{"id":2853,"date":"2022-12-01T07:51:46","date_gmt":"2022-12-01T07:51:46","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=2853"},"modified":"2023-01-31T06:46:30","modified_gmt":"2023-01-31T06:46:30","slug":"ncert-solutions-class-8-maths-chapter-1-rational-numbers-ex-1-1","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-1-rational-numbers-ex-1-1\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers Ex 1.1"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 8 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 1 (Rational Numbers)\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 8 Mathematics <strong>Chapter &#8211; 1 Rational Numbers <\/strong>Exercise 1.1 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><span style=\"color: #000000;\"><strong>Chapter 1: Rational Numbers<\/strong><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-1-rational-numbers-ex-1-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 1.2<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 1.1\u00a0<\/span><\/h2>\n<p><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">1. Using appropriate properties, find:<\/span><\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-\\frac{2}{3}\\times&amp;space;\\frac{3}{5}&amp;space;+&amp;space;\\frac{5}{2}-\\frac{3}{5}\\times&amp;space;\\frac{1}{6}}\" alt=\"\\mathbf{-\\frac{2}{3}\\times \\frac{3}{5} + \\frac{5}{2}-\\frac{3}{5}\\times \\frac{1}{6}}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{2}{3}\\times&amp;space;\\frac{3}{5}&amp;space;+&amp;space;\\frac{5}{2}-\\frac{3}{5}\\times&amp;space;\\frac{1}{6}\" alt=\"-\\frac{2}{3}\\times \\frac{3}{5} + \\frac{5}{2}-\\frac{3}{5}\\times \\frac{1}{6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{2}{3}\\times\\frac{3}{5}&amp;space;-\\frac{3}{5}\\times&amp;space;\\frac{1}{6}&amp;space;+&amp;space;\\frac{5}{2}\" alt=\"-\\frac{2}{3}\\times\\frac{3}{5} -\\frac{3}{5}\\times \\frac{1}{6} + \\frac{5}{2}\" align=\"absmiddle\" \/>\u00a0 \u00a0<\/span><span style=\"font-family: georgia, palatino, serif;\">(by commutativity)<\/span><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{5}&amp;space;\\left&amp;space;(&amp;space;-\\frac{2}{3}&amp;space;-&amp;space;\\frac{1}{6}&amp;space;\\right&amp;space;)+&amp;space;\\frac{5}{2}\" alt=\"\\frac{3}{5} \\left ( -\\frac{2}{3} - \\frac{1}{6} \\right )+ \\frac{5}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{5}\\left&amp;space;(&amp;space;\\frac{-4-1}{6}&amp;space;\\right&amp;space;)+\\frac{5}{2}\" alt=\"\\frac{3}{5}\\left ( \\frac{-4-1}{6} \\right )+\\frac{5}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{5}\\left&amp;space;(&amp;space;\\frac{-5}{6}&amp;space;\\right&amp;space;)+\\frac{5}{2}\" alt=\"\\frac{3}{5}\\left ( \\frac{-5}{6} \\right )+\\frac{5}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-15}{30}&amp;space;+\\frac{5}{2}\" alt=\"\\frac{-15}{30} +\\frac{5}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{1}{2}&amp;space;+&amp;space;\\frac{5}{2}\" alt=\"-\\frac{1}{2} + \\frac{5}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{4}{2}\" alt=\"\\frac{4}{2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= 2<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{5}\\times&amp;space;\\left&amp;space;(&amp;space;-\\frac{3}{7}&amp;space;\\right&amp;space;)-\\frac{1}{6}\\times&amp;space;\\frac{3}{2}+\\frac{1}{14}\\times&amp;space;\\frac{2}{5}}\" alt=\"\\mathbf{\\frac{2}{5}\\times \\left ( -\\frac{3}{7} \\right )-\\frac{1}{6}\\times \\frac{3}{2}+\\frac{1}{14}\\times \\frac{2}{5}}\" align=\"absmiddle\" \/><\/span><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">Solution &#8211;<\/span><\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\\times&amp;space;\\left&amp;space;(&amp;space;-\\frac{3}{7}&amp;space;\\right&amp;space;)-\\frac{1}{6}\\times&amp;space;\\frac{3}{2}+\\frac{1}{14}\\times&amp;space;\\frac{2}{5}\" alt=\"\\frac{2}{5}\\times \\left ( -\\frac{3}{7} \\right )-\\frac{1}{6}\\times \\frac{3}{2}+\\frac{1}{14}\\times \\frac{2}{5}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\\times&amp;space;\\left&amp;space;(&amp;space;-\\frac{3}{7}&amp;space;\\right&amp;space;)&amp;space;+\\frac{1}{14}\\times&amp;space;\\frac{2}{5}-\\left&amp;space;(&amp;space;\\frac{1}{6}\\times&amp;space;\\frac{3}{2}&amp;space;\\right&amp;space;)\" alt=\"\\frac{2}{5}\\times \\left ( -\\frac{3}{7} \\right ) +\\frac{1}{14}\\times \\frac{2}{5}-\\left ( \\frac{1}{6}\\times \\frac{3}{2} \\right )\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0\u00a0 (by