{"id":10425,"date":"2018-02-17T16:32:00","date_gmt":"2018-02-17T11:02:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/?p=10425"},"modified":"2019-02-01T11:05:28","modified_gmt":"2019-02-01T05:35:28","slug":"rational-numbers-class-11-notes-physical-education","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/rational-numbers-class-11-notes-physical-education\/","title":{"rendered":"Rational Numbers class 8 Notes Mathematics"},"content":{"rendered":"<p><strong>Rational Numbers class 8 Notes Mathematics<\/strong> in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Rational Numbers class 8 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school-based annual examinations. Class 8 Mathematics notes on Chapter 1 Rational Numbers class 8 Notes Mathematics are also available for download in CBSE Guide website.<\/p>\n<h2><strong>Rational Numbers class 8 Notes Mathematics<\/strong><\/h2>\n<p>Download CBSE class 8th revision notes for Chapter 1 Rational Numbers class 8 Notes Mathematics in PDF format for free. Download revision notes for \u00a0Rational Numbers class 8 Notes Mathematics and score high in exams. These are the Rational Numbers class 8 Notes Mathematics prepared by team of expert teachers. The revision notes help you revise the whole chapter in minutes. Revising notes in exam days is on of the best tips recommended by teachers during exam days.<\/p>\n<p style=\"text-align: center;\"><strong><a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-08-mathematics\/1449\/cbse-revision-notes\/7\/\">Download Revision Notes as PDF<\/a><\/strong><\/p>\n<h2><strong>CBSE Class 8 Revision Notes Maths Rational Numbers<\/strong><\/h2>\n<ul>\n<li>Rational numbers are <strong>closed<\/strong> under the operations of addition, subtraction and multiplication.<\/li>\n<li>The operations addition and multiplication are<br \/>\n(i) <strong>commutative<\/strong> for rational numbers.<br \/>\n(ii) <strong>associative <\/strong>for rational numbers.<\/li>\n<li>The rational number 0 is the <strong>additive identity<\/strong> for rational numbers.<\/li>\n<li>The rational number 1 is the <strong>multiplicative identity<\/strong> for rational numbers.<\/li>\n<li>The additive inverse of the rational number <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span>\u00a0is\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span>\u00a0and vice-versa.<\/li>\n<li>The <strong>reciprocal or multiplicative inverse<\/strong> of the rational number <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span>\u00a0is\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{c} \\over d}\" \/><\/span><\/span>\u00a0if\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span>x<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{c} \\over d}\" \/><\/span><\/span>=1<\/li>\n<li>Distributivity\u00a0\u00a0 of rational numbers: For all rational numbers a, b and c,<br \/>\na(b + c) = ab + ac \u00a0\u00a0\u00a0and\u00a0\u00a0a(b \u2013 c) = ab \u2013 ac<\/li>\n<li>Rational numbers can be represented on a number line.<\/li>\n<li>Between any two given rational numbers there are countless rational numbers. The idea of mean helps us to find rational numbers between two rational numbers.<\/li>\n<li><strong>Positive Rationals: <\/strong>Numerator and Denominator both are either positive or negative. Example: <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{4} \\over 7}, {{-3} \\over -4}\" \/><\/span><\/span><\/li>\n<li><strong>Negative Rationals:<\/strong> Numerator and Denominator both are of opposite signs. Example: <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{-2} \\over 11}, {{4} \\over -9}\" \/><\/span><\/span><\/li>\n<li><strong>Additive Inverse:<\/strong> Additive inverse (negative) <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span>+<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{-a} \\over b}\" \/><\/span><\/span>=<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{-a} \\over b}\" \/><\/span><\/span>+<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span>=0,\u00a0<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{-a} \\over b}\" \/><\/span><\/span>\u00a0is the additive inverse of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b} \\;and\\; {{a} \\over b}\" \/><\/span><\/span>\u00a0is the additive inverse of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{-a} \\over b}\" \/><\/span><\/span>.<\/li>\n<li><strong>Multiplicative Inverse (reciprocal): <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span>x<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{c} \\over d}\" \/><\/span><\/span>=1=<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{c} \\over d}\" \/><\/span><\/span>x<span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span><\/strong>\u00a0where <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{c} \\over d}\" \/><\/span><\/span>\u00a0is the reciprocal of <span class=\"cke_widget_wrapper cke_widget_inline cke_widget_selected\"><span class=\"math-tex cke_widget_element\"><img decoding=\"async\" src=\"https:\/\/elpiscart.com\/cgi-bin\/mathtex.cgi?