{"id":34,"date":"2022-04-13T06:09:52","date_gmt":"2022-04-13T06:09:52","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=34"},"modified":"2025-11-19T07:02:08","modified_gmt":"2025-11-19T07:02:08","slug":"b-5-multiply-and-divide-rational-numbers","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/b-5-multiply-and-divide-rational-numbers\/","title":{"rendered":"B.5 Multiply and divide rational numbers"},"content":{"rendered":"\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<h2 class=\"wp-block-heading has-text-align-center has-background-background-color has-text-color has-background\" style=\"color:#00056d;text-transform:uppercase\"><strong>Multiply and divide rational numbers<\/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 has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Multiplying Rational Numbers<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Definition:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To multiply two rational numbers, multiply the numerators together and the denominators together.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"143\" height=\"60\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-28.png\" alt=\"\" class=\"wp-image-14637\" style=\"width:205px;height:auto\"\/><\/figure><\/div>\n\n\n<p><strong>Steps:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Multiply the numerators: a\u00d7c<\/li>\n\n\n\n<li>Multiply the denominators: b\u00d7d<\/li>\n\n\n\n<li>Simplify the resulting fraction, if possible.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"458\" height=\"85\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-29.png\" alt=\"\" class=\"wp-image-14639\" style=\"width:508px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-29.png 458w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-29-300x56.png 300w\" sizes=\"auto, (max-width: 458px) 100vw, 458px\" \/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Multiplying by a Whole Number:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>When multiplying a rational number by a whole number, treat the whole number as a fraction with denominator 1.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"308\" height=\"51\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-30.png\" alt=\"\" class=\"wp-image-14640\" style=\"width:441px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-30.png 308w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-30-300x50.png 300w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Dividing Rational Numbers<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Definition:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To divide two rational numbers, multiply the first rational number by the reciprocal of the second rational number.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Formula:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"175\" height=\"61\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-31.png\" alt=\"\" class=\"wp-image-14641\" style=\"width:278px;height:auto\"\/><\/figure><\/div>\n\n\n<p><strong>Steps:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Find the reciprocal of the divisor (flip the numerator and the denominator of the second fraction).<\/li>\n\n\n\n<li>Multiply the first fraction by this reciprocal.<\/li>\n\n\n\n<li>Simplify the resulting fraction, if possible.<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Example:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"498\" height=\"87\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-32.png\" alt=\"\" class=\"wp-image-14642\" style=\"width:498px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-32.png 498w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-32-300x52.png 300w\" sizes=\"auto, (max-width: 498px) 100vw, 498px\" \/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Dividing by a Whole Number:<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When dividing a rational number by a whole number, treat the whole number as a fraction with denominator 1 and then find its reciprocal.<\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"307\" height=\"33\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-33.png\" alt=\"\" class=\"wp-image-14643\" style=\"width:473px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-33.png 307w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-33-300x32.png 300w\" sizes=\"auto, (max-width: 307px) 100vw, 307px\" \/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Simplifying Rational Numbers<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>After multiplying or dividing rational numbers, always simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by this number.