{"id":64,"date":"2022-04-12T12:00:06","date_gmt":"2022-04-12T12:00:06","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=64"},"modified":"2025-11-21T06:47:56","modified_gmt":"2025-11-21T06:47:56","slug":"d-6-compare-rational-numbers","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/d-6-compare-rational-numbers\/","title":{"rendered":"D.6 Compare rational numbers"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Compare and order rational numbers<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-8550df6181cd5d83aa7a08ef336a4ca1\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-large-font-size\"><strong>\ud83d\udd22 What are Rational Numbers?<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Numbers that can be written as <strong>p\/q<\/strong>, where <strong>p<\/strong> and <strong>q<\/strong> are integers and <strong>q \u2260 0<\/strong>.<\/li>\n\n\n\n<li>Examples: <strong>1\/2, -3\/4, 0, 5<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\ud83d\udccf Comparison Symbols<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>><\/strong> : Greater than<\/li>\n\n\n\n<li><strong>&lt;<\/strong> : Less than<\/li>\n\n\n\n<li><strong>=<\/strong> : Equal to<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\ud83e\uddee Step 1: Same Denominator<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Compare fractions directly if denominators are the same.<\/li>\n\n\n\n<li>\u2705 Example: <strong>3\/7 > 2\/7<\/strong> (because 3 > 2)<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\ud83e\uddee Step 2: Different Denominator<\/strong><\/p>\n\n\n\n<p>Find <strong>LCM of denominators<\/strong> to make denominators the same.<\/p>\n\n\n\n<p>\u2705 Example: Compare <strong>2\/3 and 3\/4<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>LCM of 3 &amp; 4 = 12<\/li>\n\n\n\n<li>Convert: 2\/3 = 8\/12, 3\/4 = 9\/12 \u2192 <strong>8\/12 &lt; 9\/12<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\u2795 Step 3: Use Decimal Form<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Convert fractions\/integers to <strong>decimals<\/strong> to compare.<\/li>\n\n\n\n<li>\u2705 Example: <strong>1\/2 = 0.5, 2\/5 = 0.4 \u2192 0.5 > 0.4<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\u2796 Step 4: Consider Negative Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>On the number line, numbers <strong>to the right are greater<\/strong>, numbers <strong>to the left are smaller<\/strong>.<\/li>\n\n\n\n<li>\u2705 Example: <strong>-2 &lt; -1<\/strong> (because -2 is left of -1)<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\ud83d\udccf Step 5: Compare Mixed Numbers<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Convert <strong>mixed numbers to improper fractions<\/strong> first.<\/li>\n\n\n\n<li>\u2705 Example: 1 1\/2 = 3\/2, 1 2\/3 = 5\/3 \u2192 3\/2 &lt; 5\/3<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\ud83d\udcca Quick Tip: Number Line Method<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Plot numbers on a <strong>number line<\/strong> \u2192 easier to see which is greater.<\/li>\n\n\n\n<li>\ud83d\udd39 Right \u2192 bigger<\/li>\n\n\n\n<li>\ud83d\udd39 Left \u2192 smaller<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\ud83d\udca1 Remember:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Positive > Negative<\/li>\n\n\n\n<li>Bigger numerator (same denominator) \u2192 bigger fraction<\/li>\n\n\n\n<li>Smaller denominator (same numerator) \u2192 bigger fraction<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><strong>\ud83c\udfaf Practice Makes Perfect<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always <strong>convert<\/strong> or <strong>plot<\/strong> before comparing!<\/li>\n<\/ul>\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 has-large-font-size wp-elements-1eeb049ddac67b5c832b4da3db1b9de8\" style=\"background-color:#f8b9b9\"><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-b6629e2252b86e4639be4fb1e168a17e\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-b2f035b770a5eb6c42997c6a1167a8e5\" style=\"color:#b00012\">Which sign makes the statement true?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-496b9231550c0271514fce4b3258e7d2\" style=\"color:#b00012\">1\/4 ? 1\/2<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&gt;<\/li>\n\n\n\n<li>&lt;<\/li>\n\n\n\n<li>=<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Use a common denominator.<\/p>\n\n\n\n<p>1\/4 ? 1\/2<\/p>\n\n\n\n<p>1\/4 ? 2\/4<\/p>\n\n\n\n<p>1\/4 is less than 2\/4 , so:<\/p>\n\n\n\n<p>1\/4 &lt; 2\/4<\/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-e3c83fb1a4aeb734e36097c1ae90d0df\" style=\"background-color:#fac8fc\"><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-802f0fba6bc1d09680d12cbdcb96e98c\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Which sign makes the statement true?<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-afb6971842c685d00cba5baea74ab0db\" style=\"color:#b00012\">-5\/8 ? -1\/5<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&gt;<\/li>\n\n\n\n<li>&lt;<\/li>\n\n\n\n<li>=<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Use a common denominator.<\/p>\n\n\n\n<p>-5\/8 ? -1\/5<\/p>\n\n\n\n<p>-25\/40 ? -8 \/ 40<\/p>\n\n\n\n<p>Remember that when comparing negative numbers, larger numbers like 25\/40 (if you ignore the minus sign) are less than smaller numbers like 8\/40. So:<\/p>\n\n\n\n<p>-5\/8 &lt; -1\/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-d07060efac42eb1f650cff706d18cbad\" style=\"background-color:#baf2d1\"><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-e66322c1bc90d7ab0fe7ee6b72fed3d4\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-db3f2847670e93996df80fbffc60243e\" style=\"color:#b00012\">Which sign makes the statement true? 1\/4 ? 3\/4<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&gt;<\/li>\n\n\n\n<li>&lt;<\/li>\n\n\n\n<li>=<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>1\/4 is less than 3\/4, so:<\/p>\n\n\n\n<p>1\/4&lt;3\/4<\/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\/80680\/100\/302\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-267.png\" alt=\"\" class=\"wp-image-9468\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-267.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-267-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-267-150x150.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\/81209\/430\/345\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-274.png\" alt=\"\" class=\"wp-image-9469\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-274.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-274-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-274-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Compare and order rational numbers Key Notes : \ud83d\udd22 What are Rational Numbers? \ud83d\udccf Comparison Symbols \ud83e\uddee Step 1: Same Denominator \ud83e\uddee Step 2: Different Denominator Find LCM of denominators to make denominators the same. \u2705 Example: Compare 2\/3 and 3\/4 \u2795 Step 3: Use Decimal Form \u2796 Step 4: Consider Negative Numbers \ud83d\udccf Step<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/d-6-compare-rational-numbers\/\">Continue reading <span class=\"screen-reader-text\">&#8220;D.6 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,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-64","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\/64","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=64"}],"version-history":[{"count":15,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/64\/revisions"}],"predecessor-version":[{"id":22359,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/64\/revisions\/22359"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=64"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}