{"id":164,"date":"2022-04-12T09:44:43","date_gmt":"2022-04-12T09:44:43","guid":{"rendered":"http:\/\/7thclass.deltapublications.in\/?page_id=164"},"modified":"2025-12-03T11:41:57","modified_gmt":"2025-12-03T11:41:57","slug":"h-3-compare-rational-numbers","status":"publish","type":"page","link":"https:\/\/7thclass.deltapublications.in\/index.php\/h-3-compare-rational-numbers\/","title":{"rendered":"H.3 Compare rational numbers"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Compare rational numbers<\/strong><\/h2>\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<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>A <strong>rational number<\/strong> is any number that can be written as a <strong>fraction<\/strong>:<br>\ud83d\udc49 <strong>a\/b<\/strong>, where <strong>a<\/strong> and <strong>b<\/strong> are integers and <strong>b \u2260 0<\/strong><\/li>\n\n\n\n<li>Examples: <strong>1\/2, -3\/4, 5, 0, -7\/1<\/strong><\/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\">\ud83d\udccf <strong>Convert to Same Form Before Comparing<\/strong><\/h2>\n\n\n\n<p>To compare rational numbers, convert them into:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2714\ufe0f <strong>Fractions<\/strong><\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2714\ufe0f <strong>Decimals<\/strong><\/h3>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\">\u2714\ufe0f <strong>Like denominators<\/strong><\/h3>\n\n\n\n<p>Example:<br>Compare <strong>2\/3<\/strong> and <strong>3\/5<\/strong> \u2192 Make denominators same or convert to decimals.<\/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\">\ud83d\udff0 <strong>Use Common Denominators<\/strong><\/h2>\n\n\n\n<p>\ud83c\udf1f <strong>Rule:<\/strong> When denominators are the same,<br>\u27a1\ufe0f The number with the <strong>bigger numerator<\/strong> is <strong>greater<\/strong>.<br>Example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>7\/12 > 5\/12<\/strong> \ud83d\udc4d<\/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\">\ud83d\udca1 <strong>Use Number Line<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Numbers on the <strong>right \ud83d\udc49<\/strong> are <strong>greater<\/strong> than numbers on the <strong>left \ud83d\udc48<\/strong>.<\/li>\n\n\n\n<li>Example:\n<ul class=\"wp-block-list\">\n<li><strong>\u22122<\/strong> is to the right of <strong>\u22125<\/strong>, so <strong>\u22122 > \u22125<\/strong> \ud83d\ude0a<\/li>\n<\/ul>\n<\/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\">\ud83d\udd0d <strong>Compare Using Decimals<\/strong><\/h2>\n\n\n\n<p>Convert both numbers into <strong>decimals<\/strong> for easy comparison.<br>Example:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1\/4 = <strong>0.25<\/strong><\/li>\n\n\n\n<li>2\/5 = <strong>0.40<\/strong><br>So, <strong>2\/5 > 1\/4<\/strong> \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\">\u2795\u2796 <strong>Be Careful with Negative Rational Numbers<\/strong><\/h2>\n\n\n\n<p>\ud83d\udca5 <strong>Rule:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The rational number <strong>closer to zero<\/strong> is <strong>greater<\/strong> when negative.<br>Example:<\/li>\n\n\n\n<li><strong>\u22121\/3 > \u22121\/2<\/strong><br>Because \u22121\/3 is closer to 0.<\/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\">\ud83d\udd22 <strong>Cross Multiplication Method<\/strong><\/h2>\n\n\n\n<p>Use when denominators are different:<br>Compare <strong>a\/b<\/strong> and <strong>c\/d<\/strong><br>\ud83d\udc49 Cross multiply: <strong>a \u00d7 d<\/strong> and <strong>b \u00d7 c<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If <strong>a \u00d7 d > b \u00d7 c<\/strong>, then <strong>a\/b > c\/d<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Example:<br>Compare: <strong>3\/4<\/strong> and <strong>5\/8<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>3 \u00d7 8 = 24<\/li>\n\n\n\n<li>4 \u00d7 5 = 20<br>\u27a1\ufe0f 24 > 20 so <strong>3\/4 > 5\/8<\/strong> \ud83c\udf89<\/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\udfaf <strong>Remember the Order<\/strong><\/h2>\n\n\n\n<p>\ud83d\udc49 <strong>Smallest \u2192 Largest<\/strong><br>\ud83d\udc49 <strong>Negative &lt; Zero &lt; Positive<\/strong><\/p>\n\n\n\n<p>Example order:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u22123\/2, \u22121\/4, 0, 2\/3, 5\/4<\/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 Summary Chart<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Method<\/th><th>When to Use<\/th><th>Emoji<\/th><\/tr><\/thead><tbody><tr><td>Common denominator<\/td><td>Comparing fractions<\/td><td>\u2797<\/td><\/tr><tr><td>Number line<\/td><td>Visual comparison<\/td><td>\ud83d\udcc9<\/td><\/tr><tr><td>Decimals<\/td><td>Easy comparison<\/td><td>\ud83d\udd22<\/td><\/tr><tr><td>Cross multiplication<\/td><td>Fast for unlike denominators<\/td><td>\u2716\ufe0f<\/td><\/tr><\/tbody><\/table><\/figure>\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:#ecedfe\"><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\">\u26f3 <strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p>-8 ____ -1\/2<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Remember that when comparing negative numbers, larger numbers like 8 (if you ignore the minus sign) are less than smaller numbers like 1\/2. <\/li>\n\n\n\n<li><strong>So: -8 &lt; -1\/2<\/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:#f9d8e3\"><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\">\u26f3 <strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p>-2 3\/8 _____ 0<\/p>\n<\/div><\/div>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A negative number like <strong>-2<\/strong> 3\/8 is always less than zero.<\/li>\n\n\n\n<li>So: <strong>-2 <\/strong>3\/8 &lt; 0<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f4d4f5\"><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\">\u26f3 <strong>Which sign makes the statement true?<\/strong><\/p>\n\n\n\n<p>0 ____ -5  5\/8.<\/p>\n<\/div><\/div>\n\n\n\n<p>A negative number like<strong> -5<\/strong>  5\/8 is always less than zero.<\/p>\n\n\n\n<p>So: 0 &gt; <strong>&#8211; 5<\/strong> 5\/8<\/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\/80680\/100\/146\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-268.png\" alt=\"\" class=\"wp-image-7417\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-268.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-268-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-268-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-268-400x400.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\/81268\/386\/345\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-276.png\" alt=\"\" class=\"wp-image-7418\" srcset=\"https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-276.png 500w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-276-300x300.png 300w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-276-150x150.png 150w, https:\/\/7thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-276-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Compare rational numbers Key notes: \ud83d\udd22 What are Rational Numbers? \ud83d\udccf Convert to Same Form Before Comparing To compare rational numbers, convert them into: \u2714\ufe0f Fractions \u2714\ufe0f Decimals \u2714\ufe0f Like denominators Example:Compare 2\/3 and 3\/5 \u2192 Make denominators same or convert to decimals. \ud83d\udff0 Use Common Denominators \ud83c\udf1f Rule: When denominators are the same,\u27a1\ufe0f The<a class=\"more-link\" href=\"https:\/\/7thclass.deltapublications.in\/index.php\/h-3-compare-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;H.3 Compare 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-164","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164","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=164"}],"version-history":[{"count":21,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164\/revisions"}],"predecessor-version":[{"id":17616,"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/164\/revisions\/17616"}],"wp:attachment":[{"href":"https:\/\/7thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}