{"id":172,"date":"2022-04-12T09:46:02","date_gmt":"2022-04-12T09:46:02","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=172"},"modified":"2025-12-03T11:52:38","modified_gmt":"2025-12-03T11:52:38","slug":"h-7-multiply-and-divide-rational-numbers","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/h-7-multiply-and-divide-rational-numbers\/","title":{"rendered":"H.7 Multiply and divide rational numbers"},"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 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<h2 class=\"wp-block-heading has-large-font-size\">\ud83d\udd22 <strong>What Are Rational Numbers?<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Rational numbers are numbers that can be written as <strong>a fraction<\/strong> \u2728<br>\u27a4 Example: \u00bd, \u20133, 4\/7, 0.25 \u2714\ufe0f<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u2716\ufe0f <strong>Multiplying Rational Numbers<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udccc <strong>Rule 1: Multiply the Numerators<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Top \u00d7 Top<br>Example: 2\/3 \u00d7 4\/5 = <strong>8\/15<\/strong> \ud83c\udf89<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udccc <strong>Rule 2: Multiply the Denominators<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Bottom \u00d7 Bottom<br>Example: \u20133\/4 \u00d7 2\/7 \u2192 numerator: \u20133\u00d72 = \u20136, denominator: 4\u00d77 = 28<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udccc <strong>Rule 3: Check the Sign<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(+) \u00d7 (+) = <strong>+<\/strong><\/li>\n\n\n\n<li>(\u2013) \u00d7 (\u2013) = <strong>+<\/strong><\/li>\n\n\n\n<li>(+) \u00d7 (\u2013) = <strong>\u2013<\/strong><br>\ud83d\udc49 Same signs \u2192 Positive \ud83d\ude0a<br>\ud83d\udc49 Different signs \u2192 Negative \ud83d\ude15<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83c\udfaf <strong>Shortcut:<\/strong><\/h3>\n\n\n\n<p>Try to <strong>simplify<\/strong> the fractions before multiplying to make the answer smaller and easier! \u2702\ufe0f\u2728<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\u2797 <strong>Dividing Rational Numbers<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udccc <strong>Rule 1: Keep \u2013 Change \u2013 Flip (KCF)<\/strong> \ud83d\udca1<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>KEEP<\/strong> the first fraction<\/li>\n\n\n\n<li><strong>CHANGE<\/strong> division to multiplication<\/li>\n\n\n\n<li><strong>FLIP<\/strong> the second fraction (take its reciprocal \ud83d\udd04)<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udd0d Example:<br>3\/5 \u00f7 2\/3<br>= 3\/5 \u00d7 3\/2<br>= 9\/10 \u2714\ufe0f<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\ud83d\udccc <strong>Rule 2: Check the Sign<\/strong><\/h3>\n\n\n\n<p>Same sign \u2192 Positive \ud83d\ude0a<br>Different sign \u2192 Negative \ud83d\ude15<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83e\uddee <strong>Multiplying &amp; Dividing Integers (part of rationals!)<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(+) \u00d7 (\u2013) = negative<\/li>\n\n\n\n<li>(\u2013) \u00f7 (+) = negative<\/li>\n\n\n\n<li>(\u2013) \u00d7 (\u2013) = positive<\/li>\n\n\n\n<li>(\u2013) \u00f7 (\u2013) = positive<br>\u2728 Always check the signs first!<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83c\udf08 <strong>Tips to Remember<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udd04 Flip only the <strong>second<\/strong> fraction in division<\/li>\n\n\n\n<li>\u2716\ufe0f Multiply straight across<\/li>\n\n\n\n<li>\ud83e\uddf9 Simplify at the end<\/li>\n\n\n\n<li>\ud83e\udde0 Practice makes it easy!<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\">\ud83c\udf89 <strong>Example Problems<\/strong><\/h2>\n\n\n\n<p>1\ufe0f\u20e3 2\/3 \u00d7 \u20135\/8 = \u201310\/24 \u2192 \u20135\/12<br>2\ufe0f\u20e3 \u20137\/9 \u00f7 1\/3 = \u20137\/9 \u00d7 3\/1 = \u201321\/9 \u2192 \u20137\/3<\/p>\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-large-font-size\" style=\"background-color:#f9d4f5\"><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\">\ud83d\uddfc <strong>Multiply. &#8211; 3 1\/4 x 1 3\/5 = _____<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Write the mixed numbers as improper fractions.<\/li>\n<\/ul>\n\n\n\n<p>&#8211; 3 1\/4 x 1 3\/5<\/p>\n\n\n\n<p>&#8211; 13\/4 x 8\/5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cancel common factors, then multiply.<\/li>\n<\/ul>\n\n\n\n<p>&#8211; 13\/4 x 8\/5 = &#8211; 13\/1 x 2\/5<\/p>\n\n\n\n<p>= &#8211; 13 x 2 \/  1 x 5<\/p>\n\n\n\n<p>= 26 \/ 5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplify the answer.<\/li>\n\n\n\n<li><strong>&#8211; 26\/5 = &#8211; 5 1\/5<\/strong><\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#fadee4\"><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\">\ud83d\uddfc <strong>Multiply.  &#8211; 1\/2 x 1 1\/2 = ____<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Write the mixed number as an improper fraction. <\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"146\" height=\"200\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__7_-removebg-preview.png\" alt=\"\" class=\"wp-image-3355\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Now multiply.<\/li>\n<\/ul>\n\n\n\n<p>&#8211; 1\/2 x 3\/2 = &#8211; 1 x 3 \/ 2 x 2<\/p>\n\n\n\n<p>= &#8211; 3 \/ 4<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#faf1cf\"><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\">\ud83d\uddfc <strong>Multiply. 1\/8 x 2 = _____<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Write the whole number as a fraction. <\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"100\" height=\"176\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2022\/12\/Untitled_design__9_-removebg-preview.png\" alt=\"\" class=\"wp-image-3357\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cancel common factors, then multiply.<\/li>\n<\/ul>\n\n\n\n<p>1\/8 x 2\/1 = 1\/4 x 1\/1<\/p>\n\n\n\n<p>= 1 x 1 \/ 4 x 1<\/p>\n\n\n\n<p>=1\/4<\/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\/80682\/267\/478\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-272.png\" alt=\"\" class=\"wp-image-7429\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-272.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-272-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-272-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-272-400x400.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\/81273\/233\/570\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-280.png\" alt=\"\" class=\"wp-image-7430\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-280.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-280-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-280-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-280-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Multiply and divide rational numbers Key notes: \ud83d\udd22 What Are Rational Numbers? \u2716\ufe0f Multiplying Rational Numbers \ud83d\udccc Rule 1: Multiply the Numerators \ud83d\udccc Rule 2: Multiply the Denominators \ud83d\udccc Rule 3: Check the Sign \ud83c\udfaf Shortcut: Try to simplify the fractions before multiplying to make the answer smaller and easier! \u2702\ufe0f\u2728 \u2797 Dividing Rational Numbers<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/h-7-multiply-and-divide-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.7 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,"footnotes":""},"class_list":["post-172","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.2.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"Multiply and divide rational numbers Key notes: \ud83d\udd22 What Are Rational Numbers? 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