, 2, 3\u2026)<br>\u2705 <strong>Negative whole numbers<\/strong> (\u20131, \u20132, \u20133\u2026)<br>\u2705 <strong>Zero<\/strong> (0)<\/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>\u2716\ufe0f <strong>Multiplying Integers<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Rules for Multiplication:<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Integer 1<\/th><th>Integer 2<\/th><th>Result Sign<\/th><\/tr><\/thead><tbody><tr><td>Positive \u00d7 Positive<\/td><td>\u279d<\/td><td>Positive (+)<\/td><\/tr><tr><td>Negative \u00d7 Negative<\/td><td>\u279d<\/td><td>Positive (+)<\/td><\/tr><tr><td>Positive \u00d7 Negative<\/td><td>\u279d<\/td><td>Negative (\u2013)<\/td><\/tr><tr><td>Negative \u00d7 Positive<\/td><td>\u279d<\/td><td>Negative (\u2013)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Remember:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Same signs \u2192 Positive (+)<\/strong><\/li>\n\n\n\n<li><strong>Different signs \u2192 Negative (\u2013)<\/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>\u270d\ufe0f <strong>Examples:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(+6) \u00d7 (+4) = <strong>+24<\/strong><\/li>\n\n\n\n<li>(\u20133) \u00d7 (\u20137) = <strong>+21<\/strong><\/li>\n\n\n\n<li>(\u20135) \u00d7 (+2) = <strong>\u201310<\/strong><\/li>\n\n\n\n<li>(+8) \u00d7 (\u20136) = <strong>\u201348<\/strong><\/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>\u2797 <strong>Dividing Integers<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 <strong>Rules for Division:<\/strong><\/h3>\n\n\n\n<p>(Same as multiplication!)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Integer 1<\/th><th>Integer 2<\/th><th>Result Sign<\/th><\/tr><\/thead><tbody><tr><td>Positive \u00f7 Positive<\/td><td>\u279d<\/td><td>Positive (+)<\/td><\/tr><tr><td>Negative \u00f7 Negative<\/td><td>\u279d<\/td><td>Positive (+)<\/td><\/tr><tr><td>Positive \u00f7 Negative<\/td><td>\u279d<\/td><td>Negative (\u2013)<\/td><\/tr><tr><td>Negative \u00f7 Positive<\/td><td>\u279d<\/td><td>Negative (\u2013)<\/td><\/tr><\/tbody><\/table><\/figure>\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>\u270d\ufe0f <strong>Examples:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>(+20) \u00f7 (+5) = <strong>+4<\/strong><\/li>\n\n\n\n<li>(\u201336) \u00f7 (\u20136) = <strong>+6<\/strong><\/li>\n\n\n\n<li>(+18) \u00f7 (\u20133) = <strong>\u20136<\/strong><\/li>\n\n\n\n<li>(\u201324) \u00f7 (+4) = <strong>\u20136<\/strong><\/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>\u2757 Special Note:<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Zero \u00d7 Any number = 0<\/strong><\/li>\n\n\n\n<li><strong>0 \u00f7 Any non-zero number = 0<\/strong><\/li>\n\n\n\n<li><strong>You cannot divide any number by zero!<\/strong> (Undefined)<\/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\udcdd <strong>Practice Questions:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Multiply:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u20134 \u00d7 5 = ______<\/li>\n\n\n\n<li>\u20133 \u00d7 \u20136 = ______<\/li>\n\n\n\n<li>7 \u00d7 \u20132 = ______<\/li>\n\n\n\n<li>\u20138 \u00d7 \u20131 = ______<\/li>\n\n\n\n<li>\u20139 \u00d7 0 = ______<\/li>\n<\/ol>\n\n\n\n<p><strong>Divide:<\/strong><\/p>\n\n\n\n<ol start=\"6\" class=\"wp-block-list\">\n<li>\u201324 \u00f7 6 = ______<\/li>\n\n\n\n<li>\u201336 \u00f7 \u20136 = ______<\/li>\n\n\n\n<li>40 \u00f7 \u20135 = ______<\/li>\n\n\n\n<li>\u201345 \u00f7 9 = ______<\/li>\n\n\n\n<li>0 \u00f7 7 = ______<\/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>\u2705 <strong>Answers:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u201320<\/li>\n\n\n\n<li>18<\/li>\n\n\n\n<li>\u201314<\/li>\n\n\n\n<li>8<\/li>\n\n\n\n<li>0<\/li>\n\n\n\n<li>\u20134<\/li>\n\n\n\n<li>6<\/li>\n\n\n\n<li>\u20138<\/li>\n\n\n\n<li>\u20135<\/li>\n\n\n\n<li>0<\/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>\ud83c\udfaf <strong>Tips to Remember:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiplying\/dividing <strong>same signs = Positive<\/strong><\/li>\n\n\n\n<li>Multiplying\/dividing <strong>different signs = Negative<\/strong><\/li>\n\n\n\n<li>Always follow the <strong>rules first<\/strong>, then do the calculation.<\/li>\n\n\n\n<li>Practice daily to gain confidence!<\/li>\n<\/ul>\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<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color wp-elements-fbabfcb023bc50607f024336f08ee5c4\" style=\"background-color:#fbc5e6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-bd1393815cfbc5589a784d8544476abd\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>When 2 integers have the same sign, the product is positive:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>positive \u00d7 positive = positive<\/li>\n\n\n\n<li>negative \u00d7 negative = positive<\/li>\n<\/ul>\n\n\n\n<p>When 2 integers have different signs, the product is negative:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>positive \u00d7 negative = negative<\/li>\n\n\n\n<li>negative \u00d7 positive = negative<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Ex: <\/p>\n\n\n\n<p>875 is positive.&nbsp;-95 is negative. Use the rule:<\/p>\n\n\n\n<p>positive \u00d7 negative = negative<\/p>\n\n\n\n<p>So, 875 \u00d7&nbsp;-95 is negative.<\/p>\n\n\n\n<p>Now check your answer by doing the maths.