{"id":66,"date":"2022-04-12T12:00:25","date_gmt":"2022-04-12T12:00:25","guid":{"rendered":"http:\/\/8thclass.deltapublications.in\/?page_id=66"},"modified":"2025-11-21T06:50:53","modified_gmt":"2025-11-21T06:50:53","slug":"d-7-put-rational-numbers-in-order","status":"publish","type":"page","link":"https:\/\/8thclass.deltapublications.in\/index.php\/d-7-put-rational-numbers-in-order\/","title":{"rendered":"D.7 Put rational numbers in order"},"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>Put rational numbers in order<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-video\"><video controls src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/08\/Class-8-D.7-Put-rational-numbers-in-order.mp4\"><\/video><\/figure>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-huge-font-size wp-elements-d9e058b1021c9cd90955d7a9346f5c76\" style=\"color:#74008b\"><strong>Key Notes :<\/strong><\/h3>\n\n\n\n<h2 class=\"wp-block-heading has-large-font-size\"><strong>What are Rational Numbers? \ud83e\udd14<\/strong><\/h2>\n\n\n\n<p>Rational numbers are numbers that can be written as <strong>fractions<\/strong> <code>p\/q<\/code>, where <code>p<\/code> and <code>q<\/code> are integers and <code>q \u2260 0<\/code>.<\/p>\n\n\n\n<p>They include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Positive numbers<\/strong> \u2795<\/li>\n\n\n\n<li><strong>Negative numbers<\/strong> \u2796<\/li>\n\n\n\n<li><strong>Zero<\/strong> 0\ufe0f\u20e3<\/li>\n<\/ul>\n\n\n\n<p>Examples: <code>3\/4, -2\/5, 0, 7<\/code><\/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\"><strong>Steps to Arrange Rational Numbers in Order \ud83d\udd22<\/strong><\/h2>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>Step 1: Convert to Same Form (Fractions or Decimals) \ud83d\udd04<\/strong><\/h3>\n\n\n\n<p>Convert all numbers to <strong>decimals<\/strong> or <strong>fractions with the same denominator<\/strong>.<\/p>\n\n\n\n<p>Example: Arrange <code>1\/2, -3\/4, 2\/3<\/code><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Convert to decimals: <code>1\/2 = 0.5<\/code>, <code>-3\/4 = -0.75<\/code>, <code>2\/3 \u2248 0.667<\/code><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>Step 2: Compare the Numbers \ud83d\udc40<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>For positive numbers<\/strong> \u27a1 bigger decimal\/fraction = bigger number<\/li>\n\n\n\n<li><strong>For negative numbers<\/strong> \u27a1 bigger decimal (less negative) = bigger number<\/li>\n\n\n\n<li>Example: <code>-0.75 &lt; 0.5 &lt; 0.667<\/code><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong>Step 3: Arrange in Order \u2b06\ufe0f or \u2b07\ufe0f<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Ascending Order (Smallest to Largest)<\/strong>: -0.75, 0.5, 0.667<\/li>\n\n\n\n<li><strong>Descending Order (Largest to Smallest)<\/strong>: 0.667, 0.5, -0.75<\/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\"><strong>Tips &amp; Tricks \ud83d\udca1<\/strong><\/h2>\n\n\n\n<p><strong>Always watch the signs!<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Negative numbers are <strong>smaller than zero<\/strong>. \u274c0\ufe0f\u20e3<\/li>\n<\/ul>\n\n\n\n<p><strong>Use a number line<\/strong> \ud83d\udccf<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Helps visualize which number is bigger or smaller.<\/li>\n<\/ul>\n\n\n\n<p><strong>Convert fractions first<\/strong> if denominators are different:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Example: <code>1\/3, 2\/5<\/code> \u2192 common denominator <code>15<\/code> \u2192 <code>5\/15, 6\/15<\/code><\/li>\n\n\n\n<li>Compare numerators: <code>5 &lt; 6<\/code> \u2192 <code>1\/3 &lt; 2\/5<\/code><\/li>\n<\/ul>\n\n\n\n<p><strong>Decimals make comparison easier<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><code>-3\/4 \u2248 -0.75<\/code><\/li>\n\n\n\n<li><code>2\/3 \u2248 0.667<\/code><\/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\"><strong>Example Problem \ud83d\udcdd<\/strong><\/h2>\n\n\n\n<p>Arrange in ascending order:<br><code>-1\/2, 3\/4, -2\/3, 1\/3<\/code><\/p>\n\n\n\n<p><strong>Step 