commutativity)<\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}&amp;space;\\times&amp;space;\\left&amp;space;(&amp;space;\\frac{-3}{7}+\\frac{1}{14}&amp;space;\\right)-\\frac{3}{12}\" alt=\"\\frac{2}{5} \\times \\left ( \\frac{-3}{7}+\\frac{1}{14} \\right)-\\frac{3}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}&amp;space;\\left&amp;space;(&amp;space;\\frac{-6+1}{14}&amp;space;\\right&amp;space;)&amp;space;-\\frac{3}{12}\" alt=\"\\frac{2}{5} \\left ( \\frac{-6+1}{14} \\right ) -\\frac{3}{12}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\\times&amp;space;\\left&amp;space;(&amp;space;\\frac{-5}{14}&amp;space;\\right&amp;space;)-\\frac{1}{4}\" alt=\"\\frac{2}{5}\\times \\left ( \\frac{-5}{14} \\right )-\\frac{1}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{10}{70}&amp;space;-\\frac{1}{4}\" alt=\"-\\frac{10}{70} -\\frac{1}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{1}{7}-\\frac{1}{4}\" alt=\"-\\frac{1}{7}-\\frac{1}{4}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-4-7}{28}\" alt=\"\\frac{-4-7}{28}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-11}{28}\" alt=\"\\frac{-11}{28}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>2. Write the additive inverse of each of the following:<br \/>\n(i)\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{8}}\" alt=\"\\mathbf{\\frac{2}{8}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{9}}\" alt=\"\\mathbf{\\frac{-5}{9}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-6}{-5}}\" alt=\"\\mathbf{\\frac{-6}{-5}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{-9}}\" alt=\"\\mathbf{\\frac{2}{-9}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 (v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{19}{-6}}\" alt=\"\\mathbf{\\frac{19}{-6}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{8}}\" alt=\"\\mathbf{\\frac{2}{8}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">The Additive inverse of \u00a0<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{8}\" alt=\"\\frac{2}{8}\" align=\"absmiddle\" \/>\u00a0 = \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{8}\" alt=\"\\frac{2}{8}\" align=\"absmiddle\" \/> \u00a0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{9}}\" alt=\"\\mathbf{\\frac{-5}{9}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">The additive inverse of \u00a0<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-5}{9}\" alt=\"\\frac{-5}{9}\" align=\"absmiddle\" \/> = \u00a0<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{9}\" alt=\"\\frac{5}{9}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-6}{-5}}\" alt=\"\\mathbf{\\frac{-6}{-5}}\" align=\"absmiddle\" \/> or <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{6}{5}}\" alt=\"\\mathbf{\\frac{6}{5}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">The additive inverse of \u00a0<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{5}\" alt=\"\\frac{6}{5}\" align=\"absmiddle\" \/>\u00a0 = &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{5}\" alt=\"\\frac{6}{5}\" align=\"absmiddle\" \/>\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{-9}}\" alt=\"\\mathbf{\\frac{2}{-9}}\" align=\"absmiddle\" \/> or <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-\\frac{2}{9}}\" alt=\"\\mathbf{-\\frac{2}{9}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">The additive inverse of\u00a0 &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{9}\" alt=\"\\frac{2}{9}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{9}\" alt=\"\\frac{2}{9}\" align=\"absmiddle\" \/>\u00a0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(v) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{19}{-6}}\" alt=\"\\mathbf{\\frac{19}{-6}}\" align=\"absmiddle\" \/> or <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-\\frac{19}{6}}\" alt=\"\\mathbf{-\\frac{19}{6}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The additive inverse of\u00a0 &#8211; <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{19}{6}\" alt=\"\\frac{19}{6}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{19}{6}\" alt=\"\\frac{19}{6}\" align=\"absmiddle\" \/>\u00a0<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>3. Verify that: -(-x) = x for:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{11}{15}}\" alt=\"\\mathbf{\\frac{11}{15}}\" align=\"absmiddle\" \/><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii) x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-13}{17}}\" alt=\"\\mathbf{\\frac{-13}{17}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{11}{15}}\" alt=\"\\mathbf{\\frac{11}{15}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\">\u2234 \u2013 x <\/span><span style=\"font-family: georgia, palatino, serif;\">= \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{15}\" alt=\"\\frac{11}{15}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2013 (\u2013 x) = \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(-\\frac{11}{15}&amp;space;\\right&amp;space;)\" alt=\"\\left (-\\frac{11}{15} \\right )\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{11}{15}\" alt=\"\\frac{11}{15}\" align=\"absmiddle\" \/> = x (verified)<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii) x = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-13}{17}}\" alt=\"\\mathbf{\\frac{-13}{17}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2234 \u2013 x = \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;-&amp;space;\\frac{13}{17}&amp;space;\\right&amp;space;)\" alt=\"\\left ( - \\frac{13}{17} \\right )\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{13}{17}\" alt=\"\\frac{13}{17}\" align=\"absmiddle\" \/><\/span><\/p>\n<p><span style=\"color: #000000; font-family: georgia, palatino, serif;\">\u2013 (\u2013 x) = \u2013 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;-&amp;space;\\frac{13}{17}&amp;space;\\right&amp;space;)\" alt=\"\\left ( - \\frac{13}{17} \\right )\" align=\"absmiddle\" \/> = x (verified)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>4. Find the multiplicative inverse of the following:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) -13<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-13}{19}}\" alt=\"\\mathbf{\\frac{-13}{19}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{5}}\" alt=\"\\mathbf{\\frac{1}{5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{8}}\" alt=\"\\mathbf{\\frac{-5}{8}}\" align=\"absmiddle\" \/> \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{7}}\" alt=\"\\mathbf{\\frac{-3}{7}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(v) -1 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-2}{5}}\" alt=\"\\mathbf{\\frac{-2}{5}}\" align=\"absmiddle\" \/><br \/>\n(vi) -1<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) -13<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Multiplicative inverse of -13 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-1}{13}\" alt=\"\\frac{-1}{13}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-13}{19}}\" alt=\"\\mathbf{\\frac{-13}{19}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Multiplicative inverse of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-13}{19}\" alt=\"\\frac{-13}{19}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-19}{13}\" alt=\"\\frac{-19}{13}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{5}}\" alt=\"\\mathbf{\\frac{1}{5}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Multiplicative inverse of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{5}\" alt=\"\\frac{1}{5}\" align=\"absmiddle\" \/> = 5<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-5}{8}}\" alt=\"\\mathbf{\\frac{-5}{8}}\" align=\"absmiddle\" \/> \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-3}{7}}\" alt=\"\\mathbf{\\frac{-3}{7}}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{15}{56}}\" alt=\"\\mathbf{\\frac{15}{56}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Multiplicative inverse of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{15}{56}\" alt=\"\\frac{15}{56}\" align=\"absmiddle\" \/>\u00a0 =\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{56}{15}\" alt=\"\\frac{56}{15}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(v) -1 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-2}{5}}\" alt=\"\\mathbf{\\frac{-2}{5}}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2}{5}}\" alt=\"\\mathbf{\\frac{2}{5}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">Multiplicative inverse of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{5}\" alt=\"\\frac{2}{5}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{5}{2}\" alt=\"\\frac{5}{2}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(vi) -1<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">Multiplicative inverse of -1 = -1.