<\/p>\n\n\n\n<p>875 \u00d7&nbsp;-95 =&nbsp;-83,125<\/p>\n\n\n\n<p>Yes, the answer is 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 wp-elements-ac4a0f12148b7286b9834048688b7868\" style=\"background-color:#f8baba\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-c82da39d467030f4f4ec35f8b90708b2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>When 2 integers have the same sign, the quotient is positive:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>positive \u00f7 positive = positive<\/li>\n\n\n\n<li>negative \u00f7 negative = positive<\/li>\n<\/ul>\n\n\n\n<p>When 2 integers have different signs, the quotient is negative:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>positive \u00f7 negative = negative<\/li>\n\n\n\n<li>negative \u00f7 positive = negative<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>EX: <\/p>\n\n\n\n<p>3,264 is positive.&nbsp;-48 is negative. Use the rule:<\/p>\n\n\n\n<p>positive \u00f7 negative = negative<\/p>\n\n\n\n<p>So, 3,264 \u00f7&nbsp;-48 is negative.<\/p>\n\n\n\n<p>Now check your answer by doing the maths.<\/p>\n\n\n\n<p>3,264 \u00f7&nbsp;-48 =&nbsp;-68<\/p>\n\n\n\n<p>Yes, the answer is negative.<\/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-primary-color has-text-color has-background has-link-color wp-elements-7744abc2d01d5a47a121ae48a788af11\" style=\"background-color:#f0defc\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-8406de6e9b0f0ced7631d05064ecf5b8\"><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\">\u27a1\ufe0f <strong>Divide<\/strong>:<\/p>\n\n\n\n<p>-21 \u00f7 3 =<\/p>\n<\/div><\/div>\n\n\n\n<p>First, ignore any negatives and divide:<\/p>\n\n\n\n<p>21 \u00f7 3 = 7<\/p>\n\n\n\n<p>Now find the sign of the result. Since you divided a negative number,&nbsp;-21, by a positive number, 3, the result should be negative:&nbsp;-7.<\/p>\n\n\n\n<p>So,&nbsp;-21 \u00f7 3 =&nbsp;-7.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color wp-elements-f5d366792377b55d2ff4b7de05a78fba\" style=\"background-color:#d7fade\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-9fb8988a542666882f75ebfd385a1141\"><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\">\u27a1\ufe0f<strong> Divide:<\/strong><\/p>\n\n\n\n<p>-9 \/ 9 =<\/p>\n<\/div><\/div>\n\n\n\n<p>First, ignore any negatives and divide:<\/p>\n\n\n\n<p>9\/9 = 1<\/p>\n\n\n\n<p>Now find the sign of the result. Since you divided a negative number,&nbsp;-9, by a positive number, 9, the result should be negative:&nbsp;-1.<\/p>\n\n\n\n<p>So:<\/p>\n\n\n\n<p>-9\/9 = -1<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-primary-color has-text-color has-background has-link-color wp-elements-76f2e2f8a27e00e20fd7ba588db9f6dd\" style=\"background-color:#f9d4d4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-29978d8298eec7c3c3b3387f7747a61e\"><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\">\u27a1\ufe0f Multiply:<\/p>\n\n\n\n<p>-8 \u00d7&nbsp;-5 =&nbsp;<\/p>\n<\/div><\/div>\n\n\n\n<p>First, ignore any negatives and multiply:<\/p>\n\n\n\n<p>8 \u00d7 5 = 40<\/p>\n\n\n\n<p>Now find the sign of the result. Since you multiplied a negative number,&nbsp;<sup>\u2013<\/sup>8, by a negative number,&nbsp;<sup>\u2013<\/sup>5, the result should be positive: 40.<\/p>\n\n\n\n<p>So, \u20138 \u00d7 \u20135 = 40.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-normal-font-size\" style=\"color:#d90000\"><strong>Try some practice problems!<\/strong><\/p>\n<\/div><\/div>\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\/76366\/162\/361\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-195.png\" alt=\"\" class=\"wp-image-7152\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-195.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-195-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-195-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-195-400x400.png 400w\" 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\/76373\/962\/459\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-198.png\" alt=\"\" class=\"wp-image-7153\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-198.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-198-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-198-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-198-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply and divide integers Key Notes: What Are Integers? \u2716\ufe0f Multiplying Integers \u2705 Rules for Multiplication: Integer 1 Integer 2 Result Sign Positive \u00d7 Positive \u279d Positive (+) Negative \u00d7 Negative \u279d Positive (+) Positive \u00d7 Negative \u279d Negative (\u2013) Negative \u00d7 Positive \u279d Negative (\u2013) Remember: \u270d\ufe0f Examples: \u2797 Dividing Integers \u2705 Rules for<a class=\"more-link\" href=\"https:\/\/7thclass.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,"footnotes":""},"class_list":["post-58","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/58","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=58"}],"version-history":[{"count":17,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/58\/revisions"}],"predecessor-version":[{"id":16657,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/58\/revisions\/16657"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=58"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}