1:<\/strong> Convert to decimals<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>-1\/2 = -0.5<\/li>\n\n\n\n<li>3\/4 = 0.75<\/li>\n\n\n\n<li>-2\/3 \u2248 -0.667<\/li>\n\n\n\n<li>1\/3 \u2248 0.333<\/li>\n<\/ul>\n\n\n\n<p><strong>Step 2:<\/strong> Compare<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Smallest \u2192 -0.667<\/li>\n\n\n\n<li>Then \u2192 -0.5<\/li>\n\n\n\n<li>Then \u2192 0.333<\/li>\n\n\n\n<li>Largest \u2192 0.75<\/li>\n<\/ul>\n\n\n\n<p><strong>\u2705 Answer (Ascending Order):<\/strong> <code>-2\/3, -1\/2, 1\/3, 3\/4<\/code><\/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\"><strong>Quick Reminder Chart \ud83d\uddc2\ufe0f<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th><strong>Sign<\/strong><\/th><th><strong>Order Rule<\/strong><\/th><\/tr><\/thead><tbody><tr><td>Positive \u2795<\/td><td>Bigger value \u2192 bigger number<\/td><\/tr><tr><td>Negative \u2796<\/td><td>More negative \u2192 smaller number<\/td><\/tr><tr><td>Zero 0\ufe0f\u20e3<\/td><td>In between negative and positive<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" 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-f5d567368dc06a6a1d1f7e2905858adb\" style=\"background-color:#f7e9a7\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-primary-color has-background-background-color has-text-color has-background has-link-color wp-elements-70b18362791b6d9e3fe163c899eef978\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-7707251a9ae59763eae310f7dfbc79c7\" style=\"color:#b00012\">Put&nbsp;these numbers in order from&nbsp;<strong>least<\/strong>&nbsp;to&nbsp;<strong>greatest<\/strong>.<\/p>\n\n\n\n<p class=\"has-text-align-center has-huge-font-size\">9 ,-28\/40, 6\/15, -3\/6<\/p>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;write all the numbers as&nbsp;decimals.<\/p>\n\n\n\n<p>\u201328\/40= \u20130.7<\/p>\n\n\n\n<p>6\/15= 0.4<\/p>\n\n\n\n<p>\u20133\/6= \u20130.5<\/p>\n\n\n\n<p class=\"has-text-align-left\">You want to order the numbers from least to greatest. Since negative numbers are less than positive numbers, start with them first.<\/p>\n\n\n\n<p class=\"has-text-align-left\">When comparing negative numbers, larger numbers (if you ignore the minus sign) are less than smaller numbers.<\/p>\n\n\n\n<p class=\"has-text-align-left\">\u20130.7 is less than\u20130.5.<\/p>\n\n\n\n<p class=\"has-text-align-left\">Next come the positive numbers. The positive numbers, from least to greatest, are 0.4 and 9.<\/p>\n\n\n\n<p class=\"has-text-align-left\">The numbers, written as decimals, in order from least to greatest, are:<br>\u20130.7&lt;\u20130.5&lt;0.4&lt;9<\/p>\n\n\n\n<p class=\"has-text-align-left\">So, the correct answer is:<\/p>\n\n\n\n<p class=\"has-text-align-center has-huge-font-size\">\u201328\/40 &lt; \u20133\/6 &lt; 6\/15 &lt;9<br><\/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-b5c879574c7dd0a1922ac48dd33d0413\" style=\"background-color:#edaef4\"><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 class=\"has-text-color has-link-color wp-elements-c6448103a1086a6832fb01925c0b6874\" style=\"color:#b00012\">Put these numbers in order from greatest to least.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-5-1.png\" alt=\"\" class=\"wp-image-10830\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-5-1.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-5-1-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;write all the numbers as&nbsp;decimals.<\/p>\n\n\n\n<p>18\/25 = 0.72<\/p>\n\n\n\n<p>-1\/20 = -0.05<\/p>\n\n\n\n<p>You&nbsp;want to order the numbers from greatest to least. Since positive numbers are greater than negative numbers, start with them&nbsp;first.<\/p>\n\n\n\n<p>0.72&nbsp;is the only positive number. It is the greatest number on the&nbsp;list.<\/p>\n\n\n\n<p>Next,&nbsp;come the negative numbers. When comparing negative numbers, smaller numbers (if you ignore the minus sign) are&nbsp;<em>greater<\/em>&nbsp;than larger numbers.