<strong>Example:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"274\" height=\"140\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-34.png\" alt=\"\" class=\"wp-image-14644\" style=\"width:365px;height:auto\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong><strong>Practice Problems<\/strong><\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Multiplying Rational Numbers:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"114\" height=\"105\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-27.png\" alt=\"\" class=\"wp-image-14635\" style=\"width:166px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Dividing Rational Numbers:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"107\" height=\"100\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-26.png\" alt=\"\" class=\"wp-image-14634\" style=\"width:137px;height:auto\"\/><\/figure><\/div>\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mixed Practice:<\/strong><\/li>\n<\/ul>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"93\" height=\"102\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-25.png\" alt=\"\" class=\"wp-image-14633\" style=\"width:144px;height:auto\"\/><\/figure><\/div>\n\n\n<figure class=\"wp-block-table has-normal-font-size\"><table class=\"has-text-color has-link-color has-fixed-layout\" style=\"color:#000060\"><tbody><tr><td><strong>Tips for Success<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Reciprocals:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Remember to find the reciprocal when dividing by a fraction.<\/li>\n<\/ul>\n\n\n\n<p><strong>Simplifying:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always simplify your answer to its lowest terms.<\/li>\n<\/ul>\n\n\n\n<p><strong>Multiplication and Division Rules:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Use the multiplication rule for both operations: multiply the numerators together and the denominators together for multiplication, and multiply by the reciprocal for division.<\/li>\n<\/ul>\n\n\n\n<p><strong>Check Your Work:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Double-check your multiplication and division to avoid small mistakes.<\/li>\n<\/ul>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f8c6c6\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>positive \u00d7 positive = positive<\/p>\n\n\n\n<p>positive \u00d7 negative = negative<\/p>\n\n\n\n<p>negative \u00d7 positive = negative<\/p>\n\n\n\n<p>negative \u00d7 negative = positive<\/p>\n\n\n\n<p class=\"has-background-background-color has-background\">To multiply two fractions, multiply the numerators and multiply the denominators.<\/p>\n\n\n\n<p>ex: 2\/3 \u00d7 1\/5 = 2\/15<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#c1faee\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p>positive \u00f7 positive = positive<\/p>\n\n\n\n<p>positive \u00f7 negative = negative<\/p>\n\n\n\n<p>negative \u00f7 positive = negative<\/p>\n\n\n\n<p>negative \u00f7 negative = positive<\/p>\n\n\n\n<p class=\"has-background-background-color has-background\">Dividing by a fraction is the same as multiplying by its reciprocal.<\/p>\n\n\n\n<p class=\"has-normal-font-size\">Ex: 2\/3 \u00f7 1\/3 = 2\/3 x 3\/1 =6\/3 =2<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-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:#cfe7f7\"><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>\ud83c\udfaf Multiply.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>4\/5 x 1\/4 =<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Cancel common factors, then multiply.<\/p>\n\n\n\n<p>4\/5 x 1\/4 = 1\/5 x 1\/1<\/p>\n\n\n\n<p>= 1 x 1 \/ 5 x 1<\/p>\n\n\n\n<p>= 1\/5<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#c9f9ca\"><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>\ud83c\udfaf Multiply.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>1\/2 x 2\/5 =<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Cancel common factors, then multiply.<\/p>\n\n\n\n<p>1\/2 x 2\/5 = 1\/1 x 1\/5<\/p>\n\n\n\n<p>= 1 x 1 \/ 1 x 5<\/p>\n\n\n\n<p>= 1\/5<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f99393\"><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>\ud83c\udfaf Multiply.<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>1\/4 x 2\/5 =<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Cancel common factors, then multiply.<\/p>\n\n\n\n<p>1\/4 x 2\/5 = 1\/2 x 1\/5<\/p>\n\n\n\n<p>= 1 x 1 \/ 2 x 5<\/p>\n\n\n\n<p>= 1\/10<\/p>\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\/76556\/941\/873\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-21.png\" alt=\"\" class=\"wp-image-7329\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-21.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-21-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-21-150x150.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\/76150\/674\/424\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-22.png\" alt=\"\" class=\"wp-image-7330\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-22.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-22-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-22-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Multiply and divide rational numbers key notes : Multiplying Rational Numbers Definition: Steps: Multiplying by a Whole Number: When multiplying a rational number by a whole number, treat the whole number as a fraction with denominator 1. Dividing Rational Numbers Definition: Steps: Dividing by a Whole Number: Simplifying Rational Numbers Practice Problems Tips for Success<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/b-5-multiply-and-divide-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;B.5 Multiply and divide rational numbers&#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-34","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/34","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=34"}],"version-history":[{"count":24,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/34\/revisions"}],"predecessor-version":[{"id":17268,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/34\/revisions\/17268"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=34"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}