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>5. Name the property under multiplication used in each of the following:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{5}\\times&amp;space;1&amp;space;=&amp;space;1\\times&amp;space;\\frac{-4}{5}&amp;space;=&amp;space;\\frac{-4}{5}}\" alt=\"\\mathbf{\\frac{-4}{5}\\times 1 = 1\\times \\frac{-4}{5} = \\frac{-4}{5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-13}{17}\\times&amp;space;\\frac{-2}{7}&amp;space;=&amp;space;\\frac{-2}{7}\\times&amp;space;\\frac{-13}{17}}\" alt=\"\\mathbf{\\frac{-13}{17}\\times \\frac{-2}{7} = \\frac{-2}{7}\\times \\frac{-13}{17}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-19}{20}\\times&amp;space;\\frac{29}{-19}&amp;space;=&amp;space;1}\" alt=\"\\mathbf{\\frac{-19}{20}\\times \\frac{29}{-19} = 1}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-4}{5}\\times&amp;space;1&amp;space;=&amp;space;1\\times&amp;space;\\frac{-4}{5}&amp;space;=&amp;space;\\frac{-4}{5}}\" alt=\"\\mathbf{\\frac{-4}{5}\\times 1 = 1\\times \\frac{-4}{5} = \\frac{-4}{5}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Here 1 is the multiplicative identity.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-13}{17}\\times&amp;space;\\frac{-2}{7}&amp;space;=&amp;space;\\frac{-2}{7}\\times&amp;space;\\frac{-13}{17}}\" alt=\"\\mathbf{\\frac{-13}{17}\\times \\frac{-2}{7} = \\frac{-2}{7}\\times \\frac{-13}{17}}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The property of commutativity is used in the equation.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-19}{20}\\times&amp;space;\\frac{29}{-19}&amp;space;=&amp;space;1}\" alt=\"\\mathbf{\\frac{-19}{20}\\times \\frac{29}{-19} = 1}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The multiplicative inverse is the property used in this equation.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>6. Multiply <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{6}{13}}\" alt=\"\\mathbf{\\frac{6}{13}}\" align=\"absmiddle\" \/> by the reciprocal of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{-7}{16}}\" alt=\"\\mathbf{\\frac{-7}{16}}\" align=\"absmiddle\" \/>.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Reciprocal of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{16}\" alt=\"\\frac{-7}{16}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{16}{-7}\" alt=\"\\frac{16}{-7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{16}{7}\" alt=\"-\\frac{16}{7}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">According to the question,<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{13}\" alt=\"\\frac{6}{13}\" align=\"absmiddle\" \/> \u00d7 (Reciprocal of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-7}{16}\" alt=\"\\frac{-7}{16}\" align=\"absmiddle\" \/>)<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{6}{13}\" alt=\"\\frac{6}{13}\" align=\"absmiddle\" \/> \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-\\frac{16}{7}\" alt=\"-\\frac{16}{7}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-96}{91}\" alt=\"\\frac{-96}{91}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>7. Tell what property allows you to compute <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{3}\\times&amp;space;\\left&amp;space;(&amp;space;6\\times&amp;space;\\frac{4}{3}&amp;space;\\right&amp;space;)}\" alt=\"\\mathbf{\\frac{1}{3}\\times \\left ( 6\\times \\frac{4}{3} \\right )}\" width=\"104\" height=\"44\" align=\"absmiddle\" \/> as <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\left&amp;space;(&amp;space;\\frac{1}{3}&amp;space;\\times&amp;space;6\\right&amp;space;)\\times&amp;space;\\frac{4}{3}}\" alt=\"\\mathbf{\\left ( \\frac{1}{3} \\times 6\\right )\\times \\frac{4}{3}}\" width=\"106\" height=\"44\" align=\"absmiddle\" \/>.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{3}\\times&amp;space;\\left&amp;space;(&amp;space;6\\times&amp;space;\\frac{4}{3}&amp;space;\\right&amp;space;)\" alt=\"\\frac{1}{3}\\times \\left ( 6\\times \\frac{4}{3} \\right )\" align=\"absmiddle\" \/>\u00a0 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;(&amp;space;\\frac{1}{3}&amp;space;\\times&amp;space;6\\right&amp;space;)\\times&amp;space;\\frac{4}{3}\" alt=\"\\left ( \\frac{1}{3} \\times 6\\right )\\times \\frac{4}{3}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Hence, the Associativity Property of Multiplication is used here.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>8. Is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{8}{9}}\" alt=\"\\mathbf{\\frac{8}{9}}\" align=\"absmiddle\" \/> the multiplication inverse of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-1\\frac{1}{8}}\" alt=\"\\mathbf{-1\\frac{1}{8}}\" align=\"absmiddle\" \/> <\/strong><strong>? Why or why not?