&nbsp;<\/p>\n\n\n\n<p>The&nbsp;numbers, written as decimals, in order from greatest to least,&nbsp;are:<\/p>\n\n\n\n<p>0.72 &gt; \u20130.05 &gt; \u20138<\/p>\n\n\n\n<p>So, the correct answer is:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__6_-removebg-preview.png\" alt=\"\" class=\"wp-image-10831\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__6_-removebg-preview.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__6_-removebg-preview-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\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-d1de5a43fc71ecbcb12f06c30a573570\" style=\"background-color:#9feeaf\"><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 class=\"has-text-color has-link-color wp-elements-d8f436ab933ad18ae5a2146e107bc5d1\" style=\"color:#b00012\">Put these numbers in order from least to greatest.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-7.png\" alt=\"\" class=\"wp-image-10834\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-7.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled-design-7-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>First,&nbsp;write all the numbers as&nbsp;decimals.<\/p>\n\n\n\n<p>-24\/40 = -0.6<\/p>\n\n\n\n<p>-18\/20 = -0.9<\/p>\n\n\n\n<p>6\/15 = 0.4<\/p>\n\n\n\n<p>You&nbsp;want to order the numbers from least to greatest. Since negative numbers are less than positive numbers, start with them&nbsp;first.<\/p>\n\n\n\n<p>When comparing negative numbers, larger numbers (if you ignore the minus sign) are less than smaller numbers. \u20130.9 is less than  \u20130.6.<\/p>\n\n\n\n<p>Next&nbsp;come the positive numbers. The positive numbers, from least to greatest, are&nbsp;0.4&nbsp;and&nbsp;7.<\/p>\n\n\n\n<p>The&nbsp;numbers, written as decimals, in order from least to greatest,&nbsp;are:<\/p>\n\n\n\n<p>\u20130.9 &lt; \u20130.6 &lt; 0.4 &lt; 7<\/p>\n\n\n\n<p>So, the correct answer is:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"670\" height=\"100\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__8_-removebg-preview.png\" alt=\"\" class=\"wp-image-10836\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__8_-removebg-preview.png 670w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/07\/Untitled_design__8_-removebg-preview-300x45.png 300w\" sizes=\"auto, (max-width: 670px) 100vw, 670px\" \/><\/figure>\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\/33813\/145\/821\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-266.png\" alt=\"\" class=\"wp-image-9465\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-266.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-266-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-266-150x150.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\/642\/648\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-273.png\" alt=\"\" class=\"wp-image-9466\" srcset=\"https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-273.png 500w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-273-300x300.png 300w, https:\/\/8thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-273-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Put rational numbers in order Key Notes : What are Rational Numbers? \ud83e\udd14 Rational numbers are numbers that can be written as fractions p\/q, where p and q are integers and q \u2260 0. They include: Examples: 3\/4, -2\/5, 0, 7 Steps to Arrange Rational Numbers in Order \ud83d\udd22 Step 1: Convert to Same Form<a class=\"more-link\" href=\"https:\/\/8thclass.deltapublications.in\/index.php\/d-7-put-rational-numbers-in-order\/\">Continue reading <span class=\"screen-reader-text\">&#8220;D.7 Put rational numbers in order&#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-66","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\/66","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=66"}],"version-history":[{"count":19,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/66\/revisions"}],"predecessor-version":[{"id":22361,"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/66\/revisions\/22361"}],"wp:attachment":[{"href":"https:\/\/8thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=66"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}