{{a} \\over b}\" \/><\/span><\/span>. Zero has no reciprocal. The reciprocal of 1 is1 and of -1 is -1.<\/li>\n<\/ul>\n<h2><strong>CBSE Class 8 Revision Notes and Key Points<\/strong><\/h2>\n<p>Rational Numbers class 8 Notes Mathematics. CBSE quick revision note for class-8 Mathematics, Physics, Chemistry, Biology and other subject are very helpful to revise the whole syllabus during exam days. The revision notes covers all important formulas and concepts given in the chapter. Even if you wish to have an overview of a chapter, quick revision notes are here to do it for you. These notes will certainly save your time during stressful exam days.<\/p>\n<ul>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-08-mathematics\/1449\/cbse-revision-notes\/7\/\">Mathematics<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-08-science\/1466\/cbse-revision-notes\/7\/\">Science<\/a><\/li>\n<li><a href=\"http:\/\/mycbseguide.com\/downloads\/cbse-class-08-social-science\/1485\/cbse-revision-notes\/7\/\">Social Science<\/a><\/li>\n<\/ul>\n<p>To download Rational Numbers class 8 Notes Mathematics, sample paper for class 8 Chemistry, Physics, Biology, History, Political Science, Economics, Geography, Computer Science, Home Science, Accountancy, Business Studies and Home Science; do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n<ul>\n<li><a href=\"https:\/\/mycbseguide.com\/blog\/linear-equations-in-one-variable-class-8-notes-mathematics\/\">Linear Equations in one Variable class 8 Notes Mathematics<\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/blog\/understanding-quadrilaterals-class-8-notes-mathematics\/\">Understanding Quadrilaterals class 8 Notes Mathematics<\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/blog\/practical-geometry-class-8-notes-mathematics\/\">Practical Geometry class 8 Notes Mathematics<\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/blog\/data-handling-class-8-notes-mathematics\/\">Data Handling class 8 Notes Mathematics<\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/blog\/squares-square-roots-class-8-notes-mathematics\/\">Squares and Square Roots class 8 Notes Mathematics<\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/blog\/cubes-cube-root-class-8-notes-mathematics\/\">Cubes and Cube Root class 8 Notes Mathematics<\/a><\/li>\n<li><a href=\"https:\/\/mycbseguide.com\/blog\/comparing-quantities-class-8-notes-mathematics\/\">Comparing Quantities class 8 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/algebraic-expressions-identities-class-8-notes-mathematics\/\">Algebraic Expressions and Identities class 8 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/visualising-solid-shapes-class-8-notes-mathematics\/\">Visualising solid shapes class 8 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/mensuration-class-8-notes-mathematics\/\">Mensuration class 8 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/exponents-powers-class-8-notes-mathematics\/\">Exponents and Powers class 8 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/direct-inverse-proportions-class-8-notes-mathematics\/\">Direct and Inverse Proportions class 8 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/factorisation-class-8-notes-mathematics\/\">Factorisation class 8 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/introduction-graphs-class-8-notes-mathematics\/\">Introduction to Graphs class 8 Notes Mathematics<\/a><\/li>\n<li class=\"entry-title\"><a href=\"https:\/\/mycbseguide.com\/blog\/playing-numbers-class-8-notes-mathematics\/\">Playing with Numbers class 8 Notes Mathematics<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Rational Numbers class 8 Notes Mathematics in PDF are available for free download in myCBSEguide mobile app. The best app for CBSE students now provides Rational Numbers class 8 Notes Mathematics latest chapter wise notes for quick preparation of CBSE exams and school-based annual examinations. Class 8 Mathematics notes on Chapter 1 Rational Numbers class &#8230; <a title=\"Rational Numbers class 8 Notes Mathematics\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/rational-numbers-class-11-notes-physical-education\/\" aria-label=\"More on Rational Numbers class 8 Notes Mathematics\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":10427,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[293,456],"tags":[457,150,1541,461,426,240,947],"class_list":["post-10425","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-cbse-class-08","category-revision-notes","tag-cbse-notes","tag-cbse-notes-and-key-points","tag-cbse-revision-notes","tag-mathematics-notes","tag-quick-revision","tag-quick-revision-notes","tag-rational-numbers"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Rational Numbers class 8 Notes Mathematics | myCBSEguide<\/title>\n<meta name=\"description\" content=\"Rational Numbers class 8 Notes Mathematics Chapter 1 in PDF format for free download. 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