<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-1\\frac{1}{8}\" alt=\"-1\\frac{1}{8}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{-9}{8}\" alt=\"\\frac{-9}{8}\" align=\"absmiddle\" \/><\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Since multiplicative inverse of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{9}\" alt=\"\\frac{8}{9}\" align=\"absmiddle\" \/> is <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{8}\" alt=\"\\frac{9}{8}\" align=\"absmiddle\" \/>\u00a0but not\u00a0<span id=\"MathJax-Element-16-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-92\" class=\"math\"><span id=\"MathJax-Span-93\" class=\"mrow\"><span id=\"MathJax-Span-94\" class=\"mfrac\"><span id=\"MathJax-Span-95\" class=\"mrow\"><span id=\"MathJax-Span-96\" class=\"mo\">\u2212 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{9}{8}\" alt=\"\\frac{9}{8}\" align=\"absmiddle\" \/>.<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span id=\"MathJax-Element-17-Frame\" class=\"MathJax\" style=\"font-family: georgia, palatino, serif;\" tabindex=\"0\"><span id=\"MathJax-Span-99\" class=\"math\"><span id=\"MathJax-Span-100\" class=\"mrow\"><span id=\"MathJax-Span-101\" class=\"mfrac\"><span id=\"MathJax-Span-102\" class=\"mn\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{8}{9}\" alt=\"\\frac{8}{9}\" align=\"absmiddle\" \/> <\/span><\/span><\/span><\/span><\/span><span style=\"font-family: georgia, palatino, serif;\">is not the multiplicative inverse of<\/span> <strong style=\"font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?-1\\frac{1}{8}\" alt=\"-1\\frac{1}{8}\" align=\"absmiddle\" \/><\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>9. If 0.3 is the multiplicative inverse of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{3\\frac{1}{3}}\" alt=\"\\mathbf{3\\frac{1}{3}}\" align=\"absmiddle\" \/> <\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>? Why or why not?<\/strong><\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\frac{1}{3}\" alt=\"3\\frac{1}{3}\" align=\"absmiddle\" \/>= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{10}{3}\" alt=\"\\frac{10}{3}\" align=\"absmiddle\" \/> <\/strong>and\u00a0<\/span><span style=\"font-family: georgia, palatino, serif;\">0.3 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{10}\" alt=\"\\frac{3}{10}\" align=\"absmiddle\" \/><\/span><\/span><\/p>\n<p><span style=\"color: #000000;\">Multiplicative inverse of 0.3 or <span style=\"font-family: georgia, palatino, serif;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{3}{10}\" alt=\"\\frac{3}{10}\" align=\"absmiddle\" \/><\/span> = <span style=\"font-family: georgia, palatino, serif;\"><strong><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{10}{3}\" alt=\"\\frac{10}{3}\" align=\"absmiddle\" \/><\/strong><\/span>.<\/span><\/p>\n<p><span style=\"color: #000000;\">Thus, 0.3 is the multiplicative inverse of <span style=\"font-family: georgia, palatino, serif;\"><strong><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?3\\frac{1}{3}\" alt=\"3\\frac{1}{3}\" align=\"absmiddle\" \/><\/strong><\/span>.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>10. Write:<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">(i) The rational number that does not have a reciprocal.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">(ii) The rational numbers that are equal to their reciprocals.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">(iii) The rational number that is equal to its negative.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong><br \/>\n<\/span><strong><span style=\"font-family: georgia, palatino, serif;\">(i) The rational number that does not have a reciprocal.<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">The rational number that does not have a reciprocal is 0.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2235 <\/span><span style=\"font-family: georgia, palatino, serif;\">0 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{0}{1}\" alt=\"\\frac{0}{1}\" align=\"absmiddle\" \/> is not defined<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong><span style=\"font-family: georgia, palatino, serif;\">(ii) The rational numbers that are equal to their reciprocals.<br \/>\n<\/span><\/strong><span style=\"font-family: georgia, palatino, serif;\">The rational numbers that are equal to their reciprocals are 1 and -1.