{"id":78,"date":"2022-04-12T12:02:25","date_gmt":"2022-04-12T12:02:25","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=78"},"modified":"2025-02-22T15:47:33","modified_gmt":"2025-02-22T15:47:33","slug":"e-5-multiply-and-divide-rational-numbers","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/e-5-multiply-and-divide-rational-numbers\/","title":{"rendered":"E.5 Multiply and divide rational numbers"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-background-background-color has-text-color has-background has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Multiply and divide rational numbers<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-ab8376a8ebfb22772ef7356f8b60e696\" 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-51308b5329b3222e961afc3ab9f24b6c\" style=\"color:#000060\"><strong>Understanding Rational Numbers<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>A rational number is any number that can be expressed as a fraction <strong>a\/b\u200b<\/strong>, where <strong>a<\/strong> and <strong>b<\/strong> are integers, and <strong>b \u2260 0<\/strong>.<\/li>\n\n\n\n<li>Rational numbers include integers, fractions, and terminating or repeating decimals.<\/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-ba3885b4b27107bda93cf78820ba7b3b\" style=\"color:#000060\"><strong>Multiplying Rational Numbers<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">Multiply the numerators together and multiply the denominators together: a\/b \u00d7 c\/d = a\u00d7c \/ b\u00d7d<\/p>\n\n\n\n<p class=\"has-large-font-size\">If multiplying decimals, count the total number of decimal places and place the decimal correctly in the product.<\/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-138642e38d0ec29d38a2882e44d1ef62\" style=\"color:#000060\"><strong>Sign rules<\/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>Positive \u00d7 Negative = Negative<\/li>\n\n\n\n<li>Negative \u00d7 Negative = Positive<\/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-2d600209dd025349848eb5ef2792eebb\" style=\"color:#000060\"><strong>Dividing Rational Numbers<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">To divide fractions, multiply by the reciprocal (flip the second fraction): a\/b \u00f7 c\/d = a\/b \u00d7 d\/c<\/p>\n\n\n\n<p class=\"has-large-font-size\">When dividing decimals, convert them into fractions or move the decimal point appropriately.<\/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-138642e38d0ec29d38a2882e44d1ef62\" 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>Positive \u00f7 Negative = Negative<\/li>\n\n\n\n<li>Negative \u00f7 Negative = Positive<\/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-6622bf05e12b4c397fa17056ec5cac69\" style=\"color:#000060\"><strong>Simplifying Before Multiplying or Dividing<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Reduce fractions by canceling out common factors before multiplying.<\/li>\n\n\n\n<li>Cross-cancel when multiplying fractions to simplify calculations.<\/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-2af3e2f9828d1c875b484a3f75644067\" style=\"color:#000060\"><strong>Multiplying and Dividing Mixed Numbers<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Convert mixed numbers into improper fractions before multiplying or dividing.<\/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-8f03b2e7d9ab9f0943e840e7ae88e7c0\" style=\"color:#000060\"><strong>Word Problems and Real-Life Applications<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>Understand the context of the problem before applying operations.<\/li>\n\n\n\n<li>Use multiplication and division of rational numbers in scenarios like rates, ratios, and proportions.<\/li>\n<\/ul>\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-d1bad9a5bf5dc0064a78bdc5efc56209\" style=\"background-color:#c6e1f7\"><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-primary-color has-text-color has-background has-link-color has-large-font-size wp-elements-f6091bdfc9b97ea079ae87d31ab9958d\" 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>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-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group\"><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 has-large-font-size wp-elements-2db347e356b27f804ea33dc576aade84\" style=\"background-color:#d8ecfb\"><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 Divide.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-85dc37bd3da2e14481971bc27bb4e194\" style=\"color:#b00012\"><strong>3\/10 \u00f7&nbsp;1\/3 = _____<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Turn this from a division problem into a multiplication problem by multiplying by the reciprocal.<\/p>\n\n\n\n<p>3\/10 \u00f7&nbsp;1\/3 = 3\/10  x  3\/1<\/p>\n\n\n\n<p>Now multiply.<\/p>\n\n\n\n<p>3\/10  x  3\/1 = 3 x 3 \/ 10 x 1<\/p>\n\n\n\n<p>= 9\/10<\/p>\n<\/div><\/div>\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-10b6cf502357c765dd083f3d9e3ef686\" style=\"background-color:#e1d6fc\"><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 Divide.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-16d4e852a68fbc138cd0fe9a911657fe\" style=\"color:#b00012\"><strong>-1\/5 \u00f7&nbsp;-1\/2 = ____<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Turn this from a division problem into a multiplication problem by multiplying by the reciprocal.<\/p>\n\n\n\n<p>-1\/5 \u00f7&nbsp;-1\/2 = -1\/5 x -2\/1<\/p>\n\n\n\n<p>Now multiply.<\/p>\n\n\n\n<p>-1\/5 x -2\/1 = -1 x -2 \/ 5 x 1<\/p>\n\n\n\n<p>= 2\/5<\/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-09f61d10c6d8fea42931f8dedea3afea\" style=\"background-color:#f4caca\"><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>Divide.<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-4cf66c0b496f7d54475c463237a63e8d\" style=\"color:#b00012\">1\/4 \u00f7&nbsp;-2\/3 =<\/p>\n<\/div><\/div>\n\n\n\n<p>Turn this from a division problem into a multiplication problem by multiplying by the reciprocal.<\/p>\n\n\n\n<p>1\/4 \u00f7&nbsp;-2\/3 = 1\/4 x -3\/2<\/p>\n\n\n\n<p>Now multiply. <\/p>\n\n\n\n<p>1\/4 x -3\/2 = 1 \u00d7 \u20133 \/ 4 \u00d7 2<\/p>\n\n\n\n<p>= -3\/8<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\"><strong>Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/strong><\/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\/76096\/014\/970\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-283.png\" alt=\"\" class=\"wp-image-9528\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-283.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-283-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-283-150x150.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\/85122\/987\/602\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-290.png\" alt=\"\" class=\"wp-image-9529\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-290.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-290-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-290-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply and divide rational numbers Key notes: Understanding Rational Numbers Multiplying Rational Numbers Multiply the numerators together and multiply the denominators together: a\/b \u00d7 c\/d = a\u00d7c \/ b\u00d7d If multiplying decimals, count the total number of decimal places and place the decimal correctly in the product. Sign rules: Dividing Rational Numbers To divide fractions,<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/e-5-multiply-and-divide-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.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-78","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\/78","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=78"}],"version-history":[{"count":24,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/78\/revisions"}],"predecessor-version":[{"id":19910,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/78\/revisions\/19910"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=78"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}