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">\u2235\u00a0<\/span><span style=\"font-family: georgia, palatino, serif;\">1 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{1}\" alt=\"\\frac{1}{1}\" align=\"absmiddle\" \/><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">Reciprocal of 1 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{1}\" alt=\"\\frac{1}{1}\" align=\"absmiddle\" \/>\u00a0 = 1, similarly, reciprocal of -1 = \u2013 1<br \/>\nThus, 1 and -1 are the required rational numbers.<br \/>\n<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii) The rational number that is equal to its negative.<br \/>\n<\/strong>The rational number that is equal to its negative is 0.<br \/>\n\u2235 <\/span><span style=\"font-family: georgia, palatino, serif;\">Negative of 0 = &#8211; 0 = 0<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>11. Fill in the blanks.<br \/>\n<\/strong><\/span><span style=\"font-family: georgia, palatino, serif;\">(i) Zero has _______reciprocal.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">(ii) The numbers ______and _______are their own reciprocals<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">(iii) The reciprocal of \u2013 5 is ________.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">(iv) Reciprocal of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{x}\" alt=\"\\frac{1}{x}\" align=\"absmiddle\" \/>, where x \u2260 0 is _________.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">(v) The product of two rational numbers is always a ________.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\">(vi) The reciprocal of a positive rational number is _________.<\/span><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\"><strong>Solution &#8211;<\/strong> <\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><span style=\"font-family: georgia, palatino, serif;\"><strong>(i)<\/strong> Zero has\u00a0<span style=\"text-decoration: underline;\"><strong>no<\/strong><\/span>\u00a0reciprocal.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(ii)<\/strong> The numbers\u00a0<span style=\"text-decoration: underline;\"><strong>-1\u00a0<\/strong><\/span>and\u00a0<span style=\"text-decoration: underline;\"><strong> 1\u00a0<\/strong><\/span><strong>\u00a0<\/strong>are their own reciprocals<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(iii)<\/strong> The reciprocal of \u2013 5 is <span style=\"text-decoration: underline;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{-\\frac{1}{5}}\" alt=\"\\mathbf{-\\frac{1}{5}}\" align=\"absmiddle\" \/><\/span><br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(iv)<\/strong> Reciprocal of <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{x}\" alt=\"\\frac{1}{x}\" align=\"absmiddle\" \/>, where x \u2260 0 is <span style=\"text-decoration: underline;\"><strong>x<\/strong><\/span>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(v)<\/strong> The product of two rational numbers is always a\u00a0<span style=\"text-decoration: underline;\"><strong>rational number<\/strong><\/span>.<br \/>\n<\/span><span style=\"font-family: georgia, palatino, serif;\"><strong>(vi)<\/strong> The reciprocal of a positive rational number is\u00a0<span style=\"text-decoration: underline;\"><strong>positive<\/strong><\/span>.<\/span><\/span><\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 32px;\">\n<td style=\"width: 100%; background-color: #f2e079; text-align: center; height: 32px;\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong>NCERT Class 8<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 8 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Mathematics<\/a>\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-sanskrit-ruchira\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">NCERT Solutions Class 8 Sanskrit<\/span><\/strong><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 8 Mathematics\u00a0 Chapter &#8211; 1 (Rational Numbers)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 1 Rational Numbers Exercise 1.1 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 1: Rational Numbers NCERT Solution Class 8 Maths Ex &#8211; 1.2 Exercise [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[442],"tags":[443,444,445,5],"class_list":["post-2853","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-1-rational-numbers-in-english","tag-ncert-solutions-class-8-maths-chapter-1-in-english","tag-ncert-solutions-class-8-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 8 Maths Chapter 1 Rational Numbers Ex 1.1 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 8 Mathematics\u00a0Chapter - 1 (Rational Numbers)\u00a0The NCERT Solutions in English Language for Class 8 Mathematics Chapter 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